Results: MathReg1.sas

Prediction of Performance in First-year Calculus

Variable Selection for Predicting Grade

Check dummy variables

The FREQ Procedure

The FREQ Procedure

Table sex * gender

Cross-Tabular Freq Table

Frequency
Table of sex by gender
sex gender
. 0 1 Total
 
28
0
0
28
Female
0
0
266
266
Male
0
285
0
285
Total
28
285
266
579

Table tongue * mtongue

Cross-Tabular Freq Table

Frequency
Table of tongue by mtongue
tongue(Mother Tongue (Eng or Other)) mtongue(English vs. Other)
. 0 1 Total
 
28
0
0
28
English
0
0
402
402
Other
0
149
0
149
Total
28
149
402
579

Table e1 * ethnic

Cross-Tabular Freq Table

Frequency
Table of e1 by ethnic
e1(Asian vs East Ind.) ethnic(Judged Nationality of name)
Asian Eastern European European not Eastern Middle-Eastern and Pakistani East Indian Other and DK Total
0
0
63
195
72
78
40
448
1
131
0
0
0
0
0
131
Total
131
63
195
72
78
40
579

Table e2 * ethnic

Cross-Tabular Freq Table

Frequency
Table of e2 by ethnic
e2(East Eur. vs East Ind.) ethnic(Judged Nationality of name)
Asian Eastern European European not Eastern Middle-Eastern and Pakistani East Indian Other and DK Total
0
131
0
195
72
78
40
516
1
0
63
0
0
0
0
63
Total
131
63
195
72
78
40
579

Table e3 * ethnic

Cross-Tabular Freq Table

Frequency
Table of e3 by ethnic
e3(Other Eur. vs East Ind.) ethnic(Judged Nationality of name)
Asian Eastern European European not Eastern Middle-Eastern and Pakistani East Indian Other and DK Total
0
131
63
0
72
78
40
384
1
0
0
195
0
0
0
195
Total
131
63
195
72
78
40
579

Table e4 * ethnic

Cross-Tabular Freq Table

Frequency
Table of e4 by ethnic
e4(Mid. East & Pak. vs East Ind.) ethnic(Judged Nationality of name)
Asian Eastern European European not Eastern Middle-Eastern and Pakistani East Indian Other and DK Total
0
131
63
195
0
78
40
507
1
0
0
0
72
0
0
72
Total
131
63
195
72
78
40
579

Table e6 * ethnic

Cross-Tabular Freq Table

Frequency
Table of e6 by ethnic
e6(Other/DK vs East Ind.) ethnic(Judged Nationality of name)
Asian Eastern European European not Eastern Middle-Eastern and Pakistani East Indian Other and DK Total
0
131
63
195
72
78
0
539
1
0
0
0
0
0
40
40
Total
131
63
195
72
78
40
579

Table c1 * course

Cross-Tabular Freq Table

Frequency
Table of c1 by course
c1(Catch-up) course
. 1 2 3 No Resp Total
.
99
0
0
0
0
99
0
0
0
373
39
9
421
1
0
59
0
0
0
59
Total
99
59
373
39
9
579

Table c2 * course

Cross-Tabular Freq Table

Frequency
Table of c2 by course
c2(Mainstream) course
. 1 2 3 No Resp Total
.
99
0
0
0
0
99
0
0
59
0
39
9
107
1
0
0
373
0
0
373
Total
99
59
373
39
9
579

Table c3 * course

Cross-Tabular Freq Table

Frequency
Table of c3 by course
c3(Elite) course
. 1 2 3 No Resp Total
.
99
0
0
0
0
99
0
0
59
373
0
9
441
1
0
0
0
39
0
39
Total
99
59
373
39
9
579

Prediction of Performance in First-year Calculus

Variable Selection for Predicting Grade

Model A: Predict University Calculus Grade from HS Information

The REG Procedure

Model: MODEL1

Dependent Variable: grade Final mark (if any)

The REG Procedure

MODEL1

Fit

grade

Number of Observations

Number of Observations Read 579
Number of Observations Used 323
Number of Observations with Missing Values 256

Analysis of Variance

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 3 45188 15063 73.23 <.0001
Error 319 65616 205.69147    
Corrected Total 322 110803      

Fit Statistics

Root MSE 14.34195 R-Square 0.4078
Dependent Mean 59.79257 Adj R-Sq 0.4022
Coeff Var 23.98617    

