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Table 7.1, p. 261.
data ch7tab01;
input X1 X2 X3 Y;
label x1 = 'Triceps'
x2 = 'Thigh cir.'
x3 = 'Midarm cir.'
y = 'body fat';
cards;
19.5 43.1 29.1 11.9
24.7 49.8 28.2 22.8
30.7 51.9 37.0 18.7
29.8 54.3 31.1 20.1
19.1 42.2 30.9 12.9
25.6 53.9 23.7 21.7
31.4 58.5 27.6 27.1
27.9 52.1 30.6 25.4
22.1 49.9 23.2 21.3
25.5 53.5 24.8 19.3
31.1 56.6 30.0 25.4
30.4 56.7 28.3 27.2
18.7 46.5 23.0 11.7
19.7 44.2 28.6 17.8
14.6 42.7 21.3 12.8
29.5 54.4 30.1 23.9
27.7 55.3 25.7 22.6
30.2 58.6 24.6 25.4
22.7 48.2 27.1 14.8
25.2 51.0 27.5 21.1
;
run;
Table 7.2, p. 262-263.
proc reg data = ch7tab01; model y = x1; model y = x2; model y = x1 x2; model y = x1-x3; run; quit;
The REG Procedure
Model: MODEL1
Dependent Variable: Y body fat
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 1 352.26980 352.26980 44.30 <.0001
Error 18 143.11970 7.95109
Corrected Total 19 495.38950
Root MSE 2.81977 R-Square 0.7111
Dependent Mean 20.19500 Adj R-Sq 0.6950
Coeff Var 13.96271
Parameter Estimates
Parameter Standard
Variable Label DF Estimate Error t Value Pr > |t|
Intercept Intercept 1 -1.49610 3.31923 -0.45 0.6576
X1 Triceps 1 0.85719 0.12878 6.66 <.0001
The REG Procedure
Model: MODEL2
Dependent Variable: Y body fat
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 1 381.96582 381.96582 60.62 <.0001
Error 18 113.42368 6.30132
Corrected Total 19 495.38950
Root MSE 2.51024 R-Square 0.7710
Dependent Mean 20.19500 Adj R-Sq 0.7583
Coeff Var 12.43002
Parameter Estimates
Parameter Standard
Variable Label DF Estimate Error t Value Pr > |t|
Intercept Intercept 1 -23.63449 5.65741 -4.18 0.0006
X2 Thigh cir. 1 0.85655 0.11002 7.79 <.0001
The REG Procedure
Model: MODEL3
Dependent Variable: Y body fat
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 2 385.43871 192.71935 29.80 <.0001
Error 17 109.95079 6.46769
Corrected Total 19 495.38950
Root MSE 2.54317 R-Square 0.7781
Dependent Mean 20.19500 Adj R-Sq 0.7519
Coeff Var 12.59305
Parameter Estimates
Parameter Standard
Variable Label DF Estimate Error t Value Pr > |t|
Intercept Intercept 1 -19.17425 8.36064 -2.29 0.0348
X1 Triceps 1 0.22235 0.30344 0.73 0.4737
X2 Thigh cir. 1 0.65942 0.29119 2.26 0.0369
The REG Procedure
Model: MODEL4
Dependent Variable: Y body fat
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 3 396.98461 132.32820 21.52 <.0001
Error 16 98.40489 6.15031
Corrected Total 19 495.38950
Root MSE 2.47998 R-Square 0.8014
Dependent Mean 20.19500 Adj R-Sq 0.7641
Coeff Var 12.28017
Parameter Estimates
Parameter Standard
Variable Label DF Estimate Error t Value Pr > |t|
Intercept Intercept 1 117.08469 99.78240 1.17 0.2578
X1 Triceps 1 4.33409 3.01551 1.44 0.1699
X2 Thigh cir. 1 -2.85685 2.58202 -1.11 0.2849
X3 Midarm cir. 1 -2.18606 1.59550 -1.37 0.1896
Table 7.4, p. 267.
Test1 is for the example of testing one variable, p. 269.
