Top Banner
127

ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

Jan 27, 2022

Download

Documents

dariahiddleston
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Page 1: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT
Page 2: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

FISCAL HEALTH IN TEXAS

by

WILLIAM H. MAURER, B.S. in Ed., M.Ed.

A DISSERTATION

IN

EDUCATION

Submitted to the Graduate Faculty of Texas Tech University in

Partial Fulfillment of the Requirements for

the Degree of

DOCTOR OF EDUCATION

Approved

Accepted

August, 1988

Page 3: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

T3

©1989

WILLIAM H. MAURF.R

All Rights Reserved

Page 4: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

ACKNOWLEDGMENTS

I wish to recognize and thank Dr. William Sparkman who

encouraged me to enter doctoral studies. Without his

guidance and support, I would not have been able to complete

this project. Appreciation is extended to members of the

dissertation committee. Dr. David Welton, Dr. John Champlin,

Dr. Thomas Irons and Dr. Paula Lawrence. Special thanks

also are extended to Penny Taulman, who typed this manu­

script, and to Robert Leung, who offered his skills in

computer programming.

Special appreciation goes to my wife, Patricia

Alexander Maurer, and our daughter, Sarah Elizabeth Maurer,

for their faithful love, support, patience and under­

standing. During the two years of research and writing,

they made many sacrifices that enabled me to complete my

studies.

11

Page 5: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

TABLE OF CONTENTS

ACKNOWLEDGMENTS ii

LIST OF TABLES V

LIST OF FIGURES viii

CHAPTER

I INTRODUCTION 1

Statement of the Problem 1 Delimitations 3 Limitations 4

Justification for the Study 4 Assumptions 6 Definition of Terms 6 Procedures 8 Organization of the Research Report 10

II REVIEW OF RELEVANT RESEARCH AND LITERATURE 11

Planning the School Budget 11 Fiscal Strain 13 Forecasting Techniques 15 Studies of School District Fiscal Health ... 18 Identification of Variables 24 Summary 30

III PROCEDURES AND PRESENTATION OF THE DATA , 32

Source of the Data 32 Sorting the Data and Identifying the Variables 33 Statistical Procedures 36 Analysis of the Data 61

IV PRESENTATION AND ANALYSIS OF DATA 66

Discussion of Research Questions 67

111

Page 6: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

V SUMMARY, MAJOR FINDINGS, CONCLUSIONS AND RECOMMENDATIONS 80

Summary 80 The Problem of the Study 81 Procedures 81

Major Findings 82 Conclusions 91 Recommendations 92

REFERENCES 94

APPENDICES

A TABLE A.l CORRELATION MATRIX 1980-1981 INDEPENDENT VARIABLES 1981-1982 DEPENDENT VARIABLE ALL SCHOOL DISTRICTS 97

B TABLE B.l CORRELATION MATRIX 1981-1982 INDEPENDENT VARIABLES 1982-1983 DEPENDENT VARIABLE ALL SCHOOL DISTRICTS 104

C TABLE C.l CORRELATION MATRIX 1982-1983 INDEPENDENT VARIABLES 1983-1984 DEPENDENT VARIABLE ALL SCHOOL DISTRICTS H I

IV

Page 7: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

LIST OF TABLES

2.1 VARIABLES 26

3.1 NUMBER OF SCHOOL DISTRICTS INCLUDED IN THE STUDY 34

3.2 MEAN AND STANDARD DEVIATION, 1980-1981 INDEPENDENT VARIABLES, 1981-1982, DEPENDENT VARIABLE, ALL SCHOOL DISTRICTS, N=979 37

3.3 MEAN AND STANDARD DEVIATION, 1981-1982 INDEPEDENT VARIABLES, 1982-1983 DEPENDENT VARIABLE, ALL SCHOOL DISTRICTS, N=979 39

3.4 MEAN AND STANDARD DEVIATION, 1982-1983 INDEPENDENT VARIABLES, 1983-1984 DEPENDENT VARIABLE, ALL SCHOOL DISTRICTS, N=978 41

3.5 MULTIPLE REGRESSION SUMMARY TABLE 1980-1981 INDEPENDENT VARIABLE 1981-1982 DEPENDENT VARIABLE, ALL SCHOOL DISTRICTS 45

3.6 MULTIPLE REGRESSION SUMMARY TABLE 1980-1981 INDEPENDENT VARIABLE 1981-1982 DEPENDENT VARIABLE, FIRST QUARTILE 46

3.7 MULTIPLE REGRESSION SUMMARY TABLE 1980-1981 INDEPENDENT VARIABLE 1981-1982 DEPENDENT VARIABLE, SECOND QUARTILE 47

3.8 MULTIPLE REGRESSION SUMMARY TABLE 1980-1981 INDEPENDENT VARIABLE 1981-1982 DEPENDENT VARIABLE, THIRD QUARTILE 48

3.9 MULTIPLE REGRESSION SUMMARY TABLE 1980-1981 INDEPENDENT VARIABLE 1981-1982 DEPENDENT VARIABLE, FOURTH QUARTILE 49

3.10 MULTIPLE REGRESSION SUMMARY TABLE 1981-1982 INDEPENDENT VARIABLE 1982-1983 DEPENDENT VARIABLE, ALL SCHOOL DISTRICTS 50

V

Page 8: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

3.11 MULTIPLE REGRESSION SUMMARY TABLE 1981-1982 INDEPENDENT VARIABLE 1982-1983 DEPENDENT VARIABLE, FIRST QUARTILE 51

3.12 MULTIPLE REGRESSION SUMMARY TABLE 1981-1982 INDEPENDENT VARIABLE 1982-1983 DEPENDENT VARIABLE, SECOND QUARTILE 52

3.13 MULTIPLE REGRESSION SUMMARY TABLE 1981-1982 INDEPENDENT VARIABLE 1982-1983 DEPENDENT VARIABLE, THIRD QUARTILE 53

3.14 MULTIPLE REGRESSION SUMMARY TABLE 1981-1982 INDEPENDENT VARIABLE 1982-1983 DEPENDENT VARIABLE, FOURTH QUARTILE 54

3.15 MULTIPLE REGRESSION SUMMARY TABLE 1982-1983 INDEPENDENT VARIABLE 1983-1984 DEPENDENT VARIABLE, ALL SCHOOL DISTRICTS 55

3.16 MULTIPLE REGRESSION SUMMARY TABLE 1982-1983 INDEPENDENT VARIABLE 1983-1984 DEPENDENT VARIABLE, FIRST QUARTILE 56

3.17 MULTIPLE REGRESSION SUMMARY TABLE 1982-1983 INDEPENDENT VARIABLE 1983-1984 DEPENDENT VARIABLE, SECOND QUARTILE 57

3.18 MULTIPLE REGRESSION SUMMARY TABLE 1982-1983 INDEPENDENT VARIABLE 1983-1984 DEPENDENT VARIABLE, THIRD QUARTILE 58

3.19 MULTIPLE REGRESSION SUMMARY TABLE 1982-1983 INDEPENDENT VARIABLE 1983-1984 DEPENDENT VARIABLE, FOURTH QUARTILE 59

3.20 TOTAL R^ VALUES 63

3.21 INDEPENDENT VARIABLES WITH RSQ CHANGE GREATER THAN OR EQUAL TO .01 64

VI

Page 9: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

3.22 MEANS AND STANDARD DEVIATIONS OF CASH BALANCE 65

5.1 INDEPENDENT VARIABLES WITH R^ CHANGE GREATER THAN OR EQUAL TO .05 85

5.2 FREQUENCIES OF INDEPENDENT VARIABLES WITH R^ CHANGE GREATER THAN OR EQUAL TO .05 THAT OCCURRED IN MORE THAN ONE MODEL 89

A.l CORRELATION MATRIX 1980-1981 INDEPENDENT VARIABLES 1981-1982 DEPENDENT VARIABLE ALL SCHOOL DISTRICTS 98

B.l CORRELATION MATRIX 1981-1982 INDEPENDENT VARIABLES 1982-1983 DEPENDENT VARIABLE ALL SCHOOL DISTRICTS 105

C.l CORRELATION MATRIX 1982-1983 INDEPENDENT VARIABLES 1983-1984 DEPENDENT VARIABLE ALL SCHOOL DISTRICTS 112

Vll

Page 10: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

LIST OF FIGURES

4.1 FREQUENCIES OF VARIABLES THAT ARE INCLUDED IN THE MODELS 70

4.2 VARIABLES INCLUDED IN THE MODELS FOR ALL SCHOOL DISTRICTS, FIRST QUARTILE AND FOURTH QUARTILE 75

Vlll

Page 11: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

CHAPTER I

INTRODUCTION

Statement of the Problem

Legal mandates, constrained public funds, and increased

public demands for efficient management of our schools

require that planning be an integral component of the school

budgeting process. Forecasting school district fiscal

health is an essential part of the planning process. In the

final analysis, the school budget is "the translation of

educational needs into a financial plan..." (Candoli et al.,

1984, p. 127).

Fiscal health may be defined in terms of absolute

fiscal health or relative fiscal health (Smith, 1985) .

Texas identifies a school district as being fiscally healthy

if its ending fund balance is $0.00 or more. A deficit fund

balance is illegal according to state law (Texas Education

Code, 23.45b, 1978). However, authorities in education

finance advocate that a district should maintain a balance

or reserve equal to one to three months of expenditures

(Gaylord, 1983; Roland, 1986; Walker, 1986). If a budget

does not reflect fiscal health, the school district will be

less likely to meet the needs of its students. Likewise, it

can be assumed that a school district with a higher level of

fiscal health or higher cash balance, is more able to meet

1

Page 12: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

the needs of its students than a school district with a

lower level of fiscal health or lower cash balance. Whether

it does or not is another question.

A part of budget planning and control is the local

education agency's assurance that revenues are equal to or

greater than expenditures because the legal mandate in Texas

requires that school districts -operate on a cash basis.

Decision makers at the local level prepare school district

budgets and bear the greatest responsibility for the alloca­

tion of limited financial resources. Research efforts that

can provide assistance to local districts in forecasting

budget needs have been limited. A direct causal relation­

ship has not been established between certain local school

district characteristics and the fiscal health of school

districts.

This study attempted to answer a number of questions.

First, is school district fiscal health predictable?

Second, what fiscal indicators, subject to the control of

local decision makers, can be used to forecast school

district fiscal health? Third, do different indicators have

predictive significance for school districts with a higher

level of fiscal health than for those school districts with

a lower level of fiscal health? Finally, does the

methodology employed in this study provide a viable strategy

for differentiating levels of school district fiscal health?

Page 13: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

This study included 66 specific variables, deemed as

independent, from the area of local revenue, local

expenditures by function, and local tax data, which are

found on the Texas Education Agency Official Budget for

Texas Public Schools. Stepwise multiple regression was used

as the primary statistical procedure to obtain predictive

values (Nie et al., 1975; Hull and Nie, 1981). The

independent variables were regressed against ending fund

balance, the dependent variable.

Delimitations

1. The population consisted of all public school

districts in the State of Texas, excluding state-operated

schools and school districts serving fewer than twelve

grades.

2. Data were derived from summary reports submitted

on the Texas Education Agency Official Budget for Texas

Public Schools.

3. Data were included for the years 1980-1981,

1981-1982, 1982-1983, 1983-1984, prior to the reforms of

1984. Computerized data were unavailable from Texas Educa­

tion Agency for the 1984-1985 and 1985-1986 school years.

4. Only indicators that are subject to control by

local decision makers were examined.

5. Quantitative measures were used as opposed to

qualitative measures.

Page 14: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

Limitations

1. The number of school districts varied during the

years selected for the study because of the consolidation or

creation of school districts.

2. Texas Education Agency revised the budget docu­

ments during the years selected for this study; therefore,

specific budget items vary from year to year.

3. While some independent variables were identified

on the basis of justifications provided by the literature or

authorities in the field, some a priori decisions were made

concerning other variables that were included in the study.

4. This correlational study, while both descriptive

and inferential, cannot demonstrate cause and effect.

5. This study did not examine economic conditions

such as employment, sales and property values.

6. This study did not examine qualitative measures of

fiscal health.

7. Results of this study cannot be generalized to

other states because data were confined to Texas.

Justification for the Study

Costerison (1984) identified major causes of fiscal

stress on school budgets. These include declining enroll­

ment, voter resistance to tax increases, inflation, declin­

ing state and federal aid, and employee demands. In a

period of fiscal retrenchment, school budget officers need

Page 15: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

to make decisions which will protect the fiscal health of

their organizations. Traditional research on fiscal health

has focused on demographic variables and factors relating to

state funding formulas (Lee, 1983). The value of such

research to local budget officers is limited because it

reports on factors beyond their control. There is, conse­

quently, a real need for research which gives the local

school administrator predictive control over local school

district fiscal health (Hentshcke and Yagielski, 1982a).

In Texas the fiscal burden on local school districts is

increasing (Jordan, 1985) . From 1973-74 to 1983-84 average

per pupil expenditures, not adjusted for inflation, have

increased from $910.00 to $2,960.00. Local contribution to

the total school budget increased from 41.5 percent to 46.4

percent during that same time period. This shift means that

local school administrators must assume a more proactive

responsibility for efficient use of available resources.

They can no longer depend on money from state and federal

sources to bridge the gap between mandates for new programs

and their costs. This study attempted to identify specific

indicators that local school administrators can control to

improve fiscal health.

Wegenke and Smith (1983) have identified characteris­

tics of useful fiscal data. They suggest that fiscal data

must be translatable into understandable language in order

to be useful. In addition, useful data are described as

Page 16: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

being credible throughout the term of the budget, timely and

subject to change.

This study seeks to increase the usefulness of budget

data available to local school administrators because

it defines that data in terms of its credibility or lack of

credibility to produce timely change.

Assumptions

1. Standardized data and other data provided to the

Texas Education Agency are accurate.

2. Fiscal data selected as independent variables can

be used as indicators of fiscal health.

3. Fiscal health can be influenced or controlled by

local school district administrators.

4. Fiscal health can be quantitatively defined as

cash balance.

5. School district decision making is more accurately

described as consumer behavior rather than producer behav­

ior.

Definition of Terms

Budget is a plan of financial operation embodying an

estimate of proposed expenditures for a given period or

purpose and the proposed means of financing them.

Expenditures are total charges incurred for current

expense, capital outlay and debt service.

Page 17: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

7

Fiscal data include quantitative information such as

local property taxes, total instructional payroll costs,

supplies and materials, tuition and fees that are taken from

the official school budgets.

Fiscal health, for purposes of this study, is defined

as the total fund balance that is indicated on the official

budget. School districts with higher fund balances are

fiscally healthier than school districts with lower fund

balances.

Fiscal indicators are budget items listed on the Texas

Education Agency Official Budget for Texas Public Schools

that can be controlled by local school district administra­

tors .

Fiscal strain, as used in this study, is synonymous

with fiscal stress, conditions under which school district

decision makers are forced to purchase fewer or less desir­

able inputs than in the past due to declining revenues,

increasing costs or a combination of both.

Function classification as applied to expenditures

refers to an activity or service aimed at accomplishing a

certain purpose or end; for example, instruction, instruc­

tional administration, plant maintenance and operation.

Local revenue includes revenue generated from real and

personal property taxes, services to other local education

agencies, tuition and fees from patrons, within state

Page 18: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

8

transfers, co-curricular enterprises and other local

sources.

Object classication as applied to expenditures refers

to an article or service received; for example, payroll

costs, purchased and contracted services, materials and

supplies.

Refined average daily attendance is the aggregate days

attendance of eligible students divided by the number of

days that school is in session. It is equal to the gross

average daily attendance less ineligible average daily

attendance.

Tax is a compulsory charge levied by a governmental

unit for the purpose of financing services performed for the

common benefit.

Procedures

This study was conducted using the following proce­

dures:

1. Phase one of the study consisted of two tasks to

determine the feasibility of the project. Previous research

was examined in a review of the relevant school finance and

school budget literature. Texas Education Agency was con­

tacted to determine that data were available.

2. Phase two of the study consisted of sorting the

data to extract independent and dependent variables and the

school districts that were included. Independent variables

Page 19: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

consisted of budget data selected from tax information,

expenditures by function and local revenues. The dependent

variable was ending fund balance. Data files had to be

constructed in order to prepare the data for running the

stepwise multiple regression program. Independent and

dependent variables for all school districts in the State of

Texas that offered grades kindergarten through twelve were

identified. For each school district selected data from the

official budget report were divided by the refined average

daily attendance of the school district as means of provid­

ing standard units for comparison. School districts were

ranked according to end of year fund balance divided by

refined average daily attendance and sorted into quartiles.

3. In phase three of the study, data for the whole

population and for quartiles were subjected to stepwise

multiple regression: 1980-1981 independent variables were

regressed against fiscal health in 1981-1982; 1981-1982

independent variables were regressed against fiscal health

in 1982-1983; 1982-1983 independent variables were regressed

against fiscal health in 1983-1984. Longitudinal data were

used because budget decisions to determine tax rates,

expenditures and revenues are made in the year preceding the

actual implementation of the budget. The major purpose of

this study was to analyze a strategy used to forecast school

district fiscal health.

Page 20: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

10

4. Phase four of the study consisted of analyzing and

summarizing the data for presentation and analysis. Results

of multiple regressions were compared across quartiles and

across years.

Organization of the Research Report

This research is reported in five chapters. Chapter I,

the introduction, includes the statement of the problem,

delimitations, limitations, justification for the study,

assumptions, definition of terms, procedures and organiza­

tion of the research report. Chapter II presents a review

of relevant literature and research. Chapter III consists

of the procedures and presentation of the data. Chapter IV

contains the findings and analysis of the data. Chapter V

presents a summary, major findings, conclusions and

recommendations.

Page 21: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

CHAPTER II

REVIEW OF RELEVANT RESEARCH AND LITERATURE

This chapter presents a review of the literature

related to forecasting school district fiscal health. It

presents a brief discussion of managing and planning the

school budget, and discusses fiscal strain and its causes.

It identifies forecasting techniques and the consumer

approach to school district decision making and presents

summaries of pertinent research that focuses on forecasting

school district fiscal health. A summary concludes Chapter

II.

Planning the School Budget

In times of economic turbulence, public schools as well

as the private business sector have been subjected to finan­

cial hardship. School district decision makers face the

dilemma of reconciling a decline in revenues while maintain­

ing or even expanding programs. The public calls on school

district administrators to reduce costs while demanding that

the school improve the basic skills of pupils, expand pro­

grams and provide more opportunities for special student

populations (Chabotar, 1987) . The problem is exacerbated as

staffs request higher salaries and more benefits (Hartman

and Rivenburg, 1985) , and by state and federal mandates to

implement new programs without providing additional funds to

11

Page 22: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

12

cover the costs of expanding the school program. Inflation

takes its toll on budgets even when there is no demand for

growth and expansion. In its national annual survey, the

National School Boards Association reported that in 1981,

1982 and 1983 the greatest concern of school board members

was lack of funding (Smith, 1985).

The budget is the fiscal plan that reflects the educa­

tional needs of the school district (Candoli, et al., 1984).

It operationalizes philosophies, priorities and strategies

and is the strongest measure of the priorities of local

education agencies (Hartman and Rivenburg, 1985). All

accepted definitions of budgeting include planning as a

component part, in addition to receiving funds, spending

funds and evaluating results (Burrup and Brimley, 1982).

Decisions at the local level are subject to the idiosyn­

crasies of the school district such as local politics,

economic and social conditions, beliefs, attitudes and

priorities of the decision makers. However, the budget does

provide a common basis for making comparisons, and is the

strongest measure of comparison since it closely corresponds

with operations of the school district (Hartman and

Rivenburg, 1985). In states such as Texas, which mandate a

uniform format for reporting the school district budget,

these comparisons have the potential for predictive

applications.

Page 23: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

13

Forecasting while focusing on immediate fiscal concerns

is an important part of the fiscal planning process (Wegenke

and Smith, 1983). Prudent decisions affecting the budget

consider past, present and projected trends. This process

requires that a school district establish financial review

and analysis procedures. Wegenke and Smith also specify

that fiscal data be understandable, credible, timely and

part of the overall financial picture making it subject to

change in the future. Because a budget defines fiscal

limits, local decision makers must manipulate those limits

to maximize their levels of consumption.

Fiscal Strain

The fiscal health of a school district can range from a

negative budget balance, which is illegal in Texas, to a

high budget balance. Dickmeyer (19 79) defined fiscal health

as the "ability to pay bills" (p. 161) . A school district

that is considered to be fiscally unhealthy can be described

as experiencing fiscal strain or fiscal stress. It is

difficult to define fiscal strain operationally since it is

a matter of degree; a relative term. Hentschke and

Yagielski (1982a) defined fiscal strain as the condition

that forces decision makers to purchase inputs that are less

desirable than the inputs that are currently being

purchased; that is, the combination of resources for next

year are less preferred. Zerchykov, et al. (1982) defined

Page 24: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

14

fiscal strain as organizational shrinkage. Fiscal strain

reduces the discretion of school boards. Costerison (1984)

reported that the State of Indiana defines fiscal strain as

the condition under which a school district cannot carry out

its educational duty without emergency aid; and, that

Pennsylvania defines fiscal strain using various indicators

that range from inability to meet payroll to default on bond

payments.

It is important that planners be cognizant of causes of

fiscal strain because decisions should be based on qualita­

tive as well as quantitative considerations. Lee (1983)

specified four major causes of fiscal strain. They included

decline in public confidence, unemployment, fewer voters

with school age children and declining enrollments.

Hentschke and Yagielski (1982a) added increasing prices of

inputs and changes in the input mix. Inflation, decreasing

state and federal revenues, increasing state and federal

mandates for new programs were added to the list by Hartman

and Rivenburg (1985) . Costerison (1984) expanded the list

of major causes to include 31 specific causes of fiscal

strain. Exogenous factors are listed above; however, the

local school district decision maker must exercise caution

not to introduce internal causes of fiscal strain such as

overspending, failing to adjust the tax rate, failing to

project student enrollment and staffing requirements.

Page 25: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

15

Forecasting Techniques

Chabotar (1987) identified forecasting as a critical

issue, but cautioned that forecasting should be used as one

input in the decision making process along with economic and

political factors. He confirmed, along with the studies of

Lee (1983), Smith (1985) and Ward (1985), that forecasting

can be used effectively by school district decision makers

to make fiscal decisions and that there is a great need for

linking the annual budget to long-term fiscal plans.

Chabotar identified four forecasting techniques. The

first is subjective judgment, which is not a quantitative

procedure. It is based upon the expertise and experience of

the forecaster. One example is the Delphi panel. Causal

models constitute a second forecasting technique. These

types of forecasts are based upon relationships between

revenue, expenditures and independent variables selected by

the forecaster. Examples of this type are ratio methods,

multiple correlation, regression and path analytic models.

Extrapolation is the third technique. This type of forecast

predicts the future based upon revenues and expenditures

continuing at the same rate. It depends upon using stable

data such as birth rates, economic conditions and policies.

This technique assumes the existence of a particular trend

and that the trend will continue through the years of the

forecast. Chabotar included normative approaches as a

fourth technique although he contended that they really are

Page 26: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

16

not forecasts. Instead they are descriptions of scenarios

in terms of what should be. Predictions may or may not

reflect historical trends. Normative approaches may use

statistical relationships and extrapolations for background

information. Gaylord (1983) provided caveats to

forecasting: forecasting is a conservative approach since

it cannot predict sudden and unanticipated deviations from

historical trends; it is not causal; and it requires

consistent and precise data.

School district decision making is more accurately

described as consumer rather than producer behavior because

budget decisions are a function of the interactions between

preferences and budget constraints (Hentschke and Yagielski,

1982b). These authors described three characteristics of

decision making that justify this conclusion. First, the

behavior of local decision makers reveals preferences in

dealing with theoretically unlimited wants and budget

constraints. The budget reflects what was given up in some

items in order to gain other items; that is, the consid­

eration of opportunity costs. Second, the principle of

diminishing marginal utility is applicable. The satis­

faction gained from the first unit of a good or service is

greater than the satisfaction that is derived from addi­

tional units. Third, the consumer model suggests causes and

descriptions of fiscal strain: increasing, maintaining or

decreasing levels of consumption. Hentschke and Yagielski

Page 27: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

17

(1982a) also indicated that the consumer model assumptions

are more theorectically valid and empirically descriptive

than the assumptions of the producer model which assumes an

agreed upon definition of quality and a constant level of

the quality of the output of schooling. The consumer model

allows a situation to be described as fiscal strain even

when there is an increase in the total budget. Thomas

(1980) supported the application of the consumer approach.