Parameter Estimates

Parameter Estimates
Variable Label DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t|
Intercept Intercept 1 -77.07643 10.92142 -7.06 <.0001
hsgpa High School GPA 1 1.76845 0.22097 8.00 <.0001
hscalc HS Calculus 1 0.30594 0.09750 3.14 0.0019
hsengl HS English 1 -0.38461 0.11815 -3.26 0.0013

Prediction of Performance in First-year Calculus

Variable Selection for Predicting Grade

Proportion of remaining variation for HS information

The IML Procedure

_LIT1004

hsgpa controlling for hscalc and hsengl

a

a
0.1671018

_LIT1007

hscalc controlling for hsgpa and hsengl

a

a
0.0299812

_LIT1010

hsengl controlling for hsgpa and hscalc

a

a
0.0322412

Prediction of Performance in First-year Calculus

Variable Selection for Predicting Grade

Model B: Predict University Calculus Grade from Diagnostic Test

The REG Procedure

Model: MODEL1

Dependent Variable: grade Final mark (if any)

The REG Procedure

MODEL1

Fit

grade

Number of Observations

Number of Observations Read 579
Number of Observations Used 346
Number of Observations with Missing Values 233

Analysis of Variance

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 2 23658 11829 39.88 <.0001
Error 343 101730 296.58765    
Corrected Total 345 125388      

Fit Statistics

Root MSE 17.22172 R-Square 0.1887
Dependent Mean 59.54335 Adj R-Sq 0.1840
Coeff Var 28.92299    

Parameter Estimates

Parameter Estimates
Variable Label DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t|
Intercept Intercept 1 37.85833 2.84884 13.29 <.0001
precalc Number precalculus correct 1 3.11970 0.63387 4.92 <.0001
calc Number calculus correct 1 1.80048 0.41033 4.39 <.0001

Prediction of Performance in First-year Calculus

Variable Selection for Predicting Grade

Model C: Do the diagnostic test and HS info both contribute?

The REG Procedure

Model: MODEL1

Dependent Variable: grade Final mark (if any)

The REG Procedure

MODEL1

Fit

grade

Number of Observations

Number of Observations Read 579
Number of Observations Used 289
Number of Observations with Missing Values 290

Analysis of Variance

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 5 44178 8835.57302 47.36 <.0001
Error 283 52793 186.54641    
Corrected Total 288 96970      

Fit Statistics

Root MSE 13.65820 R-Square 0.4556
Dependent Mean 60.57785 Adj R-Sq 0.4460
Coeff Var 22.54652    

Parameter Estimates

Parameter Estimates
Variable Label DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t|
Intercept Intercept 1 -71.41781 11.14193 -6.41 <.0001
hsgpa High School GPA 1 1.59051 0.22122 7.19 <.0001
hscalc HS Calculus 1 0.25421 0.10166 2.50 0.0130
hsengl HS English 1 -0.34853 0.12057 -2.89 0.0041
precalc Number precalculus correct 1 1.53973 0.55954 2.75 0.0063
calc Number calculus correct 1 0.68279 0.37603 1.82 0.0705

Prediction of Performance in First-year Calculus

Variable Selection for Predicting Grade

Model C: Do the diagnostic test and HS info both contribute?

The REG Procedure

Model: MODEL1

Test Diagnostic_Test

Results

Test Diagnostic_Test Results for Dependent Variable grade
Source DF Mean
Square		 F Value Pr > F
Numerator 2 1544.04857 8.28 0.0003
Denominator 283 186.54641    

Prediction of Performance in First-year Calculus

Variable Selection for Predicting Grade

Model C: Do the diagnostic test and HS info both contribute?

The REG Procedure

Model: MODEL1

Test HS_Information

Results

Test HS_Information Results for Dependent Variable grade
Source DF Mean
Square		 F Value Pr > F
Numerator 3 8761.88810 46.97 <.0001
Denominator 283 186.54641    

Prediction of Performance in First-year Calculus

Variable Selection for Predicting Grade

Proportion of remaining variation explained by diagnostic test

The IML Procedure

_LIT1001

Precalc and calc controlling for hsgpa hscalc hsengl

a

a
0.0552811

Prediction of Performance in First-year Calculus

Variable Selection for Predicting Grade

Model D: See if Course makes a contribution

The REG Procedure

Model: MODEL1

Dependent Variable: grade Final mark (if any)

The REG Procedure

MODEL1

Fit

grade

Number of Observations

Number of Observations Read 579
Number of Observations Used 289
Number of Observations with Missing Values 290