Test2 is for the example of testing two variables at once, p. 270-271.
proc reg data = ch7tab01; model y = x1-x3/ss1; test1: test x3 = 0; test2: test x2=x3=0; run; quit;
The REG Procedure
Model: MODEL1
Dependent Variable: Y body fat
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 3 396.98461 132.32820 21.52 <.0001
Error 16 98.40489 6.15031
Corrected Total 19 495.38950
Root MSE 2.47998 R-Square 0.8014
Dependent Mean 20.19500 Adj R-Sq 0.7641
Coeff Var 12.28017
Parameter Estimates
Parameter Standard
Variable Label DF Estimate Error t Value Pr > |t| Type I SS
Intercept Intercept 1 117.08469 99.78240 1.17 0.2578 8156.76050
X1 Triceps 1 4.33409 3.01551 1.44 0.1699 352.26980
X2 Thigh cir. 1 -2.85685 2.58202 -1.11 0.2849 33.16891
X3 Midarm cir. 1 -2.18606 1.59550 -1.37 0.1896 11.54590
The REG Procedure
Model: MODEL1
Test test1 Results for Dependent Variable Y
Mean
Source DF Square F Value Pr > F
Numerator 1 11.54590 1.88 0.1896
Denominator 16 6.15031
The REG Procedure
Model: MODEL1
Test test2 Results for Dependent Variable Y
Mean
Source DF Square F Value Pr > F
Numerator 2 22.35741 3.64 0.0500
Denominator 16 6.15031
Coefficients of partial determination, p. 275.
ry1.2 and ry2.1 are from the first model.
ry3.12 is the coef. from X3 in the second model.
proc reg data = ch7tab01; model y = x1 x2 / pcorr2; model y = x1-x3 / pcorr2; run; quit;
The REG Procedure
Model: MODEL1
Dependent Variable: Y body fat
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 2 385.43871 192.71935 29.80 <.0001
Error 17 109.95079 6.46769
Corrected Total 19 495.38950
Root MSE 2.54317 R-Square 0.7781
Dependent Mean 20.19500 Adj R-Sq 0.7519
Coeff Var 12.59305
Parameter Estimates
Squared
Parameter Standard Partial
Variable Label DF Estimate Error t Value Pr > |t| Corr Type II
Intercept Intercept 1 -19.17425 8.36064 -2.29 0.0348 .
X1 Triceps 1 0.22235 0.30344 0.73 0.4737 0.03062
X2 Thigh cir. 1 0.65942 0.29119 2.26 0.0369 0.23176
The REG Procedure
Model: MODEL2
Dependent Variable: Y body fat
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 3 396.98461 132.32820 21.52 <.0001
Error 16 98.40489 6.15031
Corrected Total 19 495.38950
Root MSE 2.47998 R-Square 0.8014
Dependent Mean 20.19500 Adj R-Sq 0.7641
Coeff Var 12.28017
Parameter Estimates
Squared
Parameter Standard Partial
Variable Label DF Estimate Error t Value Pr > |t| Corr Type II
Intercept Intercept 1 117.08469 99.78240 1.17 0.2578 .
X1 Triceps 1 4.33409 3.01551 1.44 0.1699 0.11435
X2 Thigh cir. 1 -2.85685 2.58202 -1.11 0.2849 0.07108
X3 Midarm cir. 1 -2.18606 1.59550 -1.37 0.1896 0.10501
Inputting the Dwaine Studio Data from Ch. 6, Table 5 (p. 241).
data ch6fig05;
input x1 x2 y;
label y = 'sales'
x1 = 'targtpop'
x2 = 'dispoinc';
cards;
68.5 16.7 174.4
45.2 16.8 164.4
91.3 18.2 244.2
47.8 16.3 154.6
46.9 17.3 181.6
66.1 18.2 207.5
49.5 15.9 152.8
52.0 17.2 163.2
48.9 16.6 145.4
38.4 16.0 137.2
87.9 18.3 241.9
72.8 17.1 191.1
88.4 17.4 232.0
42.9 15.8 145.3
52.5 17.8 161.1
85.7 18.4 209.7
41.3 16.5 146.4
51.7 16.3 144.0
89.6 18.1 232.6
82.7 19.1 224.1
52.3 16.0 166.5
;
run;
Creating the standardized variables of the Dwaine Studios Data, p. 282.
proc sql;
create table temp as
select *, ( y - mean(y) )/( std(y)*( sqrt( count(y)-1 ) ) ) as yprime,
( x1 - mean(x1) )/( std(x1)*( sqrt( count(x1)-1 ) ) ) as x1prime,
( x2 - mean(x2) )/( std(x2)*( sqrt( count(x2)-1 ) ) ) as x2prime
from ch6fig05;
quit;
Table 7.5a, p. 283.