He stated that the producer approach is inadequate because

it is based on the factory model which oversimplifies the

decision making behavior. It fails to recognize and con­

sider the "multiplicity of decision makers, the diversity of

goals, the complex nature of educational inputs and intri­

cate relationships ... between resources and outcomes" (p.

252) . It is very difficult to determine the utility of

inputs. Alternatives are not comprehensive nor of equal

financial magnitude or consequence (Hentschke and Yagielski,

1982b).

The literature and research cited above provide justi­

fication for choosing multiple linear regression and corre­

lation as a strategy for forecasting school district fiscal

health. Chabotar (1987) indicated that using regression and

correlation statistics to create a causal model is the best

forecasting technique. Its credibility is based on the use

of hard data and the statistical power of the procedures.

Ward (1985) used multiple regression to create a causal

Page 28: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

18

model using bond ratings. Ward's model exhibited 85%

accuracy in predicting presence or absence of fiscal strain.

Studies of School District Fiscal Health

Murphy (1980) tried to determine if financial, demo­

graphic, economic, electoral or environmental variables

could be identified that would characterize school districts

in Ohio that were financially troubled or that were experi­

encing fiscal strain. He identified financially troubled

districts as those that were forced to close between 1976

and 1978, and districts that received emergency loans from

the state. All other school districts were considered to be

fiscally healthy. The study used analysis of variance to

differentiate variables that distinguished the two groups of

school districts. Murphy concluded that:

1. Financially troubled districts are primarily classified as central city and rural.

2. Over-staffing is not a factor contribut­ing to the fiscal problems of financially troubled districts.

3. Financially troubled districts are concentrated in the northern and southern sections of the state.

4. Financially troubled districts are spread over more geographical space. This differ­ence was not translated into significantly higher per pupil transportation expenses.

5. Financially troubled districts are characterized by high proportions of special cost students.

6. Financially troubled districts cannot be characterized as declining enrollment districts.

Page 29: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

19

7. Financially troubled districts can be characterized as low fiscal capacity districts in terms of having lower median family income. There was not a significant difference when fiscal capacity was defined in ... equalized assessed valuation per pupil.

8. Financially troubled districts had a significantly lower equalized millage rate. Unequalized and debt millages were not signifi­cantly different between financially troubled and non-troubled districts.

9. Financially troubled districts are low revenue districts. Almost all the difference is in locally raised revenue.

10. Financially troubled districts are characterized as high health and interest expense districts and as low instruction, general control, and plant maintenance expense districts.

11. Financially troubled districts appear to pass fewer requests for millage.

(Murphy, 1980, pp. 177-184)

The variables in Murphy's study that met the criteria

of being subject to change or under the control of local

decision makers are particularly relevant to the current

study. Murphy concluded that the level of staffing was not

a factor that contributed to fiscal strain. However,

personnel costs were significant because they constituted

the largest portion of a school district's expenditures due

to the labor intensive nature of schooling. Murphy also

noted that locally raised revenue accounted for most of the

difference between financially troubled and non-troubled

districts. Financially troubled school districts were

characterized by high health and interest expenses while

Page 30: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

20

expenditures for instruction, general control and plant

maintenance were low.

Berny attempted to identify the variables that could be

used to discriminate between financially troubled and

non-troubled rural school districts using a causal-

comparative research method. Multiple discriminant analysis

was conducted to determine the relative influence of six

fiscal and demographic variables: geographical size,

special cost children, fiscal capacity, tax effort, total

general revenue and excess staff. Financially troubled

school districts were those districts that closed and those

districts that applied for preclosing audits. Berny

concluded that:

1. There was no discernible statistical difference between the rural districts defined as financially troubled and non-troubled for any of the years studied on any of the variables tested.

2. None of the selected variables possessed a higher discriminating capacity than any of the others.

3. When examined from a nonlinear point of view, there was no interactive or cumulative effect of the selected variables that exceeded the effect of any one alone.

(Berny, 1982, p. 480)

It is significant that the variables investigated in

Berny's study did not discriminate troubled from non-

troubled rural school districts. It appears that the

variables were not relevant to the question studied.

However, his results contradicted certain conclusions of

Page 31: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

21

Murphy (1980) who used a larger sample that included rural,

urban and suburban districts. Murphy found that financially

troubled districts were characterized by large geographic

area, high proportions of special cost students, low fiscal

capacity, low tax effort and low revenue. Berny agreed with

Murphy (1980) that staffing levels did not discriminate

levels of fiscal health.

Lee (1983) attempted to predict fiscally distressed

school districts using ratio analysis. School districts

that received emergency state loans in 1981 were identified

as experiencing fiscal distress; 36 of the 615 school

districts in Ohio were eliminated from the study because of

problems with data. Lee analyzed financial and staffing

ratios using multiple discrimination analysis and correla­

tion. He used the qualitative dependent variable of dis­

tressed or not distressed. Five ratios, which displayed

predictive significance, were used in the fiscal distress

predictive model included the following:

1. True Day's Cash Ratio = (12/31/80 Cash Balance-Encumbrances) / (1980 Current Expendi­tures/365 days)

2. True Ending Cash Balance Ratio (12/31/80 Cash Balance-Encumbrances) / (1980 Total Operating Funds)

3. Salaries/Operating Ratio = 1980 Salaries & Wages / 1980 Total Operating Funds

4. Salaries-Fringes/Operating Ratio = 1980 Salaries & Wages + Fringe Benefits / 1980 Total Operating Funds

Page 32: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

22

5. Investment Earnings Ratio = 1980 Invest­ment Earnings / 19 80 Total Operating Funds

Lee concluded that:

1. Financial ratios have the ability to forecast fiscal distress as early as one year in advance. ... historical data were able to forecast over 90 percent of the districts that eventually experience financial problems.

2. Liquidity ratios demonstrated strength in forecasting financial problems in school districts. Unlike private business enterprise ... education ... is more sensitive to cash balance fluctuations.

3. Elementary/secondary institutions are labor intensive. In this study, the percent of operating funds spent for salaries, wages and fringe benefits proved to be potent indicators of impending fiscal doom.

4. Although not the primary cog in the fiscal distress model, the Investment Earnings ratio enhances the accuracy of the model.

5. ... expenditures and revenues per pupil have little or no value in forecasting fiscal distress. These conclusions do not recommend the banishment of per pupil expenditure data, but caution their use in respect to fiscal health.

6. There were no relationships found between elevated staffing levels and fiscal distress.

7. Trend ratios, measuring changes between the beginning and ending fiscal periods of 1980 did not demonstrate any predictive significance in the Fiscal Distress model.

8. The borrowing or loan repayment ratios were not found to have any predictive relation­ships with fiscal distress.

(Lee, 1983, pp. 261-262)

Authorities in school finance have labelled Lee's study

a milestone in predictive research (Lee, 1983). Conclusions

Page 33: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

23

4, 5, 6 and 8 are of interest since they discuss variables

used in this study. Lee's study was the impetus for Smith's

work.

Smith (1985) based his forecasting study on Lee's

research. Smith redefined fiscal health, the dependent

variable, in quantitative terms, defined the variables using

raw data, examined more areas and analyzed a time frame of

three years rather than one year. His population consisted

of all 616 school districts in Ohio. Independent variables

included specific indicators in the categories of liquidity,

salaries and capital projects funds. Smith concluded that:

1. ... school district fiscal health lends itself to considerable predictability.

2. ... predictability improves with shorter prognostic periods.

3. ... predictive models, as developed in this study, are highly temporal — that is, they are unique to each fiscal period.

4. ... the consistent nature gf the find­ings, particularly the pattern of R values and the rankings ... demonstrate the general validity for the approach taken by this study.

5. ... a relatively few indicators, when considered together with all the indicators examined, contribute to the predictability of school district fiscal health. The five most important, in descending order, are: (1) person­nel costs; (2) local receipts; (3) liquidity; (4) purchased services; and (5) investment earnings.

6. ... some of the indicators examined are weak predictors of school district fiscal health, when considered together with the other variables examined. They are, in descending order of importance: (1) material, supply and textbook expenditures; (2) capital outlay expenditures; (3)

Page 34: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

24

voted and effective millage; and (4) capital project fund indicators.

7. ... indicators maintain their relative importance irrespective of the prognostic period.

(Smith, 1985, pp. 139-140)

This study builds upon Smith's work. Raw data were

used as independent variables; levels of fiscal health have

been identified in order to make comparisons within each

year and across years. The techniques were applied to the

present study of school district budgets in Texas using a

function/object type of budget format.

Identification of Variables

The selection of independent variables was based

primarily upon criteria established by Smith (1985) which

require that:

1. Its numerical value must be capable of being changed by local decision makers.

2. Its potential usefulness (in making forecasts) is indicated by relevant literature; and

3. The data used to compute it must be readily available and accurate.

(Smith, 1985, p. 84)

In addition to Smith's criteria, fiscal indicators were

selected as independent variables because the best projec­

tions are based upon the lowest level of detail; that is,

the most specific information that is available, not lump

sums (Chabotar, 1987). Also, these independent variables

Page 35: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

25

are used consistently throughout the state, are relatively

easy for all school districts to provide, and are compre­

hensible and usable in terms of budget decisions ("Is Your

Budget in Tune?", 1981).

Research studies cited above validate the variables

that were selected for this study. Those studies were

conducted in other states; therefore, the variables do not

have exactly the same labels as those that are used in the

Texas budget format. Some of the variables used by Murphy

(1980) were tax rate, locally-raised revenue, health

expense, plant maintenance and personnel costs. Berny

(1982) included fiscal capacity and tax effort. Lee (1983)

constructed ratios using cash balance and expenditures.

Smith (1985) included personnel costs, local receipts,

material, supply and textbook expenditures and local

receipts.

Table 2.1 lists and defines the independent variables

and indicates the years in which they are found in the

budgets. A total of 66 variables was identified and used in

this study. Texas Education Agency revised the budget

reporting form during the years included in this study;

therefore, the same fiscal indicators are not found in each

year, although the budget format remained the same. The

major revisions that affected this study were made after

1981-1982, when tax data categories for maintenance taxes

and debt service taxes were combined into totals for the

fiscal years 1982-1983 and 1983-1984.

Page 36: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

26

Fiscal Year

1980- 1981- 1982-1981 1982 1983

X X

Maintenance Taxes

1983-1984

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

Table 2.1

VARIABLES

Variable Identification and Explanation

VI Balance of funds

Vll Assessed valuation

V12 Tax rate/$100

V13 Gross taxes assessed

V14 Discounts and adjustments

V15 Net taxes assessed

Vl6 Estimated uncollectible current taxes

V17 Net taxes collectible on current year's levy

V18 Total current year deferred revenue (...to be collected in subsequent years)

VI9 Current year tax revenue

V20 Prior years tax revenue

V21 Penalties, interest and other tax revenue

Debt Service Taxes

X

X

X

X

X

X

X

X

X

V22 Assessed valuation

V23 Tax rate/$100

V24 Gross taxes assessed

V25 Discounts and adjustments

Page 37: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

X X

X X

X X

27

TABLE 2.1 (continued)

^ ^ V26 Net taxes assessed

^ ^ V27 Estimated uncollectible current taxes

X V28 Net taxes collectible on current year's levy

V29 Total current year deferred revenue (...to be collected in subsequent years)

V30 Current year tax revenue

V31 Prior years tax revenue

^ ^ V32 Penalties, interest and other tax revenue

Total Tax Data (Maintenance Plus Debt Service)

X V33 Total appraised value per tax roll

X V34 Total appraised value for school tax purposes

X V35 Calculated tax levy

X V36 Additional tax levy generated due to bond rate charged against exempted homestead property

X V37 Tax levy loss due to tax freeze

X V38 Other adjustments, and discounts

X V39 Net taxes assessed

Expenditures by Function

X X X V50 Instruction

X V51 Instructional computing

X X X V52 Instructional administration

Page 38: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

28

TABLE 2.1 (continued)

X X X V53 Instructional resources and

media services

X X X V54 School administration

X X X V55 Instructional research and development

X X X V56 Curriculum and personnel development

X X X V57 Communications and dissemination

X X X V58 Guidance and counseling services

X X X V59 Attendance and social work services

X X X V60 Health services

X X X V61 Pupil transportation -regular

X X X V62 Pupil transportation -

exceptional children

X X X V63 C o - c u r r i c u l a r a c t i v i t i e s

X X X V64 Food s e r v i c e s

X X X V65 G e n e r a l a d m i n i s t r a t i o n

X X X V66 Debt s e r v i c e

X X X V67 P l a n t m a i n t e n a n c e and o p e r a t i o n

X X X V68 Facilities acquisition and

construction

X X X V69 Management (Data Processing)

X X X V70 Computer processing X X V71 Development (Data Processing)

Page 39: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

29

TABLE 2 . 1 ( c o n t i n u e d )

X X X V72 I n t e r f a c i n g ( T e c h n i c a l

a s s i s t a n c e )

X X X V73 Community s e r v i c e s

Revenue from L o c a l and I n t e r m e d i a t e S o u r c e s

X X X V80 L o c a l m a i n t e n a n c e t a x

X X X V81 Debt s e r v i c e t a x

X X X V82 L o c a l r e v e n u e from s e r v i c e s t o o t h e r LEA's and ESC's

X X X V83 T u i t i o n and f e e s from p a t r o n s

X X X V84 T r a n s f e r s from w i t h i n t h e s t a t e

X V85 Transportation fees from patrons

X X

X X

X X

X X

X X

X V86 Enterprise funds

X V87 Other revenue from local sources

X V88 Revenue from intermediate sources

X V89 Non-revenue receipts (proceeds from bonds, loans, lease/pur­chases, etc.)

X V90 Revenues from outside the state

X V91 Transfers in

Page 40: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

30

Consequently, the number of variables examined each year of

this study is less than 66. Variables were assigned numbers

arbitrarily; VI is the fund balance; Vll through V39 are tax

data; V50 through V73 are expenditures by function; and V80

through V91 are revenues.

Summary

Chapter II discussed the recent evolution of a rela­

tively new area of school finance. The importance of con­

tinuous planning was emphasized because the school budget

reflects educational needs and priorities and can be used as

a measure of comparison among school districts. Causes of

fiscal stress were identified along with forecasting techni­

ques in order to facilitate the budget planning process. It

was discussed that school district budget planners take a

consumer approach to decision making. Studies by Murphy

(1980), Berny (1982), Lee (1983) and Smith (1985) indicated

that multiple regression and correlation techniques were

appropriate statistical procedures to use in this study.

These studies also identified criteria to use in selecting

variables. Tax data, expenditures by function, and revenue

subject to the control of local decision makers were

selected as variables for this study and divided by refined

average daily attendance to provide common units of

comparison. The methodology was selected based upon the

Page 41: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

31

studies cited in this chapter and because of the structure

of the budget that is mandated by Texas.

Page 42: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

CHAPTER III

PROCEDURES AND PRESENTATION OF THE DATA

The purpose of this study was to analyze a strategy for

forecasting school district fiscal health in Texas. Cash

balance was selected as the quantitative measure of school

district fiscal health, the dependent variable, and the

fiscal indicators of tax data, expenditures by function and

revenues divided by refined average daily attendance were

the independent variables. The goal of this study was to

determine if the relationships between the dependent vari­

ables and the independent variables could be used to predict

fiscal health.

The purpose of this chapter is to describe the research

procedures. Phases of the study are outlined; the popula­

tion is defined; statistical strategies are identified; and

data are presented.

Source of the Data

In phase one, fiscal data for the official budgets were

obtained from Texas Education Agency Division of Policy

Analysis. Master computer files included all fiscal data

that were submitted by each school district to the Texas

Education Agency, district names and identification numbers,

32

Page 43: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

33

and refined average daily attendance for all school dis­

tricts and Education Service Centers in the state.

Fiscal data were taken from the Texas Education Agency

Official Budget for Texas Public Schools for the fiscal

years 1980-1981, 1981-1982, 1982-1983 and 1983-1984.

Sorting the Data and Identifying the Variables

Phase two of the study consisted of sorting the data.

Variables were identified and data files were constructed.

Texas Education Agency provided dumps of their fiscal files

which included extraneous data that had to be eliminated.

The population for this study consisted of all school

districts in the State of Texas that offered programs for

grades kindergarten through twelve. Deleted from the study

were school districts that did not offer those grades and

Education Service Centers which were identified according to

information in the Texas Education Agency School Directory

for the years included in the study. As shown in Table 3.1,

the total number of school districts included in the study,

the N of cases, varies from year to year because school

districts were either consolidated or created. Differences

in the N of cases did not affect the results of the multiple

regressions because this study examined budget characteris­

tics in general and not the fiscal performance nor budgets

of individual school districts.

Page 44: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

34

TABLE 3.1

NUMBER OF SCHOOL DISTRICTS INCLUDED IN THE STUDY

1980- 1981- 1982- 1983-Quartile 1981 1982 1983 1984

1 245 245 245 245 2 245 245 245 245 3 245 245 244 245 4 244 244 244 245 Total N 979 979 978 979

Page 45: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

35

A number of data files were set up in order to process

the data and to provide a means of checking the process.

The data files include the following information: names of

all school districts and their refined average daily

attendance listed by county-district identification number;

all school districts with all budget items included in the

study listed in order of county-district identification

number; all school districts ranked according to fund

balance divided by refined average daily attendance

(dependent variable); all school districts with all budget

items selected for this study divided by refined average

daily attendance and ranked according to fund balance

divided by refined average daily attendance; and, all school

districts with all dependent and independent variables

listed in order by county-district identification numbers.

Budget categories selected for use in this study were

divided by the refined average daily attendance. This

provided a common means of comparison. School districts

were ranked according to the dependent variable and the data

for each year were divided into quartiles so that compari­

sons could be made among four levels of fiscal health within

each year and across years.

Statistical Procedures

Phase three of the study consisted of statistical

analysis of the data. The data files were organized to

Page 46: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

36

facilitate the use of stepwise multiple regression. Statis­

tical Package for the Social Sciences (Nie et al. 1975;

Hull and Nie, 1981) was employed using the facilities of the

Texas Tech University Academic Computing Services.

The first step in the statistical analysis of the data

was to generate descriptive statistics that were examined to

determine whether multiple regression procedures were appro­

priate. The mean and standard deviation of dependent and

independent variables for all school districts, displayed in

Tables 3.2, 3.3 and 3.4 were generated along with

correlation matrices for all variables for all school

districts, which are located in Appendix A, Appendix B and

Appendix C. These statistics provide a preliminary

understanding of the data that were selected for the study.

Pearson product-moment correlations were calculated for all

possible pairs of dependent and independent variables.

Because no controls were made for the influence of other

variables, these are called zero-order correlations (Nie et

al. 1975).

Page 47: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

TABLE 3.2

MEAN AND STANDARD DEVIATION, 1980-1981 INDEPENDENT VARIABLES, 1981-1982 DEPENDENT VARIABLES,

ALL SCHOOL DISTRICTS N = 979

37

VARIABLE

VI Vll V12 V13 V14 V15 V16 V18 V19 V20 V21 V22 V23 V24 V25 V26 V27 V29 V30 V31 V32 V50 V52 V53 V54 V55 V56 V57 V58 V59 V60 V61 V62 V63 V64 V65 V66 V67 V68 V69 V70

MEAN

518.715 125976.959

2.414 1001.284 10.644 990.640 19.520 971.120 945.612 16.676 3.944

126339.420 0.328

151.860 1.574

150.285 3.028

147.257 142.781 3.125 0.796

1289.235 23.664 35.742 105.178 1.008 0.096 0.207 34.499 1.723 13.970 124.580 3.194 49.469 18.224 266.287 161.739 290.020 248.929 0.264 0.321

STD. DEV.

752.814 237334.284

3.481 1051.052 27.935

1037.147 39.186

1024.908 1010.951 23.642 8.435

237286.628 0.528

173.009 5.667

170.845 4.919

169.306 166.265 4.726 3.678

460.413 42.810 28.115 59.733 11.934 4.146 1.389 39.134 5.424 32.569 98.852 14.240 48.369 44.175 214.863 171.176 271.208 797.294 4.763 3.254

Page 48: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

38

TABLE 3 . 2 ( c o n t i n u e d )

VARIABLE MEAN STD. DEV,

V71 0.000 0.000 V72 0.017 0.483 V73 5.868 61.708 V80 966.233 1016.473 V81 146.702 167.781 V82 2.894 20.743 V83 2.846 6.106 V85 0.372 1.657 V86 3.168 18.179 V87 43.558 155.899 V88 18.898 63.339 V84 3.481 15.371 V90 0.158 4.831 V89 52.585 445.019

Page 49: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

39

TABLE 3 . 3

MEAN AND STANDARD DEVIATION, 1 9 8 1 - 1 9 8 2 INDEPENDENT VARIABLES,

1 9 8 2 - 1 9 8 3 DEPENDENT VARIABLES, ALL SCHOOL DISTRICTS

N = 979

VARIABLE MEAN

VI Vll V12 V13 V14 V15 V16 V17 V18 V19 V20 V21 V22 V23 V24 V25 V26 V27 V28 V29 V30 V31 V32 V50 V52 V53 V54 V55 V56 V57 V58 V59 V60 V61 V62 V63 V64 V65 V66 V67 V68

628.047 236004.075

16.487 1142.359 11.274

1131.085 19.428

1111.656 30.751

1080.905 16.551 4.249

236601.623 2.362

176.065 1.822

174.243 3.172

171.071 5.698

165.372 3.481 6.734

1450.647 26.342 41.454 124.465 0.775 1.661 0.329 38.559 1.786 15.534 138.904 3.702 58.869 21.893 296.041 191.928 333.330 274.286

STD. DEV.

965.273 711478.493

23.440 1166.779

29.309 1151.273

30.269 1138.290

40.473 1128.079

28.973 8.432

711423.671 4.145

208.300 5.844

205.482 5.678

203.067 8.768

199.138 5.742 1.294

565.893 40.668 33.503 71.732 11.129

9.760 0.067

40.547 5.081

36.743 106.878

12.396 56.439 49.158

228.559 216.809 257.858 930.963

Page 50: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

40

TABLE 3 . 3 ( c o n t i n u e d )

VARIABLE MEAN STD. DEV.

45.566 2.887 1.125 0.513

54.897 1133.702

200.718 29.569

7.014 61.279 22.423

122.032 72.118

9.748 547.921

V69 V70 V71 V72 V73 V80 V81 V82 V83 V84 V86 V87 V88 V90 V89

1.849 0.438 0.053 0.032 5.721

1103.705 169.587 4.325 3.487 5.224 4.526 51.357 20.795 0.454 67.128

Page 51: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

41

TABLE 3.4

MEAN AND STANDARD DEVIATION, 1982-1983 INDEPENDENT VARIABLES, 1983-1984 DEPENDENT VARIABLES,

ALL SCHOOL DISTRICTS N = 978

VARIABLE MEAN STD. DEV.

VI V50 V51 V52 V53 V54 V55 V56 V57 V58 V59 V60 V61 V62 V63 V64 V65 V66 V67 V68 V69 V70 V71 V72 V73 V80 V81 V82 V83 V84 V86 V87 V88 V90 V91 V89 V33 V34 V12 V23

669.925 1591.870

2.833 29.128 45.652 139.761 0.714 2.084 0.445 42.288 2.029 16.956 145.628 4.331 96.985 181.620 307.741 207.628 355.756 310.063 0.184 0.938 0.361 0.022 5.647

1217.141 192.205 4.667 4.485 8.123

110.843 77.056 19.986 0.394 4.199 72.743

346473.771 291496.260

14.172 1.940

865.890 534.814

12.442 44.986 33.839 75.090 11.048

8.504 2.491

42.888 5.663

39.731 108.363

13.204 71.469 71.827

217.773 262.320 243.840 907.272

2.298 4.579

10.209 0.285

52.334 1207.168

246.312 23.245

8.850 35.570 88.024

145.264 71.780

7.671 32.156

446.868 948656.139 936934.602

21.130 3.541

Page 52: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

42

TABLE 3 . 4 ( c o n t i n u e d )

VARIABLE MEAN STD. DEV.