Analysis of Variance

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 7 44713 6387.53844 34.35 <.0001
Error 281 52258 185.97057    
Corrected Total 288 96970      

Fit Statistics

Root MSE 13.63710 R-Square 0.4611
Dependent Mean 60.57785 Adj R-Sq 0.4477
Coeff Var 22.51170    

Parameter Estimates

Parameter Estimates
Variable Label DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t|
Intercept Intercept 1 -72.42495 11.28800 -6.42 <.0001
hsgpa High School GPA 1 1.57595 0.22105 7.13 <.0001
hscalc HS Calculus 1 0.28249 0.10294 2.74 0.0065
hsengl HS English 1 -0.35419 0.12145 -2.92 0.0038
precalc Number precalculus correct 1 1.60358 0.56058 2.86 0.0045
calc Number calculus correct 1 0.73326 0.37721 1.94 0.0529
c1 Catch-up 1 5.24279 4.35514 1.20 0.2297
c3 Elite 1 -3.17149 2.78087 -1.14 0.2551

Prediction of Performance in First-year Calculus

Variable Selection for Predicting Grade

Model D: See if Course makes a contribution

The REG Procedure

Model: MODEL1

Test Course

Results

Test Course Results for Dependent Variable grade
Source DF Mean
Square		 F Value Pr > F
Numerator 2 267.45197 1.44 0.2391
Denominator 281 185.97057    

Prediction of Performance in First-year Calculus

Variable Selection for Predicting Grade

Model D: See if Course makes a contribution

The REG Procedure

Model: MODEL1

Test Diagnostic_Test

Results

Test Diagnostic_Test Results for Dependent Variable grade
Source DF Mean
Square		 F Value Pr > F
Numerator 2 1684.57843 9.06 0.0002
Denominator 281 185.97057    

Prediction of Performance in First-year Calculus

Variable Selection for Predicting Grade

Model D again with proc glm

The GLM Procedure

The GLM Procedure

Data

Class Levels

Class Level Information
Class Levels Values
course 3 1 2 3

Number of Observations

Number of Observations Read 579
Number of Observations Used 289

Prediction of Performance in First-year Calculus

Variable Selection for Predicting Grade

Model D again with proc glm

The GLM Procedure

Dependent Variable: grade Final mark (if any)

Analysis of Variance

grade

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 7 44712.76907 6387.53844 34.35 <.0001
Error 281 52257.72920 185.97057    
Corrected Total 288 96970.49827      

Fit Statistics

R-Square Coeff Var Root MSE grade Mean
0.461097 22.51170 13.63710 60.57785

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
hsgpa 1 34512.00462 34512.00462 185.58 <.0001
hscalc 1 4744.09530 4744.09530 25.51 <.0001
hsengl 1 1833.66807 1833.66807 9.86 0.0019
precalc 1 2473.04238 2473.04238 13.30 0.0003
calc 1 615.05475 615.05475 3.31 0.0700
course 2 534.90395 267.45197 1.44 0.2391

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
hsgpa 1 9452.626595 9452.626595 50.83 <.0001
hscalc 1 1400.568197 1400.568197 7.53 0.0065
hsengl 1 1581.653505 1581.653505 8.50 0.0038
precalc 1 1521.786932 1521.786932 8.18 0.0045
calc 1 702.730145 702.730145 3.78 0.0529
course 2 534.903948 267.451974 1.44 0.2391

Contrasts

Contrast DF Contrast SS Mean Square F Value Pr > F
Replicate Test of Course 2 534.903948 267.451974 1.44 0.2391
Diagnostic Test F = 9.06 2 3369.156864 1684.578432 9.06 0.0002

Prediction of Performance in First-year Calculus

Variable Selection for Predicting Grade

Model E: Include Language, Sex and Ethnic Background

The REG Procedure

Model: MODEL1

Dependent Variable: grade Final mark (if any)

The REG Procedure

MODEL1

Fit

grade

Number of Observations

Number of Observations Read 579
Number of Observations Used 287
Number of Observations with Missing Values 292

Analysis of Variance

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 12 46396 3866.29446 21.01 <.0001
Error 274 50434 184.06417    
Corrected Total 286 96829      

Fit Statistics

Root MSE 13.56702 R-Square 0.4791
Dependent Mean 60.59582 Adj R-Sq 0.4563
Coeff Var 22.38937    

