Here, pal! Regress this! presented by Miles Hamby, PhD Principle, Ariel Training Consultants MilesFlight.20megsfree.com drhamby@cox.net Or, How to Use.
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Here, pal!
Regress this!
presented by
Miles Hamby, PhD
Principle, Ariel Training ConsultantsMilesFlight.20megsfree.com
drhamby@cox.net
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 .
Quarters to Completion
Age
Gender
Marital Status
Black
Native American
Asian
Hisp
Unkn
Alien
GPA
XFER CR
Undergrad Status
Tutoring Sessoin Date
Accounting
Business
Quarters to Completion
Age
Gender
Marital Status
Black
Native American
Asian
Hisp
Unkn
Alien
GPA
XFER CR
Undergrad Status
Tutoring Sessoin Date
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
Tutoring Sessoin Date
(Constant)
AGE
Gender
Marital Status
Black
Native American
Asian
Hisp
Unkn
Alien
GPA
XFER CR
Undergrad Status
Tutoring Sessoin Date
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
Tutoring Sessoin Date
(Constant)
AGE
Gender
Marital Status
Black
Native American
Asian
Hisp
Unkn
Alien
GPA
XFER CR
Undergrad Status
Tutoring Sessoin Date
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)
• 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
Tutoring Sessoin Date
(Constant)
AGE
Gender
Marital Status
Black
Native American
Asian
Hisp
Unkn
Alien
GPA
XFER CR
Undergrad Status
Tutoring Sessoin Date
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)
• Married/Divorced tends to shorten completion time
(B= -.0405), but is not significant (Sig. = .309, >.05)
• 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
Tutoring Sessoin Date
(Constant)
AGE
Gender
Marital Status
Black
Native American
Asian
Hisp
Unkn
Alien
GPA
XFER CR
Undergrad Status
Tutoring Sessoin Date
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)
• Married/Divorced tends to shorten completion time
(B= -.0405), but is not significant (Sig. = .309, >.05)
• 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
Tutoring Sessoin Date
(Constant)
AGE
Gender
Marital Status
Black
Native American
Asian
Hisp
Unkn
Alien
GPA
XFER CR
Undergrad Status
Tutoring Sessoin Date
Accounting
Business
Model1
2
3
B Std. Error
UnstandardizedCoefficients
Beta
Standardized
Coefficients
t Sig.
Dependent Variable: Quarters to Completiona.
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
Tutoring Sessoin Date
(Constant)
AGE
Gender
Marital Status
Black
Native American
Asian
Hisp
Unkn
Alien
GPA
XFER CR
Undergrad Status
Tutoring Sessoin Date
Accounting
Business
Model1
2
3
B Std. Error
UnstandardizedCoefficients
Beta
Standardized
Coefficients
t Sig.
Dependent Variable: Quarters to Completiona.
The SlopesModel 3 Interpretation
• 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
Tutoring Sessoin Date
(Constant)
AGE
Gender
Marital Status
Black
Native American
Asian
Hisp
Unkn
Alien
GPA
XFER CR
Undergrad Status
Tutoring Sessoin Date
Accounting
Business
Model1
2
3
B Std. Error
UnstandardizedCoefficients
Beta
Standardized
Coefficients
t Sig.
Dependent Variable: Quarters to Completiona.
The SlopesModel 3 Interpretation
• Xfer lengthens slightly; GPA shortens, but not significant
• Female (neg) tends to shorten time (B = -.329) over Male
• 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
Tutoring Sessoin Date
(Constant)
AGE
Gender
Marital Status
Black
Native American
Asian
Hisp
Unkn
Alien
GPA
XFER CR
Undergrad Status
Tutoring Sessoin Date
Accounting
Business
Model1
2
3
B Std. Error
UnstandardizedCoefficients
Beta
Standardized
Coefficients
t Sig.
Dependent Variable: Quarters to Completiona.
The SlopesModel 3 Interpretation
• Xfer lengthens slightly; GPA shortens, but not significant
• Female (neg) tends to shorten time (B = -.329) over Male
• 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
Tutoring Sessoin Date
(Constant)
AGE
Gender
Marital Status
Black
Native American
Asian
Hisp
Unkn
Alien
GPA
XFER CR
Undergrad Status
Tutoring Sessoin Date
Accounting
Business
Model1
2
3
B Std. Error
UnstandardizedCoefficients
Beta
Standardized
Coefficients
t Sig.
Dependent Variable: Quarters to Completiona.
The SlopesModel 3 Interpretation
• Xfer lengthens slightly; GPA shortens, but not significant
• Female (neg) tends to shorten time (B = -.329) over Male
• 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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