1345.724 7.250

29.171 45.310

1323.975

V35 V36 V37 V38 V39

1466.868 1.169 18.537 16.835

1432.980

Page 53: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

43

In the final phase of statistical analysis, data were

subjected to stepwise multiple regression which yielded

prediction equations (Cornett and Beckner, 1975; Kerlinger,

1973; Kim and Kohout, 1975) based on correlation. Multiple

linear regression was selected because this multivariate

procedure can be used to analyze effects of more than one

independent variable on a dependent variable. It is the

most useful and flexible method because any number of

continuous or categorical variables can be analyzed; and it

is appropriate for non-experimental variables to examine

within-group variance (Kerlinger, 1973).

The stepwise regression program examined each variable

that was selected for analysis. The computer entered one

variable at a time in single steps beginning with the

variable that explained the greatest amount of variance with

the dependent variable and continuing in descending order of

importance. Three options were used to determine which

variables were included in the regression equation generated

by the program (Nie, et al. 1975). The first option

permits the programmer to select or limit the number of

variables that may be included in the predictor list. The

second option is the determination of the minimum value of

the F ratio that the programmer will accept for variables to

be included in the equation. F ratios were computed for

independent variables not yet included. The F ratio was the

value that would be obtained if the variable were included

Page 54: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

44

on the next step. The tolerance of an independent variable

was the third option. Tolerance is the proportion of the

variance of that variable not explained by the variables

already included.

The values of the options selected for this study

exceeded the default values. All variables were included in

the analysis. The F value was set at .05; the default value

is .01. The tolerance index was set at .20; the default

value is .001. More conservative default values were

selected to make the data more manageable and to include in

the equation those variables that had greater explanatory

power.

A total of 15 stepwise regressions was conducted.

Independent variables for 1980-1981 were regressed against

the dependent variable for 1981-1982; independent variables

for 1981-1982 were regressed against the dependent variables

for 1982-1983; independent variables for 1982-1983 were

regressed against the dependent variable for 1983-1984. The

regression program yielded a number of statistics that

described the relationship between fiscal indicators, the

independent variables and cash balance, the dependent

variable.

Summary Tables 3.5 through 3.19 display values of

2 2 multiple R, R , R change, simple R and B, the regression

2 coefficient, for independent variables with R change

greater than or equal to .01. Multiple R, the multiple

Page 55: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

45

CQ t-H ' ^ o^

• «—1

CN m KD

• rH

O a\ ^

• i n

o en r^

• 1

vo cr> vo

• o

«

IT) •

ro

W 1 ^ ffi < E-t

W h^ ffi < E-i

>H K

en w t ^ CQ < H ff;

H

< H W

< <: « EH S > < U s p w

s o H W W w «

o w K

w h^ fi^ M EH t ^ D S

EH

2 H Q 2; H CM H D IS H

i H 00 cr» i - i 1

o 00 <T> i H

> M «

EH EH

S W W M Q P IS H t- CU O K O Q ffi

U CN CO 00 cr. f j rH t^ 1 <

T-H 00 CT\ rH

W tJ CU s H W

w o 2 <: re u a w «

w p rt: D O W

tf

2: o H EH

<:

a is H

W

w OQ <

>

H

H EH

D

H

OQ

H Pi < >

CN

ro rH

ro o

ro CM o

cy> 00 o ro

00 ro t-H

• O

KD 00 O

• O

00 CM O

• o

rH CM o

• o

CM rH O

« o

00 ro r H

IT) CM CM

ro i n CM

"^ r-CM

r^ 00 CM

CM

ro ro o in

CN in

ro in

o in

00 r-t >

V^ 00 >

o CM >

* * T-i >

in

in

Page 56: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

46

PQ cri CM ro

• o 1

r^ i n 00

• CM 1

O ^ CM

• rH

^ V£) :< •

o 1

cr» o> 00

• i n r-\

^ 00 I ^

• i-{

Pi

V£> •

ro

W 1^ PQ < EH

W t-q W m H <: h i H EH PQ 1-5

< P3 >^ H <C Pi p; H < < «

s > < S > H D EH •q W IS EH H

H IS EH 2 : P W « O IS Q < H H ^ ; D w cu w a W W P< W D W EH p; IS Q W O H « W CM H Pi rH 00 fa

00 <T\ W cr> tH i-:i «-! 1 eu 1 -H H O 00 EH 00 CTi ^q cr. rH D H

s

H Hi PU S H W

H U S < K U

a w Pi

H Pi < P

a w Pi

Pi

IS

o M ^ < o a H

2 : H

W W i-:i CQ < H p; < >

w hi (h M tH ^J D S

W t-q PQ < M Pi < >

r-CM CM

• o 1

VD V£) rH

• O 1

r>-r-o

• o

o 00 o

• o 1

o CO T-i

• o 1

VD CM O

• o 1

in o

ro CM o

rH O

o

o rsi o

o o o

o o o

^ r-o

00 00 o

<y\ o rH

<y\ rH T-^

V£> i n r-t

r^ CM CN

• o

ro t^ CM

• o

00 a\ CN

• o

o ro ro

• o

i n * * ro

• o

i n a\ ro

• o

^ o 00

• in CM

>

CN T-\

CM >

O y£> >

m CM >

i n CN >

-p (n

§

Page 57: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

PQ CM 00

in

o I

CM in 00

CM

r •

ro

W hi PQ < ir^

W t^ W CQ W <; hi H EH CQ t^

< PQ X M <: Pi Pi H < rt: Pi s > <; w S > h P EH H W S EH EH

H IS P: IS Q H <: O IS Q P M w IS a Ui CU K CO fa CU Q fa O fa 2 Pi s p o O H U fa CM fa Pi rH 00 W

00 a \ fa <r> rH ^^ H 1 PH I H H O 00 EH 00 O^ t-1 C5 H P H

Pi

fa 1-1

H W

fa

u o w Pi

fa Pi < p o w Pi

ro CM

o I

00

o 00 o

ro o

00 x-\

o •

o

ro 1-i

o •

o

** r-i

o •

o

ro T-^

o •

o

o r-{ O

• o

00 r H O

• o

(N ro o

• o

VD 'sr O

• o

o i n o

• o

o r o

• o

IS

o H EH <: p a fa IS H

W fa t-1 CQ < H Pi < >

Pi

fa Hi P4 H E H hi

P

s

fa hi PQ < H

Pi

>

ro in rH CM

CM VD CM

ro >

O 00 VD CN 00 rH > > >

in crv o •

in ro CM

8

Page 58: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

48

PQ

169

• o

468

• o 1

398

• o 1

702

• o

Pi

00 •

ro

fa hi PQ < b^

fa hi PQ

w fa

< hi fa EH

>H Pi (rf s s p w IS

PQ hi < PQ H < Pi H <: Pi > <

> fa ^ hQ IS EH H fa IS EH P fa Pi

o IS p <: H W W fa Pi o fa Pi

fa t ^ PH H EH h:i P S

fa IS P cu fa a fa P4 P fa P IS P Pi H H

CM ffi r H 00 EH 00 CTi CJ\ y-^ H 1

1 H O 00 00 a\ (T» T-i rH

fa hQ P4

s H W

fa o IS < K u o w Pi

fa Pi < p a w Pi

«

IS o H EH < P a fa

2; H

W fa hQ PQ < H PS < >

fa ^A Cu H EH hi P s

fa hi CQ < H Pi < >

1—1

in i H

• o

'^r o^ o

• o 1

00 CM 1-i

• o 1

T-i

in o

• o

CM CM O

CM O O

o o o

CN CN O

r-^ o

00 in o

o r^ o

r-{ in rH

• O

r^ rH CM

• O

CM ^ CN

• O

'5J< \D CM

• O

•«* \D r-i

430

o ro in K£> i n > >

00

>

Page 59: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

49

CQ VD r-i o

• CM

a\ VD ro

• o

00 00 VD

• o

^ in in

• ^

CM CN CTi

-36

Pi

C3> •

ro

fa hi OQ < iri

fa hQ W PQ fa < h:i fa EH PQ h^

< CQ >< H <C Pi Pi H < < ^ S > < fa § > 1-1 P EH W IS EH

H EH

fa IS Pi IS P fa O Z P H fa 2 W CU fa CO fa PU fa P fa Pi IS p U H fa CM Pi TH 00

00 <y> fa 0^ rH ^A H 1 P< 1 H H O 00 EH 00 a\ nq cr. rH P -H S

< P O

E EH Pi P O fa

fa hQ CU S H in

fa o IS < ffi u a en Pi

fa « < p a w p;

Pi

z o H EH < P a fa

fa hi OA H EH h l p S

cn fa 1-3 CQ < H Pi < >

fa hi CQ < H Pi < >

VD 00 ro

VD o ro

in in CM

vo a\ «H

VD o rH

CN r^ ^ r-i o o

rH O O

o^ ^ rH

. o

cr> in CN

• o

rH O ro

. o

a\ rH ro

• o

r-i ro ro

• o

vo 00 ro

cr> o in

<j\ ^ in

in VD in

vo r-in

o t-\

00

V87

V20

V65

V16

V12

(Cons

Page 60: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

50

CQ r -" r ro

• o

H 00 VO

• o

CM ^ ro

• CM

t ^ in r~

• o

'^ ro ro

• ro 1

CM ro VD

• T-i

ro

fa hi PQ < E H

fa 1-1 cn CQ fa < h^ ^ OQ

< >H H Pi Pi < <

>

IS fa p IS

p cn

IS O H fa cn P4 cn fa fa p Pi IS o H fa Pi CN

00

fa cr> i^ H

fa 1 ^ OQ < H

Pi

>

IS fa P IS fa P4 fa p

Cl4 H EH hi P

s

I T-i 00 cr>

cn EH O H Pi EH cn

hi o o ffi u

ro cn 00

I CN 00

hi

<

Pi

fa hQ

s H cn

fa

<

u a cn Pi

fa Pi < p a cn

Pi

Pi

IS

o H EH < P

a fa

^ H

cn fa hQ CQ < H Pi < >

fa hi Oi H EH h^ P S

fa (-1 CQ < H Pi < >

o o

ro 00 ro

vo

ro

CM vo ro

o CM

VD rH

O

o vo 1-i

• o

rH "* r-i

• O

r-in o

• o

rH rH O

• O

ro T-\

o •

o

CM r H O

• o

o vo

CN O ro

in ro ro

00 ro

o

o o ' d '

• o

cr» '^ in

• o

G^ cr> in

• o

a\ o vo

• o

o CM VO

• o

00 ro vo

• o

ro ^ 00

• in

in T-i

>

<Ti 00 >

r-00 >

in VD >

rr VD >

r>> CM >

g u

Page 61: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

51

CQ ro rsi ro

• o

^ 00 ^

• o 1

CM i n ro

• o 1

00 ro ^

t

o

CM ^ ro

• ^

i n VD CM

• o 1

Pi

rH T-i

• ro

fa hi CQ < b^

fa hQ cn OQ fa < h i fa EH PQ h i

< PQ >H H < P^ Pi H << •< Pi S > < fa S > hi P EH H cn 3 EH EH

fa IS p; IS P fa < O IS P P H fa IS a cn p< fa cn fa Pn EH

fa p fa cn Pi IS P Pi O H H fa ro fa Pi CM 00

00 a\ fa CTi rH h i H 1 CU I CM H rH 00 EH 00 0^ h i C^ rH P H

s

fa hi Oi

s H cn

fa o s < ffi u a cn Pi

fa « < p a cn

Pi

Pi

IS o H EH < P a fa

IS H

cn fa (-1 CQ < H Pi < >

fa h l PH H EH hi P s

fa hQ CQ < H Pi < >

'cr * * T~<

• o

rH [ ^

o • o

1

CM " 5 ^

T-i •

O 1

CTt i n o

• o

00 VD o

• o

ro 00 o

• o 1

o (N O

CM o

ro T-i

o o

T-i

o o

o o

o rH

o o

o CN o

00 ^ o

T-i VD O

i n r-o

CN CN i-H

CM ro T-i

^ ^ x-i

9

O

<y> rH CM

• O

r--«* CN

• O

i n r-" CM

• o

o> * * ro

• o

ro vo ro

• o

i n ro vo

• 00 VD

§

00 o VD >

' ^ VD >

i n i n >

r CM >

CM VD >

-P CO G 0 U

Page 62: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

52

PQ

.164

o

.726

CN

862

o

191

CN

118

o 1

340

o

501

rH

111

o 1

368

r-i

.916

CM 1

CM rH

t

ro

fa hi CQ < iri

fa hQ PQ

cn fa

< h i fa bi

>H Pi

P cn

PQ yA < PQ H < p; H < Pi > <: fa

> h i ^ H IS EH EH fa IS Pi

IS P fa <

o H cn cn fa « O fa P:

fa hQ P4 H ^ hQ p

s

IS P P fa S O PH fa fa PH P P fa IS 2 P O H U

ro fa CN 00 cn 0 0 <T> OS T-i rH 1

1 CN rH 00 CO CJ O^ T-i rH

IS

o H < P

o fa IS H

cn fa hQ OQ < H

Pi

>

fa hQ P4

H

cn

fa O IS < ffi u a cn Pi

fa Pi < p a cn

Pi

p;

fa h i P4 H EH hi P

fa h i CQ < H Pi < >

CM in

o CM o

T-i

o

VD

o

o o 00

o

00 CM VD O

ro

o cr> o

o I

o I

o I

ro

o

VD T-i

o

o

ro T-i

o

o

o T-i

o o

rH

o

o

o rH

o

o

T-i

o

o

in T-i

o

o

o

o

ro CM o

o ^ o

ro i n o

' 5 * '

VD O

^ r-o

r-00 o

r--cr> o

T-i

rH rH

I ^ CM rH

00 VD T-i

CN in T-i

o o CM

o ro CM

ro in CM

ro CM

in CN

CN rH ro o

ro ro

in ro

i n ro 00

• o CN

CM T-i

r^ CM i n ro > >

IT) >

vo 00 >

ro vo >

i n CM >

vo vo >

a\ CN >

r-CM >

§

Page 63: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

53

PQ vo o ^

• o 1

<y\ in ^

• o 1

00 ro o • o 1

^ T-i

o • o

Pi

ro rH

• ro

fa hQ PQ < iri

fa 1-1 cn OQ fa < hQ fa EH CQ hQ

< CQ >i i-i f^ Pi tf H < <: Pi s > < s > w P EH hQ cn IS EH H

fa IS EH IS P fa Pi O IS P < H fa S P cn cu fa a cn fa P4 fa p fa p Pi IS p Pi O H H fa ro « Pi CM 00 EH

00 cr. fa Cr» rH 1-1 H 1 C^ 1 CM H rH 00 EH CO a> hQ <y> rH P H S

fa hi P4

s H cn

fa O S < ffi u o cn Pi

fa Pi < p a cn Pi

IS

o H < P a fa

Pi

fa hQ pu H EH hi P

cn fa hi CQ < H Pi < >

fa 1 ^ CQ < H Pi < >

00 VD CM

• O

^ 04 rH

• o 1

i n r^ rH

• o

CM o CM

• o

CN

o CM T-i

o o

o rH O

o

rH O

o

CM r-o

* * 00 o

* * <T\ o

00 o rH

CO VD CN

O

CM o ro

CM

ro

in in

CTi

CM

§

ro »H >

VD CO >

'^r (N >

O i n >

4J cn g p U

Page 64: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

54

PQ

.850

o

.486

CM

.158

o 1

.549

00 1

423

ro

196

o 1

143

r^ ^

878

ro

070

vo 1

449

o 1

Pi

'sr T-i

. ro

fa hi PQ < EH

fa hi cn PQ fa < hQ fa EH CQ hQ

< PQ >i ^-^ < Pi Pi H < < Pi s > < w S > hQ P EH H cn IS EH EH

fa S Pi IS P fa < o 2: p P H fa IS O cn pu fa cn fa P ffi fa P fa EH « 21 p Pi O H P fa ro O Pi <N 00 fa

00 as fa CJ rH hQ «H 1 PH I CM H rH 00 EH 00 <r» ^q a* rH P H S

fa hQ Cm S H

cn

fa o z < K u a cn Pi

fa Pi < P a cn

Pi

Pi

IS o H ^ < P a fa

2: H

cn fa hi CQ < H Pi < >

fa hQ CU H b^ 1-1 P s

fa t J ffl < H p; < >

.503

o

.327

o

209

o 056

o 1

114

o

072

o

118

o

206

o

.129

o

.115

o

ro in CM

o o

ro

o TH

o o

o o

rH

o o

TH

o

o

ro rH

o

o

ro rH O

o o o

ro in CN

ro CN ro

vo vo ro

ro 00 ro

in as ro

as o 'd '

ro CM ^

VD ro »*

o in ' ^

T-i

vo ' ^

ro o in o

00 vo in

• o

in o vo

• o

as rH VO

• o

00 CN VO

• o

as ro vo

• o

o in VD

• o

o vo VD

• o

o r~> VD

• O

as r^ VD

• o

CM VU (M

063

§

as 00 >

,-i vo >

o VD >

CO rH >

CO vo >

r-CM >

o CO >

' ^ vo >

r-vo >

4J CO C u u

Page 65: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

55

OQ ro 00 in • o

as 1-i CO • o

in

ro

fa hi CQ < E H

fa hi cn OQ fa <

P cn

o H

1 ^ CQ <

>H H Pi Pi < <

>

iri

fa P IS fa

cn cu cn fa

fa hQ CQ < cn H b^ Pi u

fa Pi

p IS

O H fa p; ro

00 fa as hQ tH PH I H CM EH CO hi as P H S

< >

EH IS fa P ^ fa Oi fa ffi P U

cn

CO as

H Pi iri cn H p hQ O o

I ro 00 as

hi hQ <

Pi

fa hi P4

s H cn

fa o IS < u

a cn Pi

fa p; < p o cn

Pi

Pi

r-rH in • o

ro vo CM • o

r vo CM • o

00 rH o • o

VD CM

VD 00 CN

IS o H B^ < P a fa IS H

cn fa hi OQ < H Pi < >

fa t - 1 Oi H ^ ( P s

fa hi CQ <: H Pi < >

r-

.51

o

as ro >

in ro in

ro vo a\

• in

CO >

CO

g

Page 66: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

56

OQ VO VD ro • o

^ rH rH • o 1

CN VD ro •

rH 1

r cr> rf • o 'sr

ro as ro • o

fO CO VD • o 1

00 ro o • o 1

Pi

fa hQ

s H cn

ro vo ro as

vo o

ro o

'vt* o a\ o

o I

o I

o I

o I

vo

ro

fa O IS < U

a cn Pi

vo CM o • o

r-rH O •

O

o I-I o • o

rH rH O • o

CM rH o • o

rH T-i

o • o

o rH O • o

fa hi OQ < ti

fa Pi < P a cn Pi

vo CM O

^ •cy O

"^ in o

in vo o

r-r-o

as 00 o

as as o

IS

o H < P

a fa

Pi

fa hQ

H

P

ro VD rH

• o

as o CM

CM ro CM

vo i n CN

as

rsi

00 a\ CM

i n rH

ro o

vo

00

CN

2: H

cn fa hQ CQ < H Pi < >

fa

OQ < H

Pi

>

00 i n >

VD CM

g g 5 00 ro >

CM T-i >

00 >

-P CO

Page 67: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

57

OQ rH * * CM

• O

rH T-i rH

• o

VD CM O

• o 1

ro

fa hi OQ <

fa hi cn OQ fa < hi

OQ <

>H H p; Pi <

s p cn

IS

o

>

iri IS fa P IS

H fa cn Oi cn fa fa p

fa hQ OQ < H Pi < fa > hi

IS H

Pi o fa Pi ro

CO fa as h:i H P4 I H CN EH 00

Pi < p a p 2: o u

^ fa 00 cn

T-i I

ro 00 as

EH

fa P IS fa Oi fa p

hi p

cr>

2 O H EH < P a fa

Pi

fa hi

PH

H

cn

fa o

u a cn Pi

fa Pi < p a cn

Pi

Pi

fa 1 ^ p^ H

hQ P S

cn fa (^ OQ <: H Pi < >

fa hi 03 < H Pi < >

cr> o

o a\ o o

vo rH O o

ro T-i

o o

o o

VD CN O

as ro o

<T> ro rH

CM VD

as ro

ro

CM o as

• ro CM

g

CN ' ^ in >

in ro >

4-> CO

c P U

Page 68: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

58

PQ CM 00 CO • o

^ r vo • CM 1

ro vo CO • o 1

ro o .H •

O

ro '* ro • o

r-r CM • o 1

Pi

CO

ro

fa hQ PQ <

fa h i cn CQ fa

hQ CQ <

X H

Pi Pi

> p cn

IS o

IS fa p

fa cn P cn fa fa P Pi ^ o H fa Pi ro

00 fa as hQ H PLI I H CM EH 00 h i as P H

fa h : | OQ < H Pi < >

p

fa hi

EH IS EH fa (^

< P

fa O Oi fa p p Pi

H

00 EH as T-i I

ro 00 as

cn

fa O IS <

u

a cn Pi

fa Pi < p a cn

fa t ^ CU s

'r in 1-i

• o

ro rH 1-H

O 1

'r a\ o

t o 1

^ in T-i

• o

** as o • o

ro ^ o • o 1

Pi

IS o H ^ < P a fa s H

cn fa hi CQ < H Pi < >

fa hi 0* H EH ^A P S

fa iJ CQ < H Pi < >

ro CN o CN

o

ro rH O O

rH O

O

CM rH

o

o

o T-i

o o

ro rsi o

in ^ o

00 in o

vo r o

CO CO o

a\ as o

'r in T-i

• o

CM T-i CM •

O

CM ^ CN •

O

r>-r CN • o

CO as CN • o

in rH ro • o

o CN 'a* •

542

ro as in >

o vo >

r vo >

CN in >

4-» CO

§

Page 69: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

59

OQ r-T-i

r •

o

CO CO r •

rH

O ro ro •

1

in CM o • ro 1

T-i

in o •

VD ro

as in in •

^

CM o a\

9

O

Pi

<T> T-i

• ro

fa hi 01 < ^

fa hQ cn PQ fa <; hQ fa EH m hi

< CQ >H H < Pi Pi H < < Pi S > < fa S > hQ P EH H cn IS EH EH

fa IS Pi IS p fa <: O IS P P H fa 2; O cn cu fa cn fa a. ffi fa P fa EH Pi IS p p; O H P fa ^ o Pi ro CO fa

CO as fa Cr> rH hQ H 1 PH I CO H CN CO EH CO o^ hi O^ rH P rH S

fa 1^ cu S H cn

fa o IS < ffi

u o cn Pi

fa p; < p a cn

Pi

Pi

IS

o H EH < P

a fa

s H

cn fa tJ CQ < H Pi < >

fa hi PH H EH tJ P

s

fa hQ CQ < H Pi < >

in r-ro

r-Oi CM

CM T-i O

r vo rH

VO VO rH

ro as CM

vo ro ro

o r 00 ro rH o o

rH

o

o

ro rH O o

ro rH O o

o

o

o r-r- vo

CTv o T-i CM

o

CN CN

ro CN

ro vo CM

in r ro •

o

T-i CN 'r •

O

ro ^ ^ •

o

as in •^ • o

ro r-'^ •

o

r 00 ** • o

ro TH in • o

r--CN o •

061

in ro >

00 >

o ro o^ ro in vo vo VD in vo > > > > >

-P CO

c 8

Page 70: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

60

correlation coefficient, indicates the correlation between

the dependent variable and the weighted sum of the indepen­

dent variables. 2

R , the coefficient of determination, indicates the

amount of variability in the dependent variable that can be

explained by an independent variable; that is, the strength

of the relationship (Nie et al. 1975) . This statistic is

the square of the multiple correlation coefficient. Cause 2

and effect relationships cannot be determined from R . 2

The amount of change in R , RSQ Change, indicates the 2

amount of change in R at each successive step. This sta­

tistic was used to determine at what step the addition of

independent variables did not add significantly to the

amount of variance that was already explained by variables

already included in the regression equation.