Parameter Estimates

Parameter Estimates
Variable Label DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t|
Intercept Intercept 1 -60.53085 11.87140 -5.10 <.0001
hsgpa High School GPA 1 1.57906 0.22245 7.10 <.0001
hscalc HS Calculus 1 0.22034 0.10273 2.14 0.0328
hsengl HS English 1 -0.36429 0.12827 -2.84 0.0048
precalc Number precalculus correct 1 1.74734 0.56723 3.08 0.0023
calc Number calculus correct 1 0.65177 0.38352 1.70 0.0904
mtongue English vs. Other 1 -4.76328 2.19585 -2.17 0.0309
gender   1 1.89029 1.72632 1.09 0.2745
e1 Asian vs East Ind. 1 -5.49703 2.77555 -1.98 0.0486
e2 East Eur. vs East Ind. 1 -5.46550 3.21790 -1.70 0.0906
e3 Other Eur. vs East Ind. 1 -4.09079 2.54033 -1.61 0.1085
e4 Mid. East & Pak. vs East Ind. 1 -5.98768 3.23591 -1.85 0.0653
e6 Other/DK vs East Ind. 1 -1.05791 5.63847 -0.19 0.8513

Prediction of Performance in First-year Calculus

Variable Selection for Predicting Grade

Model E: Include Language, Sex and Ethnic Background

The REG Procedure

Model: MODEL1

Test TroubleVars

Results

Test TroubleVars Results for Dependent Variable grade
Source DF Mean
Square		 F Value Pr > F
Numerator 7 305.41011 1.66 0.1191
Denominator 274 184.06417    

Prediction of Performance in First-year Calculus

Variable Selection for Predicting Grade

Model E: Include Language, Sex and Ethnic Background

The REG Procedure

Model: MODEL1

Test Nationality

Results

Test Nationality Results for Dependent Variable grade
Source DF Mean
Square		 F Value Pr > F
Numerator 5 206.04701 1.12 0.3502
Denominator 274 184.06417    

Prediction of Performance in First-year Calculus

Variable Selection for Predicting Grade

Model F: Discarding Gender and Nationality

The REG Procedure

Model: MODEL1

Dependent Variable: grade Final mark (if any)

The REG Procedure

MODEL1

Fit

grade

Number of Observations

Number of Observations Read 579
Number of Observations Used 287
Number of Observations with Missing Values 292

Analysis of Variance

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 6 45177 7529.47663 40.82 <.0001
Error 280 51652 184.47234    
Corrected Total 286 96829      

Fit Statistics

Root MSE 13.58206 R-Square 0.4666
Dependent Mean 60.59582 Adj R-Sq 0.4551
Coeff Var 22.41419    

Parameter Estimates

Parameter Estimates
Variable Label DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t|
Intercept Intercept 1 -67.81236 11.26953 -6.02 <.0001
hsgpa High School GPA 1 1.57276 0.22101 7.12 <.0001
hscalc HS Calculus 1 0.22495 0.10213 2.20 0.0284
hsengl HS English 1 -0.29798 0.12258 -2.43 0.0157
precalc Number precalculus correct 1 1.60480 0.55970 2.87 0.0045
calc Number calculus correct 1 0.61933 0.37553 1.65 0.1002
mtongue English vs. Other 1 -4.74223 2.12444 -2.23 0.0264

Prediction of Performance in First-year Calculus

Variable Selection for Predicting Grade

Model F: Discarding Gender and Nationality

The REG Procedure

Model: MODEL1

Test EnglishTongue

Results

Test EnglishTongue Results for Dependent Variable grade
Source DF Mean
Square		 F Value Pr > F
Numerator 2 1253.11163 6.79 0.0013
Denominator 280 184.47234    

Prediction of Performance in First-year Calculus

Variable Selection for Predicting Grade

Proportion of remaining variation explained by mother tongue

The IML Procedure

_LIT1001

Mtongue controlling for hsgpa hscalc hsengl precalc calc

a

a
0.0174504

Prediction of Performance in First-year Calculus

Variable Selection for Predicting Grade

Model G: Drop mtongue and calc

Compare R-Square = 0.4556, Adj R-Sq = 0.4460 From Model 3

The REG Procedure

Model: MODEL1

Dependent Variable: grade Final mark (if any)

The REG Procedure

MODEL1

Fit

grade

Number of Observations

Number of Observations Read 579
Number of Observations Used 289
Number of Observations with Missing Values 290

Analysis of Variance

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 4 43563 10891 57.91 <.0001
Error 284 53408 188.05524    
Corrected Total 288 96970      

