Here, pal! Regress this! presented by Miles Hamby, PhD Principle, Ariel Training Consultants MilesFlight.20megsfree.com [email protected] Or, How to Use.

Here, pal!

Regress this!

presented by

Miles Hamby, PhD

Principle, Ariel Training ConsultantsMilesFlight.20megsfree.com

[email protected]

Or, How to Use Regression to Tell You Just About Everything

Part 1

Typical – Descriptive Statistics

Frequencies – numbers of things

eg – How many female students have graduated over the last 6 years?

Mean – measure of central tendency

eg – What is the average time to complete an academic program for students with 12 hours transfer credit?

Standard Deviation – measure of dispersion

eg – 68% of completing students graduate within how many terms?

Shortcoming of Descriptive Statistics

They do not predict.

They can tell you what it is –

but they can’t tell you what it will be

eg -

Can we predict how many female students will graduate and when?

Regression predicts!

Can we predict when a student with no transfer credit will graduate?

Can we predict the likelihood of graduation of a student based on gender?

How to Use Regression to Predict

Question –

What kind of student takes the

longest time to graduate?

What kind of student never graduates?

Typical way –

• Start with specific cohort (eg, Fall 1993)

• Select a single group (eg, 1-12 transfer credits)

• Count number who graduate each term

• Compute percentage ~

25 graduated 100 started = 25%

Conclusion – For Fall 93 cohort, graduation rate = 25% after 12 terms for those with 1-12 transfer credits

Exiguousness of Typical Method –

• DV implied, not specified (and therefore not tested)

• Does not measure strength of association to graduation time (correlation) or amount of effect (slope) on graduation time

eg – compare age’s effect to transfer credits’ effect

• Graduation Rate does not predict time-in-program or time-to-completion

• Must repeat procedure for each time block

Time to graduation for each variable not discrete - includes all other variables

Typical Method, e.g.

Time to GraduationVariable

X = 16 terms, S = 5 termsFemales ~

X = 13 terms, S = 4 terms1-12 Xfer Cr ~

X = 18 terms, S = 9 termsMarried ~

But how about a single, black, man with 17 transfer credits?

Must repeat procedure for single students, then repeat for black students, then repeat for males then repeat for 13 – 20 transfer credits, then ‘eyeball’ how they correlate.

Is there a way to determine how much of the 16 terms time for females (previous ex.) would be

ameliorated by being a single, black, male with 17 transfer credit hours?

There is a way!

Regress it!

Effects of gender, age, transfer credits, marital status, citizenship, ethnicity, and more, directly on time to complete are measurable and comparable

Pick a profile and I’ll tell you how long it will take for that student to graduate!

Procedure –

2. Identify independent variables (IV) that possibly effect graduation rates – gender, ethnicity, marital status, age, transfer credits, income

4. Run linear regression to determine:

(b) significance of difference in means of IVs

(c) regression model (y = a+b1X1…bnXn) to predict Time by IVs

(a) correlations between Time and IVs

1. Identify dependent variable (DV) – i.e, the question you are asking – eg, Time to Graduate (Time)

3. Collect data

Regression can tell you everything!

# Terms = a + .4*marital + .2*Gender + .06*Age - .18*xfer

EG –

For a single male, age 32, with 18 transfer credits - we can expect a graduation time of 32 terms

# Terms = 33 terms + .4*0 + .2*0 + .06*32 - 1.7*18

32 terms = 33 terms + 0 + 0 + 2 - 3

DV ~ Time to Graduation (# terms - ratio)

Adding Variables

IV ~ Gender (F or M - nominal)

Ethnic (B, H, W, NA, API, Alien - nominal)

Alien (Alien or US - nominal)

Marital status (si, ma, di – nominal)

Age (# years - ratio)

Transfer credits (# hours - ratio)

Tutoring done (# sessions – ratio; Y/N - nominal

Coding Your Variables

Scale (ratio) variables (time to completion, age, etc) – use number directly

eg, Age = 32 years, use ’32’

Time to Comp (terms) = 12 terms, use ’12’

Coding Your Variables

Nominal Variables – use ‘dummies’

What are Dummy Variables?

Variables used to quantify nominal

variables i.e., Nominal (qualitative) variables

assigned a quantitative number and treated as a quantitative variable.

Dummy Variables

eg – Ethnic - African-American, Hispanic, White

Major – Bus, Account, Computers, English, LA

Religion – Christian, Jew, Muslim, Hindu

Dichotomous variable – two categorieseg - Male or Female

Married or Single

Has had tutoring or hasn’t

US Citizen or Alien

Graduate student or Undergrad

Polychotomous variable – several categories of the variable

Dummy Variables

‘Ethnic’

Make B, NA/AN, W, API,H, Unk unique variables

Code as 1 = ‘presence of characteristic’ (‘Black’-ness) or 0 = ‘absence of characteristic’

eg, ‘Gender’

Code Male = 0, Female = 1 (or vice-versa)

1 = ‘presence of characteristic’ (femaleness)

0 = ‘absence of characteristic’

