[SAS Program]
data ati;
input (y x1 x3)(1.0 1.0 2.0);
x4 = x1 * x3;
cards;
2105
1107
2110
2115
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5021
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;
proc means n mean var std;
var y x3;
title 'ATI example -- Pedhazur data p. 464';
proc reg;
m1: model y = x3/stb;
m2: model y = x3 x1/stb;
m3: model y = x3 x1 x4/stb;
plot y*x3='*';
data part2;
set ati;
if x1 = 1;
proc reg;
model y = x3;
plot y*x3='*';
data part3;
set ati;
if x1 = 0;
proc reg;
model y = x3;
plot y*x3='*';
run;
.
VAR LABELS Y,RATINGS OF TEACHERS/
X1,TEACHING STYLE/
X3,TOLERANCE OF AMBIGUITY/
X4,INTERACTION--X1*X3.
[SAS Output]
ATI example -- Pedhazur data p. 464
Variable N Mean Variance Std Dev
------------------------------------------------------
Y 40 4.2000000 3.6000000 1.8973666
X3 40 31.2500000 307.0128205 17.5217813
------------------------------------------------------
Model: M1
Dependent Variable: Y
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 1 0.46979 0.46979 0.128 0.7229
Error 38 139.93021 3.68237
C Total 39 140.40000
Root MSE 1.91895 R-square 0.0033
Dep Mean 4.20000 Adj R-sq -0.0229
C.V. 45.68932
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 4.395745 0.62641436 7.017 0.0001
X3 1 -0.006264 0.01753692 -0.357 0.7229
Standardized
Variable DF Estimate
INTERCEP 1 0.00000000
X3 1 -0.05784518
Model: M2
Dependent Variable: Y
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 2 2.21859 1.10930 0.297 0.7448
Error 37 138.18141 3.73463
C Total 39 140.40000
Root MSE 1.93252 R-square 0.0158
Dep Mean 4.20000 Adj R-sq -0.0374
C.V. 46.01238
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 4.215571 0.68358527 6.167 0.0001
X3 1 -0.007210 0.01771493 -0.407 0.6864
X1 1 0.419466 0.61298532 0.684 0.4980
Standardized
Variable DF Estimate
INTERCEP 1 0.00000000
X3 1 -0.06658025
X1 1 0.11194726
Model: M3
Dependent Variable: Y
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 3 127.33242 42.44414 116.930 0.0001
Error 36 13.06758 0.36299
C Total 39 140.40000
Root MSE 0.60249 R-square 0.9069
Dep Mean 4.20000 Adj R-sq 0.8992
C.V. 14.34488
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 7.193213 0.26672429 26.969 0.0001
X3 1 -0.106796 0.00769903 -13.871 0.0001
X1 1 -5.999715 0.39505737 -15.187 0.0001
X4 1 0.205155 0.01105036 18.565 0.0001
Standardized
Variable DF Estimate
INTERCEP 1 0.00000000
X3 1 -0.98624259
X1 1 -1.60120554
X4 1 2.21758127
--+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+---
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--+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+---
5 10 15 20 25 30 35 40 45 50 55 60 65
X3
ATI example -- Pedhazur data p. 464 - x3 = 1
Model: MODEL1
Dependent Variable: Y
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 1 55.88756 55.88756 145.531 0.0001
Error 18 6.91244 0.38402
C Total 19 62.80000
Root MSE 0.61970 R-square 0.8899
Dep Mean 4.40000 Adj R-sq 0.8838
C.V. 14.08403
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 1.193498 0.29975052 3.982 0.0009
X3 1 0.098359 0.00815335 12.064 0.0001
--+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+---
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--+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+---
5 10 15 20 25 30 35 40 45 50 55 60 65
X3
ATI example -- Pedhazur data p. 464 - x3 = 0
Model: MODEL1
Dependent Variable: Y
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 1 69.84487 69.84487 204.254 0.0001
Error 18 6.15513 0.34195
C Total 19 76.00000
Root MSE 0.58477 R-square 0.9190
Dep Mean 4.00000 Adj R-sq 0.9145
C.V. 14.61916
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 7.193213 0.25888016 27.786 0.0001
X3 1 -0.106796 0.00747260 -14.292 0.0001
--+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+---
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--+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+---
5 10 15 20 25 30 35 40 45 50 55 60 65