Simple R, the zero-order correlation coefficient, is

included in the summary tables for convenience. This sta­

tistic indicates the strength and direction of the rela­

tionship between variables.

B is the partial regression coefficient. It represents

the expected change in the dependent variable for each

change of one unit in an independent variable when the other

variables in the equation are held constant (Nie et al.

1975). Combined effects of variables are additive.

Finally, the constant is provided. This statistic is

the Y intercept. The F ratio and beta values are not

Page 71: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

61

included in the summary tables because the stepwise regres­

sion program excluded independent variables that did not

meet or exceed the value of the specified F ratio and the

variables are presented in descending order of their beta

values.

Analysis of the Data

Phase four of the study consisted of analyzing the data

generated by the stepwise multiple regression program. The

data were analyzed to answer the research questions. First,

is school district fiscal health predictable? Second, what

fiscal indicators, subject to the control of local decision

makers, can be used to forecast school district fiscal

health? Third, do different indicators have predictive

significance for school districts with a higher level of

fiscal health than for those school districts with a lower

level of fiscal health? Finally, does the methodology

employed in this study provide a viable strategy for differ­

entiating levels of school district fiscal health?

The data in the summary tables includes all independent

variables that met the criteria chosen for the F ratio and

tolerance options. The researcher decided to further reduce

the number of variables by limiting the models to those

2 variables that displayed a change m R greater than or

equal to .01; that is, those variables that accounted for

one percent or more of the variance in the dependent

Page 72: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

62 2

variable. The R value for each model is displayed in Table

2 3.20. R values were examined to compare the amount of

variability in the dependent variables that were attributed

2 to each model. The R values for all 15 regression runs are

displayed in Table 3.20.

Table 3.21 identifies those variables, the values of

2 the change in R for each, and the budget category of each

variable. Although 15 multiple regressions were run, dis­

cussions and further analysis will focus on the data that

were obtained for all school districts, the first quartile

2 and the fourth quartile. The R values of the models for

2 the extremes were higher than the R values for the second

and third quartiles except for the models derived from the

1981-1982 independent variables.

Table 3.22 displays the means and standard deviations

of cash balance for models that include all school dis­

tricts; first quartile and fourth quartile. It appears that

the low values of R^, from Table 3.20, for the first quar­

tile correspond with the low cash balance as displayed in

Table 3.22. Higher cash balances were found for the fourth

quartile and for all school districts. The means of cash

balance for all school districts for all years included in

the study displayed the greatest variability according to

the values of the standard deviations.

Page 73: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

TABLE 3.20

TOTAL R VALUES

63

Independent Variables

Dependent Variables

All School Districts

First Quartile

Second Quartile

Third Quartile

Fourth Quartile

1980-1981 1981-1982 1982-1983

1-1982

.285

.128

.070

.070

.331

1982-1983

.394

.095

.134

.108

.461

1983-198

.286

.099

.050

.099

.249

Page 74: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

64

CN

ro

fa h i

fa O IS <

u •-< o

a . cn a o iri

in ^ H < 12 P a cn fa fa h i PQ < H IS Pi <

p; o

>

EH

fa P IS fa Pi P o fa p IS

in

Pi fa EH

< fa

ro CO a\

I

CM 00 as

-P

CM 00 as

I

I-H 00 as

O Cn cn C Pi fO

U

Q) r-i X! fO

•H 5H

>

u o

3 -P OQ fO

U

0)

O C cn to p; i i :

u 0)

rH

•H u to >

CO CTt

I

o 00 as

4J O

cn IT> ^3 (U 13 4J OQ fO

U

(U

a C cn to Pi ^

u

<u

to • H

SH

to >

(U o cn cn

T l CU

OQ to

* u

r^ 00 VD rH CM O

VD r^ O rH CM rH O CM rH rH iH rH rH rH O O O O O O O

o r^ 00 'r ro ro rH ^ ro rH rH rH rH rH rH O O O O O O

as r-ro 00 > >

CO vo CM 00 CM r^ in in in r- ro rH 00 > > > > > > >

i n P>- o ro ON ro i n ro CO vo vo vo i n vo > > > > > > >

in Pi W f a f a f a E H E H P i E H p i W f a f a f a W

O rH r^ rH r o CM VD - ^ i n rH rH rH 1-1 r H O O O O

O r-- ro '^ rH O CN CM rH rH rH rH

o o o o o o

in o^ r^ in 'ST r-TH 00 00 vo vo CM > > > > > >

CO o ' ^ i n r^ CN i n vo vo i n rvi VD > > > > > >

E H p i P i f a f a E H fafafafaEHfa

CO VD CO rH CM ro 00 CM CM rH rH O O O O

TH ro ^ o O o m c>i T-i c^ T-i T-i o o o o o o

00 i ^ o 'S" i n rH CO CN rH VD > > > > >

^ CN rH o ro i n VD rH CM vo CM CN > > > > > >

EH Pi EH EH fa fa EH EH W E-I EH

r o o r o r ^ r ^ « ! * ^ r o r o ^ - ^ i n t ^ ' ^ r r H - r H r H r H r H r H r H C N O O O O O O O O O

o ^ r ^ r H O o o o o r ^ o ^ ^ ^ C O O O V O V D r H V D C M O O V O V D > > > > > > > > > >

piPifafaEHfaEHpifafa

CTi O CM r - CN «;}' rH « * rH rH T H rH O O O

r^ o i n VO CM CO CM vo rH rH > > > > >

Pi EH fa EH EH

Q)

>

Pi

Pi

o • H 4J U

c 4H

Q) }H :3 4-> • H TJ C G)

X fa

fa

to

to

r-i 0 0

j : :

o

CO j j

u •H U -P to

•H cn p

Q) rH •H

+J -p cn u u to

•H 13

fa a

rH x: -H •p -p }H U 3 to O J3 fa a

X to EH

Ii

in

Page 75: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

65

00

as T-i

I ro 00 cr>

U

to 4J

O

to +J TJ to

cn p

to

s

r-ro ' ^

• i n 00 00

CM as CM

• O VD

O i n vo

• CM ^ CM

i n CM a\

• as vo vo

r-vo as

• T-i

o t -H

i n a\ as

• CN CM r-

CM CM

• ro fa hi

cn IS o H in < H > fa fa U P IS

< Pi ^ < OQ

p

< cn EH <

cn u p fa IS o < cn

I fa

ro CO cr> rH I

CM 00 as

CM CO

as rH I

rH CO

cn

•73 }H

u

O •H

to +J TJ to

to 4J cn p

to Q)

o •H

to -P Ti 10 to 4J cn p

ro

CN

vo VD

as

CO

CN

in

in VD

in in

in ro

• in

CM

o in

r-"sr o

• CO CM VO

CM rsi o

• ro as

as o vo

• CM in VD

VD

in

d to Q) S

t-i 0 0 XJ u cn t-\

t-i

i n rH r^

• 00 rH

in

cn 4J U

•H VH 4-> cn

•H < p

•P cn u

•H fa

^ vo VD

• r-r~-

Q) rH •H •P U to :3 o

o o as

9

VD

13

2

Q) rH

45 -H JJ 4J U U p to 0 J3 fa O

Page 76: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

CHAPTER IV

PRESENTATION AND ANALYSIS OF DATA

The purpose of this chapter is to investigate the

research questions that were presented in Chapter I. The

questions are addressed separately using stepwise multiple

regression as the primary statistical method in order to

examine the relationships between the independent variables

of tax data, expenditures by function, and local revenues,

and the dependent variable, cash balance. For purposes of

reporting and analyzing the statistical results, several

groups of school districts were used. The first group

included all school districts in Texas (N for 1980-1981 and

1981-1982 was 979; N for 1982-1983 was 978). Next the

districts were divided into quartiles on the basis of fiscal

health as measured by cash balance divided by refined

average daily attendance. Because there appeared to be

little differences in the two middle quartiles, the decision

was made to focus the analysis on the first quartile (N=245)

and the fourth quartile (N=244), which represented the

extremes. In addition, a three-year time period was used to

provide a longitudinal analysis of the results.

66

Page 77: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

67

Discussion of Research Questions

1. Is fiscal health predictable?

This question was investigated by subjecting the

variables to stepwise multiple regression. Independent

variables for 1980-1981 were regressed against the dependent

variable for 1981-1982; 1981-1982 independent variables were

regressed against the dependent variable for 1982-1983;

1982-1983 independent variables were regressed against the

dependent variable for 1983-1984. For all models, variables

were restricted to those that contributed one percent or

more to the variability of the dependent variable.

2 An examination of the R values for the models for all

school districts and for school districts in the first and

fourth quartiles in Table 3.20 indicates that 9.5 percent to

46.1 percent of the variance in the dependent variable could

be attributed to the independent variables that were

included in the models. For the 1980-1981 models, the

2 values of R were 28.5 percent for all school districts,

12.8 percent for the first quartile, and 33.1 percent for

the fourth quartile. For the 1981-1982 models, the values

of R were 39.4 percent for all school districts, 9.5 per­

cent for the first quartile, and 46.1 percent for the fourth 2

quartile. For the 1982-1983 models, the values of R were

28.6 percent for all school districts, 9.9 percent for the

first quartile, and 24.9 percent for the fourth quartile.

Page 78: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

68 2

The R values indicate that the models derived in this

study do not have a high level of predictive significance.

Only moderate predictive values were found for all school

districts and for school districts in the fourth quartile. 2

The values of R for the models in the first quartile were

too low to be of value in predicting school district fiscal

health. It appears that there are other intervening factors

beyond the scope of this study that would improve the

ability of regression models to predict school district

fiscal health. Therefore, school district fiscal health

cannot be predicted with accuracy using the methods employed

in this study.

2. What fiscal indicators, subject to the control of

local decision makers, can be used to forecast school

district fiscal health?

Fiscal indicators that are subject to control by local

decision makers were examined, for example, tax rate/$100,

current year tax revenue, adjustments- and discounts,

instructional administration, health services, plant mainte­

nance and operation, tuition and fees from patrons, enter­

prise funds, non-revenue receipts, and so forth. The

regression program was run using 54 independent variables

for 1980-1981; 55 independent variables were included in

1981-1982; 44 independent variables were analyzed in 1982-

1983. The SPSS stepwise multiple regression program

included all independent variables that were statistically

Page 79: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

69

significant at the .05 level in the regression equation.

Because most of the variables accounted for a very small

amount of the variance, the number of variables that were

included in the models was reduced further by identifying

those that exhibited a change in R greater than or equal to

.01; that is, those independent variables that had the

greatest influence in the regression equation. The vari-

ables that displayed R values greater than or equal to .01

and the frequencies with which they appear in the models are

summarized in Figure 4.1.

The number of variables included in the models varies

from two to ten, with five, six or seven variables being

included most often. Most of the variables that exhibited 2

values of R greater than or equal to .01 were expenditures

by function and tax data rather than revenue items. Because

cash balance basically reflects the difference between

expenditures and revenue, with 9 8 percent of local revenue

derived from local tax collections, it appears that school

district decision makers should exercise greatest discretion

in establishing tax rates and adjustments to tax rates along

with how they decide to spend revenues. Cash balance

depends upon tax rates and expenditures as well as revenue.

Even with low revenues, expenditures can be adjusted to

enhance cash balance.

Page 80: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

70

Frequency Variable Identification

Maintenance Taxes (1980-1981, 1981-1982)

3 V12 Tax rate/$100

1 V14 Discounts and adjustments

1 V15 Net taxes assessed

1 V16 Estimated uncollectible taxes

2 VI8 Total current year deferred revenue

2 V20 Prior years tax revenue

1 V21 Penalties, interest, and other tax

revenue

Debt Service Taxes (1980-1981, 1981-1982)

1 V23 Tax rate/$100

1 V25 Discounts and adjustments

3 V27 Estimated uncollectible current taxes

Total Tax Data (1982-1983)

1 V35 Calculated tax levy

1 V38 Other adjustments and discounts

1 V39 Net taxes assessed

Expenditures by Function

1 V53 Instructional resources and media

services

1 V54 School administration

1 V55 Instructional research and development

FIGURE 4.1

FREQUENCIES OF VARIABLES THAT ARE INCLUDED IN THE MODELS

Page 81: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

71

1 V56 Curriculum and personnel development

2 V58 Guidance and counseling services

4 V60 Health services

1 V61 Pupil transportation-regular

1 V62 Pupil transportation-exceptional

1 V63 Co-curricular activities

4 V64 Food services

4 V65 General administration

1 V67 Plant maintenance and operation

1 V68 Facilities acquisition and construction

1 V69 Management (Data processing)

1 V72 Interfacing (Technical assistance)

Revenue from Local and Intermediate Sources

1 V80 Local maintenance tax

7 V87 Other revenue from local sources

2 V89 Non-revenue receipts (proceeds from bonds, loans, lease/purchases, etc.)

FIGURE 4.1 (continued)

Page 82: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

72

According to the data in Figure 4.1, only six

independent variables occur in the different models more

than two times. They are: V12 - maintenance tax rate/$100,

V27—estimated uncollectible current debt services taxes,

(V12 and V27 occur only in 1980-1981 and 1981-1982 because

of revisions in the budget format. Maintenance and debt

service tax data were combined after 1982.), V60—health

services, V64—food services, V65—general administration

and V87—other revenue from local sources.

Tax rate seems to occur frequently because it is the

basic determinant of local tax revenue, the largest source

of local revenue. Regardless of the appraised value per tax

roll and to compensate for uncollectible tax revenues, the

tax rate must be adjusted to meet the local revenue needs of

the school district.

Estimated uncollectible debt service taxes, V27,

occurred in three of the nine models, all of which occurred

using 1981-1982 independent variables. This variable

displayed a negative correlation with cash balance only in

the fourth quartile. School districts can estimate the

amount of taxes that cannot be collected by examining the

history of tax collections and economic conditions, but they

have less control over uncollectible taxes than they do over

other tax items in the budget. Results indicate that this

variable is a significant factor related to fiscal health.

Page 83: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

73

Both health services, V60, and food services, V64, are

pupil services that occur in four of nine models. Health

services had a negative correlation in all models where it

occurred except in the fourth quartile in 1982-1983. Food

services displayed negative correlations with cash balance

where it occurred in the first quartiles in 1980-1981 and

1981-1982. Food services may be self-supporting or subsi­

dized. Where it appeared in the model for all school

districts and the fourth quartile for 1981-1982, it had a

positive correlation with cash balance. Increasing demands

are placed on schools to provide services related to educa­

tion that are not direct instructional services. It appears

that the high costs of providing these services must be met

by the local school districts.

Variable 65, general administration, also occurs in

four models. It had a positive correlation in all models.

This function detail encompasses all activities that include

overall administrative responsibilities, including such

areas as the board of education, superintendent's office,

security, staff accounting, tax administration and computer

services. Costs include salaries, supplies and equipment.

Variable 87, other revenue from local sources, occurs

most frequently appearing in seven of the models. It has a

negative correlation with cash balance only in the model for

the first quartile for 1982-1983. This function includes

earnings from permanent funds and endowments, temporary

Page 84: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

74

deposits and investments, net receipts from revolving funds

or clearing accounts, rent, gifts and bequests and any other

revenues from local sources. It appears that school

districts were very enterprising and were able to generate

local revenues from sources other than taxes. This variable 2

ranked first, second or third in its R change in models for

all school districts and for school districts in the fourth

quartile. It contributed the least of all variables that

were included for the first quartile for 1982-1983. The

values of the change in R for V87 range from .010 to .149.

This indicates that local decision makers must continue to

explore alternate sources of revenue.

3. Do different indicators have predictive signifi­

cance for school districts with a higher level of fiscal

health than for those school districts with a lower level of

fiscal health?

Figure 4.2 displays the variables that were included in

the models for all school districts, the first quartile and

the fourth quartile. While models within the same year do

not include all the same independent variables, they do have

some variables in common. For 1980-1981, variables 87, 65

and 20 appear in models for all school districts and in the

model for the fourth quartile which have the highest means

of cash balance. Variable 12 appears in the first quartile

and the fourth quartile. Variables 18, 14, 64, 21, 60, 23,

25 and 16 appear only in one model.

Page 85: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

75

1980-1981

All School Districts

First Quartile

Fourth Quartile

V18 Total current year deferred revenue V87 Other revenue from local sources V20 Prior years tax revenue V14 Discounts and adjustments V65 General administration

V64 Food services V12 Maintenance tax rate/$100 V21 Penalties, interest and other tax revenue V60 Health services V23 Debt service tax rate/$100 V25 Debt service discounts and adjustments

V87 Other revenue from local sources V20 Maintenance tax prior years tax revenue V65 General administration V16 Estimated uncollectible current maintenance

taxes V12 Maintenance tax rate/$100

1981-1982

All School Districts

First Quartile

Fourth Quartile

V15 Net maintenance taxes assessed V87 Other revenue from local sources V89 Non-revenue receipts (proceeds from bonds,

loans, lease/purchase agreements, etc.) V65 General administration V64 Food services V27 Estimated uncollectible current debt

service taxes

V58 Guidance and counseling services V60 Health services V64 Food services V55 Instructional research and development V27 Estimated uncollectible current debt

service taxes V62 Pupil transportation-exceptional V89 Non-revenue receipts (proceeds from bonds,

loans, lease/purchase agreements, etc.) V87 Other revenue from local sources V61 Pupil transportation-regular

FIGURE 4.2

VARIABLES INCLUDED IN THE MODELS FOR ALL SCHOOL DISTRICTS, FIRST QUARTILE

AND FOURTH QUARTILE

Page 86: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

76

total current year V60 Health services V18 Maintenance taxes

deferred revenue V68 Facilities acquisition and construction V27 Estimated uncollectible current debt

service taxes V80 Local maintenance tax V64 Food services V67 Plant maintenance and operation

1982-1983

All V39 School Districts V87

Net taxes assessed (maintenance plus debt service) Other revenue from local sources

First Quartile

V58 Guidance and counseling services V54 School administration V56 Curriculum and personnel development V72 Interfacing (technical assistance) V38 Other adjustments and discounts (mainte­

nance plus debt service) V12 Maintenance tax rate/$100 V8 7 Other revenue from local sources

Fourth Quartile

V35 Calculated tax levy (maintenance plus debt service)

V87 Other revenue from local sources V60 Health services V63 Co-curricular activities V69 Management (data processing) V53 Instructional resources and media services V65 General administration

FIGURE 4.2 (continued)

Page 87: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

77

In the models for 1981-1982, variables 89 and 87 appear

in all school districts and the fourth quartile. Variable

60 appears in the first quartile and the fourth quartile.

Variables 64 and 27 can be found in all three models for

this year. Variables 15, 65, 58, 55, 62, 61, 18, 68, 80 and

67 appear only once in different models.

The models for 1982-1983 display the least amount of

variables in common. Variable 87 appears in all three

models. The other variables, 39, 58, 54, 56, 72, 38, 12,

35, 60, 63, 69, 53 and 65 appear only once in different

models. Therefore, the models for 1982-1983 provide the

greatest discrimination among different levels of fiscal

health.

The differences between the means of cash balance for

all school districts and the fourth quartile are less than

the differences in the means between the first and fourth

quartiles, and between the first quartile and all school

districts. Therefore, we might expect to find more

similarities in the models for those groups than for groups

that have greater differences in the means of their cash

balances as is the case with variables 87, 65 and 20 in the

models for all school districts and school districts in the

fourth quartile. Variables that appear in more than one

group seem to be more significant in predicting fiscal

health than variables that appear only in one model.

Variable 12, maintenance tax rate/$100, was likely to be a

Page 88: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

78

significant variable in all models because it determines the

amount of local tax revenue that a school district could

expect to collect, subject to adjustments and discounts.

The models for the first and fourth quartiles have the

least variables in common. Therefore, research question

number three can be answered in the affirmative. Different

indicators have predictive significance for school districts

with a higher level of fiscal health than for those school

districts with a lower level of fiscal health.

4. Does the methodology employed in this study

provide a viable strategy for differentiating levels of

school district fiscal health?

The statistical methods employed in this study are

accepted standard procedures for predicting and forecasting.

The question of whether the methodology employed in this

study provides a viable strategy for differentiating levels

of school district fiscal health requires an examination of

the variables that were included in the regression models.

If this were a viable strategy, the models in different

years should include the same variables so that the

method/models could be used in any year to predict fiscal

health in the following year.

Referring again to Figure 4.2, we see that variable 87

is the only variable that occurs in the models for all

school districts in all three years. V87, other revenue

Page 89: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

79

from local sources, includes earnings from permanent funds

and endowments, earnings from temporary deposits and

investments, net receipts from revolving funds or clearing

accounts, rent, gifts and bequest, and any other

miscellaneous revenue from local sources. As mentioned

above, it appears that school districts are finding ways to

generate local revenue from sources other than taxes.

In the models for school districts in the first

quartile, variables 60 and 64 appear in 1980-1982 and

1981-1982. Variable 12 appears in 1980-1981 and 1982-1983.

Variable 58 appears in the models for 1981-1982 and

1982-1983. For models in the fourth quartile, variable 87

appears in all three years; variable 65 can be found in

1980-1981 and 1982-1983. Differences in the models among

years seem to be due to changes in economic and/or political

conditions. Therefore, the methodology employed in this

study did not provide a strategy for accurately forecasting

levels of school district fiscal health.

Page 90: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

CHAPTER V

SUMMARY, MAJOR FINDINGS,

CONCLUSIONS AND RECOMMENDATIONS

The purpose of this chapter is to briefly summarize the

study, present major findings, present conclusions and to

make recommendations using the data that were presented and

analyzed in Chapter IV. Conclusions will be made regarding

the relationships between the independent variables,

specific budget categories and the dependent variable, cash

balance. Each research question as well as the overall

perspective of the study will be addressed.

Summary

Because school district budgets are prepared at the

local level, local decision makers bear the greatest

responsibility for the fiscal health of their school

districts. Educational needs and priorities are translated -1

into fiscal indicators or budget categories. The major .1

purpose of this study was to contribute to school finance

research by examining the relationships between fiscal

indicators and fiscal health so that budget planners could

exercise greater control over the fiscal health of their

school districts.

80

Page 91: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

81

The Problem of the Study

The focus of this study was to forecast school district

fiscal health by identifying budget categories that had the

greatest impact on cash balance. A major assumption was

that fiscal security could be improved by increasing cash

balance. The problem was restated in four research

questions.

1. Is school district fiscal health predictable?

2. What fiscal indicators, subject to the control of

local decision makers, can be used to forecast school

district fiscal health?

3. Do different indicators have predictive

significance for school districts with a higher level of

fiscal health than for those school districts with a lower

level of fiscal health?

4. Does the methodology employed in this study

provide a viable strategy for forecasting levels of school

district fiscal health?

Procedures

The research for this study was conducted in four

phases. The purpose of Phase I was to determine the

feasibility of the study by reviewing the relevant school

budget and school finance literature and by contacting the

Texas Education Agency to establish that data were

available. Phase II of the study consisted of sorting the

Page 92: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

82

data to isolate the variables and to construct files to run

the stepwise multiple regression program. Phase III

consisted of analysis by running the stepwise multiple

regression program. Results of the computer program were

analyzed and summarized in Phase IV for presentation and

analysis.

Major Findings

To analyze the data, stepwise multiple regression

models were examined for three groups. Fiscal health was

used to divide the school districts into quartiles and an

analysis was conducted for all school districts. Summary

data were analyzed for all school districts and the

extremes, which are the school districts in the first and

fourth quartiles. Findings for each research question will

be addressed separately.

1. Is school district fiscal health predictable?

For the models using the 1980 independent variables,

fiscal health was not predictable for the school districts 2

in the first quartile. The value of R was only .128.