proc print data = temp (obs= 10); var y x1 x2; run; proc means data = temp mean std ; var y x1 x2; run;
Obs y x1 x2 1 174.4 68.5 16.7 2 164.4 45.2 16.8 3 244.2 91.3 18.2 4 154.6 47.8 16.3 5 181.6 46.9 17.3 6 207.5 66.1 18.2 7 152.8 49.5 15.9 8 163.2 52.0 17.2 9 145.4 48.9 16.6 10 137.2 38.4 16.0 The MEANS Procedure Variable Label Mean Std Dev ---------------------------------------------------- y sales 181.9047619 36.1913039 x1 targtpop 62.0190476 18.6203281 x2 dispoinc 17.1428571 0.9703460 ----------------------------------------------------
Table 7.5b, p. 283.
proc print data = temp; var yprime x1prime x2prime; run;
Obs yprime x1prime x2prime 1 -0.04637 0.07783 -0.10205 2 -0.10815 -0.20198 -0.07901 3 0.38489 0.35163 0.24361 4 -0.16870 -0.17075 -0.19423 5 -0.00188 -0.18156 0.03621 6 0.15814 0.04901 0.24361 7 -0.17982 -0.15034 -0.28640 8 -0.11557 -0.12032 0.01317 9 -0.22554 -0.15754 -0.12510 10 -0.27621 -0.28364 -0.26336 11 0.37068 0.31080 0.26665 12 0.05681 0.12947 -0.00988 13 0.30951 0.31680 0.05926 14 -0.22616 -0.22960 -0.30945 15 -0.12854 -0.11431 0.15143 16 0.17173 0.28438 0.28970 17 -0.21937 -0.24881 -0.14814 18 -0.23419 -0.12392 -0.19423 19 0.31322 0.33121 0.22056 20 0.26070 0.24835 0.45100 21 -0.09518 -0.11671 -0.26336
Table 7.5c, p. 283.
proc reg data = temp; model yprime = x1prime x2prime; run; quit;
The REG Procedure
Model: MODEL1
Dependent Variable: yprime
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 2 0.91675 0.45837 99.10 <.0001
Error 18 0.08325 0.00463
Corrected Total 20 1.00000
Root MSE 0.06801 R-Square 0.9167
Dependent Mean 3.23815E-17 Adj R-Sq 0.9075
Coeff Var 2.100236E17
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 -8.9542E-18 0.01484 -0.00 1.0000
x1prime 1 0.74837 0.10896 6.87 <.0001
x2prime 1 0.25110 0.10896 2.30 0.0333
Inputting the data of the Work Crew data.
data ch7tab06;
input x1 x2 y;
label x1 = 'Crew size'
x2 = 'Bonus Pay'
y = 'Crew productivity';
cards;
4 2 42
4 2 39
4 3 48
4 3 51
6 2 49
6 2 53
6 3 61
6 3 60
;
run;
Table 7.6, p. 286.
proc print data = ch7tab06; run;
Obs x1 x2 y 1 4 2 42 2 4 2 39 3 4 3 48 4 4 3 51 5 6 2 49 6 6 2 53 7 6 3 61 8 6 3 60
Table 7.7, p. 287.