Dummy Variables

B: 1 = yes, 0 = no

AN: 1 = yes, 0 = no

W: 1= yes, 0 = no

API: 1 = yes, 0 = no

H: 1 = yes, 0 = no

Unk: 1 = yes, 0 = no

Alien: 1 = yes, 2 = no

Marital: 1 = MA/DI 0 = SI

Gender: 1 = F, 0 = M

Age: number years

Transfer credits: number

# Terms = 3 terms + .2*1 + .3*32 + 1.2*10 + .4*3

# Terms = 32 terms + [.2*1+.2*0+.2*0 +.2*0] (ethnic)

+ .5*0 (Alien) + .4*1 (marital)

+ .2*1 (gender)

+ .06*32 (age)

- 1.7*10 (xfer credits)

e.g. ~

Black, US Citizen, single, female, married, 32 years old, 10 transfer credits:

As Used in the Regression

Nominal Variables – Dichotomous - 2 values

Create new column for dummy variable or recode original

1 = presence of characteristic of interest

0 = not the characteristic of interest (absence of characteristic)

1F-490G001F

0US0SI1U000M

1GREEN1MA1U110M

1P-R1MA0G001F

0US1DI1U110M

0US0SI1U121F

1F-10SI1U131F

ALIENVISAMARITMARITLU/GLEVELTUTRDTUTSESGENDRSEX

Nominal Variables – more than 2 values

Create new columns for dummy variables – one for each value

1 = presence of characteristic (value)

0 = absence of characteristic

0010004001ACC

0000102100CIS

0000011010BUS

1001000100CIS

0001003010BUS

0100005001ACC

0000011001ACC

0UNKN5HISP4ASIAN3WHITE2NATAM1BLACKETHNICCISBUSACCMAJOR

Run the Regression

SPSS

The Results!Descriptive Statistics

30.530 6.339 6263

37.1677 8.7830 6263

.52 .50 6263

8.57 1.86 6263

.36 .53 6263

1.31E-02 .25 6263

.15 .42 6263

5.36E-02 .31 6263

.11 .38 6263

.19 .39 6263

3.5771 .3695 6263

45.1997 41.9258 6263

.69 .46 6263

98635.26 100119.01 6263

.12 .32 6263

.29 .46 6263

Quarters to Completion

AGE

Gender

Marital Status

Black

Native American

Asian

Hisp

Unkn

Alien

GPA

XFER CR

Undergrad Status

Tutoring Sessoin Date

Accounting

Business

Mean Std. Deviation N

Regression ModelsVariables Entered/Removedb

Alien,Black,MaritalStatus,Unkn,Gender,AGE,Asian,Hisp,NativeAmerican

a

. Enter

TutoringSessoinDate,XFER CR,GPA ,UndergradStatus

a

. Enter

Accounting,Business

a . Enter

Model1

2

3

VariablesEntered

VariablesRemoved Method

All requested variables entered.a.

Dependent Variable: Quarters to Completionb.

Variable CorrelationsCorrelations

1.000 -.148 .053 -.027 .013 .014 -.013 -.009 .040 -.016 .046 .158 -.144 .068 .093 .190

-.148 1.000 .005 -.004 .073 -.008 -.170 -.023 -.042 -.250 .117 .030 .038 .022 -.006 -.002

.053 .005 1.000 -.021 .110 -.029 -.038 -.036 -.030 -.058 -.032 -.066 -.049 .069 .142 .225

-.027 -.004 -.021 1.000 -.012 -.012 -.003 .005 .024 -.010 -.011 -.033 .014 -.031 .002 -.021

.013 .073 .110 -.012 1.000 .406 .015 .232 .096 -.009 -.228 -.135 -.045 .014 -.014 .057

.014 -.008 -.029 -.012 .406 1.000 .536 .733 .600 .065 .022 -.025 -.043 .010 .008 -.004

-.013 -.170 -.038 -.003 .015 .536 1.000 .374 .259 .361 .036 -.094 -.155 -.009 .003 -.047

-.009 -.023 -.036 .005 .232 .733 .374 1.000 .434 .058 -.030 -.013 -.013 -.018 .016 -.002

.040 -.042 -.030 .024 .096 .600 .259 .434 1.000 .060 .052 -.019 -.057 .035 .027 -.001

-.016 -.250 -.058 -.010 -.009 .065 .361 .058 .060 1.000 -.025 -.208 -.211 -.030 .022 -.008

.046 .117 -.032 -.011 -.228 .022 .036 -.030 .052 -.025 1.000 .090 -.222 .093 .006 .039

.158 .030 -.066 -.033 -.135 -.025 -.094 -.013 -.019 -.208 .090 1.000 .460 -.164 .040 -.119

-.144 .038 -.049 .014 -.045 -.043 -.155 -.013 -.057 -.211 -.222 .460 1.000 -.438 .029 -.270

.068 .022 .069 -.031 .014 .010 -.009 -.018 .035 -.030 .093 -.164 -.438 1.000 -.029 .122

.093 -.006 .142 .002 -.014 .008 .003 .016 .027 .022 .006 .040 .029 -.029 1.000 -.238

.190 -.002 .225 -.021 .057 -.004 -.047 -.002 -.001 -.008 .039 -.119 -.270 .122 -.238 1.000