Moderate values of R^, .285 and .331 were obtained for all

school districts and for the fourth quartile, respectively. 2

For 1981-1982 independent variables, R for all school

districts was .394; R^ for the first quartile was .095; and

R2 ^ Q ^ j g fourth quartile was .461, which was the highest

Page 93: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

83

value found in the study. Fiscal health for the first

quartile could not be predicted reliably. 2

The lowest R values for the models for all school

districts and for the fourth quartile were found in the

portion of the study that used 1982-1983 independent 2 -)

variables. R for all school districts was .286; R for the

first quartile was .099; R^ for the fourth quartile was

.249.

2

A consistent pattern of R values was found across the

years; that is, the highest values were found in the models

for all school districts and for the models in the fourth 2

quartile. The lowest values of R were displayed by models in the first quartile. It appears that the amount of vari-

2

ance that is explained by the change in R increases as the

amount of cash balance increases. Local decision makers can

control factors to improve fiscal health; that is, to

increase cash balance. However, as reported above, the 2

values of R for models derived from this study indicate

that school district fiscal health cannot be reliably

predicted.

2. What fiscal indicators, subject to the control of

local decision makers, can be used to forecast school

district fiscal health?

In the analysis of the statistical data, models

included only those variables that contributed one percent

or more to the variance in fiscal health. The models did

Page 94: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

84

not contain the same variables, which was to be expected for

models in the same group of school districts across years.

The model for the first quartile should have included the

same variables if it were useful to predict fiscal health

across years.

The data also indicated that variables that occur in 2

more than one model do not exhibit the same influence, R

change, upon fiscal health. This is another indication of

the differences among the models for different groups. The 2

same values of R change were not expected- because school

districts were sorted into groups according to cash balance.

One perspective for answering question two is to focus 2

on change in R ; that is, the amount of variability in the

dependent variable, cash balance, that could be attributed

to each of the independent variables. The analysis and 2

discussion focused on independent variables that had R

changes greater than or equal to .01 or only one percent.

Those independent variables comprise the models. It is

useful and more practical to limit the independent variables

2 that displayed a change in R of five percent or more.

Table 5.1 displays those independent variables in descending

order of R^ change. For variables that appear in more than

one model, the largest value of R is provided in the table.

Page 95: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

85

TABLE 5.1

INDEPENDENT VARIABLES WITH R^ CHANGE GREATER THAN OR EQUAL TO .05

Variable R^ Change

V39 Net total taxes assessed (1982-1983) .267

V89 Non-revenue receipts .253

V15 Net maintenance taxes assessed .160

(1980-1981, 1981-1982)

V87 Other revenue from local sources .149

V35 Calculated total tax levy (1982-1983) .140 V18 Total current year deferred maintenance .138

revenue (1980-1981, 1981-1982)

V20 Prior years maintenance tax revenue .110 (1980-1981, 1981-1982)

V64 Food services .051

Page 96: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

86

Net total taxes assessed obtained the highest value of 2 R change. It accounted for 26.7 percent of the variance in

cash balance for the model that included all school

districts using 1982-1983 independent variables.

Nonrevenue receipts displayed the second highest value 2

of R change by accounting for 25.3 percent of the

variability in cash balance for the model that included

school districts in the fourth quartile for 1981-1982.

Revenue in this category includes proceeds from sales of

bonds, land, buildings, equipment, insurance recovery,

lease-purchases and loans. 2 Net maintenance taxes assessed obtained the R change

value of .160 in the fourth quartile for 1981-1982. This

item reflects adjustments made to gross taxes assessed.

Other revenue from local sources, V87, ranked fourth 2

with an R value of .149. This item includes earnings from

permanent funds, endowments, temporary deposits,

investments, rent, gifts and bequests.

Calculated total tax levy includes taxes levied for

maintenance and debt service, which were not identified

separately in the budget document after 1982. The value of

change in R^ was .140 in the model for school districts in

the fourth quartile for 1982-1983. Total current year deferred maintenance revenue

2 obtained .138 as the value of R change in the model for all

school districts in 1980-1981. Deferred maintenance revenue

Page 97: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

87

is revenue that was targeted for day-to-day operations that

is not collected during the current budget year.

Prior years maintenance tax revenue displayed .110 as 2

the R value for the model that included school districts in

the fourth quartile in 1980-1981. This variable includes

maintenance tax revenue assessed in a previous year that is

collectible in the current year.

2

The final independent variable that displayed an R

value equal to or greater than .05 was food services. This

expenditure includes all expenses associated with providing

meals or snacks such as preparing and serving food,

operating kitchens and storage. Costs include

administration and supervision of food services.

Five of the independent variables presented above are

tax data. It appears that, as a group, tax data have the

greatest impact on the variability of cash balance. This

could be expected since tax structure is the driving

mechanism for the largest amount of locally generated

revenues. It also is noteworthy that three of the tax

categories are maintenance which were separated from debt

categories for 1980-1981 and 1981-1982.

Two of the independent variables are revenue data.

Nonrevenue receipts and other revenue from local sources

indicate that school districts need to be entrepreneurs to

enhance fiscal security by generating revenues through

business transactions such as setting up trusts, renting.

Page 98: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

88

buying and selling property as the markets make such

transactions advantageous.

Food services is the final independent variable

included in this category. As an enterprise service, it is

another area in which school districts can produce profits.

Another perspective for answering question two is to

examine the frequency with which each variable occurs in the

models identified by this study. Variable 87, other revenue

from local sources, appears in seven of the nine models

prepared in this study, which gives it the highest

frequency. Variable 60, health services, V64, food services

and V65, general administration, each appear four times.

Variable 12, tax rate/$100, and V27, estimated uncollectible

current taxes, both appear three times. Variable 18, total

current year deferred maintenance revenue, V20, prior years

tax revenue, V58, guidance and counseling services, and V89,

nonrevenue receipts, appear two times.

A third strategy for identifying the most important

fiscal indicators is to identify those independent variables 2

that exhibit both the highest values of R change and that

appear with the greatest frequencies in the models. Only

five fiscal indicators meet the combined criteria for

selection in this third group and are listed in Table 5.2.

3. Do different indicators have predictive

significance for school districts with a higher level of

Page 99: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

89

TABLE 5.2

FREQUENCIES OF INDEPENDENT VARIABLES WITH R^ CHANGE GREATER THAN OR EQUAL TO .05 THAT

OCCURRED IN MORE THAN ONE MODEL

VARIABLE FREQUENCY R^ CHANGE

V89 Nonrevenue receipts 2 .253

V87 Other revenue from local 7 .149 sources

V18 Total current year deferred 2 .138 maintenance revenue (1980-1981, 1981-1982)

V20 Prior years maintenance tax 2 .110 revenue (1980-1981, 1981-1982)

V64 Food services 4 .051

Page 100: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

90

fiscal health than for those school districts with a lower

level of fiscal health?

Different fiscal indicators are included in the models

for the first and fourth quartiles for 1980-1981 independent

variables. For 1981-1982 independent variables, V27,

estimated uncollectible current debt service taxes, and V64,

food services, appear in both the first and fourth quar­

tiles. The first and fourth quartiles for 1982-1983 share

only V87, other revenue from local sources. Therefore, it

appears that different fiscal indicators have predictive

significance for school districts with a higher level of

fiscal health than for school districts with a lower level

of fiscal health. This seems to indicate a correspondence

between cash balance and the models that were identified as

2 having higher values of R .

4. Does the methodology employed in this study

provide a viable strategy for forecasting school district

fiscal health?

The data generated by the methodology employed in this

study appear to indicate that this methodology does not

provide a viable strategy for forecasting school district

health. Overall, the values of R change are low. The

models for the same quartiles across years do not include

the same fiscal indicators. A viable strategy would yield

higher R^ values and the fiscal indicators included in

models would be consistent.

Page 101: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

91

Conclusions

The perspective of this study focuses on short term

budget decisions. The variables that were analyzed were

budget items planned one year in advance. Studies by Murphy

(1980), Berny (1982), Lee (1983) and Smith (1985) produced

more reliable forecasting models and found stronger rela­

tionships between independent variables and dependent

variables by using variables that reflected long term

decisions such as bond ratings and trend ratios that com­

pared relationships between indebtedness and total budget,

investment earnings and operating funds, encumbrances and

cash expenditures per day. Their results appear to indicate

that variables reflecting long term budget decisions are

more closely related to cash balance than are the variables

that were used in this study. The results of this study do

not show a strong relationship between the fiscal indicators

that were analyzed and cash balance.

A second indication of the weakness in the strategy to

forecast school district health that was analyzed in this

study is that different variables appeared in the models

across different years. A reliable strategy would use

models that include the same variables. It appears that

other factors affect school district fiscal health more than

those identified in this study. Factors beyond local

control influence local budgets; however, local decision

makers determine local school district budgets; that is, how

Page 102: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

92

money is used. It was interesting to note that although

costs of instruction constitute the largest portion of a

school district budget, instructional costs did not have the

strongest influence upon variability of cash balance. This

could be due to mandates that require certain levels of

staffing. A school district has less flexibility in per­

sonnel matters than it does in enterprise activities.

Cash balance was used as the dependent variable. A

problem that was recognized at the outset of this study was

that cash balance could not be partitioned into balances

from local, state or federal revenues. Also, cash balance

did not include amounts held in reserve accounts.

Recommendations

While this study did not yield a predictive validity

associated with this strategy for forecasting school dis­

trict fiscal health, the goal of determining a viable method

for such predictions remains of significant importance.

Therefore, the following recommendations are proposed:

1. Examine variables associated with long term budget

decisions such as indebtedness, trends or ratios.

2. Examine more recent data because of changes due to

the reforms of 1984 to determine whether the changes in

mandates influence the predictability of school district

fiscal health.

Page 103: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

93

3. Examine factors such as fiscal capacity and tax

effort relative to other school districts.

4. Examine and explore methods by which school

districts can pursue entrepreneurial activities to earn

money through cash and securities transactions and by

renting, buying and selling assets and properties whenever

feasible.

5. Examine means of reducing uncollectible tax

revenues.

Page 104: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

REFERENCES

Berny, C.A. (1982) . Selected variables as discriminators between financially troubled and non-troubled rural Ohio school districts. Journal of Education Finance, 7, 473-483. ""

Burrup, P. E. & Education in Allyn and Bacon.

Brimley, Jr., V. (1982). a Climate of Change. (3rd ed

Financing Boston:

Candoli, I. (1984)

C , Hack, W. G., Ray, J. R. , & Stollar, D. H. School Business Administration: A Planning

Approach. Newton, MA: Allyn and Bacon.

Chabotar, K. J. educational Finance, 12,

(1987). Use of retrenchment. 351-368.

financial Journal

forecasting in of Education

Cornett, J. D. & Statistics for

Beckner, W. the Behavioral

(1975) . Sciences.

Charles E. Merrill Publishing Company.

Introductory Columbus, OH:

Costerison, D. L. Distressed

(1984) . State Assistance to Financially School Districts. (ERIC Document

Reproduction Service No. ED. 246 536) .

Dickmeyer, N. (1979). Assessing the financial health institutions. Education Record, 60, (2), 159-168.

of

Gaylord, T. A. (1983) Planning: Phase

An Approach to Quantitative Fiscal I Report

Department of Development. ED 239 551).

Juneau, AK: Alaska State Education, Statewide Office of Budget (ERIC Document Reproduction Service No.

Hartman, W. T. & Rivenburg, J. W. (19 85). Budget allocation patterns: school district choices for available resources. Journal of Education Finance, 2, 219-235.

Hentschke, G. C. & Yagielske, Jr. (1982a). Fiscal strain — past and future. Educational Horizons, 61, (1), 12-17.

Hentschke, G- C. & Yagielske, Jr. (1982b). School district fiscal strain: implications for state and federal financial assistance. Journal of Education Finance, 8, 52-82.

94

Page 105: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

95

Hentschke, G. C. & Yagielske, Jr. (1983). Response to F. Howard Nelson. Journal of Education Finance, 9, 245-250. -~

Hull, C. H. & Nie, N. H. (1981). SPSS Update 7-9: New Procedures and Facilities for Releases 7-9. New York: McGraw-Hill Book Company.

Is Your Budget in Tune? (1981). The Executive Educator, 3, 25-29.

Jordan, K. F. (1985) . Education vital signs: finance. The Executive Educator, 7 (10), A 11-A 14.

Kerlinger, F. A. (1973). Foundations of Behavioral Research (2nd ed.). New York: Holt, Rinehart and Winston.

Kim, J. & Kahout, F. J. (1975) . Multiple regression analysis: Subprogram regression. In Nie, N. H., Hull, C. H., Jenkins, J. G., Steinbrenner, K., & Bent, D. H., Statistical Package for the Social Sciences. (2nd ed.), 320-367. New York: McGraw-Hill Book Company.

Lee, R. A. (1983). Financial and staffing ratio analysis: predicting fiscal distress in school districts. Journal of Education Finance, 9, 256-263.

Murphy, J. F. (1980) . An analysis of financially troubled school districts in Ohio. Dissertation Abstracts International, 41, 34219A-34220A. (Univeristy Microfilms No. 8100209) .

National School Boards Association (1985). Seventh annual survey of board members. American School Board Journal, 172, (1), 29-32.

Nie, N. H., Hull, C H., Jenkins, J. G., Steinbrenner, K., & Bent, D. H., Statistical Package for the Social Sciences. (2nd ed.). New York: McGraw-Hill Book Company.

Roland, C. (1986). Telephone interview. Austin: Texas Education Agency, Audit Division.

Smith, C. A. (1985) . Forecasting school district fiscal health. Dissertation Abstracts International, 46, 10-A. (University Microfilms No. AAD85-26254).

Texas Education Agency. (1981). 1980-1981 Texas School Directory. Austin, TX: Author.

Page 106: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

96

Texas Education Agency. (1982). 1981-1982 Texas School Directory. Austin, TX: Author.

Texas Education Agency. (1983). 1982-1983 Texas School Directory. Austin, TX: Author.

Texas Education Agency. (1984). 1983-1984 Texas School Directory. Austin, TX: Author.

Texas Education Agency. (1985) . House Bill 72 and subsequent educational legislation: comprehensive references and explanations. Austin, TX: Author.

Texas Education Agency. (1986). Bulletin 679: Financial Accounting Manual (6th ed., change no: 19). Austin, TX: Author.

Texas Education Code, Volume 2, Vernon's Texas Codes Annotated, 23.45b (1978).

Thomas, J. A. (1980). Resource allocation in school districts and classrooms. Journal of Education Finance, 5 , 246-261.

Walker, B. D. (1986) . Telephone interview. Odessa, TX: Ector County Independent School District.

Ward, J. G. (1985). Predicting fiscal stress in large city school districts. Journal of Education Finance, 11, 89-104.

Wegenke, G. L. & Smith, D. B. (1983) . Data Needs for Financial Planners. Ann Arbor, MI: Paper presented at the annual meeting of the Michigan Education Research Association, (ERIC Document Reproduction Service No. ED 238 154) .

Zerchykov, R. , Owen, H., & Weaver, W. T. (1982). A Review of the Literature and an Annotated Bibliography on Managing Decline in School Systems. Boston: Institute for Responsive Education.

Page 107: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

APPENDIX A

97

Page 108: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

98

CN >

o o I

'sr rsj o o oj r>» CM 0> CM rH CN r-«-CN rH CM O ( N rsj

• • • • • • o o o o o o

CM ro vo »* vo rH r^ r^ ro vo ^ VD r^ in o o ^ o ro ro o

• • • • • t •

o o o o o o o I I

CN >

r H

• <

fa hQ OQ <: in

cn fa iJ fa m i-Q < OQ H < Pi H cn

X < Pi EH H > < U Pi > H in in P5 < IS EH EH s fa IS cn

P fa H IS IS P P O fa IS H P< fa hQ EH fa PH O < P fa O

ORREL

81 IN

982 D

L SCH

U CT r H hQ r H 1 <

1 r H O 00 00 as as rH

o CM >

as r H >

00 T-i

>

VD T-i

>

i n T-i

>

•^ T-i

>

ro r H >

CO'* cNrHrocr>r*-CM vocM cNrs jCMrors j ro O O O O O r H O O

o o o o

CTv in o r vo o o o f** cy> rH rH vo o

o o o o o

in t^ ro ro rH o 0^ CO CM 0^ ro ro CM CN CN rH CM O

r CM CT\ ro vo o o O O CN rH VO rH rH TH rH rH O O O O

.171

.461

o

.128

o o 1

VD VD CM O H O

O O

a\ ^ o r-* vo o

o o 1

rH CN rH rH O O

O O 1

CO 00 00 VD CM rH

O O 1

CM CN rH O O rH

O O

VO rH 00 O CN O

O O 1 1

as ro o o o o

o o 1

as vo 00 as rM CN

o o o o 1

rH ro CT\ ro in in ^ vo ^ O CM rH

o o o o

' ^ r^ r«- in o in rvj rs] rH o vo o

o o o 1

r* C3 r^ ^ Cr> rH o o o

o o o

rH ro r^ CM 00 r^ i n ' ^ o

o o o o o o

^ '^ CM 'sr in ra 00 VD CO o 00 <y» CM H CM O CM CM

o o o o o o o I I I

VD vo rH 00 O CM vo <y> in ro rH CM 00 VD o o VD o in r-

o o o o o o

O in CT\ ro ro o rH rH O vo O O 0 0 0 ^ * 0 0

o o o o o o o I I i

CN in in 00 o CN rH rsi o '* o in vo rH O O CM H rH H O

o o o o o o

cr> crs 00 rH i n cy r^ CN CTv (T» o " * o r-ro <T> <T> CM rH <X> O

O O O O O O

rH CM <Ti r o rH CO 00 VO r^ rH 00 CO CM rH CM O CN CM

O O O O O O O I I I

VO in ro o CN rH CT» in ro rH CM 00 in o o vo o in r

o o o o o o o

t ^ o o r o r H c r > o o o oo<y»cT>cr»vo'*vDrH ^ O ' s ^ i ' ^ o o r o o

o o o o o o

r^ 00 00 00 o^ in cr> vo t^ rH r* 00 rn \D T-i O T-i 1-i

o o o o o o o I I I

CJ CM -^ cn rH 00 i n r o rH rH O i n rH CO o o ro o ^ ^ CNJ o

o o o o o o o o

t ^ a > r ^ c T > o o o i n o i n aasc^asasO'^rn r^ ino>rocy>cT»o« j rHvoo

o o o o o o

ro 00 o ro CN o^ 00 r^ 00 rH CO 00 CM rH CM O CM CN

o o o o o o o I i I

vo i n ro * * CTi CN vo o> in ro rH rH CO r-o o VD o in ^ o

o o o o o o o o o o o o o o o o o o o o o o I I I

CM r H >

^ ^ ^ o o o ^ r ^ r o c ? ^ ^ * o o r ^ 0 O t ^ 0 O C M C O 0 O C M 0 0 C T > i n r O r H r o r H r o r o c N H O C M

O ^ ^ J rvj rH CT\ ro o ro r ro CN rH O rH O rH rH

O O '^ in rH -^ iH ro ** in 1* ro CN rH O "iT rH O O O

oooooooooo o o o o o o I I I I i i

o o o o o o o 1 1 I I I I

corHO<r>rHcocT» in in<T>r^ C r > r H V O O r O O O C N V D C T » r ^ O V O r O V O C N V O V D r H O C T \ 0

^ CM O rH CN r » rs) <y» CM r H r>a r>j rvj rH CM O CN CM

CN ^ vo ^ r^ CM 00 r^ ro vo ^ vo r^ in o o ' ^ o ro ro o

o o o o o o o o o o o o o o o o o o o o o o o o I I

fa

OQ < H Pi < >

cr»co<r»cy»cNCMCN i n r ^ v o c T i r H O O ^ V D C O r ^ r H r « V O r O r H O ^ C N r H r o o r O r H r o r o c N r H C M O

^ rH vo i^ VD ro r o r* 'sj' t^ r rH O rH O H rH

VD rH CN VD O O t <T» O VD ro rH O O O CM O rH rsj O

O O O O O O O O O O O O O O O O O O

r H C N r O - ^ i n V D O O C T v O r H C N ro r H r H r H r H r H r H H r H C N C M C : ^ Ql > > > > > > > > > > > >

^ in VD r^ cr» o

o o o o o o o I I

iH r j o CN ro ' ^ in ro ro in in in in in > > > > > > >

Page 109: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

99

CN CN >

CM >

O rsj >

as T-i >

00 T-i >

VD T-i >

in rH >

rH >

ro T-i

>

CM rH >

fa

CQ

^ Z l ^ ^ Z l Z l ^ ^ ^ v D i H i n r H r H o o c o o c T . C M o o r ^ o r H r ^ c o r ^ c o t n ? ^ ? ^ S ^ i 5 r S r ^ S ^ " ^ ^ c M l n < 7 ^ o o o r ^ o o ^ o c M o k i n ^ o o r - ^ r H o o o o c N o v o i n o r o i n ^ c N r o o o o o o o v o C N O O O O O I H O O O ^ - ^ ^ * ^ ^ ~ * * o o o c p O O O O O O O O O O 0 < T > 0 0 0 o o o o o o o o o o

' ' I cn I i i I I I I I ^ o 15 J5; P; ^ ^ [;; S ; : : J 2 ? S ^ ^ i n o o v o r - v o ^ v o c n o cn CM r - ^ ro S o o S S r 2 S i C ^ 9 S: : :^ iQ: i^ :Z^ m o r o r n - ^ r v j o r o o o r j r o o o . - i O O O O O r H O O r H C N O O O O O O O O r H O O O O O O O O O O ^ ^ ^ * ^ ^ ^ * * ^ ? ? ? OOOOO ooooo ocnooo ooooo ooooo

' ' ' I I cn I i i i I II i Q ? ^ S l 5 J ^ i £ l ^ S 2 ! < 3 ^ ^ r o r o • ^ o o o r s i r o t ^ o o c n O r H ^ i ^ i ^ r - ^ S S ^ ?^ £ j J^ J^ E^ ^ H I S ^ ' D ' ^ r 0 O C N l H a ^ . - H O i n V O O i H r O C M r H C M O O O O r H C N C M r H r H C N O r H O O O O O O r H O O O O O O O O O O

• • • • ^ * * * * . . . . . • • • . . » . . . . o c p o c p o o o o o o o o o o o c T i O o o o o o o o o o o o o

• ' I I c: I I I I I I

^ ^ S ^ i S S S ^ C i i C C N C o o r H v o roocMCN<J^ c n c N ' ^ o r o c n o ^ v o i n o 2 S r ^ 2 2 ^ r ^ 5 ^ * ' ^ v o r ^ - ^ o o o o o o o v D c n o o o c o o o r H - " ^ ^ r H r n c N O O r H O r H V O O V D i n V D C M V O r H O r H O O O O ^ C N O O O O O r H O O O

OOOO OOOOO OOOOO OOOOOO ooooo ooooo • I CTi I I I I I I I

?!! ! ;^?^S2 v D 5 ; " ^ c M r M v o - ^ v o c N t ^ r o o r H l n c T ^ i n r H i n r H r H c n < y > r - i n c n CMOCMOO ' ^ ' ^ r H C N c n v o t ^ r o c o o o o o o v o c n o o o o o c o r H rr fT T-i T-i r-i O O r H O r H V O O V D i n V D C M V O r H O r H O O O O ^ C M O O O O O r H O O O O O O O O O O O O O O O O O 0 0 ^ 0 0 0 O O O O O O O O O O

I I c n I I I I I I I

CM'>PCNvo c o r o c o O r H rHiHTTVOrH f ^ o r ^ t ^ c M o i n i n o o v D cMcr>vo in r^ i - H r H i n i n ' i ^ O ^ r O ^ ' d ' ^ O C M r H C M O O r H V D a ^ O O ^ r O r H r H O r O O C M O O O O r H t — I r H r H r H C N O r H O O O O O V D C M O O O O O O O O O O

OOOO OOOOO OOOOO ocnooo ooooo ooooo I I C7 I I I I I I

c n r ^ o c n O ' s r c n c n o r ^ o r o r H v o rHOrHCTicy\ c N r H i n c N r H as t^ in m o C M O r O O O i n ' ^ r H r H C T i V O r ^ r O O O O O O O O O O O C O O O O O O r H ^ ' ^ r H r H C N O O r H O r H V O O V D i n V O C N V O H O r H O O O O C N O O O O O r H O O O