proc reg data = ch7tab06; model y = x1 x2; model y = x1; model y = x2; run;
The REG Procedure
Model: MODEL1
Dependent Variable: y Crew productivity
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 2 402.25000 201.12500 57.06 0.0004
Error 5 17.62500 3.52500
Corrected Total 7 419.87500
Root MSE 1.87750 R-Square 0.9580
Dependent Mean 50.37500 Adj R-Sq 0.9412
Coeff Var 3.72704
Parameter Estimates
Parameter Standard
Variable Label DF Estimate Error t Value Pr > |t|
Intercept Intercept 1 0.37500 4.74045 0.08 0.9400
x1 Crew size 1 5.37500 0.66380 8.10 0.0005
x2 Bonus Pay 1 9.25000 1.32759 6.97 0.0009
The REG Procedure
Model: MODEL2
Dependent Variable: y Crew productivity
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 1 231.12500 231.12500 7.35 0.0351
Error 6 188.75000 31.45833
Corrected Total 7 419.87500
Root MSE 5.60877 R-Square 0.5505
Dependent Mean 50.37500 Adj R-Sq 0.4755
Coeff Var 11.13404
Parameter Estimates
Parameter Standard
Variable Label DF Estimate Error t Value Pr > |t|
Intercept Intercept 1 23.50000 10.11136 2.32 0.0591
x1 Crew size 1 5.37500 1.98300 2.71 0.0351
The REG Procedure
Model: MODEL3
Dependent Variable: y Crew productivity
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 1 171.12500 171.12500 4.13 0.0885
Error 6 248.75000 41.45833
Corrected Total 7 419.87500
Root MSE 6.43881 R-Square 0.4076
Dependent Mean 50.37500 Adj R-Sq 0.3088
Coeff Var 12.78177
Parameter Estimates
Parameter Standard
Variable Label DF Estimate Error t Value Pr > |t|
Intercept Intercept 1 27.25000 11.60774 2.35 0.0572
x2 Bonus Pay 1 9.25000 4.55293 2.03 0.0885
Fig. 7.3, p. 290. The scatter macro can be used for making a scatterplot matrix.
%scatter(data = Ch7tab01, var = x1 x2 x3);
Showing correlations of x1 to x3.
proc corr data = ch7tab01; var x1-x3; run;
The CORR Procedure
3 Variables: X1 X2 X3
Simple Statistics
Variable N Mean Std Dev Sum Minimum Maximum Label
X1 20 25.30500 5.02326 506.10000 14.60000 31.40000 Triceps
X2 20 51.17000 5.23461 1023 42.20000 58.60000 Thigh cir.
X3 20 27.62000 3.64715 552.40000 21.30000 37.00000 Midarm cir.
Pearson Correlation Coefficients, N = 20
Prob > |r| under H0: Rho=0
X1 X2 X3
X1 1.00000 0.92384 0.45778
Triceps <.0001 0.0424
X2 0.92384 1.00000 0.08467
Thigh cir. <.0001 0.7227
X3 0.45778 0.08467 1.00000
Midarm cir. 0.0424 0.7227
Inputting data in table 7.9, p. 302.
data ch7tab09;
input y x1 x2;
label y = 'cycles'
x1 = 'Charge rate'
x2 = 'Temperature';
cards;
150 0.6 10
86 1.0 10
49 1.4 10
288 0.6 20
157 1.0 20
131 1.0 20
184 1.0 20
109 1.4 20
279 0.6 30
235 1.0 30
224 1.4 30
;
run;
* Recoding the variables. ;
proc sql;
create table temp as
select *, (x1-mean(x1))/.4 as lx1, (x2-mean(x2))/10 as lx2,
((x1-mean(x1))/.4)*((x1-mean(x1))/.4) as lx1sq,
((x2-mean(x2))/10)*((x2-mean(x2))/10) as lx2sq,
((x1-mean(x1))/.4)*((x2-mean(x2))/10) as lx1x2,
x1*x1 as x1sq, x2*x2 as x2sq
from ch7tab09;
quit;
Correlations at the bottom of p. 302.