Fit Statistics

Root MSE 13.71332 R-Square 0.4492
Dependent Mean 60.57785 Adj R-Sq 0.4415
Coeff Var 22.63752    

Parameter Estimates

Parameter Estimates
Variable Label DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t|
Intercept Intercept 1 -74.11274 11.08720 -6.68 <.0001
hsgpa High School GPA 1 1.60015 0.22205 7.21 <.0001
hscalc HS Calculus 1 0.29640 0.09937 2.98 0.0031
hsengl HS English 1 -0.35439 0.12101 -2.93 0.0037
precalc Number precalculus correct 1 1.90277 0.52470 3.63 0.0003

Prediction of Performance in First-year Calculus

Variable Selection for Predicting Grade

Proportion of remaining variation explained by Pre-calculus

The IML Procedure

_LIT1001

precalc controlling for hsgpa hscalc hsengl

a

a
0.0443403

Prediction of Performance in First-year Calculus

Variable Selection for Predicting Grade

Model H: Combine precalc and calc instead of dropping calc

Compare R-Square = 0.4492 from Model 7

The REG Procedure

Model: MODEL1

Dependent Variable: grade Final mark (if any)

The REG Procedure

MODEL1

Fit

grade

Number of Observations

Number of Observations Read 579
Number of Observations Used 289
Number of Observations with Missing Values 290

Analysis of Variance

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 4 43951 10988 58.86 <.0001
Error 284 53019 186.68704    
Corrected Total 288 96970      

Fit Statistics

Root MSE 13.66335 R-Square 0.4532
Dependent Mean 60.57785 Adj R-Sq 0.4455
Coeff Var 22.55502    

Parameter Estimates

Parameter Estimates
Variable Label DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t|
Intercept Intercept 1 -70.49310 11.11446 -6.34 <.0001
hsgpa High School GPA 1 1.60612 0.22085 7.27 <.0001
hscalc HS Calculus 1 0.24685 0.10148 2.43 0.0156
hsengl HS English 1 -0.35057 0.12060 -2.91 0.0039
totscore Total # right on diagnostic test 1 0.98964 0.25277 3.92 0.0001

Prediction of Performance in First-year Calculus

Variable Selection for Predicting Grade

Model H: Combine precalc and calc instead of dropping calc

Compare R-Square = 0.4492 from Model 7

The REG Procedure

Model: MODEL1

Dependent Variable: grade Final mark (if any)

Observation-wise Statistics

grade

Residual Plots

Panel 1

Panel of scatterplots of residuals by regressors for grade.

Prediction of Performance in First-year Calculus

Variable Selection for Predicting Grade

Proportion of remaining variation explained by Pre-calculus

The IML Procedure

_LIT1001

totscore controlling for hsgpa hscalc hsengl

a

a
0.0513297

_LIT1007

For prediction, I am happy with Model 8: hsgpa hscalc hsengl totscore

Prediction of Performance in First-year Calculus

Variable Selection for Predicting Grade

Model I: Same as Model H but including Mother Tongue

The REG Procedure

Model: MODEL1

Dependent Variable: grade Final mark (if any)

The REG Procedure

MODEL1

Fit

grade

Number of Observations

Number of Observations Read 579
Number of Observations Used 287
Number of Observations with Missing Values 292

Analysis of Variance

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 5 44881 8976.29511 48.56 <.0001
Error 281 51948 184.86704    
Corrected Total 286 96829      

Fit Statistics

Root MSE 13.59658 R-Square 0.4635
Dependent Mean 60.59582 Adj R-Sq 0.4540
Coeff Var 22.43815    

Parameter Estimates

Parameter Estimates
Variable Label DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t|
Intercept Intercept 1 -66.75516 11.25053 -5.93 <.0001
hsgpa High School GPA 1 1.58918 0.22087 7.20 <.0001
hscalc HS Calculus 1 0.21759 0.10208 2.13 0.0339
hsengl HS English 1 -0.30024 0.12270 -2.45 0.0150
totscore Total # right on diagnostic test 1 0.97213 0.25185 3.86 0.0001
mtongue English vs. Other 1 -4.69657 2.12640 -2.21 0.0280

Prediction of Performance in First-year Calculus

Variable Selection for Predicting Grade

Try automatic (stepwise) selection

The REG Procedure

Model: MODEL1

Dependent Variable: grade Final mark (if any)

The REG Procedure

MODEL1

Stepwise Selection Method

grade

Number of Observations

Number of Observations Read 579
Number of Observations Used 287
Number of Observations with Missing Values 292

