Results: MathLogReg1.sas

Prediction of Performance in First-year Calculus

Logistic Regression with dummy variables on the Math data

Check course2 and dummy vars -- and why so many no course?

The FREQ Procedure

The FREQ Procedure

Table course * course2

Cross-Tabular Freq Table

Frequency
Table of course by course2
course course2
. Catch-up Mainstrm Elite Total
.
99
0
0
0
99
Catch-up
0
59
0
0
59
Mainstrm
0
0
373
0
373
Elite
0
0
0
39
39
No Resp
9
0
0
0
9
Total
108
59
373
39
579

Table c1 * course2

Cross-Tabular Freq Table

Frequency
Table of c1 by course2
c1(Catch-up) course2
. Catch-up Mainstrm Elite Total
.
108
0
0
0
108
0
0
0
373
39
412
1
0
59
0
0
59
Total
108
59
373
39
579

Table c2 * course2

Cross-Tabular Freq Table

Frequency
Table of c2 by course2
c2(Mainstream) course2
. Catch-up Mainstrm Elite Total
.
108
0
0
0
108
0
0
59
0
39
98
1
0
0
373
0
373
Total
108
59
373
39
579

Table c3 * course2

Cross-Tabular Freq Table

Frequency
Table of c3 by course2
c3(Elite) course2
. Catch-up Mainstrm Elite Total
.
108
0
0
0
108
0
0
59
373
0
432
1
0
0
0
39
39
Total
108
59
373
39
579

Prediction of Performance in First-year Calculus

Logistic Regression with dummy variables on the Math data

A few simple Chi-squared tests to predict passed

The FREQ Procedure

The FREQ Procedure

Table course2 * passed

Cross-Tabular Freq Table

Frequency
Row Pct
Table of course2 by passed
course2 passed(Passed the course)
No Yes Total
Catch-up
44
74.58
15
25.42
59
 
Mainstrm
149
39.95
224
60.05
373
 
Elite
8
20.51
31
79.49
39
 
Total
201
270
471
Frequency Missing = 108

Statistics for Table of course2 by passed

Chi-Square Tests

Statistic DF Value Prob
Chi-Square 2 33.5096 <.0001
Likelihood Ratio Chi-Square 2 34.4171 <.0001
Mantel-Haenszel Chi-Square 1 31.6717 <.0001
Phi Coefficient   0.2667  
Contingency Coefficient   0.2577  
Cramer's V   0.2667  

Effective Sample Size = 471
Frequency Missing = 108

WARNING: 19% of the data are missing.

Table sex * passed

Cross-Tabular Freq Table

Frequency
Row Pct
Table of sex by passed
sex passed(Passed the course)
No Yes Total
Female
118
44.36
148
55.64
266
 
Male
138
48.42
147
51.58
285
 
Total
256
295
551
Frequency Missing = 28

Statistics for Table of sex by passed

Chi-Square Tests

Statistic DF Value Prob
Chi-Square 1 0.9118 0.3396
Likelihood Ratio Chi-Square 1 0.9122 0.3395
Continuity Adj. Chi-Square 1 0.7559 0.3846
Mantel-Haenszel Chi-Square 1 0.9101 0.3401
Phi Coefficient   -0.0407  
Contingency Coefficient   0.0406  
Cramer's V   -0.0407  

Fisher's Exact Test

Fisher's Exact Test
Cell (1,1) Frequency (F) 118
Left-sided Pr <= F 0.1923
Right-sided Pr >= F 0.8509
   
Table Probability (P) 0.0432
Two-sided Pr <= P 0.3484

Effective Sample Size = 551
Frequency Missing = 28

Table ethnic * passed

Cross-Tabular Freq Table

Frequency
Row Pct
Table of ethnic by passed
ethnic(Judged Nationality of name) passed(Passed the course)
No Yes Total
Asian
65
49.62
66
50.38
131
 
Eastern European
30
47.62
33
52.38
63
 
European not Eastern
88
45.13
107
54.87
195
 
Middle-Eastern and Pakistani
33
45.83
39
54.17
72
 
East Indian
31
39.74
47
60.26
78
 
Other and DK
27
67.50
13
32.50
40
 
Total
274
305
579

Statistics for Table of ethnic by passed

Chi-Square Tests

Statistic DF Value Prob
Chi-Square 5 9.0500 0.1071
Likelihood Ratio Chi-Square 5 9.1556 0.1030
Mantel-Haenszel Chi-Square 1 0.0788 0.7789
Phi Coefficient   0.1250  
Contingency Coefficient   0.1241  
Cramer's V   0.1250  

Sample Size = 579

Table tongue * passed

Cross-Tabular Freq Table

Frequency
Row Pct
Table of tongue by passed
tongue(Mother Tongue (Eng or Other)) passed(Passed the course)
No Yes Total
English
187
46.52
215
53.48
402
 
Other
69
46.31
80
53.69
149
 
Total
256
295
551
Frequency Missing = 28

Statistics for Table of tongue by passed

Chi-Square Tests

Statistic DF Value Prob
Chi-Square 1 0.0019 0.9652
Likelihood Ratio Chi-Square 1 0.0019 0.9652
Continuity Adj. Chi-Square 1 0.0000 1.0000
Mantel-Haenszel Chi-Square 1 0.0019 0.9652
Phi Coefficient   0.0019  
Contingency Coefficient   0.0019  
Cramer's V   0.0019  

Fisher's Exact Test

Fisher's Exact Test
Cell (1,1) Frequency (F) 187
Left-sided Pr <= F 0.5552
Right-sided Pr >= F 0.5214
   
Table Probability (P) 0.0765
Two-sided Pr <= P 1.0000

Effective Sample Size = 551
Frequency Missing = 28

Prediction of Performance in First-year Calculus

Logistic Regression with dummy variables on the Math data

Course2 by passed with dummy vars: Compare LR Chisq = 34.4171

The LOGISTIC Procedure

The LOGISTIC Procedure

Model Information

Model Information
Data Set WORK.MATHEX  
Response Variable passed Passed the course
Number of Response Levels 2  
Model binary logit  
Optimization Technique Fisher's scoring  

Observations Summary

Number of Observations Read 579
Number of Observations Used 471

Response Profile

Response Profile
Ordered
Value		 passed Total
Frequency
1 Yes 270
2 No 201

Probability modeled is passed='Yes'.

Note:108 observations were deleted due to missing values for the response or explanatory variables.

Convergence Status

Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Fit Statistics

Model Fit Statistics
Criterion Intercept Only Intercept and Covariates
AIC 644.800 614.383
SC 648.955 626.847
-2 Log L 642.800 608.383

Global Tests

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 34.4171 2 <.0001
Score 33.5096 2 <.0001
Wald 29.2854 2 <.0001

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept 1 0.4077 0.1057 14.8733 0.0001
c1 1 -1.4838 0.3171 21.8931 <.0001
c3 1 0.9468 0.4104 5.3226 0.0211

Odds Ratios

Odds Ratio Estimates
Effect Point Estimate 95% Wald
Confidence Limits
c1 0.227 0.122 0.422
c3 2.578 1.153 5.762

Association Statistics

Association of Predicted Probabilities and Observed Responses
Percent Concordant 29.2 Somers' D 0.215
Percent Discordant 7.6 Gamma 0.585
Percent Tied 63.2 Tau-a 0.106
Pairs 54270 c 0.608

Test Statement Results

Linear Hypotheses Testing Results
Label Wald
Chi-Square		 DF Pr > ChiSq
Course1_vs_2 21.8931 1 <.0001
Course1_vs_3 23.9536 1 <.0001
Course2_vs_3 5.3226 1 0.0211

Prediction of Performance in First-year Calculus

Logistic Regression with dummy variables on the Math data

Estimate prob. of passing for for course=3: Compare 31/39 = 0.7949

The IML Procedure

probpass

  probpass
Estimated probability of passing course 3 is 0.7948643

Prediction of Performance in First-year Calculus

Logistic Regression with dummy variables on the Math data

Use the Class statement

The LOGISTIC Procedure

The LOGISTIC Procedure

Model Information

Model Information
Data Set WORK.MATHEX  
Response Variable passed Passed the course
Number of Response Levels 2  
Model binary logit  
Optimization Technique Fisher's scoring  

Observations Summary

Number of Observations Read 579
Number of Observations Used 471

Response Profile

Response Profile
Ordered
Value		 passed Total
Frequency
1 Yes 270
2 No 201

Probability modeled is passed='Yes'.

Note:108 observations were deleted due to missing values for the response or explanatory variables.

Class Level Information

Class Level Information
Class Value Design Variables
course2 Catch-up 1 0
  Elite 0 1
  Mainstrm 0 0

Convergence Status

Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Fit Statistics

Model Fit Statistics
Criterion Intercept Only Intercept and Covariates
AIC 644.800 614.383
SC 648.955 626.847
-2 Log L 642.800 608.383

Global Tests

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 34.4171 2 <.0001
Score 33.5096 2 <.0001
Wald 29.2854 2 <.0001

Type 3 Tests

Type 3 Analysis of Effects
Effect DF Wald
Chi-Square		 Pr > ChiSq
course2 2 29.2854 <.0001

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter   DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept   1 0.4077 0.1057 14.8733 0.0001
course2 Catch-up 1 -1.4838 0.3171 21.8931 <.0001
course2 Elite 1 0.9468 0.4104 5.3226 0.0211

Odds Ratios

Odds Ratio Estimates
Effect Point Estimate 95% Wald
Confidence Limits
course2 Catch-up vs Mainstrm 0.227 0.122 0.422
course2 Elite vs Mainstrm 2.578 1.153 5.762

Association Statistics

Association of Predicted Probabilities and Observed Responses
Percent Concordant 29.2 Somers' D 0.215
Percent Discordant 7.6 Gamma 0.585
Percent Tied 63.2 Tau-a 0.106
Pairs 54270 c 0.608

Wald Test for Contrasts

Contrast Test Results
Contrast DF Wald
Chi-Square		 Pr > ChiSq
Catch-up vs Mainstream 1 21.8931 <.0001
Elite vs Mainstream 1 5.3226 0.0211
Catch-up vs Elite 1 23.9536 <.0001