proc corr data = temp; var x1 x1sq x2 x2sq lx1 lx1sq lx2 lx2sq; run;
The CORR Procedure
8 Variables: x1 x1sq x2 x2sq lx1 lx1sq lx2 lx2sq
Simple Statistics
Variable N Mean Std Dev Sum Minimum Maximum Label
x1 11 1.00000 0.30984 11.00000 0.60000 1.40000 Charge rate
x1sq 11 1.08727 0.62529 11.96000 0.36000 1.96000
x2 11 20.00000 7.74597 220.00000 10.00000 30.00000 Temperature
x2sq 11 454.54545 314.20896 5000 100.00000 900.00000
lx1 11 0 0.77460 0 -1.00000 1.00000
lx1sq 11 0.54545 0.52223 6.00000 0 1.00000
lx2 11 0 0.77460 0 -1.00000 1.00000
lx2sq 11 0.54545 0.52223 6.00000 0 1.00000
Pearson Correlation Coefficients, N = 11
Prob > |r| under H0: Rho=0
x1 x1sq x2 x2sq lx1 lx1sq lx2 lx2sq
x1 1.00000 0.99103 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000
Charge rate <.0001 1.0000 1.0000 <.0001 1.0000 1.0000 1.0000
x1sq 0.99103 1.00000 0.00000 0.00592 0.99103 0.13363 0.00000 0.03563
<.0001 1.0000 0.9862 <.0001 0.6953 1.0000 0.9172
x2 0.00000 0.00000 1.00000 0.98609 0.00000 0.00000 1.00000 0.00000
Temperature 1.0000 1.0000 <.0001 1.0000 1.0000 <.0001 1.0000
x2sq 0.00000 0.00592 0.98609 1.00000 0.00000 0.04432 0.98609 0.16621
1.0000 0.9862 <.0001 1.0000 0.8970 <.0001 0.6253
lx1 1.00000 0.99103 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000
<.0001 <.0001 1.0000 1.0000 1.0000 1.0000 1.0000
lx1sq 0.00000 0.13363 0.00000 0.04432 0.00000 1.00000 0.00000 0.26667
1.0000 0.6953 1.0000 0.8970 1.0000 1.0000 0.4280
lx2 0.00000 0.00000 1.00000 0.98609 0.00000 0.00000 1.00000 0.00000
1.0000 1.0000 <.0001 <.0001 1.0000 1.0000 1.0000
lx2sq 0.00000 0.03563 0.00000 0.16621 0.00000 0.26667 0.00000 1.00000
1.0000 0.9172 1.0000 0.6253 1.0000 0.4280 1.0000
Table 7.9, p. 303.
proc print data = temp; run; proc means data = temp mean; var x1 x2; run;
Obs y x1 x2 lx1 lx2 lx1sq lx2sq lx1x2 x1sq x2sq 1 150 0.6 10 -1 -1 1 1 1 0.36 100 2 86 1.0 10 0 -1 0 1 -0 1.00 100 3 49 1.4 10 1 -1 1 1 -1 1.96 100 4 288 0.6 20 -1 0 1 0 0 0.36 400 5 157 1.0 20 0 0 0 0 0 1.00 400 6 131 1.0 20 0 0 0 0 0 1.00 400 7 184 1.0 20 0 0 0 0 0 1.00 400 8 109 1.4 20 1 0 1 0 0 1.96 400 9 279 0.6 30 -1 1 1 1 -1 0.36 900 10 235 1.0 30 0 1 0 1 0 1.00 900 11 224 1.4 30 1 1 1 1 1 1.96 900 The MEANS Procedure Variable Label Mean --------------------------------------- x1 Charge rate 1.0000000 x2 Temperature 20.0000000 ---------------------------------------
Table 7.7, p. 304.
Fig. 7.8a-7.8c, p. 304.
Test1 is the Partial F-test on p. 306.
proc reg data = temp; model y = lx1 lx2 lx1sq lx2sq lx1x2/ss1; plot r.*p. r.*lx1 r.*lx2; output out=tempout p=fitted r=residual; test lx1sq=lx2sq=lx1x2=0; run; quit;
The REG Procedure
Model: MODEL1
Dependent Variable: y cycles
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 5 55366 11073 10.57 0.0109
Error 5 5240.43860 1048.08772
Corrected Total 10 60606
Root MSE 32.37418 R-Square 0.9135
Dependent Mean 172.00000 Adj R-Sq 0.8271
Coeff Var 18.82220
Parameter Estimates
Parameter Standard
Variable Label DF Estimate Error t Value Pr > |t| Type I SS
Intercept Intercept 1 162.84211 16.60761 9.81 0.0002 325424
lx1 1 -55.83333 13.21670 -4.22 0.0083 18704
lx2 1 75.50000 13.21670 5.71 0.0023 34202
lx1sq 1 27.39474 20.34008 1.35 0.2359 1645.96667
lx2sq 1 -10.60526 20.34008 -0.52 0.6244 284.92807
lx1x2 1 11.50000 16.18709 0.71 0.5092 529.00000
The REG Procedure
Test 1 Results for Dependent Variable y
Mean
Source DF Square F Value Pr > F
Numerator 3 819.96491 0.78 0.5527
Denominator 5 1048.08772
Fig. 7.8a, p. 304.
Fig. 7.8b, p. 304.
Fig. 7.8c, p. 304.