. .000 .000 .017 .147 .129 .152 .245 .001 .101 .000 .000 .000 .000 .000 .000

.000 . .338 .369 .000 .255 .000 .035 .000 .000 .000 .009 .001 .040 .305 .425

.000 .338 . .051 .000 .011 .001 .002 .008 .000 .005 .000 .000 .000 .000 .000

.017 .369 .051 . .172 .167 .411 .332 .030 .213 .197 .004 .132 .007 .441 .048

.147 .000 .000 .172 . .000 .115 .000 .000 .230 .000 .000 .000 .132 .137 .000

.129 .255 .011 .167 .000 . .000 .000 .000 .000 .043 .023 .000 .217 .252 .361

.152 .000 .001 .411 .115 .000 . .000 .000 .000 .002 .000 .000 .248 .397 .000

.245 .035 .002 .332 .000 .000 .000 . .000 .000 .009 .148 .152 .080 .109 .431

.001 .000 .008 .030 .000 .000 .000 .000 . .000 .000 .067 .000 .003 .017 .463

.101 .000 .000 .213 .230 .000 .000 .000 .000 . .025 .000 .000 .010 .039 .253

.000 .000 .005 .197 .000 .043 .002 .009 .000 .025 . .000 .000 .000 .306 .001

.000 .009 .000 .004 .000 .023 .000 .148 .067 .000 .000 . .000 .000 .001 .000

.000 .001 .000 .132 .000 .000 .000 .152 .000 .000 .000 .000 . .000 .010 .000

.000 .040 .000 .007 .132 .217 .248 .080 .003 .010 .000 .000 .000 . .012 .000

.000 .305 .000 .441 .137 .252 .397 .109 .017 .039 .306 .001 .010 .012 . .000

.000 .425 .000 .048 .000 .361 .000 .431 .463 .253 .001 .000 .000 .000 .000 .


Age

Gender

Marital Status

Black

Native American

Asian

Hisp

Unkn

Alien

GPA

XFER CR

Undergrad Status


Accounting

Business


Age

Gender

Marital Status

Black

Native American

Asian

Hisp

Unkn

Alien

GPA

XFER CR

Undergrad Status


Accounting

Business

Pearson Correlation

Sig. (1-tailed)

Quarters toCompletion AGE Gender Marital Status Black

NativeAmerican Asian Hisp Unkn Alien GPA XFER CR

UndergradStatus

TutoringSessoin Date Accounting Business

Note – although some variables are highly correlated to each other, the correlation (R) may not be significant

The Regression

ANOVA

ANOVAd

8038.936 9 893.215 22.926 .000a

243617.2 6253 38.960

251656.1 6262

29666.471 13 2282.036 64.239 .000b

221989.6 6249 35.524

251656.1 6262

38749.290 15 2583.286 75.797 .000c

212906.8 6247 34.081

251656.1 6262

Regression

Residual

Total

Regression

Residual

Total

Regression

Residual

Total

Model1

2

3

Sum ofSquares df Mean Square F Sig.

Predictors: (Constant), Alien, Black, Marital Status, Unkn, Gender, AGE, Asian, Hisp,Native American

a.

Predictors: (Constant), Alien, Black, Marital Status, Unkn, Gender, AGE, Asian, Hisp,Native American, Tutoring Sessoin Date, XFER CR, GPA , Undergrad Status

b.

Predictors: (Constant), Alien, Black, Marital Status, Unkn, Gender, AGE, Asian, Hisp,Native American, Tutoring Sessoin Date, XFER CR, GPA , Undergrad Status,Accounting, Business

c.

Dependent Variable: Quarters to Completiond.

Test of significance of the F statistic indicates all three the regression models are statistically significant (Sig. < .05)

i.e, the variation was not by chance – another set of data would probably show the same results.

The Regression

ANOVA

ANOVAd

8038.936 9 893.215 22.926 .000a

243617.2 6253 38.960

251656.1 6262

29666.471 13 2282.036 64.239 .000b

221989.6 6249 35.524

251656.1 6262

38749.290 15 2583.286 75.797 .000c

212906.8 6247 34.081

251656.1 6262

Regression

Residual

Total

Regression

Residual

Total

Regression

Residual

Total

Model1

2

3

Sum ofSquares df Mean Square F Sig.

Predictors: (Constant), Alien, Black, Marital Status, Unkn, Gender, AGE, Asian, Hisp,Native American

a.

Predictors: (Constant), Alien, Black, Marital Status, Unkn, Gender, AGE, Asian, Hisp,Native American, Tutoring Sessoin Date, XFER CR, GPA , Undergrad Status

b.

Predictors: (Constant), Alien, Black, Marital Status, Unkn, Gender, AGE, Asian, Hisp,Native American, Tutoring Sessoin Date, XFER CR, GPA , Undergrad Status,Accounting, Business

c.

Dependent Variable: Quarters to Completiond.

The larger the F (ratio of the mean square of the Regression and mean square of the Error/Residual), the more robust the regression equation.

I.e., the smaller the mean square residual, indicates smaller error or departure from the regression line.

893.21538.960

= 22.926F =

Interpretation –

Mean Square Error/Residual of Model 1 is > Mean Square Error of Model 2

Variation about the Regression Line

Y

QT

RS

to C

ompl

etio

n

0 +

error

y

ŷ

Model 1 error

y

ŷ

Model 2

The Regression Correlation (R)

Model 3 returns the highest correlation (R = .392) with 15.4% (R2 = .154) of the variation in Time to Completion (in Qtrs) being explained by the variables Alien, Ethnicity, Marital status, Gender, Age, Tutoring, Transfer credits, U/G status, and Major.