Step 1

Stepwise Selection: Step 1

ANOVA

Variable hsgpa Entered: R-Square = 0.3579 and C(p) = 54.7774

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 1 34656 34656 158.87 <.0001
Error 285 62173 218.14988    
Corrected Total 286 96829      

Parameter Estimates

Variable Parameter
Estimate		 Standard
Error		 Type II SS F Value Pr > F
Intercept -87.53291 11.78465 12035 55.17 <.0001
hsgpa 1.82997 0.14519 34656 158.87 <.0001

Bounds on condition number: 1, 1

Step 2

Stepwise Selection: Step 2

ANOVA

Variable hscalc Entered: R-Square = 0.4053 and C(p) = 31.8742

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 2 39240 19620 96.76 <.0001
Error 284 57589 202.77793    
Corrected Total 286 96829      

Parameter Estimates

Variable Parameter
Estimate		 Standard
Error		 Type II SS F Value Pr > F
Intercept -78.92940 11.50506 9543.77385 47.07 <.0001
hsgpa 1.28138 0.18140 10118 49.90 <.0001
hscalc 0.45656 0.09603 4583.78372 22.60 <.0001

Bounds on condition number: 1.6795, 6.7178

Step 3

Stepwise Selection: Step 3

ANOVA

Variable precalc Entered: R-Square = 0.4344 and C(p) = 18.5640

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 3 42058 14019 72.44 <.0001
Error 283 54771 193.53665    
Corrected Total 286 96829      

Parameter Estimates

Variable Parameter
Estimate		 Standard
Error		 Type II SS F Value Pr > F
Intercept -77.39176 11.24707 9163.77010 47.35 <.0001
hsgpa 1.20854 0.17825 8896.80932 45.97 <.0001
hscalc 0.38611 0.09561 3156.10670 16.31 <.0001
precalc 2.03629 0.53364 2818.06020 14.56 0.0002

Bounds on condition number: 1.7445, 13.72

Step 4

Stepwise Selection: Step 4

ANOVA

Variable hsengl Entered: R-Square = 0.4514 and C(p) = 11.6202

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 4 43704 10926 58.00 <.0001
Error 282 53125 188.38526    
Corrected Total 286 96829      

Parameter Estimates

Variable Parameter
Estimate		 Standard
Error		 Type II SS F Value Pr > F
Intercept -74.38595 11.14286 8395.27582 44.56 <.0001
hsgpa 1.61314 0.22284 9871.54525 52.40 <.0001
hscalc 0.28738 0.10007 1553.64075 8.25 0.0044
hsengl -0.35871 0.12135 1646.22898 8.74 0.0034
precalc 1.95702 0.52717 2596.17989 13.78 0.0002

Bounds on condition number: 2.7281, 29.826

Step 5

Stepwise Selection: Step 5

ANOVA

Variable mtongue Entered: R-Square = 0.4614 and C(p) = 8.3468

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 5 44675 8935.02380 48.14 <.0001
Error 281 52154 185.60141    
Corrected Total 286 96829      

Parameter Estimates

Variable Parameter
Estimate		 Standard
Error		 Type II SS F Value Pr > F
Intercept -70.13523 11.21533 7258.21332 39.11 <.0001
hsgpa 1.58158 0.22162 9452.36264 50.93 <.0001
hscalc 0.26190 0.09995 1274.37374 6.87 0.0093
hsengl -0.30256 0.12292 1124.43880 6.06 0.0144
precalc 1.93902 0.52332 2548.06067 13.73 0.0003
mtongue -4.86990 2.12951 970.64664 5.23 0.0229

Bounds on condition number: 2.7387, 43.231

All variables left in the model are significant at the 0.0500 level.

No other variable met the 0.0500 significance level for entry into the model.

Selection Summary

Summary of Stepwise Selection
Step Variable
Entered		 Variable
Removed		 Label Number
Vars In		 Partial
R-Square		 Model
R-Square		 C(p) F Value Pr > F
1 hsgpa   High School GPA 1 0.3579 0.3579 54.7774 158.87 <.0001
2 hscalc   HS Calculus 2 0.0473 0.4053 31.8742 22.60 <.0001
3 precalc   Number precalculus correct 3 0.0291 0.4344 18.5640 14.56 0.0002
4 hsengl   HS English 4 0.0170 0.4514 11.6202 8.74 0.0034
5 mtongue   English vs. Other 5 0.0100 0.4614 8.3468 5.23 0.0229