Fig. 7.8d, p. 304.
proc univariate data = tempout noprint; qqplot residual/ normal; run;
First Order Models using transformed and not transformed variables, p. 306. The CLB option provides the confidence limits for the parameters on p. 307.
proc reg data = temp; model y = lx1 lx2; model y = x1 x2/ clb; output out=tempout p=fitted; run; quit;
The REG Procedure
Model: MODEL1
Dependent Variable: y cycles
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 2 52906 26453 27.48 0.0003
Error 8 7700.33333 962.54167
Corrected Total 10 60606
Root MSE 31.02486 R-Square 0.8729
Dependent Mean 172.00000 Adj R-Sq 0.8412
Coeff Var 18.03771
Parameter Estimates
Parameter Standard
Variable Label DF Estimate Error t Value Pr > |t|
Intercept Intercept 1 172.00000 9.35435 18.39 <.0001
lx1 1 -55.83333 12.66584 -4.41 0.0023
lx2 1 75.50000 12.66584 5.96 0.0003
The REG Procedure
Model: MODEL2
Dependent Variable: y cycles
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 2 52906 26453 27.48 0.0003
Error 8 7700.33333 962.54167
Corrected Total 10 60606
Root MSE 31.02486 R-Square 0.8729
Dependent Mean 172.00000 Adj R-Sq 0.8412
Coeff Var 18.03771
Parameter Estimates
Parameter Standard
Variable Label DF Estimate Error t Value Pr > |t|
Intercept Intercept 1 160.58333 41.61545 3.86 0.0048
x1 Charge rate 1 -139.58333 31.66461 -4.41 0.0023
x2 Temperature 1 7.55000 1.26658 5.96 0.0003
Parameter Estimates
Variable Label DF 95% Confidence Limits
Intercept Intercept 1 64.61793 256.54874
x1 Charge rate 1 -212.60206 -66.56461
x2 Temperature 1 4.62925 10.47075
Fig. 7.9, p. 307.
We are using the fitted values from the last model in the previous proc reg.
proc g3d data = tempout;
plot x2*x1 = fitted ;
label fitted = 'Number of Cycles'
x1 = 'Charge Rate'
x2 = 'Temperature';
run;
We cannot find the data files for section 7.8, pages 308-313. The 3d graphs can be made using 3D Graphs using SAS and SAS Teaching Tools- Graphs for Visualizing Interactions of Continuous Variables in Multiple Regression.
Creating centered variables for the Body Fat dataset from table 7.1, p. 261.
proc sql; create table temp as select *, y - mean(y) as cy, x1 - mean(x1) as cx1, x2 - mean(x2) as cx2, x3 - mean(x3) as cx3 from ch7tab01; quit; data temp; set temp; cx1x2 = cx1*cx2; cx1x3 = cx1*cx3; cx2x3 = cx2*cx3; run;
Fitting the Regression model (7.93), p. 315. The SS1 option lets you obtain the extra sums of squares. Test1 is the test of the interaction terms.
proc reg data = temp; model y = cx1 cx2 cx3 cx1x2 cx1x3 cx2x3/ss1; test1: test cx1x2 = cx1x3 = cx2x3 = 0; run; quit;
The REG Procedure
Model: MODEL1
Dependent Variable: Y body fat
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 6 407.69950 67.94992 10.07 0.0003
Error 13 87.69000 6.74538
Corrected Total 19 495.38950
Root MSE 2.59719 R-Square 0.8230
Dependent Mean 20.19500 Adj R-Sq 0.7413
Coeff Var 12.86055
Parameter Estimates
Parameter Standard
Variable Label DF Estimate Error t Value Pr > |t| Type I SS
Intercept Intercept 1 20.52689 1.07363 19.12 <.0001 8156.76050
cx1 1 3.43781 3.57867 0.96 0.3543 352.26980
cx2 1 -2.09472 3.03677 -0.69 0.5025 33.16891
cx3 1 -1.61634 1.90721 -0.85 0.4121 11.54590
cx1x2 1 0.00888 0.03085 0.29 0.7781 1.49572
cx1x3 1 -0.08479 0.07342 -1.15 0.2689 2.70433
cx2x3 1 0.09042 0.09200 0.98 0.3437 6.51484
The REG Procedure
Model: MODEL1
Test test1 Results for Dependent Variable Y
Mean
Source DF Square F Value Pr > F
Numerator 3 3.57163 0.53 0.6699
Denominator 13 6.74538
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