Model Summary

.179a .032 .031 6.242 .032 22.926 9 6253 .000

.343b .118 .116 5.960 .086 152.204 4 6249 .000

.392c .154 .152 5.838 .036 133.252 2 6247 .000

Model1

2

3

R R SquareAdjustedR Square

Std. Error ofthe Estimate

R SquareChange F Change df1 df2 Sig. F Change

Change Statistics

Predictors: (Constant), Alien, Black, Marital Status, Unkn, Gender, AGE, Asian, Hisp, Native Americana.

Predictors: (Constant), Alien, Black, Marital Status, Unkn, Gender, AGE, Asian, Hisp, Native American, Tutoring Sessoin Date,XFER CR, GPA , Undergrad Status

b.

Predictors: (Constant), Alien, Black, Marital Status, Unkn, Gender, AGE, Asian, Hisp, Native American, Tutoring Sessoin Date,XFER CR, GPA , Undergrad Status, Accounting, Business

c.

Coefficientsa

35.612 .533 66.835 .000

-.120 .009 -.166 -12.817 .000

.624 .160 .049 3.910 .000

-9.27E-02 .043 -.027 -2.180 .029

.101 .179 .008 .568 .570

1.127 .676 .044 1.668 .095

-.625 .257 -.041 -2.434 .015

-.891 .373 -.044 -2.389 .017

.670 .270 .040 2.477 .013

-.692 .224 -.043 -3.081 .002

37.068 .983 37.723 .000

-.119 .009 -.165 -13.170 .000

.656 .153 .052 4.290 .000

-4.64E-02 .041 -.014 -1.142 .253

.397 .179 .033 2.211 .027

.928 .655 .036 1.418 .156

-.874 .247 -.058 -3.535 .000

-.724 .358 -.036 -2.023 .043

.551 .259 .033 2.129 .033

-.601 .220 -.037 -2.736 .006

-.311 .226 -.018 -1.376 .169

4.418E-02 .002 .292 20.994 .000

-4.013 .216 -.292 -18.588 .000

-9.36E-07 .000 -.015 -1.103 .270

35.577 .968 36.768 .000

-.117 .009 -.162 -13.256 .000

-.110 .157 -.009 -.701 .483

-4.05E-02 .040 -.012 -1.017 .309

.439 .176 .036 2.497 .013

.719 .641 .028 1.120 .263

-.553 .243 -.037 -2.275 .023

-.830 .351 -.041 -2.366 .018

.531 .254 .032 2.092 .036

-.618 .216 -.038 -2.867 .004

-.277 .221 -.016 -1.254 .210

4.285E-02 .002 .283 20.762 .000

-3.259 .218 -.237 -14.959 .000

-4.71E-07 .000 -.007 -.566 .571

2.638 .240 .135 10.970 .000

2.651 .181 .191 14.686 .000

(Constant)

AGE

Gender

Marital Status

Black

Native American

Asian

Hisp

Unkn

Alien

(Constant)

AGE

Gender

Marital Status

Black

Native American

Asian

Hisp

Unkn

Alien

GPA

XFER CR

Undergrad Status


(Constant)

AGE

Gender

Marital Status

Black

Native American

Asian

Hisp

Unkn

Alien

GPA

XFER CR

Undergrad Status


Accounting

Business

Model1

2

3

B Std. Error

UnstandardizedCoefficients

Beta

Standardized

Coefficients

t Sig.

Dependent Variable: Quarters to Completiona.

The SlopesModel 3 Interpretation

• The older the student, the shorter the time to completion (B = -.117)

Y

QT

RS

to C

ompl

etio

n

Interpretation –

Age slope shallow, slight effect on Qtrs to Completion

Model 3 Slopes Graph – AGE

AGE B = - .117

35.577

0 yrs 70 yrs

Coefficientsa

35.612 .533 66.835 .000

-.120 .009 -.166 -12.817 .000

.624 .160 .049 3.910 .000

-9.27E-02 .043 -.027 -2.180 .029

.101 .179 .008 .568 .570

1.127 .676 .044 1.668 .095

-.625 .257 -.041 -2.434 .015

-.891 .373 -.044 -2.389 .017

.670 .270 .040 2.477 .013

-.692 .224 -.043 -3.081 .002

37.068 .983 37.723 .000

-.119 .009 -.165 -13.170 .000

.656 .153 .052 4.290 .000

-4.64E-02 .041 -.014 -1.142 .253

.397 .179 .033 2.211 .027

.928 .655 .036 1.418 .156

-.874 .247 -.058 -3.535 .000

-.724 .358 -.036 -2.023 .043

.551 .259 .033 2.129 .033

-.601 .220 -.037 -2.736 .006

-.311 .226 -.018 -1.376 .169

4.418E-02 .002 .292 20.994 .000

-4.013 .216 -.292 -18.588 .000

-9.36E-07 .000 -.015 -1.103 .270

35.577 .968 36.768 .000

-.117 .009 -.162 -13.256 .000

-.110 .157 -.009 -.701 .483

-4.05E-02 .040 -.012 -1.017 .309

.439 .176 .036 2.497 .013

.719 .641 .028 1.120 .263

-.553 .243 -.037 -2.275 .023

-.830 .351 -.041 -2.366 .018

.531 .254 .032 2.092 .036

-.618 .216 -.038 -2.867 .004

-.277 .221 -.016 -1.254 .210

4.285E-02 .002 .283 20.762 .000

-3.259 .218 -.237 -14.959 .000

-4.71E-07 .000 -.007 -.566 .571

2.638 .240 .135 10.970 .000

2.651 .181 .191 14.686 .000

(Constant)