OOOO ooooo ooooo OCTNOOO O O O O O O O O O O

I I cn I i l l I I I o c N ' d ' V D o o c M o u o r H r o o H V D o o r o o c n u o c N C M r o o r o r o i n r ^ o c M O C N O o r - c M o o o o r o o c o r o r « - C N r - > o O o a > o o o r - i n r o i n u o ' ^ r n r o O O r H O o r o o r o r o r o r n r o o o C M O O O ^ r H O O o o r H r n o o o

OOOO ooooo ooooo oc3^ooo ooooo ooooo I (7\ I I I I I I

o t ^ r H O ( T i i n c n c n r H r ^ c N r o o i n O O O C M O O O rornvocMCM r o o ' d ' i n o r o o r o c h ' * r r r H r H a \ v o r ^ r o o o o r H o o o o o ^ c o o c o o o r H i n i n r H r H C N O O r H O r H V O O V D i n V D C M V O r H O 0 0 0 0 0 ^ C M O O O O O r H O O O

OOOO OOOOO OOOOO OOOOOO OOOOO ooooo I I cn I I I I I I I

^ r ^ r ^ c o ' ; r l n o o a ^ l n o m c M v o i ^ o o o - ^ o o c N ^ r c M r o i n C M ^ ^ O C M ' ^ T C M r ^ o i n r o ' * O r H a ^ v o c M r n r o o v o o c N r o o o roCT>Lnt^ in o o H O r H O o ^ ^ O O O r H C N V O r H r O O O O O O O r O r H O H O O O r H O O O

O O O O o o o o o O O O O O o c n o o o o o o o o o o o o o l l l l l I I I c n i l l l l I I

^ r o o o v o r o ^ r ^ v o c T t v o r H i n r H r H O O O O O O O c M c o r ^ o o r ^ c o v o c o L n «*rHO^vD r o r o ' i ^ i n c M c M L n a ^ c o o r ^ o o ' ^ o c N o r ^ u o r H o o r ^ i - n o o O O C N O v o i n o r o i n < * c M r o o o o o o o v o C M O O O O O r H o o o

OOOO ooooo ooooo oo^ooo ooooo ooooo I I \ as llll II

r H i n C N O O O O ^ r ^ ' S f i n r n r O r H C M i n r H O O O H O ^ ' i i ' ^ ^ t ^ r H C M r ^ r O O r H L j J i J ^ ^ C N ^ O C M O r ^ " < * C M r H r H C M O H r H V O r - O - ^ i n r O r H - ^ r H r H - « * O O O O o c M O C N C N r o r H C M r H O o o o o r o r H O O O O r o o o o o

, , , , • • • • •

O O O O o o o o o o o o o o o < y > o o o o o o o o o o o o o I I I ' r * ' I I I I

VD r- CO cn O rH CN ro ^ VD VO VD VD VO > > > > >

in VO r- 00 CT\ vo vo vo vo vo > > > > >

O rH

555? CN ro o r r- CO > > >

rH CM ro i n VD CO 00 00 00 00 > > > > >

r^ CO ^ o o> 00 C30 00 a^ 00 > > > > >

Page 110: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

100

ro in >

in ** r^ ^ <7N in r^ vo ro o o o

O O O O

vo 0^ CN iH CM O t^ CT^ VD vo ro o o I-H o

'^r cr> 00 CM o in ro CM CO 'i r «* ro CM CM ro

o rH CM o r~-00 o CO o ro o o o o o

o o o o o o o o o o o o o <r» o as

CN i n >

o r^ in «H 'd' •^ T-i m T-i •<!r I-H TH O rH o

o o o o o

in o r* cn CM i n i n ^ o fH ^ rH rH rH vo

rH ^ *:}< rH VD O CM r^ rH rH O O O O O

O VD VO O CM ^ CM CM O O O O O O O

O O O O O O O O O O I I

o o o cr> o I I I cn I

o in >

CM ro >

ro >

o ro >

i n 00 ro

00 00 0^ rH rH CM CM CO O rH ro ro o rH o o o o o o

rH o «-i CO cn VD vo in in rH ro o CM «* ^

^ a^ o VD r-o CN o ro ro '^ ^ vo rH ^

vo ro cn o rH rH CN in o o ooooo

o o o o o o o o o o O O O (Ti o I cn I

.236

o

.180

o

.076

o

.074

o 1

.134

o 1

.129

o

.015

o

TOO

*

o 1

.018

o

.026

o 1

.043

o 1

.292

o

.012

o 1

.053

o 1

.235

o

600"

o .050

o

.194

o

rH rH

o o 1

.007

o 1

.005

o

.003

o

.016

o

.076

o

.026

o 1

.012

o 1

.056

o

.010

o 1

017

o .016

o 1

025

o 1

.038

o 1

035

o 059

o 1

070

o 1

104

o 007

o 1

010

o

021

o 1

033

o 1

079

o 1

291

o

014

o 1

061

o 1

219

o

037

o 1

102

o 1

090

o

096

o

224

o

957

o

047

o 1

085

o 1

272

o

186

o

071

o

377

o

008

o 1

015

o 1

013.

o

003

o 1

025

o

113

o

O rH O CN O O

cn o cn

O CO o ro o o as o cn

O rH O CM o o as o cn

as CM >

00 i n 00 CM 00 cn in r^ CN rH (Tv CN O iH O

o o o o o

o 00 i n * * r-<y CN cn o r~-CN CM rH O O

CO r- CN .H rH in rH ro o CM O O O rH O

ro ro r^ VD ^ 00 rH CO in vo CM CM O cn CM

rH rH 00 O ro 00 rH t-H O rvi ro O rH o o

o o o o o o o o o o I I o o o o o o o o <r» o as

CN >

C5 i H * * VD CM 0 0 o^ o ^ ^ ' ^ o CM ro CM rH O O

00 ro rH i n "«T O ro O rH CM o o o o o

rH r^ -er in CN ro rH CM o ro o o o o o

vo "sr r- ^ VD o o o r-- o O O O CM O

o^ CO ro o vo rH ro VD O rH rH O O O O

O O O O O O I I

o o o o o o o o o o l l l l l

o o o o o I I

o o o cn o cn I

vo CM >

i n CN >

CM >

ro CM >

fa hQ OQ < H Pi < >

i n o ^ o o c T v r H O C o o o r ^ r o i n t ^ v o r ^ r H O C M r H r H v o i n c M T H C M O ^ O C S I c N a \ c n i n c o c N r H o o c N o ^ o ^ ^ i n r n r o o c N c o r H O o i n v o c O f H r H o r s i r o a ^ o ^ C M O r H O C M C M I H O O o o O r H O CMrs iocncM r o o H o o

O O O O O O O o o o o o o o o o o o o o o o O O O C T > 0 1 I I as

[ ^ c N v o r H i n c N r H r ^ o t ^ ^ H C M t ^ r o v o o i n C N ' ^ o ^ r o r o < r > r s i o ^ o r o V D i n v o r - r H r ^ c o r H ro<7^ ro rH ro r o i n o r o r o o r o r ^ v o H v o v o o o o o r o ^ r O f Y - ) , _ I O O O r H O r H O O O O O r H O r-i T-i a cn T-i O O r H O O

o o o o o o o o o o o o o o o o o o o o o o o o o o c r > o I I I as

l n a ^ v o o ^ ^ ^ o c M 1 H a ^ o o r ^ L n i n r ^ ^ ^ a ^ r ^ ' * c N r n r o o o i n c M o o ^ r o o c M a^CT^CNO^o^vDoo<NrH o o c N O ^ o ^ ^ i n n r o o c M o O r H O i n v o t ^ r n r s i o c M m 0 ^ r O O ^ O ^ C M O r H O C M C M r H O O O O O r H O C M C M O O N C M r O O r H O O

ooooooooo ooooo ooooo ooooo oooo^o I I I cn

o ^ c N r ^ o c M i n ' ! * o o r * ~ i n cN'«l 'CNa^ro C N t ^ r o r H o ^ c o r H r n r o o o o o r o t ^ o < * r H v D r H ^ ^ r H o a ^ c N ' 5 * ' ^ ^ a ^ r o c M ' * ' * CMOOO^VDVD as T-i T-i t^ cn i — l O ' ^ O r H ( v ^ , _ | f n r s l f * 1 f * 1 r H r H O r H r H r H O O O O O O O O O O r H C M O r H O O O O

C5000000000 OOOOO OOOOO ooooo oooovo

<: rLnvD^~*o^OrHCMOCM C M C N C N C N C M r o r o p L n i n > > > > > > > > > >

ro in VD r- CO 0> O rH (N in in VD VO VO > > > > >

ro in vo r VD vo VD VD vo > > > > >

00 0^ O rH CM

Page 111: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

101

r r o 00 00 CO r-r^ CM 00 "sr «* o

r- r^ VD 00 o CM O rH cr, O rH ro ro

in >

CM in >

V5

0

CM

ro >

o • o

as in o • o

CN CM O

O

O T-i

o

in • o

rH CM O •

O 1

rH ro vo O

^ in o

CN • o

00 rH O • o 1

CN CM T-i

O

CM O fH

O • o 1

o CM O • o 1

r ^ o o

CM o o

o • o

r-cn o • o 1

CN as o o 1

vo T-i

o

o • o 1

^ VD O • o

ro vo o o 1

o o o

o • o

o in o • o

iH O O

O

VO CM O

O • o

r vo o • o

o in T-i

o

T-i T-i

o

o • o

ro vo o • o 1

cn ro rn o

00 T-i

o

o • o 1

r-rH O • o

o ro O

o

VD O o

o • o 1

00 rH o • o 1

.H CM O

o 1

o o o

o • o 1

in T-i

o • o 1

cn -^ o o 1

CN CM O

O O O O O O I I I I

O O O O O O l l l l

ro >

in CM vo in o ro r-i as '^ O T-i T-i O O CN O O O

• « • • • • O O O O O O I I I I

00 CN rH o cn 'sr VD CM ro CN O CO O O O O O O

• • • • • • O O O O O O

l l l l

o ro >

in * * cn cr> rH (Ti o cn o^ ro CM ro o CN cn o o o

• • . * • • O O O O O O I i I

r r ro ro r~ r^ CN r^ vo ^ o rH vo O O rH o o o

O O O O O O I I

as CM >

in r^ CO r-> rH o o 00 <J ro CM ^ o rsi cn o o o

O O O O O O I I I

rH ro rH r^ 00 t^ r- vo * * O H VD O O tH O O O

O O O O O O I I

CM >

r o CM CO r H VD r H 00 o o CM ro o rH o ro o o o

O O O O O O I I

o rH 00 CO in ro r^ CM rH in ^ rH O O O O O O

• * • • • • O O O O O O

VD CN >

o ^ CO r- CM o o CO C3 ro CN <* o CM a^ o o o

O O O O O O I I I

ro ro o in VD r^ (^ vo * * o rH vo O O rH O O O

• • * • < • O O O O O O

I I

rH r- ro O CM rH 00 in ^ r- cT\ in

V2

5

'^ CM >

ro CM >

fa i-q OQ < H Pi < >

o o • o 1

ro O o • o

r ro o • o 1

ro

5

vo rH O

VD CO CM

t

O

^ r~ o • o 1

o 00 >

ro • o

r as as

9

O

o rH ro • o

tH

g

O

o • o

r ro o • o 1

ro o rH • o

CM 00 >

o o • o

rH CM O • o

CM in o • o 1

ro g

o • o 1

rH ^ O • o 1 CM VO O • o 1

in CO >

fJS O • o

in r o • o

in o o • o

vo

I—I rH • o

r VD o • o

o o o • o 1

r

T-i 9

O

CM •d" rH .

O

cn T-i

o • o

00

IN O • o

»*

o o • o 1 VD VO o • o

^ 00 00 00 00 > > > >

V — ' 1—1

O O • • o o 1 1

VD in T-i VD

o o . • o o 1 o cn o o o o * • o o

o as ??

Page 112: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

102

in VD >

ro rH ro in 00 ro rs] o o ^ o o

O O O O

in o CJ o vo r- o CM rH vo O O O O VD

VD ro r r ^ CM 00 r^ r^ CO rH O O rH o o

o cr> o o o cn I I o o o o o

I I I

ro CN vo ro CO 00 VD CM O CM O rH O O O

O O O O O I I

'sr VD >

r^ o r- TT CM 00 CN vo r^ o '?r CM ^ o o

o o o o o

"^ o ^ r^ VD ro o tH rH cy> rH o o o in

in ^ 'i r CM vo rH rH 00 r^ O CN O O O ^

o o^ o o o (y> I

o o o o o I I I

CM ro CM ro r^ r^ in «* rH o O rH O O O

o o o o o I I I

ro vo >

CM VO >

r H VO > .0

50

o 1

.033

o

.345

o

.467

o .015

o

.434

o

.407

o

.055

o

.581

o

.275

o

.014

o 1

.112

o

.430

o

.014

o .444

o

o rH T-i

O

.007

o 1

.051

o

.006

o 1

.009

o 1

.006

o 1

.071

o

.008

o 1

.080

o 1

.000

as as

.000

cn cn

.000

as as

rH T-i O o 1

.006

o 1

.024

o 1

TOO

o

TOO

o

.004

o 1

622

o

008

o

647

o

285

o 030

o 1

100

o

016

o 1

010

o 1

T-i rH o o

084

o 1

035

o

128

o

073

o 1

017

o

086

o 1

088

o

015

o 1

036

o 1

066

o

100

o

630

o

103

o

630

o 1

203

o

020

o 1

015

o

002

o 1

O T-i T-i O o o o o 1 1

r- o O rH

o o o o 1

CM CM o ro O o o o

1

o vo >

r^ 00 ro ' ^ CM rH in vo CM rH o rsj

O O O O

CO cn O VD VD vo a ro o o O O rH O O

CN o r* VD cn rH O O CM ^ O O O O rH

ro rsi cr> o CO ro rsi o o o o o o o o

o o o o o I I

O CT\ O O O I as

o o o o o I I

ro 00 'O' CO ro in ro o ro iH o o o o o

o o o o o

cn in >

VD "^ r^ O CN rH <! VD r^ in O rH o o o o o o o o

i I I

cr« o r^ cr> r^ in rH ro ro iH rH o o o o

in o ro in r-o o o O 00 o o o o o

in ro ' ^ ro rH tH ro vo r- o o o o o o

o o o o o l l l l l

o cn o o o i at I I

o o o o o I I I

ro VD 'd" o 00 rH VD 'a' tH O O O O O O O O O O O l l l l l

CO in >

^ ro * * r- ro CM tH ro ^ r^ o CM tH ro O CM tH CM

in CM vo ro CO ^ r- r- o CM O O rH o o

ro O rH VD O r^ o vo in ro O O O O rH

in r^ in rH VD in vo ** ro ro o o o o o

O O O O O O o o o o o I I I

o cn o o o as o o o o o

r- rsi ** vo CM in CO ro CM o o o o o o

o o o o o I I

in >

00 CN 00 vo a\ ro vo cn ^ rH vo CM O CM O O O O O O O

CN r- r^ in 00 r^ VD rH vo O o o o o o

o o o r^ r^ r^ o vo o o CM O CM O O

in o^ CM r^ ro r~> rH VD VD o O O rH O O

O O O O O O O o o o o o I I

O CT» O O O as

o o o o o

in cn CN o O CM CN o r^ o o o o o

o o o o o I I I

VD in >

V O ' ^ ^ C T t V O O O t H O O r H ^ t H r H i n C M ' * t H r H O O O O O O

00 O r - VD CM rH rH O t H rH O O O O O

CM o r^ vo o o o o H ro o o o o o

^ VD CO O "^ O H CO rH rH O O O O tH

CO in '?r r^ 00 o r^ CM o o o o o o o

o o o o o o o o o o o o o I I

o cn o o o as I

o o o o o I I

o o o o o I I I

in in >

in >

fa hQ

< H

c N i n v o r H r o v o r o r ^ t H r ^ r H r o r H r o t H C N O r o O O O O O O O r H C M o o o o o o o o o

I C 0 ' * ' * V O r H 0 0 r H < * C ^ V O r ^ t H C M r ^ c M O i H r ^ ' 3 < r H O O O t H O C M C N O ^ r O oooooooooo

I I

L n v D ^ * ~ o o o ^ O t H C N r o ^ i n i n i n i n i n v o v o v o v p v p > > > > > > > > > >

CO in vo vo 'd' rH ro ro CM o O CM O tH o

. . * • • o o o o o

I CM in ro 00 ro ro CM in rsj CN CN ro o o

• • • • • o o o o o

in VD r^ CO o^ vo vo vo vo vo > > > > >

CM o ro o r~ o o o o r-o o o o o

. • • • • o a> o o o

cn I I rH O i n vo CM rsi O r H CM CO o o o o **

• • • • • O CTi O O O

cn I •JC

o H CN ro o

^ o ON ro o as cn 1-i T-i as rH o o o ro

• • • • . o o o o o

I rH CM 00 VD t H ro in o in VO CN O O O O

• • • • • o o o o o

I I I

rH CN ro in VD 00 00 00 00 00 > > > > >

00 iH cx) rvj ';r O CM O O O o o o o o

• • • • • o o o o o

l l l l ro ro o VD CN ^ a> VD rH o o o o o o

• • • • • o o o o o

r- 00 -^ o <y\ 00 CO 00 a > > > >

Page 113: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

103

ro 00 >

rvj ^ ro vo iH CM vo o o o

O O O O l l l l

r - 00 CM rH rH ro o o o

• • • o o o

CN 00 >

CO

>l

o 00 >

ro

>

CM

>

>

o

>

00 CM O

• o I

00 CM 00 O CM O

• • o o

I

rH VD CM VD O rH O O O

• • • o o o

I I

C7 rH ro in o o rM o O O O O

• • • * O O O O

I I ooooo ooooo ooooo

• • • . • as as as as as as as as as as

O ro ro ^ ro ro O O O 00 rH rH O O O rH rH O

• • • * . . o o o o o o a\ I I

CM r>- o 00 o tH rsi rsj rH ro o o o o o

• • • • * o o o o o

l l l l

O O VD rH rH CM CN r^ VD rr O O O O tH

• • • • .

o o o o o

vo rH ro cr> o 00 CO rH ^ i n O O O O rH

• • I . *

O O O O O I I

o ro cn rH ro rsi O tH rH o o o o o o

• . . . • o o o o o

I I I

in 00 o '^ o CN O O O tH o o o o o

• • • • . o o o o o

l l l l

ooooo ooooo ooooo • . . • .

as as as as as as as as as as

CT\ r^ vo ro 00 tH rH rH CM O O O O O O

• « • • • o o o o o i I I

VD cn rH rsj O rH O rH O

• * • o o o I I

00 r^ ^ O tH VD o o o

• • . o o o I I

r^ i n rH rH rH CM o o o

• . . o o o I I I

rH ro r^ rH O O o o o

• t .

o o o I I I

CO rH r-O O 00 o o o

• • * o o o I I

o o o o o o o o o

• . * as as as as as as

CM rH CN OJ O O o o o

• . . o o o I I I

o cn >

00 >

ro o o

• o I

r^ as O rH o o

• • o o

I

0)

a o u <u

Xi

+J o c c fd u •p

c Q)

• H

u • H MH MH Q) O U C O

•H •P fC

rH Q) U U O U

as vo >

CO VD >

vo >

VD VD >

fa t-:i OQ < H

< >

i n o CM CM VO CM r^ O O O O O rH O O O O O O O O

•^ CN <r> CM VD rH rH O O tH O O O O O

O O O O cn as •K

O O O O I I

o o o o o

^ - o o a ^ O r H C N r o O l H C N v D v o v o r ^ r ^ r ^ r ^ o o c o o o > > > > > > > > > >

CM rH vo H O O O O O

.273

041

o

.403

000

o 1

.028

o 1

.024

o 1

.164

o

092

o

.111

as as

.000

cn a\

000

cn as

.000

o 1

.048

o

TOO

o

.018

o 1

.025

o

800'

o

.013

o 1

.180

o

640

o

.276

o

.380

o

99

3'

o

.957

o 1

.036

o 1

.012

o 1

.026

o 1

.024

o

.044

o 1

.017

o 1

.037

o 1

.046

o 1

.045

o 1

.009

o 1

.004

o 1

.092

o 1

173

o

.047

o

.080

o 1

.002

o 1

.167

o

.128

o 1

013

o 1

022

o 1

.027

o o 1 1

O rH T-i cn o in o o 1

in »* O CM o o o o 1 1

cn ro rH t^

o o o o o I I

r o i n v o r - c o " ^ o c r * pooopocopo co<y»co

CO 00 >

CO >

vo 00 >

in 00 >

fa hQ OQ < H Pi

i n o CO CM O rH o o o

• • • o o o I I

r^ rH r^ rH O CM O O O O O O

• • . . O O O O l l l l

ro rH ^ ^ r^ rH ro tH o o O O O O O

o o I

o I

o o I

i n 00 CM i n r^ ^ CM rH 'g' ro O rH O O O O O O

• • • * . . O O O O O O i I I I I I

VD r^ 00 ^ O <J 00 00 00 CO o^ 00 > > > > > >

4H •H

(D 4J C

•H U

Cu

cn •H o o o

• as as

rH

>

<

Page 114: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

APPENDIX B

104

Page 115: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

105

rsj rsj >

00 rH O^ OJ rH tH in ro O O O rH

VD cn ^ rsj rH in o in CO in O rH o o o

O O O O o o o o o

ro 00 r^ ro CM ro vo rH T-i cn T-i <z>

• t • .

