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Inputting Salary Survey data, table 5.1, p. 124.
data p124; input S X E M; cards; 13876 1 1 1 11608 1 3 0 18701 1 3 1 11283 1 2 0 11767 1 3 0 20872 2 2 1 11772 2 2 0 10535 2 1 0 12195 2 3 0 12313 3 2 0 14975 3 1 1 21371 3 2 1 19800 3 3 1 11417 4 1 0 20263 4 3 1 13231 4 3 0 12884 4 2 0 13245 5 2 0 13677 5 3 0 15965 5 1 1 12336 6 1 0 21352 6 3 1 13839 6 2 0 22884 6 2 1 16978 7 1 1 14803 8 2 0 17404 8 1 1 22184 8 3 1 13548 8 1 0 14467 10 1 0 15942 10 2 0 23174 10 3 1 23780 10 2 1 25410 11 2 1 14861 11 1 0 16882 12 2 0 24170 12 3 1 15990 13 1 0 26330 13 2 1 17949 14 2 0 25685 15 3 1 27837 16 2 1 18838 16 2 0 17483 16 1 0 19207 17 2 0 19346 20 1 0 ; run;
Creating the dummy coding for the variable e.
data p124; set p124; e1 = .; if e = 1 then e1 = 1; else e1 = 0; e2 = .; if e = 2 then e2 = 1; else e2 = 0; run; proc freq data = p124; tables e e1 e2; run;
The FREQ Procedure
Cumulative Cumulative
E Frequency Percent Frequency Percent
-----------------------------------------------------
1 14 30.43 14 30.43
2 19 41.30 33 71.74
3 13 28.26 46 100.00
Cumulative Cumulative
e1 Frequency Percent Frequency Percent
-------------------------------------------------------
0 32 69.57 32 69.57
1 14 30.43 46 100.00
Cumulative Cumulative
e2 Frequency Percent Frequency Percent
-------------------------------------------------------
0 27 58.70 27 58.70
1 19 41.30 46 100.00
Creating the category variables used in table 5.2, p. 126.
data p124; set p124; category = .; if e = 1 and m = 0 then category = 1; if e = 1 and m = 1 then category = 2; if e = 2 and m = 0 then category = 3; if e = 2 and m = 1 then category = 4; if e = 3 and m = 0 then category = 5; if e = 3 and m = 1 then category = 6; run;
Table 5.3, p. 126, fig. 5.1, p. 127 and fig. 5.2, p. 128.
proc reg data = p124; var category; model s = x e1 e2 m; plot student.*x student.*category; run; quit;
The REG Procedure
Model: MODEL1
Dependent Variable: S
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 4 957816858 239454214 226.84 <.0001
Error 41 43280719 1055627
Corrected Total 45 1001097577
Root MSE 1027.43725 R-Square 0.9568
Dependent Mean 17270 Adj R-Sq 0.9525
Coeff Var 5.94919
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 11032 383.21713 28.79 <.0001
X 1 546.18402 30.51919 17.90 <.0001
e1 1 -2996.21026 411.75271 -7.28 <.0001
e2 1 147.82495 387.65932 0.38 0.7049
M 1 6883.53101 313.91898 21.93 <.0001
Creating the interaction variables, p. 128.
data p124; set p124; me1= m*e1; me2 = m*e2; run;
Table 5.4 and fig. 5.3, p. 129.
symbol v=dot h=.8 c=blue; proc reg data = p124; model s = x e1 e2 m me1 me2; plot student.*x; run; quit;
The REG Procedure
Model: MODEL1
Dependent Variable: S
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 6 999919409 166653235 5516.60 <.0001
Error 39 1178168 30209
Corrected Total 45 1001097577
Root MSE 173.80861 R-Square 0.9988
Dependent Mean 17270 Adj R-Sq 0.9986
Coeff Var 1.00641
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 11203 79.06545 141.70 <.0001
X 1 496.98701 5.56642 89.28 <.0001
e1 1 -1730.74832 105.33389 -16.43 <.0001
e2 1 -349.07769 97.56790 -3.58 0.0009
M 1 7047.41202 102.58919 68.70 <.0001
me1 1 -3066.03512 149.33044 -20.53 <.0001
me2 1 1836.48795 131.16736 14.00 <.0001
Deleting observation 33, repeating the regression with interactions, table 5.5 and fig. 5.4-5.5, p. 129-130.
data missing33; set p124; id = _N_; /* creates the id variable */ if id = 33 then delete; run; symbol1 c=blue v=dot; proc reg data = missing33; var category; model s = x e1 e2 m me1 me2; plot student.*x student.*category; run; quit;
The REG Procedure
Model: MODEL1
Dependent Variable: S
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 6 957607113 159601186 35428.0 <.0001
Error 38 171188 4504.95052
Corrected Total 44 957778301
Root MSE 67.11893 R-Square 0.9998
Dependent Mean 17126 Adj R-Sq 0.9998
Coeff Var 0.39192
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 11200 30.53338 366.80 <.0001
X 1 498.41777 2.15169 231.64 <.0001
e1 1 -1741.33595 40.68250 -42.80 <.0001
e2 1 -357.04226 37.68114 -9.48 <.0001
M 1 7040.58014 39.61907 177.71 <.0001
me1 1 -3051.76329 57.67420 -52.91 <.0001
me2 1 1997.53060 51.78498 38.57 <.0001
Table 5.6, Estimates of the Base Salary, p. 131.