AGE

Gender

Marital Status

Black

Native American

Asian

Hisp

Unkn

Alien

(Constant)

AGE

Gender

Marital Status

Black

Native American

Asian

Hisp

Unkn

Alien

GPA

XFER CR

Undergrad Status


(Constant)

AGE

Gender

Marital Status

Black

Native American

Asian

Hisp

Unkn

Alien

GPA

XFER CR

Undergrad Status


Accounting

Business

Model1

2

3

B Std. Error


Beta

Standardized

Coefficients

t Sig.




• Married/Divorced tends to shorten completion time

(B= -.0405), but is not significant (Sig. = .309, >.05)

Y

QT

RS

to C

ompl

etio

n

Interpretation –

Married/Divorced very shallow, but not significant (Sig. <.000)

Model 3 Slopes Graph – Married/Divorced

Married B = - .0405

35.577

0 (Single)

1 (Married/Divorced)

Coefficientsa

35.612 .533 66.835 .000

-.120 .009 -.166 -12.817 .000

.624 .160 .049 3.910 .000

-9.27E-02 .043 -.027 -2.180 .029

.101 .179 .008 .568 .570

1.127 .676 .044 1.668 .095

-.625 .257 -.041 -2.434 .015

-.891 .373 -.044 -2.389 .017

.670 .270 .040 2.477 .013

-.692 .224 -.043 -3.081 .002

37.068 .983 37.723 .000

-.119 .009 -.165 -13.170 .000

.656 .153 .052 4.290 .000

-4.64E-02 .041 -.014 -1.142 .253

.397 .179 .033 2.211 .027

.928 .655 .036 1.418 .156

-.874 .247 -.058 -3.535 .000

-.724 .358 -.036 -2.023 .043

.551 .259 .033 2.129 .033

-.601 .220 -.037 -2.736 .006

-.311 .226 -.018 -1.376 .169

4.418E-02 .002 .292 20.994 .000

-4.013 .216 -.292 -18.588 .000

-9.36E-07 .000 -.015 -1.103 .270

35.577 .968 36.768 .000

-.117 .009 -.162 -13.256 .000

-.110 .157 -.009 -.701 .483

-4.05E-02 .040 -.012 -1.017 .309

.439 .176 .036 2.497 .013

.719 .641 .028 1.120 .263

-.553 .243 -.037 -2.275 .023

-.830 .351 -.041 -2.366 .018

.531 .254 .032 2.092 .036

-.618 .216 -.038 -2.867 .004

-.277 .221 -.016 -1.254 .210

4.285E-02 .002 .283 20.762 .000

-3.259 .218 -.237 -14.959 .000

-4.71E-07 .000 -.007 -.566 .571

2.638 .240 .135 10.970 .000

2.651 .181 .191 14.686 .000

(Constant)

AGE

Gender

Marital Status

Black

Native American

Asian

Hisp

Unkn

Alien

(Constant)

AGE

Gender

Marital Status

Black

Native American

Asian

Hisp

Unkn

Alien

GPA

XFER CR

Undergrad Status


(Constant)

AGE

Gender

Marital Status

Black

Native American

Asian

Hisp

Unkn

Alien

GPA

XFER CR

Undergrad Status


Accounting

Business

Model1

2

3

B Std. Error


Beta

Standardized

Coefficients

t Sig.






• Undergraduates tend to take considerably less time to complete than graduates

(B = -3.259)

Y

QT

RS

to C

ompl

etio

n

Interpretation –

Undergraduates steep, tend to shorten Qtrs to Completion considerably over Graduates

Model 3 Slopes Graph – Undergraduate vs Graduate

Under B = - 3.259

35.577

0 (Graduate)

1 (Undergraduate)

Coefficientsa

35.612 .533 66.835 .000

-.120 .009 -.166 -12.817 .000

.624 .160 .049 3.910 .000

-9.27E-02 .043 -.027 -2.180 .029

.101 .179 .008 .568 .570

1.127 .676 .044 1.668 .095

-.625 .257 -.041 -2.434 .015

-.891 .373 -.044 -2.389 .017

.670 .270 .040 2.477 .013

-.692 .224 -.043 -3.081 .002

37.068 .983 37.723 .000

-.119 .009 -.165 -13.170 .000

.656 .153 .052 4.290 .000

-4.64E-02 .041 -.014 -1.142 .253

.397 .179 .033 2.211 .027

.928 .655 .036 1.418 .156

-.874 .247 -.058 -3.535 .000

-.724 .358 -.036 -2.023 .043

.551 .259 .033 2.129 .033

-.601 .220 -.037 -2.736 .006

-.311 .226 -.018 -1.376 .169

4.418E-02 .002 .292 20.994 .000

-4.013 .216 -.292 -18.588 .000

-9.36E-07 .000 -.015 -1.103 .270

35.577 .968 36.768 .000

-.117 .009 -.162 -13.256 .000

-.110 .157 -.009 -.701 .483

-4.05E-02 .040 -.012 -1.017 .309

.439 .176 .036 2.497 .013

.719 .641 .028 1.120 .263

-.553 .243 -.037 -2.275 .023

-.830 .351 -.041 -2.366 .018

.531 .254 .032 2.092 .036

-.618 .216 -.038 -2.867 .004

-.277 .221 -.016 -1.254 .210

4.285E-02 .002 .283 20.762 .000

-3.259 .218 -.237 -14.959 .000

-4.71E-07 .000 -.007 -.566 .571

2.638 .240 .135 10.970 .000

2.651 .181 .191 14.686 .000

(Constant)