O O O O

CM >

in in CM vo CO VD o ro o ^ CM O O O O

• • • • . o o o o o

in r^ ro ro rH o ^ o r j o O O O rH o

• . • . • o o o o o

r^ in cTt rH 00 rH ^ '?r •^ H o o

• • * • O O O O

o rsi >

as T-i >

rH • OQ

fa i-Q OQ < in

cn fa t-Q fa OQ hQ < OQ H < Pi H cn

X < Pi EH H > < U « > H in in Pi < IS EH EH s fa IS cn P fa H IS IS P P O fa IS H P< fa HQ EH fa P4 O < P fa O

ORREL

82 IN

983 D

L SCH

U O^ rH KI rH 1 < 1 CM rH 00 CO as as T-i

00 rH >

VD rH >

in rH >

'd' rH >

ro rH >

o rsj

i n T-i cn cn CM ' r

o o

00 o^ ^ VD cr» r o rsj cy> i H

o o o

CO CO i n ro rH r^ rH t ^ ^ rH ^ rH

O O O O

o^ o^ o o> r~~ cn as t^ as cn "«*• cn rsj (T» rH

o in CO CM vo o CN cy\ in rH CM in O ro CM

rH in ro r^ rsj in CO in ^ vo ro o ro o ro

O O O O O o o o o o

i n C3 00 CM CM ro t^ rsi vo " r rsj o o o o

rsj in ro o ^ vo O VD ^ '^ o o o ^ o

o o o o o

vo ro CO rH in o r*j cn in rH CN in O ro CM

o o o o o

O ' ^ rsj rH o in CO in ro vo ro o ro o ro

o o o o o

in o in r* * * cr» in o CM cn rsj rsi o rH o

o o o o o

vo cy» ro CO in rsi Tl* rH O rH rH i n tH O tH

o o o o o

CM ro r^ rH in rH rsi (y» in H rsj in o ro rsi

o o o o o

as CO T—i T—i as ' ^ cj> in ro in ro o ro o ro

o o o o o

as T—i as T—i T-i CO rH ro tH r* r J vo in rsi in o in o

o o o o o

O r^ CN O CM o r- rH " r ro oj ro o rsi vo

o o o o o

in ro VD ro rH rsj vo rsj rH ro rsj o rsi o CM

O O O O O O

CO as as as co oo r^ ro <y» ro cr» vo cr> ro in C3^ cy> rM (T> rH

o o o o o

^ vo in rsi 00 rH rsi cn in CM rsi in o ro CM

o o o o o

O CO CM tH O in o^ in ro vo ro O ro O ro

00 CO o • o 1

00 "«* ro

^ vo ro in r o O VD o • • • o o o i

o CM ro O ^ rH rH rH O

O O O O

^ o in ro r^ in r- o o o vo o

O O O O I I

vo ro rH CT\ o r- in "^ o o ro o

O O O O

ro r-* r-» ^ r-o ^ r^ o o o vo o

O O O O I I

in rH rsj TT rH O CT\ ^ o o rM o

O O O O I I I

ro vo in ro r^ ^ [^ o o o vo o

O O O O O O O o o o o o o o o o o O O O O I I

rsj rH >

L n ^ v o L n ^ ( T > c N C T > VOCNVOr^VOCNVOrO C M r H C M r H C M r H r s J r H

o^ iH ro ^ ^ * * rH O ro O rH O rsj rH O

vo rH r»- C7 in ro ^ ro o^ ro rH O rH O rH

O O O O O O O O o o o o o o o o o o l l l l l

Cr» O 00 rH <y» TH VD rH O rH ro CM

O O O O I I I

r H v o r ^ r o r H r o o o i n m r H r s l t ^ C M i n C N t ^ C M O o i n r o i n r s i i n o i n o

CO o^ o^ ro CM rH CT> i n H VD O CT» O rsj rH

rH o ro O C3 rH ' ^ rH i n rH CM O CN o rsj

O O O O O O O O O o o o o o o o o o o

vo rsj 00 un KD m T-i '^ o o ^ o O O O O I I

v D r o o ^ l n o L n o o f ^ v o c » l n r o o ^ ^ ^ o r o o ^ v o o ^ o ^ r H t H r o H ^ r s j r o H r o o

r* r* o H in ro in ^ ro r^ rH rH O CN rH

o rH 00 ro 00 ro vo CM <y> CM rsi rH rsi o rsj

55» vo vo r^ ^ CM 00 ^ o o rsj o

o o o o o o o o o o o o o o o o o o o o O O O O

fa

OQ < H pa < >

r H C M r o ^ i n v D r » o o < y i O

> > > > > > > > > >

rH rsi ro ^ in v o r - * o o c r » o r n r s i o r s j

Page 116: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

106

rsi rsi >

r j >

o CN >

as T-i >

CO rH >

VO rH >

i n rH >

rH >

ro 1-i >

rsi rH >

fa

OQ < H Pi

>

2 J ^ ^ J ^ ! 5 ^ rii^S!?!:22 o o 00 rH ro o v o t ^ r s i ( T » ro t^ r o - ^ "^ r- rsi rH 3 2 S R R S S S ^ : ^ 2 V D O j O O r O C M C M r H O r O r H t H i n r o i ^ t H rH o ^ ^ r H r H O O O O O O r s I O r H O r H O r H O O O O O O C M O O O O O O O • • • • • • • • • . . .

O O O O O O o o o o o o o o o o o o o o o o o o o o O O O ' ' I I

S S J ^ Q j n S ^ H J S ^ ^ ' " ' o o r H i n v o o ^ •«a'r--vocorH r - r o r s i o i n r H f ^ r o o S § o S ^ R P ^ Z ) ; : ^ S ^ ^ 2 : i Q ^ r H r O O C M H i ^ t H ^ U ^ C M ? ^ O C N O r H O O O O O O r H O O O r H O O O O O O O O r H O O O O O O O

• • • • • • • • • » . • * • • . • • • • • • • > . . . . . O O O C I J O C p O O O O O o o o o o o o o o o o o o o o O O O

• • • I I I I I I n : ! r X 2 ! J 5 ' ^ ! r 1 corsjcy»rsicri o j r - r o o o r H ^ r s i o c r » i n as\o ID "^ cn T-i -^ i-i ^ ^ ° o ^ r i f ^ i n v o r o ^ ^ r o r - i n r s i c M r H ^ r M O c : ^ o ^ l n r ^ t ^ r H J ^ ^ J N i n i n o o o r H O r H v o o v o v o v o r o r ^ c N o o o o o c n r o o o o O r H r H

O O O O O O o o o o o o o o o o o o o o o O O C D O C J C 5 0 C D I I I I I I I

i f 2 ! 5 ^ ' ^ : : 1 ' ^ r s i r ^ r n r - r n r H c n r o c N r ^ o o ' ^ r o L n c s j r ^ i n r H v o v o r ^ v o o ^ ^ £ ^ ! I J £ ^ ' ~ ' c M o o c T i o c n i n r H r H i n v o r s j i n o ^ i n ^ i n c r ^ r o r s i r H o o r H r H O O O O O O r H O r H r H r s I t H r H r H O O O O r H C M O O O O O r H O

O O O O O O O O O O O o o o o o o o o o o o o o o o O O O I I I I

r H r ^ c N v o o o r H v D ' ^ o c M O cMoo 'd ' vo i n r o r o c T > r * - o cy>inoo«?j"CN o r - » o i n v o o o i n r H C M invD"<j<rHin r o r ^ i n r s j r M r H ^ ^ r H O o ( T i i n c N r ^ r H ro^*r^a i n i n O O O r H O r H V D O V O V O V O r O t ^ r s l O O O O r H c n r o o o o O r H r H

O O O O O O O O O O O o o o o o o o o o o o o o o o O O O I I I I I I I

( y » r ^ c o r o r o r H r n r ^ ' a ^ v o c n v o c o r o i n c o cNCT»cNrHO o i n r o o c M o o o i n r H ( y » r H r H t H r H C M i n i ^ O O r O i n r H r O V D O O O r * j r s I C M r H r O ^ O O O V O r H C N C M O O O O O r H r O O r O C M r O r H r O O O O O O O O r H O O O O O O

O O O O O O o o o o o o o o o o o o o o o o o o o o O O O l l l l I I I I

r H o ^ r H v o r ^ o vDvorocMrH r H o r o r ^ ^ cn cn as CO as as r^ co m -^ o v o c r * i n v D o o i n r H C M i n v D ^ r H i n rooo incNCN r H ^ r H O c y \ cy» in rs j r ^ rH r o r * r H i n i n o o o r H O r H v o o v D v o v o r o r ^ r s i o o o o o c r » r o o o o O r H r H

OOOOOO OOOOO OOOOO ooooo ooooo loo I I I I I I o

i n c N i n v o c M V D o i n r n r o i n v o i n r H i n c N m o i n o r - cMcr»r^ t^vD rHCMin i n c M i n o o i n r - r o c o m c M cNCNH<r»rH r H ' d ' r H o o c M r s i o v o o o o o o o C M C M O O O O O O r O O r O ^ r o r s i r O r H o o o o o i n C M O O O O O r H

O O O O O O o o o o o o o o o o O O O O O o o o o o O O O I I I I I I I I

o r ^ r H i n r ^ o r ^ i n ^ ^ r o o r o < T » r o r * ^ r o r o o ^ o o c o a \ L n c o i n ^ O V D C N i n v D c o i n r H C N i n v o ^ r H i n r o r ^ i n c M C M r H ^ a ' r H o c y i CT\incNt^rH r o r ^ c M i n i n O O O r H O t H V D O V O V O V O r O t ^ C N o o o o o < T » r O O O O O r H r H

O O O O O O O O O O O O O O O O o o o o o o o o o o O O O

o o v o L n r H a ^ c N i n c M O ^ i n ( T > C M O H C N r o r o i n c M r * - l n c o o ^ v D r H inrHCM c^ m T-i T-i \D '^ C M C N r o o o o r ^ o c n r * * ^ CNCMCMroro v o r o c N i n r * r o o c o O O O O O C N r H O ^ O r H C M V O O C M O O O O O O C N r H r H H O O O O

l O O O O O O O O O O o o o o o o o o o o O O O O O O O O l l l l I I I I I l l l l l I I I I

o ^ r o o ^ i n r H i n v o i n o r o o o i n c o o o r o r H O O ' * c M i n r H ' « * i n O C N O O v o r H o o r o r H ^ i n r H O O v o o r H r o r o o o o o r H H r o r s j r H O V D O ro ' s r cn c N f » i o o o c N o r ^ r o o r o ' ^ r o c M ^ r H o o o o o i n c M o o o O r H O

ocDCDCJCDCD o o o o o O O O O O O O O O O o o c D c p c D c p o o I I I I I l l l l

O N _ j , * c N C M r * r ^ r n r o r H i n (y>rsicocMro r s i i n o o c o v o t : r 0 0 * ^ 2 ! ^ 5 i ! 5 ' T ^ O ^ ^ ^ r H C M r H ivf O H - ^ r^ O V O i n O O i n rH rH rH rH rH 0^ CM rO O IQ 2 ^ 3 : i£^ S ^ O H O O o o ro o CM rsi ro rsi rsi rH o o o o o ro rsi o o o o ro o

. . . . • • . . . . . . . . O O O O O O o o o o o o o o o o o o c D c D O o o o o o c p o o

l l l l l I I I I

ro •«* in vo r* CO <y» o rH CM ro in vo vp vp vp > > > > >

';!< in vo t^ 00 vo vo vo VD vo > > > > >

c n o r H C M r o o r H C M r o ' ^ v o r ^ o o

Page 117: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

107

IM rsj >

1-i rM >

o IM >

as r H >

CO r H

>

VD r H

>

i n r H >

^ r H

>

ro r H >

rg r H >

1—1

r H >

r H >

fa l-q OQ < H

VA

R

i n o o

• o

CO o o

o 1

r H o

• o 1

r H rsi o

• o 1

00 r H O

• o 1

o rH o

• o 1

00 r H o

o 1

-s * T-i

o

o 1

00 T-i o

• o 1

o CN O

• O 1

00

ro rsi o

o 1

i n rsi o

• o 1

as T-i o

. o

as o o

• o 1

as T-i

o • o

i n

o •

o 1

00 r H O

o

i n i n o

o

as r H o

• o

00 rsj o

. o 1

i n O 1-i O O

O O 1

i n ro r H 00 O ro

• • o o

1

o as

o i n >

CM ro >

r H ro >

o ro >

cn CN >

CO CN >

r^ rsi >

VD rsj

>

i n rsi >

<* rsi >

ro rsi >

rsj

CN >

fa a OQ < H

VA

R

rsj CO VD in CO ' ^ rsi in rM ^ in o

O O O rH ^ ' ^ o in o r o o ro o rsi

in 00 H 00 <T» ^ r H Tjt Tj< r H

in H ^ ^ vo O O O O

rH r>* rsj ro cy» o rsi o> -?}• o o o o o o

o o o o o I I

in rH o r- VD o in in ro o o o o o o

ooooo o o o o o

ooooo

CN O r* CT> CM ro in in in O O O O O . . . . . o o o o o I I I

.413

o

i n VD

o

rsj

o

1-i rM

o

o as cn CO "«* ro

o o

as vo cn CM cn CM

o o

1-i ^ 1-i CM •^ rsj

o o

.383

o

vo cn 1-i

o

cn T-i cn

o

VD o rsj

o

t H

o

r- rH rH ro rH O

O O 1 1

ro CM i n - ^ rsi o

o o

T-i in vo o o o

o o 1

m 1-i

rsj o

o o

^ vo CO ro o o

o o

i n o o ro o o

o 1

00 o ro

o

i n o o

o

rsj o ro

o

vo 00 o

o

o 1

rsj vo rg

o

rn o o

o 1

.007

o

00

rH

O

•>* O O

o 1

i n r» CM r H

o

i n as o

o

rsi rH o

o o 1

.024

o 1

vo o o

o

rsi o

o 1

i n o o

o

ro CM o o

1

045

o

i n o

o

00 ro o

o

i n o

o

o o

o 1

in in rH rH rsi CM O O O

O O O 1 1

^ rH 00 ro 'sr VO rH O O

O O O 1

rsi ro <T» CM O rH O O O

O O O 1

rsi o vo ro ' ^ VD rH O O

O O O 1

\D as as CM O O O O O

O O O 1

CO o < ^ T-i o o

o o 1

i n o ^ in 1-i o

o o

rH 00 ro ^ O 1-i

o o 1

o i n ^ in 1-i o

o o

in CM as vo o o

o o

^ o o rsi rsi o O O H

O O O i 1 1

^ ro r^ vo vo vo ro rsj rH

O O O

cn o r^ ^ VD in O O O

O O O 1 1

cn vo CM in in VD ro CM rH

O O O

CO vo in rH ro vo rH O O

O O O

vo o^ VD CO o 00 ro cr» vo cy> ro o " r <y> "^ cyi rsj CM

in CM rH f^ CM ' ^ ' ^ o i n t^ CM O ro CN rH

' ^ VD rsj o in o in ro •^ vo O O rH o o

rH VD CO ' ^ rH * * i n i n i n VO rH O ro CM rH

O O O O O O o o o o o O O O O O o o o o o

r H O C M O ' s T r H c n cTNOors joo in '<3«r^oocn cn as ^ cn as r ^ v o r - v o t ^ o ^ H i n i n i n r ^ cMrHCM's ro o o r s i r ^ i n r s i ^ r H ' S T r H ' ^ r H t H r H O r H O O O O O O O r H O r H r s l r H

O O O O O O O OOOOO OOOOO ooooo I I I

c N O ^ L n ( J ^ ^ c o o o i n o r H i n c N i n v o r H O * * i n i n o o r ^ r o cnc3^rocy^voo^rorH ^ ^ ^ o i n r * o i n r o ' ^ r v o " ^ m i n i n v o ' * c n ' * o > ^ c y > r s i c M o j o r o r s i r H o O r H O O r H o r o r s i r H

o o o o o o o o ooooo o o o o o o o o o o

cy>cMOorsjroCT\VDO^CT\ r « c n r o r o c N i n i n o o ^ v o C M r ^ r o r H i n r o o ^ r o c N r o c T ^ c M l n H i n r ^ m r H r H r o i n o r s j r - * c M H v o r s i o o ( v ^ ^ r o r o r o r s i r o r H r H o H r H r H O o o c M r H O o o o o o

CDOOOOOOOO ooooo o o o o o ooooo " llll lllll II

g > . f r ) o . , _ ( o r o o c r » v o r s j o o ' ^ O ' ^ o c n m n i n v o i n o r o o o i n r H V O r H ^ r H i n r H V O i n rH -^VOrHCO Cn i-i "^ ID rH C O V D O r H r O o c M ^ r s i o c M O C s j o o ^ o c M r o o o o r s j o r ^ r o o r o ' ^ r r o o o o o o o o o o o ooooo o o o o o o o o o o I I I I I I

r o ' s r i n v o r - ^ o o c n o r H rsi o rsi ro ^ in in in in uo in > > > > >

vo r^ 00 o^ o in in in in vo > > > > >

rH rsi ro ^ in VD VD vo vo VD > > > > >

Page 118: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

108

o ID >

rH 00 r r o 00 VD rH O rH O CN VD rH O O

00 VD CM VD CO ro rM o r 1^ ^ in O O O VD CM rH

o j 00 rH ro CN ro r^ o ro rH r^ VD CM o O CM O CM rH O O

o o o o o O O O O O O O O O O O O O I I I

r«j ro >

o in ro o VD 00 CM ^ o o rH O O O O

CN CO r«- CO CN ro CN 00 rj« ^ rH CN O O O O CM O

O O O O O O O O O O O

00 VD r* ro r^ VD CO ^ rH ro Cy> '^r rH O H O O O O O O

. . . . . . . O O O O O O O

I I I I

ro >

o ro >

cn rsi >

00 rsi >

rM >

VD rsj >

inoor;»covD r^r -<yt^rorH roocovDcyivor^ ^^JdP iOO :Z!J£J^«^^f^ rHCN^CMSrHO r s j o o o o o o o o r M o o o o o o o o

• • • • • O C D O O O O O O O O O O O O O O O O

. ' ^ f ^J^ r2 : i ' c o o r - o c n r > - cnrHcoor>.'«*o iiJJ^f)J:i^2^ CMinrHVDcy>rsi r t r o o t ^ r o r s i m C J ^ r O i n O O O O O r O O ^ O O O C M r H r H O r s l o o o o o O O O O O O oooc3c:><i>c>

I I I

i 2 ^ 5 ^ S ^ r-cy>r-roorH oorors icncnoo ^ C N r H i n O O r H C 3 ^ r H ' ; f ^ C M r O C M r s l C T l ^ O O ^ O ' ^ O O o o o o v o O O O O O O r H o o o o o O O O O O O O O O O O O O

I i I I I I I

vDO>^inro o^'i'corHcrtr^ OrHcr tocNroo intHrorHCTN cNinrHinCT^CN inrocMr^rocNin o ^ r o i n o o O O o r o o ^ o OOOrHrHOrs i

o o o o o O O O O O O O O O O O O O I I I

"ia r-CMoovD vDorsivDinr^ ininrHrH<T»rHr^ C O O ^ O O O C M r H r H O C O r H ' * r s l r H C M r O r H O m r O r H r H r H O O O O O O O O O O O O O O

o o o o o O O O O O O O O O O O O O I l l l l

inrHrovoro cr»rocoooooo OrHcncTvo oo incNrorHcn rsiinrHincrvrsi in rors jvororo^ < T > r O i n O O O O O r 0 < y » O O O O r H r H C M C M o o o o o O O O O O O O O O O O O O

I I I

i n rsi >

CN >

ro rsj >

rsi rsi >

fa hQ OQ < H Pi

r ^ V O V D C N C O ^ r s I r H t ^ ' ^ l ' r H C M r o i n c T i i n c M r H V D i n ' ^ T r H i n r H C M O r H I ^ O C N O C M r » V D r H < T t ^ r H C N O O O O O C N " ? r O O O O O H O r s I

O O O O O O O O O O O O O O O O O O I i I I I I

ID T-i cn ID cn o>ror^rHcoco as T-i as as cn c^ cn incMrorHcr* rsjinrHino^cN •sj'rocNvDrorsiin o ^ r o l n o o o o o r o o ^ o o o o H r H O C N

O O O O O O O O O O O O O O O O O O

o>OLnroo ^ ^ KD oo as as cxjinrHo^cNcovo c n o r ^ r H O CMtHro<y>rsirH CNororsirHorsi fvj,_l,_IOO O O O O r O O O O O O O O H

o o o o o O O O O O O O O O O O O O I l l l l I I I I I I

inoocororH o o ' ^ c N i n o ^ i n o c N c o o o i n CMOOOO rH rH ro rsj rH o VD o ro <«* cn O rH CNOrHOO O O O i n C N O O O O t H O O O cDOCDcJo O O O O O O o o o o o c p o

I I I I I I I

VD r* CO a\ o rH CN ro O rH CM ro "^ VD r 00 o o

Page 119: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

109

ro VO >

ro o cy> ro ro CN o CN ' ^ TJ< CN CO o "^ i n ^ ro i n rH o o

cr» <y> VD a^ rH rsi CM O O ro ^ vo rsi ro o o o vo ro o o

00 00 as as c^ CO o ^ cy rsi o CM O O rH rH o o

O O O O O O O O O O O O O I I

O O O O O O I I

rsj VD >

1 ^ 1 ^ O O ^ r H r o V D O i n i n v D v o r o r H o r o o o O O O O O O

o o I I

O CM O ro O VD i n ro rH o H i n rH i n O O O O O O O

o i n CN vo rH rsj rH CM rsi rj< O CM O O O O O O

O O O O O O I I I

O O O O O O O I I I I

O O O O O O I I I I

VD >

VD r^ ro CO i n rH o ro ^

O O O

00 rH 00 rsi VD CTt cn vo ro cn rH CM un rH i n o o o

CM r^ VD ro rsi i n ro rsi CM CM ^ ^ rsj 00 O O O VD H rH O

00 i n o r^ rsi r-* H o o i n CM rsi rH O rH rH O O

O O O O O O I I

O O O O O O O I I I

O O O O O O I I

o VD >

<y> i n f^ o <T> ro i n ro rH rH O rH

O O O O

i n 00 r^ r- i n ^ cn O rH rH o o O rH CM O O O

^ ro ^ rsj VD H * * O O CN vo VD O O O O O H O O rH

O O rH VD O^ O rH O O rsi O rH O O H O O O

O O O O O O O O O O O O O I I I

O O O O O O I I I

as ID >

VD t ^ i n o o> CM i n cn ro rsi O rH O O O

o o o o o I I I

i n '<;»' rH o^ ro CO o ro CM rM rH rsi rH O O O O O

00 rH o^ r^ o^ o^ r^ i n o o i n ro rH vo O O O O O O O

CM t^ r^ (Ti r^ r* rsj "sr o i n o rsj O O O O O O

O O O O O O l l l l l

O O O O O O O I I I I

O O O O O O I I I I

00 i n >

ro O 'iJ' CN rH i n CO rH ro i n cn r^ rH ro O rH o o

r - »* CO i n cTt rsj CO ro ^ ro H r^ O rH rH o o o

vo in o cn ^ rr O vo CO H ^ o oj O O O rH rH O rH

VO <y» VD rH cn 00 ro - ^ 00 rsi o o O O H O O O

O O O O O O O O O O O O O O O O O O O I I

O O O O O O I I

i n >

o rH ro o vo ^ r>-rM VO ro rH rH O 00 rH O O O O O O

CO CM i n rsi VD rsj vo VD ro rH o i n o o o o o rsj

r^ 00 'sr 00 00 rH CM O "^ rH rH i n H ' ^ O CM O O O O H

^ * * ro t^ ^ rH O t ^ rsi O O rH O H O O O O

O O O O O O O O O O O O O O O O O O O O I I

O O O O O O I I I

VD i n >

r o r H O O ' ^ r o i n r o r H i n r H C M V D C M i n o O O O O O O O O O

VD rH ro r* VD H ^ ro H O O H O O O O O O

' ^ rH CM i n VD CO CM o o o i n o o rH O O O O O O O

CN vo rH ro i n ^ O - ^ VD CM CM rH O O O O O O

O O O O O O O O O O O O O O I I

O O O O O O O I I I

O O O O O O

in in >

in >

i n r H r * ^ i n r ^ c M o r s i V D C M C M O r M O r H O C O O O O O O O O r H r H

CM r r rsj cr» CM rH rsi vo r* o o o O rH O rH O O

CN ^ i n ro t ^ cy> rH o o o 00 r^ o rH O O O O rH O O

rH rsi O 00 ' i ^ VD o o o rH rsi o O CM O O O O

o o o o o o o o o I I

CN ascni-iy£>oii-ti-*^asi-i v D ' s f i n o r o o r o o ^ ^ O O O C N O C N r O t H O r O

. . . . . . . . . . O O O O O O O O O O

O O O O O O

o ' ^ i n H rH ro 00 i n (Tv CT\ rH rsj ro rM "^ o o o

. . . . . . O O O O O O

O O O O O O o I I I I

rsj 00 ^ cy» o ro CM O CN VD vo VD r o ^ o o o i n CM o o

• • • • • • • O O O O O O O

I I I

O O O O O O I I I

rH 00 CM ^ ro ro CO ro o 00 o o H o rsi o o o

• • • • • • O O O O O O

ro i n >

rsj i n >

fa (J OQ < H Pi

^ i n r ^ o o r ^ o r o i n o v o o ^ v o o ^ ^ o o O L n v D O ^ v o

^ O r H O r O r H H C M O - ^ r O

O O O O O O O O O O O

c n o o i n ' ^ r ^ ' ^ o c M V D o o v o c N V O n O O C M r H O C y » V D O r s I ^ O r H r H O O r H i n O J r H r H r H O O

. . . . . . . • • • • • o O O O O O O O O O o o

I I I

r o ' ^ i n v o r ^ c o o ^ O r H C M c*};^'