proc glm data = missing33; class e m ; model s = x e e*m; lsmean e*m/ at x=0 stderr cl; run; quit;
The GLM Procedure
Class Level Information
Class Levels Values
E 3 1 2 3
M 2 0 1
Number of observations 45
The GLM Procedure
Dependent Variable: S
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 6 957607113.1 159601185.5 35428.0 <.0001
Error 38 171188.1 4505.0
Corrected Total 44 957778301.2
R-Square Coeff Var Root MSE S Mean
0.999821 0.391923 67.11893 17125.53
Source DF Type I SS Mean Square F Value Pr > F
X 1 276059254.3 276059254.3 61279.1 <.0001
E 2 153242718.2 76621359.1 17008.3 <.0001
E*M 3 528305140.6 176101713.5 39090.7 <.0001
Source DF Type III SS Mean Square F Value Pr > F
X 1 241723277.6 241723277.6 53657.3 <.0001
E 2 119359886.9 59679943.4 13247.6 <.0001
E*M 3 528305140.6 176101713.5 39090.7 <.0001
The GLM Procedure
Least Squares Means at X=0
Standard
E M S LSMEAN Error Pr > |t|
1 0 9458.3778 31.0407 <.0001
1 1 13447.1947 31.7437 <.0001
2 0 10842.6715 26.1571 <.0001
2 1 19880.7823 32.9443 <.0001
3 0 11199.7138 30.5334 <.0001
3 1 18240.2939 28.5471 <.0001
E M S LSMEAN 95% Confidence Limits
1 0 9458.377848 9395.539200 9521.216497
1 1 13447 13383 13511
2 0 10843 10790 10896
2 1 19881 19814 19947
3 0 11200 11138 11262
3 1 18240 18183 18298
Table 5.7, the Pre-employment Testing Program data, p. 134.
data p134; input TEST RACE JPERF; cards; 0.28 1 1.83 0.97 1 4.59 1.25 1 2.97 2.46 1 8.14 2.51 1 8.00 1.17 1 3.30 1.78 1 7.53 1.21 1 2.03 1.63 1 5.00 1.98 1 8.04 2.36 0 3.25 2.11 0 5.30 0.45 0 1.39 1.76 0 4.69 2.09 0 6.56 1.50 0 3.00 1.25 0 5.85 0.72 0 1.90 0.42 0 3.85 1.53 0 2.95 ; run;
Table 5.8 and fig. 5.7, p. 135.
symbol v=dot h=.8 c=blue; proc reg data = p134; model jperf = test; plot student.*test; run; quit;
The REG Procedure
Model: MODEL1
Dependent Variable: JPERF
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 1 48.72296 48.72296 19.25 0.0004
Error 18 45.56830 2.53157
Corrected Total 19 94.29125
Root MSE 1.59109 R-Square 0.5167
Dependent Mean 4.50850 Adj R-Sq 0.4899
Coeff Var 35.29093
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 1.03497 0.86803 1.19 0.2486
TEST 1 2.36053 0.53807 4.39 0.0004
data temp;
set p134;
racetest = race*test;
run;
Table 5.9 and fig. 5.8, p. 135.
symbol v=dot h=.8 c=blue; proc reg data = temp; model jperf = test race racetest; plot student.*test; run; quit;
The REG Procedure
Model: MODEL1
Dependent Variable: JPERF
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 3 62.63578 20.87859 10.55 0.0005
Error 16 31.65547 1.97847
Corrected Total 19 94.29125
Root MSE 1.40658 R-Square 0.6643
Dependent Mean 4.50850 Adj R-Sq 0.6013
Coeff Var 31.19840
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 2.01028 1.05011 1.91 0.0736
TEST 1 1.31340 0.67037 1.96 0.0677
RACE 1 -1.91317 1.54032 -1.24 0.2321
racetest 1 1.99755 0.95444 2.09 0.0527
Table 5.10 and fig. 5.10-5.11, p. 136-137.
proc sort data = p134; by race; run; proc reg data = p134; by race; model jperf = test; plot student.*test; run; quit;
RACE=0
The REG Procedure
Model: MODEL1
Dependent Variable: JPERF
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 1 7.59441 7.59441 3.32 0.1059
Error 8 18.29863 2.28733
Corrected Total 9 25.89304
Root MSE 1.51239 R-Square 0.2933
Dependent Mean 3.87400 Adj R-Sq 0.2050
Coeff Var 39.03954
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 2.01028 1.12911 1.78 0.1129
TEST 1 1.31340 0.72080 1.82 0.1059
RACE=1
The REG Procedure
Model: MODEL1
Dependent Variable: JPERF
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 1 46.98957 46.98957 28.14 0.0007
Error 8 13.35684 1.66960
Corrected Total 9 60.34641
Root MSE 1.29213 R-Square 0.7787
Dependent Mean 5.14300 Adj R-Sq 0.7510
Coeff Var 25.12409
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 0.09712 1.03519 0.09 0.9276
TEST 1 3.31095 0.62411 5.31 0.0007
Fig. 5.9, p. 136.
proc reg data = p134 noprint; var race; model jperf = test; plot student.*race; run; quit;
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