AGE

Gender

Marital Status

Black

Native American

Asian

Hisp

Unkn

Alien

(Constant)

AGE

Gender

Marital Status

Black

Native American

Asian

Hisp

Unkn

Alien

GPA

XFER CR

Undergrad Status


(Constant)

AGE

Gender

Marital Status

Black

Native American

Asian

Hisp

Unkn

Alien

GPA

XFER CR

Undergrad Status


Accounting

Business

Model1

2

3

B Std. Error


Beta

Standardized

Coefficients

t Sig.






• Undergraduates tend to take considerably less time to complete than graduates

(B = -3.259)

• Tutoring shortens time very slightly (B = -.0471), but is not significant (Sig. =.571)

Y

QT

RS

to C

ompl

etio

n

Interpretation –

Undergraduates steep, tend to shorten Qtrs to Completion considerably over Graduates, but not significant (Sig. .571 > .05)

Model 3 Slopes Graph – Undergraduate vs Graduate

Tutored B = - .00000047135.577

0 (No Tutoring)

1 (Tutored)

Coefficientsa

35.612 .533 66.835 .000

-.120 .009 -.166 -12.817 .000

.624 .160 .049 3.910 .000

-9.27E-02 .043 -.027 -2.180 .029

.101 .179 .008 .568 .570

1.127 .676 .044 1.668 .095

-.625 .257 -.041 -2.434 .015

-.891 .373 -.044 -2.389 .017

.670 .270 .040 2.477 .013

-.692 .224 -.043 -3.081 .002

37.068 .983 37.723 .000

-.119 .009 -.165 -13.170 .000

.656 .153 .052 4.290 .000

-4.64E-02 .041 -.014 -1.142 .253

.397 .179 .033 2.211 .027

.928 .655 .036 1.418 .156

-.874 .247 -.058 -3.535 .000

-.724 .358 -.036 -2.023 .043

.551 .259 .033 2.129 .033

-.601 .220 -.037 -2.736 .006

-.311 .226 -.018 -1.376 .169

4.418E-02 .002 .292 20.994 .000

-4.013 .216 -.292 -18.588 .000

-9.36E-07 .000 -.015 -1.103 .270

35.577 .968 36.768 .000

-.117 .009 -.162 -13.256 .000

-.110 .157 -.009 -.701 .483

-4.05E-02 .040 -.012 -1.017 .309

.439 .176 .036 2.497 .013

.719 .641 .028 1.120 .263

-.553 .243 -.037 -2.275 .023

-.830 .351 -.041 -2.366 .018

.531 .254 .032 2.092 .036

-.618 .216 -.038 -2.867 .004

-.277 .221 -.016 -1.254 .210

4.285E-02 .002 .283 20.762 .000

-3.259 .218 -.237 -14.959 .000

-4.71E-07 .000 -.007 -.566 .571

2.638 .240 .135 10.970 .000

2.651 .181 .191 14.686 .000

(Constant)

AGE

Gender

Marital Status

Black

Native American

Asian

Hisp

Unkn

Alien

(Constant)

AGE

Gender

Marital Status

Black

Native American

Asian

Hisp

Unkn

Alien

GPA

XFER CR

Undergrad Status


(Constant)

AGE

Gender

Marital Status

Black

Native American

Asian

Hisp

Unkn

Alien

GPA

XFER CR

Undergrad Status


Accounting

Business

Model1

2

3

B Std. Error


Beta

Standardized

Coefficients

t Sig.


The SlopesMode 3 Interpretation

• Xfer slightly lengthens time (B=.04285) very slightly; GPA shortens time but is not significant (Sig. >.05)

Y

QT

RS

to C

ompl

etio

n

Xfer B = - .04285

Interpretation –

Xfer & GPA very shallow, but GPA not significant (Sig. <.000)