00 o^ rH ro "^ rsi r - rH i n o CN ' ^ CM ro 'sr rH O O

. . . . . . O O O O O O

VD o^ CO CO o r^ rH ro r* rH O rH rH O O O O O

. . . . . . O O O O O O

I I

i n VD r^ 00 as o VD VD vo VD VD r^ > > > > > >

rH o o CN VD ro ro rsi CM H in o ^ as o o rH in ro o o

• . . . . . . O O O O O O o

I rsi o o rH rH ^ r^ rH o o^ o ^ i n vo O O O O O O rH

. . . . . . . O O O O O O o

rH rsj ro O rH CM ro

as as cn yo cn CO ro rsj o r^ ro ro o o rsj o o o

• • • • • • O O O O O O

I VD i n ro r^ ro o CM r-- VD ro o ro O O rH O O O

• • • • • • O O O O O O I I I

^ VD t^ CO o <y>

Page 120: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

110

CO >

CO O rH O CN in ro ro O O O O

. . . . O O O O I I

O ' i j ' r r 00 f^ ro CN rr tH rH O CM

. . . . O O O O

o 00 >

in VD ro o in CN r rH ro ro o o o o

. . . . . o o o o o

I I

^ o 00 cn r>- CM rH rH rH rH O O

. . . . O O O O

ro

>

rsj

>

in r o 00 in ' f O^ tH O "^ O CN O O O O O O

• . . . . . o o o o o o

CM 00 CN cr> in o r o o in o *!* o o o o o o o o o

• » . . . . . o o o o o o o

i I I I

VD ^ O 00 og o o o O O O O

. . . . O O O O

I i I

rH r f rH r^ O rH O O O O O O

. . . . O O O O

I I

>

f^ rH O O O CM O O O

. . . O O O

I I

o vo CN ro o rsj o o o o o o o o o

. . . . . o o o o o l l l l l

ro cyt CM in rH O O O O O O O

. . . . O O O O l l l l

o >

rH o ro CM rsj o o '^ O O O O

. . . . O O O O

ro VD in o 00 cn rH rH rH ro o o o o o

. . . . . o o o o o

I I I

00 O t ^ 00 O ro O rH O O O O

. . . . O O O O

I I

o cr» >

i n o o

• o I

as VD >

ro O CN rH ^ 'sr O O O rH O O O O O

. . . . . O O O O O

l l l l

^ rsi r ro r H O rH o o O O O O O

• • • • • o o o o o

I I I

cn T-i 1-i ^ O rH o o O O O O

. . . . O O O O l l l l

00 00 >

00 r-o rsj o o

• • o o I I

00 vo >

rH VD ro i n rH O rH rH rH rsj ro CN O O O O O CM

. . . . . . O O O O O O I I

i n 00 CO o VD rsi O O rH o in o o o o

• • • • • o o o o o

I I I

r^ CO 00 rH vo ro rH cn rsi o o rsi

. . . . O O O O

CO >

vo r o o o o

rsj

O O O

VD >

i n 00 rH rH rsj ro VD <y> rH ^ O rH VD CN o o o o o o r-

ro in 00 r 'jj* rsi oj o ro rH ro o o o o

O O O O O O O I I I

o o o o o

CM ^ O VD rH i n rH O rsi rH o O

O O O O I I

VD 00 >

o rH r r rH TJ* O O O O O O

. . . . O O O O l l l l

VD VD >

r ^ o o C T \ c o o i n r o o v D r H c r > c M ' * o i n r o i n o o o o o r o

i n ro *!»• CO rH in rsi '^ o ro o o o o o

o o o o o o o o o o o o o

ID •^ ID 1-i 1-i 1-i C^ T-i OJ rH o ro

O O O O

CO >

'^ rsj cy» r H c n rH O O O O o o o o o

. . . . . o o o o o

l l l l l

i n VD >

VD >

fa

OQ < H Pi

^ ^ o r ^ o c r > v o ' * o ^ r^"5;t«orMrHCNrorHr^ r H i n r H O O O O O V O

cn r^ oo T-i a\ vo 00 ro vo o rH O rH O O

ooooooooo l l l l

^HOO^cooo^*LnvDO^rH inr^cr i rHrHvorHcsirs j ro i n r M ^ r H O O O O O V D

o o o o o I I

o ro rH rsi in VD 00 rH rH VD CN O H o ro

o o o o o o o o o o I I I

o o o o o I I

L n v D r - c o a > O r H C N r o o rH rsi ro - r VD

i n o <T» r^ r in rsi o rH rH o o

O O O O I

^ i n o (Ti ID T-i C^ ID rH rH O O

O O O O

r- 00 o cr>

ro 00 >

rsj 00 >

fa hQ OQ < H

Pi

>

00 r ro vo rH r 00 o CO r^ i n CM O O O O O O

. . . . . . O O O O O O

I I ro ^ ^ rH VD vo r>> O O O rH CM O O O O O O O O O

. . . . . . . O O O O O O O

I l l l l

ro ' ^ vo r^ 00 o <T>

Page 121: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

APPENDIX C

111

Page 122: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

112

o vo >

rH O rH rsj CO r * ^ ^ ^ <yi r H rH O rH O

. . . . . O O O O O

o r* ^ rsj o in o ^ o rH O CM rH o o

^ cn as O O rH O O O

o o o o o O O O

as in >

t^ ro 00 rsi o O ro 'd' rH o in rsj O H rH rH O rH

. . . . . . o o o o o o

I I I

<y> cn VD ^ ro CM rH ro o vo o o o o o

. . . . . o o o o o l l l l

VD cy> CM

o in o O rH O

. . . O O O

00 ID >

r o 00 CN 00 vo O CM o rH VD a^ '^ (y> ^ CM r o O rH O O rH

o o

1-i T-i <D cn \D cn rH in o r-» O rH O O O

o o o o o i I

o o o o o

r^ VD '^f o '^ r^ O O O

O O O

in >

r H .

u

fa f j OQ < b^

cn fa cn i-:i fa OQ f-q < m H <c Pi H cn

X < oi in H > < u Pi > H in in Pi < IS EH EH S fa IS cn

P fa H 2 IS P P O fa IS H PH fa hQ EH fa P< O < P fa o

ORREL

83 IN

984 D

L SCH

U 0^ rH KP rH 1 < 1 ro

OJ 00 CO cn as rH

vo in >

in in >

^ in >

ro in >

rsi in >

00 ' ^ rH cn r^ CM O O O O O O

as 1^ cn as •^ in r^ in O rH o o

O O O O

00 CO ro vo in CM rH VD o rsj o o o o o

cn o rH o 00 00 ^ in vo r^ o o o o o

o ' * vo '^ ro 00 r* rsi CN 00 o o o o H

o o o o o I I I I

H ro O VD i n rH CM rH ro CM O O O O O

o o o o o

VO ro ro in O O rsi rH rH 00 o o o o o

o o o o o

ro i n H C3> "^ o o 00 in rH o o o o o

o o o o o

CM 00 00 o i n O 00 ro O O rH O O O O

o o o o o

VD i n o i n t ^ CM ' ^ r** r o VD r J cn O O O rH O rH

o o o o o

ro rM r* ro cn vo H -"^ CM [^ CN o ' ^ ro ro

o o o o o

rsi ro VD in ro CN o o CT\ r j CM in rH o o

O O O O O O

rH ro ro ^ in r^ ro ';r in ro 00 vo OJ o^ ^ O tH O CN rH O

o o o o o

00 VD rsi rH in ro ro O vo ro rH o ro OJ rsi

o o o o o

VD cn r» o o ' ^ CM rH r o CO CM ' ^ rH O O

O O O O O O O

v D v o r ^ r s i r ^ v D V D i n o v o c M O H ' ^ r ^ r o r H O O t H r H ' s r r s J r H

o o o o o

rH CM 00 i n 00 a^ ro CM ro O H O O rH

O O O O O

^ i n o C3 OJ ^ ro rH ro ro o o o o o

i n CM CN o in OJ O O O

O O O

VD '^r <T> o vo in O O O

O O O

rH r^ r^ o in o O O O O O O

ro o ^ Ol CM ro O O O

O O O I I

«* in vo O rH 00 O O O

O O O

^ ro CN O O VD O O O

o o o o o o o o O O O O O I I I

o o o o o O O O

in >

c M r ^ c n ^ i n o o i r H r H O i n r H O O ' ^ O O C T * O H r H O r O O r H O O

00 o ro 00 [^ VD CM vo r^ cr> O O rH O O

ro t^ CM VD in ro rH ro o o^ O rH O O O

o o o o o o o o o O O O O O o o o o o

r-. o 'a* O O O O O O

O O O I I I

o in >

C N ' * o o v D O r o a ^ r H V O « * r o ^ ' * r o o ^ v D O O ^ o o ^ r H C N r O ' ^ O O O C N O C M

i n ^ 00 <T> r-o o r^ CO cn in o '^ ^ vo

in cy> r* o ^ VD •<* r o O rH rn KD T-i rn <Z3

O O O O O O O O O O o o o o o O O O O O

cn o vo ro o ro O O O

o o I

fa hQ OQ < H Pi < >

C M ' * ' * o o o ^ o o o o o ^ * L n c N ^ O r O r H r H H C M O O ' d ' H r O r H o r o r o o o o o o o

(TV r^ ro r^ r-« ro OJ rH vo Ol

ro o ro CM ^

o vo o in o 00 r^ 00 rH rH 01 ro rH rH O

ooooooooooo I I I

Q , _ l r s I r O " « : r l n v D ^ * o o c T ^ o

o o o o o

rH OJ ro ' a* in vo vo vo VD vo > > > > >

o o o o o

vo r^ 00 <T> o VD VD VD VD r^ > > > > >

ro o^ 00 O rH ro O O O

O o I

rH Ol ro

555

Page 123: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

113

o vo >

cn in >

CO in >

in >

VD in >

in in >

in >

ro in >

rsi in >

in >

o in >

fa hQ OQ < H Pi

r H O ' ^ o j r H o i r o o r ^ r o r H o r o r H i ^ r o i n o i n v o c o i n o r H O v o r H ^ t H r H r H o o as T-i KD CO cn rOCMOO r H O O O O O r H O O O O t ^ t ^ O O r H O O O r H

O O O O O O O o o o o o O O O O O O O O I I I I l l l l

C M r ^ ^ r H o i n r o o o r ^ o o c o v o " ^ r ^ o c o c y * o ^ v o VD'<3< ' *CT\0 ' * rH inrHCMrOVD i n r H r H V D O o i r^vo O O O O O O O o o o o o O r H r H O O O O O

O O O O O O O o o o o o o o o o o O O O I I I I I I I I I I I I I I I I

O I O O i n o r O C M ' ; * * inCNtHCNVO (J\<T\CMrsirsI O H r H r H O O r O r O V O C N r O O C » O r O ^ i n v O r H C N ' * ^ O C N r H O O H O O r H O O O O O J C M O l C N r H O Q i-i i-i

O O O O O O O O O O O O O O O O O O O O I l l l l

c N C N O c N r H i n o i n v o ^ r o o ' s r o o i n r H r o v o * * O V O r H V D r H t H C N r H O O r O O J rHOOVOrHCM ^ ( N r H O O O r H O O O O O H O O O O O O O O O O

O O O O O O O o o o o o O O O O O O O O I I I I I I I I I I

o c M i n r M v D o v D i n o i v o r ^ r * o o i r ^ i n c r ^ o j ^ r v o i n o c N o r o v D O r o r H O j o c N r o ^ C M ^ o j <o rn -^ O O O O O O O o o o o o o o o o o O O O O O O O O O O O O O O O o o o o o O O O

I I I l l l l i n v o c M r o c M o i n ' s r r s i o o o c o r H r H o i v o o ^ cMvor^ c y » O r H r o o r o o r H O r H O < T » o c N r H O O o j r o o O r H O O O O O o o o o o r H O O r H O O O r H

O O O O O O O o o o o o o o o o o O O O I I I I I I I l l l l

i n C N r H O O i n C O O r H VOrHVOrOCN O O r O O r H ^ rOrOCM V D C N O r O ^ C r i C N V O O O r O O O OOCOVOVOrO OCNVD i n c N o o o o c M o o o o c M c M o o i n o o o i n

O O O O O O O o o o o o o o o o o O O O I I I I I

r o o r ~ r ^ c N o o i n r - r n r o o j i n o o o o r - r o ^ v o t n ^ o i n r o u o ' ^ ^ o oorHrHCMin i n ^ ^ r ^ o r * * o o o i n C N O O O O C N O O O O H r H O r H i n O O C M i n

O O O O O O O o o o o o o o o o o O O O I I l l l l

f O o o o i n c N V D v o r o r H v o c N O * c T i r o i n r H o o 0 ( y » r H O ^ r ^ r O O O V O V O C M r H r H l ^ CX3<y»rOrHCM O H r H O O r H r H O O r H O O O O O O H H O O CDCDO

C 3 C I > C I > C D < D O O o o o o o O O O O O O O O I I I I I I I

r ^ o o r ^ m r H r H o i r o r H H ' ^ r H ojcM««j'<y»rH Hr ; : :2? o S c N O ^ J S c g oorH<y>rHcr> a^ ^ OJ cy» Ol fN oo a^ S o O O H O C D o o o o o O O O H O O O r H

. . . . . . . . . . . . • • • O O O O O O O o o o o o O O O O O c p o o

I I I I I I l l l l

r o r f t v o r s i o r ^ c n vocr»r^ rHoo v o c o o o r o o j o i n i n

I^ rH O tH O O Ol rH O O O ^^ '^ ' ^ O r- O O Ol r-

O O O o ' o ' O O O O C^ CD O O O C> O CD O O O

.«««««r t / -^ i r> r r \ m c T » r o o o " ^ r o r o t ^ r * - o r ^ r ^

O O O O O O O O CD O O O o o o o o O O O

O rH CM ro VD r- 00 o H a> ro ^ CM ro in VD ro H Ol ro ro > > > > >

r^ CO <?> ro ro ro > > >

Page 124: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

114

CM

>

ro tH r^ vo O O rH O O O O O

O O O O I I

vo <r> i n ro o^ O^ rH r^ O CM tH O O O O

ro o CM ro r-O rH rH rH O O O O O O

O 00 rH ro ro ro rH o o 'sr o o o o o

o o o o o o o o o o l l l l l

o o o o o I i I

>

o

>

cr> vo >

CO VD >

vo >

r^ ro in o r^ O O rH rH O o o o o o

00 in tH ro cn O O OJ o o o o o o o

000

o o 1

O r-l iH O

O O O 1 1 1

OJ O OJ CN "^ CM O O O

O O 1

VO ^ ro CM o o

o o 1

OJ CM O O O O

O 1

048

rH in in r* in o ro o o o o o o o o

• • • • • o o o o o I I I I

vo vo ^ cn cn o o o o o o o o o o

a in vo in 00 1-i r-i 1-i CD O O O O O O

• • • • • o o o o o l l l l

00 00 i n CO rH ^ O ro CM rH o o o o o

.144

.007

o

.049

.007

o 1

.008

o

.018

o

TO

O'

o 1

1-i rH o o 1

.025

o

.005

o

.022

o

.004

o

.006

o .047

o

.035

o

.068

o .253

o

.798

o

.026

o

.504

o

.228

o 1

.006

o

.019

o

.007

o

.026

o

069

o .079

o 1

.018

o 1

.021

o .032

o 1

.024

o

003

o 1

.065

o

.062

o

401

o

.203

o 1

.013

o 1

014

o 1

.131

o 1

004

o 1

017

o 1

.003

o

006

o 1

073

o

.021

o 1

042

o

413

o

.039

o 1

010

o

210

o

.393

o 1

010

o

214

o

.386

o 1

099

o

040

o 1

.351

o 1

on

o 1

288

o

.073

o

073

o

334

o

.773

o o 1

CO o O -J

o o o o 1

tH as cn CM O 1-i

o o 1

VD in in o o o

O O O O o o o o o o o o o o I I o o o o o o o o o o

I I

VD VD >

in rH ro in in CM vo CM i n rH CN in o o o

o o o o o

o> r^ r^ rH CM rH O O vo H o o ro cn o

rH in in vo CM i n rH rH 00 rH O O O CM rH

cn r^ rH VD rH o ro CO ro ^ O O rH rH rH

CM ^ CO ' ^ 00 Ol r~- VD ro o tH ro " r o o

o o o o o I I

o o o o o o o o o o o o o o o I I

in VD >

<D 1-i rn as iD as rH OJ CM r^ i n CN rH vo rH O O O

i n rH VD 00 o ro o o CN Ol O O r^ rH o

Ol in vo in CN rH ^ r^ ro VD CN O O CM tH

<r> 0 0 CT\ VD ';r O rH rH Ol O O O O ro ro

CJS (T CM 00 r-r- o r- ' ^ rH vo rH VD O O

O O O O O O I I

o o o o o I I

o o o o o o o o o o o o o o o

VD >

i n CO ^ 00 i n CO <? CN O^ CT> i n 00 O CM in o ^ o o o o

o> ^ cn r^ VD cn cn as as cn o o ">* o o

^ vo vo ro '«* rH rH r^ Cr» rH rH O OJ O H

O ro ro VO cn O O O Cr> 00 O O O CM CM

O O O O O O O O O O O O o o o o o o o o o o I I

r- rH r^ ^ ro in rH r^ CT> r--ro o ^ o o

o o o o o I I

ro vo >

r o r H ' ^ r o c M i n v o r o o o o o c N v o i n o o r r i n c N i n r H O O o

o^ o^ vo "^ ^ r r H ro cn r^ o o vo CM o

Cr> 00 CM rH o cn rH r- o r-* O O rH CM rH

VD O in ^ CM VD rH r- r-- VD O O O OJ CM

ro o 'S* cn 00 i n CM ro VD o rH O VD O O

o o o o o o o o I I

o o o o o o o o o o o o o o o o o o o o I I

CM VD >

C N O ^ o o o c ^ r M r o o ^ t H i n r H C N O r H O O r H C M O O r H O O O O O ' ^ r

o o o o o o o o o I I I I I I

in - r ro o^ ro rH O ro O rH o o o o o

• • • • • o o o o o

r o^ 00 ** o CO ro rH o CM o o o o o

. . . . . o o o o o

I I I

in " r cn ro rH rH rH CM vo r^ o o o o o

• • • • • o o o o o I I

o^ o^ 00 ^ tH CM r^ CM rH O rH O O O O

• • * • • O O O O O I I I

vo >

fa hQ OQ < H

Pi

>

r o c M l n ^ ^ ( ^ c M r ^ o o ^ c M r H C n ^ C N r H i n r ^ O r O t H r H r O ' ^ r V O r H i n r H O O O

o o o o o o o o c p c p I I I

ro CM O rH CM CM O rH rH ro O O VO rH O . . . . .

O O O O O

cn CM CO cn o vo CM 'r o vo rH O O rH rH . . . . .

O O O O O

rMr^'«rlnvD^-cocT^OrH C^'JTl^^J^ S S S VD VD vo vp vp {^ i: r^ r^ on m m

ro ^ VD r-- CO r ^ r ^ o o o o o o OOOOOOOOOO

' r in r^ r^ vo rH o 00 r^ in o o o ro ro

. . . . . o o o o o

o 1-i as cn ^ as as CO cn cn > > > > >

in in ro o 00 o ro 00 r^ in ^ o in o o

. . . . . o o o o o

CM ro in so r^ rH rsi ro ro ro > > > > >

Page 125: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

115

rsi

>

^ T-i CM O O O

. . o o

I

as CO >

o CM CM ro rH rH CM i n O O O O

. . . . O O O O

in 00 VD 00 in O rH cn rH O H O O O rH

. . . . . O O O O O

I I

>

vo >

O r H o o

. . o o

I I

o o

00 vo >

ro o T-i

'«*' ro ro

• o o

r^ vo vo r^ CM r*-

. . o o

cn >

o l"^ >

cn vo >

ro o

• o

ro o o

ro o

• o

ro r--o

o as >

CO 00 >

00 >

VD CO >

o ro o

• o 1

CM r H

o • o

1

CM * * O

• o

o o o

• o 1

VD r H O

• o 1

in 1—i

o •

o

';r o o

. o 1

r H CM O

• O 1

in o o

• o

o o o

• o

r^ ^ ^ ^ VD

O o o ** ro o o o o o

. . . . . o o o o o

l l l l

CO VD ro ro O O O rH o o o o o o

. . . . . o o o o o 1 1 1

r ^ ro o vo rH CO r^ Ol o O O O rH o

• t • • •

o o o o o 1

00 r o^ ro in ' ^ cn o^ o ro rH rH rH O O

. . . . . O O O O O

r- o 00 in ro rH CM CM 00 rH o o o o o

• • • • • o o o o o 1 1

ro in ro o ro r-i CD T-i 1-i T-i O O O O O

. . . . . o o o o o

1

r o r - Ol rH rH O O CM t ^ O o o o o o

. . . . . o o o o o

1 1

r^ C7 CM i n i n rH CN O ON rH rH O O O rH

. . . . . O O O O O

1 1

O rH O rH CM i n '53" rH 00 i n CN O O O CM

. . . . . o o o o o i 1

CM ^ in '^ o CM i n rH i n Ol o o o o o

• • • • t

o o o o o 1

vo VD >

o^ cn r-o vo T-i ^

o o 00 >

cn rH rH rH cn O CM CM rH CM O O O O rH

O O O O O I i I

ro <y> Ol CM r^ ro o rH ro o o o o o o

o o o o o I I I

rH 00 r^ CM ^ CM O i n CM CN o o o o o o o o o o I I

in vo >

O ' J'

CM vo . .

o o

ro 00 >

00 o VD in ro o\ CN o o in rH ro­o o o o o o

r^ o rH vo ro rH 00 r - r^ rH O O O rH O

in ro CN ro VD o o CM ro o tH O O O rH

O O O O O O I I I I

o o o o o I I I

o o o o o I I I

vo >

as VD CN ^

. . o o

OJ 00 >

in VD in r^ in rH r^ CN rH ^ r o CM CM rH O O O O O O O

rH in CO VD ro r o O O rH o o o o o o

r- in o o r^ O rH O CM O o o o o o

O O O O O O O I I I

o o o o o I I

o o o o o

ro vo >

O CN in ro ro vo

• • o o

00 >

V D C O ^ ^ i n r H r ^ r H O ' ^ C N O r O H O r H O O O O C M t H O O

in r^ ro ro VD vo ro '5j« CM cn rH rH rH rH r o

Ol o ro CM ro 00 r o CM 00 00 ^ O O rH ^

o o o o o o o o I I

o o o o o o o o o o

CN VD >

vo r^ Ol CN o o o o

I I

o 00 >

v o r ^ r o o o ^ r s i r ^ " ^ ^ r H O r H r H C N C M O O r H r O O r H O O C M r H O O

rH CM i n VD CO 00 r - VD 00 VD O ^ ^ Ol o

o o o o o o o o o I I

o o o o o

rr r- VD VD in r^ r ta* CM r^ o^ o o ^ o^

o o o o o

vo >

fa

OQ < H Pi < >

CM ro in 00 CN in

. . o o

00 as cn cn > >

cn

>

fa iJ OQ < H

>

i H r ^ v D c n r o c M r o o i n v o O O r H O C M r H r H r H O O O O O O O O O O O O O

in VD in o (7 o Ol CM ^ ro o o o o o

oooooooooo l l l l l

O H r s i r o ' j ^ v D r ^ o o o r H o o o o o o c o o o o o o o o o a ^ o ^ > > > > > > > > > >

o o o o o I I

<* tH 00 cn o r^ tH o ^ r-O O O rH O

o^ ro ^ CN ro 00 ro ro rH CM > > > > >

o o o o o

in VD r CO cn ro ro ro ro ro > > > > >

Page 126: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT

116

CO ro >

o CN

ro >

vo ro >

in ro >

080

182

• o

065

ro in o *r o o

• • o o 1

OJ o rH 00 o o

• • o o 1 1

r^ cn ^ cn <* as

O O O O

ro CM >

^ in ro in CM rH rH r o r o rH o o o o o

. . . . . o o o o o

Ol 1-i

>

in o CM o vo OJ 00 "«;r ro CM ' ^ «!j* tH CM O O O CM

. . . . . . O O O O O O

'S3'

ro >

a^ in in rH o "* ^ o ' r vo ro CM VD VD O O *^ O O CN "^

o o o o o I I I

o o

ro ro >

fa hQ OQ < H Pi < >

• t r i n c M r H r o r H r o c n c r > c M ' * r ~ r O ' - i v o v o ( r > o o ' ! f O O C M ' *

O O O O O O O O I I I

r r c M r o i n v o r - o o o j f O f H C M r o r o r p c n C ?

Page 127: ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT