Results: MathReg2.sas

Gender, Ethnicity and Math performance

Basic Regression Diagnostics

Model I: hsgpa hscalc hsengl totscore mtongue

The REG Procedure

Model: MODEL1

Dependent Variable: grade Final mark

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

Gender, Ethnicity and Math performance

Basic Regression Diagnostics

Model I: hsgpa hscalc hsengl totscore mtongue

The REG Procedure

Model: MODEL1

Dependent Variable: grade Final mark

Observation-wise Statistics

grade

Residual Plots

Panel 1

Panel of scatterplots of residuals by regressors for grade.

Gender, Ethnicity and Math performance

Basic Regression Diagnostics

Model I: hsgpa hscalc hsengl totscore mtongue

The IML Procedure

ceiling

  ceiling
Investigate x if hat values are > 0.2 or greater than 0.0622837

Gender, Ethnicity and Math performance

Basic Regression Diagnostics

Model I: hsgpa hscalc hsengl totscore mtongue

The UNIVARIATE Procedure

Variable: hatval (Leverage)

The Univariate Procedure

hatval

Moments

Moments
N 287 Sum Weights 287
Mean 0.02090592 Sum Observations 6
Std Deviation 0.01192835 Variance 0.00014229
Skewness 1.31916828 Kurtosis 3.40708239
Uncorrected SS 0.16612922 Corrected SS 0.04069368
Coeff Variation 57.0572838 Std Error Mean 0.00070411

Basic Measures of Location and Variability

Basic Statistical Measures
Location Variability
Mean 0.020906 Std Deviation 0.01193
Median 0.018252 Variance 0.0001423
Mode . Range 0.08517
    Interquartile Range 0.01526

Tests For Location

Tests for Location: Mu0=0
Test Statistic p Value
Student's t t 29.69134 Pr > |t| <.0001
Sign M 143.5 Pr >= |M| <.0001
Signed Rank S 20664 Pr >= |S| <.0001

Quantiles

Quantiles (Definition 5)
Level Quantile
100% Max 0.08972749
99% 0.05160047
95% 0.04360103
90% 0.03793186
75% Q3 0.02749305
50% Median 0.01825205
25% Q1 0.01223160
10% 0.00769741
5% 0.00638436
1% 0.00513980
0% Min 0.00455388

Extreme Observations

Extreme Observations
Lowest Highest
Value Obs Value Obs
0.00455388 346 0.0471874 487
0.00509502 112 0.0499569 186
0.00513980 511 0.0516005 383
0.00530355 277 0.0624349 340
0.00535597 543 0.0897275 50

Missing Values

Missing Values
Missing
Value		 Count Percent Of
All Obs Missing Obs
. 106 26.97 100.00

Plots for hatval

Plots for hatval

The SGPlot Procedure

The SGPlot Procedure

The SGPlot Procedure

Gender, Ethnicity and Math performance

Basic Regression Diagnostics

Model I: hsgpa hscalc hsengl totscore mtongue

The Print Procedure

Data Set WORK.EXPLOR

Obs id hatval hsgpa hscalc hsengl totscore mtongue grade delstud
575 340 0.062435 88.0 96 56 14 0 95 0.32023
579 50 0.089727 93.5 97 57 15 0 81 -1.49938

Gender, Ethnicity and Math performance

Basic Regression Diagnostics

Re-running without participants 50 and 340

The REG Procedure

Model: MODEL1

Dependent Variable: grade Final mark

The Reg Procedure

MODEL1

Fit

grade

Number of Observations

Number of Observations Read 577
Number of Observations Used 285
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 43692 8738.47274 47.32 <.0001
Error 279 51526 184.68184    
Corrected Total 284 95219      

Fit Statistics

Root MSE 13.58977 R-Square 0.4589
Dependent Mean 60.40351 Adj R-Sq 0.4492
Coeff Var 22.49831    

Parameter Estimates

Parameter Estimates
Variable Label DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t|
Intercept Intercept 1 -67.98238 11.28142 -6.03 <.0001
hsgpa High School GPA 1 1.65482 0.22857 7.24 <.0001
hscalc HS Calculus 1 0.20532 0.10248 2.00 0.0461
hsengl HS English 1 -0.33993 0.12909 -2.63 0.0089
totscore Total # right on diagnostic test 1 0.98719 0.25219 3.91 0.0001
mtongue English vs. Other 1 -4.86520 2.13506 -2.28 0.0234

Gender, Ethnicity and Math performance

Basic Regression Diagnostics

Critical value for Joint t-test on Studentized Deleted Residuals

The IML Procedure

Alpha

Alpha
0.000173

Critval

Critval
3.8061889

Gender, Ethnicity and Math performance

Basic Regression Diagnostics

Studentized Deleted Residuals

The UNIVARIATE Procedure

Variable: delstud (Studentized Residual without Current Obs)

The Univariate Procedure

delstud

Moments

Moments
N 287 Sum Weights 287
Mean -0.0011951 Sum Observations -0.3429943
Std Deviation 1.00735115 Variance 1.01475633
Skewness -0.7188188 Kurtosis 1.03846069
Uncorrected SS 290.220721 Corrected SS 290.220311
Coeff Variation -84289.959 Std Error Mean 0.05946206

Basic Measures of Location and Variability

Basic Statistical Measures
Location Variability
Mean -0.00120 Std Deviation 1.00735
Median 0.11540 Variance 1.01476
Mode . Range 6.28032
    Interquartile Range 1.18810

Tests For Location

Tests for Location: Mu0=0
Test Statistic p Value
Student's t t -0.0201 Pr > |t| 0.9840
Sign M 6.5 Pr >= |M| 0.4788
Signed Rank S 1533 Pr >= |S| 0.2767

Tests For Normality

Tests for Normality
Test Statistic p Value
Shapiro-Wilk W 0.97046 Pr < W <0.0001
Kolmogorov-Smirnov D 0.067348 Pr > D <0.0100
Cramer-von Mises W-Sq 0.328101 Pr > W-Sq <0.0050
Anderson-Darling A-Sq 2.071763 Pr > A-Sq <0.0050

Quantiles

Quantiles (Definition 5)
Level Quantile
100% Max 2.410620
99% 1.999026
95% 1.540531
90% 1.168669
75% Q3 0.683132
50% Median 0.115404
25% Q1 -0.504969
10% -1.366051
5% -1.892008
1% -3.047289
0% Min -3.869696

Extreme Observations

Extreme Observations
Lowest Highest
Value Obs Value Obs
-3.86970 521 1.80660 554
-3.40744 450 1.87512 227
-3.04729 380 1.99903 519
-2.86101 238 2.05720 506
-2.57695 259 2.41062 304

Missing Values

Missing Values
Missing
Value		 Count Percent Of
All Obs Missing Obs
. 292 50.43 100.00

Plots for delstud

Plots for delstud

Gender, Ethnicity and Math performance

Basic Regression Diagnostics

Large Negative Studentized Deleted Residual

The Print Procedure

Data Set WORK.EXPLOR

Obs id precalc calc sex totscore outcome passed grade hsgpa hscalc havecalc hsengl tongue class rater1 rater2 ethnic e1 e2 e3 e4 e5 e6 gender mtongue c1 c2 c3 yhat resid hatval delstud
521 176 3 6 Male 9 Failed No 1 69.8 76 Yes 60 Other Elite Asian Asian Asian 1 0 0 0 0 0 0 0 0 0 1 51.4408 -50.4408 0.035218 -3.86970

The SGPlot Procedure

The SGPlot Procedure

The SGPlot Procedure

The SGPlot Procedure

The SGPlot Procedure

The SGPlot Procedure

The SGPlot Procedure

The SGPlot Procedure

The SGPlot Procedure

The SGPlot Procedure

The SGPlot Procedure

The SGPlot Procedure