Model 3 Slopes Graph – GPA & Transfer Credits

GPA0 1.00 2.00 3.00 4.00Xfer0 50 100 150

GPA B = - .277

35.577

Coefficientsa

35.612 .533 66.835 .000

-.120 .009 -.166 -12.817 .000

.624 .160 .049 3.910 .000

-9.27E-02 .043 -.027 -2.180 .029

.101 .179 .008 .568 .570

1.127 .676 .044 1.668 .095

-.625 .257 -.041 -2.434 .015

-.891 .373 -.044 -2.389 .017

.670 .270 .040 2.477 .013

-.692 .224 -.043 -3.081 .002

37.068 .983 37.723 .000

-.119 .009 -.165 -13.170 .000

.656 .153 .052 4.290 .000

-4.64E-02 .041 -.014 -1.142 .253

.397 .179 .033 2.211 .027

.928 .655 .036 1.418 .156

-.874 .247 -.058 -3.535 .000

-.724 .358 -.036 -2.023 .043

.551 .259 .033 2.129 .033

-.601 .220 -.037 -2.736 .006

-.311 .226 -.018 -1.376 .169

4.418E-02 .002 .292 20.994 .000

-4.013 .216 -.292 -18.588 .000

-9.36E-07 .000 -.015 -1.103 .270

35.577 .968 36.768 .000

-.117 .009 -.162 -13.256 .000

-.110 .157 -.009 -.701 .483

-4.05E-02 .040 -.012 -1.017 .309

.439 .176 .036 2.497 .013

.719 .641 .028 1.120 .263

-.553 .243 -.037 -2.275 .023

-.830 .351 -.041 -2.366 .018

.531 .254 .032 2.092 .036

-.618 .216 -.038 -2.867 .004

-.277 .221 -.016 -1.254 .210

4.285E-02 .002 .283 20.762 .000

-3.259 .218 -.237 -14.959 .000

-4.71E-07 .000 -.007 -.566 .571

2.638 .240 .135 10.970 .000

2.651 .181 .191 14.686 .000

(Constant)

AGE

Gender

Marital Status

Black

Native American

Asian

Hisp

Unkn

Alien

(Constant)

AGE

Gender

Marital Status

Black

Native American

Asian

Hisp

Unkn

Alien

GPA

XFER CR

Undergrad Status


(Constant)

AGE

Gender

Marital Status

Black

Native American

Asian

Hisp

Unkn

Alien

GPA

XFER CR

Undergrad Status


Accounting

Business

Model1

2

3

B Std. Error


Beta

Standardized

Coefficients

t Sig.



• Xfer lengthens slightly; GPA shortens, but not significant

• Female (neg) tends to shorten time (B = -.110) over Male

0 (Male)

1 (Female)

Y

X

QT

RS

to C

ompl

etio

n

Gender B = - .110

Interpretation –

Female Qtrs to Completion tend to be predictably shorter than Male Qtrs

Model 3 Slopes Graph - Gender

35.577

Coefficientsa

35.612 .533 66.835 .000

-.120 .009 -.166 -12.817 .000

.624 .160 .049 3.910 .000

-9.27E-02 .043 -.027 -2.180 .029

.101 .179 .008 .568 .570

1.127 .676 .044 1.668 .095

-.625 .257 -.041 -2.434 .015

-.891 .373 -.044 -2.389 .017

.670 .270 .040 2.477 .013

-.692 .224 -.043 -3.081 .002

37.068 .983 37.723 .000

-.119 .009 -.165 -13.170 .000

.656 .153 .052 4.290 .000

-4.64E-02 .041 -.014 -1.142 .253

.397 .179 .033 2.211 .027

.928 .655 .036 1.418 .156

-.874 .247 -.058 -3.535 .000

-.724 .358 -.036 -2.023 .043

.551 .259 .033 2.129 .033

-.601 .220 -.037 -2.736 .006

-.311 .226 -.018 -1.376 .169

4.418E-02 .002 .292 20.994 .000

-4.013 .216 -.292 -18.588 .000

-9.36E-07 .000 -.015 -1.103 .270

35.577 .968 36.768 .000

-.117 .009 -.162 -13.256 .000

-.110 .157 -.009 -.701 .483

-4.05E-02 .040 -.012 -1.017 .309

.439 .176 .036 2.497 .013

.719 .641 .028 1.120 .263

-.553 .243 -.037 -2.275 .023

-.830 .351 -.041 -2.366 .018

.531 .254 .032 2.092 .036

-.618 .216 -.038 -2.867 .004

-.277 .221 -.016 -1.254 .210

4.285E-02 .002 .283 20.762 .000

-3.259 .218 -.237 -14.959 .000

-4.71E-07 .000 -.007 -.566 .571

2.638 .240 .135 10.970 .000

2.651 .181 .191 14.686 .000

(Constant)

AGE

Gender

Marital Status

Black

Native American

Asian

Hisp

Unkn

Alien

(Constant)

AGE

Gender

Marital Status

Black

Native American

Asian

Hisp

Unkn

Alien

GPA

XFER CR

Undergrad Status


(Constant)

AGE

Gender

Marital Status

Black

Native American

Asian

Hisp

Unkn

Alien

GPA

XFER CR

Undergrad Status


Accounting

Business

Model1

2

3

B Std. Error


Beta

Standardized

Coefficients

t Sig.





• Black, Nat Am & Unkn take longer than Whites (+ B) (NA not significant) Hisp & Asians tend to take shorter than Whites (-B)

Y

X

QT

RS

to C

ompl

etio

n

Interpretation –

Black, Asian & Unknown tend to take longer than Whites (+ B); Hispanic & Native American tend to take shorter than Whites (-B)

Model 3 Slopes Graph -Ethnicity

White B = 0

Black B = .439

Hispanic B = - .830

Unknown .531

Native A

m B = .719

Asian -.553

Coefficientsa

35.612 .533 66.835 .000

-.120 .009 -.166 -12.817 .000

.624 .160 .049 3.910 .000

-9.27E-02 .043 -.027 -2.180 .029

.101 .179 .008 .568 .570

1.127 .676 .044 1.668 .095

-.625 .257 -.041 -2.434 .015

-.891 .373 -.044 -2.389 .017

.670 .270 .040 2.477 .013

-.692 .224 -.043 -3.081 .002

37.068 .983 37.723 .000

-.119 .009 -.165 -13.170 .000

.656 .153 .052 4.290 .000

-4.64E-02 .041 -.014 -1.142 .253

.397 .179 .033 2.211 .027

.928 .655 .036 1.418 .156

-.874 .247 -.058 -3.535 .000

-.724 .358 -.036 -2.023 .043

.551 .259 .033 2.129 .033

-.601 .220 -.037 -2.736 .006

-.311 .226 -.018 -1.376 .169

4.418E-02 .002 .292 20.994 .000

-4.013 .216 -.292 -18.588 .000

-9.36E-07 .000 -.015 -1.103 .270

35.577 .968 36.768 .000

-.117 .009 -.162 -13.256 .000

-.110 .157 -.009 -.701 .483

-4.05E-02 .040 -.012 -1.017 .309

.439 .176 .036 2.497 .013

.719 .641 .028 1.120 .263

-.553 .243 -.037 -2.275 .023

-.830 .351 -.041 -2.366 .018

.531 .254 .032 2.092 .036

-.618 .216 -.038 -2.867 .004

-.277 .221 -.016 -1.254 .210

4.285E-02 .002 .283 20.762 .000

-3.259 .218 -.237 -14.959 .000

-4.71E-07 .000 -.007 -.566 .571

2.638 .240 .135 10.970 .000

2.651 .181 .191 14.686 .000

(Constant)

AGE

Gender

Marital Status

Black

Native American

Asian

Hisp

Unkn

Alien

(Constant)

AGE

Gender

Marital Status

Black

Native American

Asian

Hisp

Unkn

Alien

GPA

XFER CR

Undergrad Status


(Constant)

AGE

Gender

Marital Status

Black

Native American

Asian

Hisp

Unkn

Alien

GPA

XFER CR

Undergrad Status


Accounting

Business

Model1

2

3

B Std. Error


Beta

Standardized

Coefficients

t Sig.





• Black, Nat Am & Unkn take longer than Whites (+ B); Hisp & Asians tend to take shorter than Whites (-B)

• Alien tends to take less time than US citizen (B = -.618)

Alien B = - .6180

(US)

1 (Alien)

Y

X

QT

RS

to C

ompl

etio

n

Interpretation –

Alien tends to take less time than US citizen (B = .279)

Model 3 Slopes Graph - Alien

Coefficientsa

35.612 .533 66.835 .000

-.120 .009 -.166 -12.817 .000

.624 .160 .049 3.910 .000

-9.27E-02 .043 -.027 -2.180 .029

.101 .179 .008 .568 .570

1.127 .676 .044 1.668 .095

-.625 .257 -.041 -2.434 .015

-.891 .373 -.044 -2.389 .017

.670 .270 .040 2.477 .013

-.692 .224 -.043 -3.081 .002

37.068 .983 37.723 .000

-.119 .009 -.165 -13.170 .000

.656 .153 .052 4.290 .000

-4.64E-02 .041 -.014 -1.142 .253

.397 .179 .033 2.211 .027

.928 .655 .036 1.418 .156

-.874 .247 -.058 -3.535 .000

-.724 .358 -.036 -2.023 .043

.551 .259 .033 2.129 .033

-.601 .220 -.037 -2.736 .006

-.311 .226 -.018 -1.376 .169

4.418E-02 .002 .292 20.994 .000

-4.013 .216 -.292 -18.588 .000

-9.36E-07 .000 -.015 -1.103 .270

35.577 .968 36.768 .000

-.117 .009 -.162 -13.256 .000

-.110 .157 -.009 -.701 .483

-4.05E-02 .040 -.012 -1.017 .309

.439 .176 .036 2.497 .013

.719 .641 .028 1.120 .263

-.553 .243 -.037 -2.275 .023

-.830 .351 -.041 -2.366 .018

.531 .254 .032 2.092 .036

-.618 .216 -.038 -2.867 .004

-.277 .221 -.016 -1.254 .210

4.285E-02 .002 .283 20.762 .000

-3.259 .218 -.237 -14.959 .000

-4.71E-07 .000 -.007 -.566 .571

2.638 .240 .135 10.970 .000

2.651 .181 .191 14.686 .000

(Constant)

AGE

Gender

Marital Status

Black

Native American

Asian

Hisp

Unkn

Alien

(Constant)

AGE

Gender

Marital Status

Black

Native American

Asian

Hisp

Unkn

Alien

GPA

XFER CR

Undergrad Status


(Constant)

AGE

Gender

Marital Status

Black

Native American

Asian

Hisp

Unkn

Alien

GPA

XFER CR

Undergrad Status


Accounting

Business

Model1

2

3

B Std. Error


Beta

Standardized

Coefficients

t Sig.





• Black, Nat Am & Unkn take longer than Whites (+ B); Hisp & Asians tend to take shorter than Whites (-B)

• Alien tends to take less time than US citizens (B = -.618)

• Acc & Bus considerable effect (B= 2.638, 2.651); pos. relative to CIS slope ‘0’

Interpretation –Accounting & Business steepest slopes (2.638, 2.651); positive relative to CIS slope ‘0’

Y

X

QT

RS

to C

ompl

etio

nModel 3 Slopes Graph - Major

Computers B = 0

Business

B = 2.651

Accounting B = 2.638

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