data oneway;
input group y1 y2 y3 x1 x2;
cards;
1 19.6 5.15 9.5 1 1
1 15.4 5.75 9.1 1 1
1 22.3 4.35 3.3 1 1
1 24.3 7.55 5.0 1 1
1 22.5 8.50 6.0 1 1
1 20.5 10.25 5.0 1 1
1 14.1 5.95 18.8 1 1
1 13.0 6.30 16.5 1 1
1 14.1 5.45 8.9 1 1
1 16.7 3.75 6.0 1 1
1 16.8 5.10 7.4 1 1
2 17.1 9.00 7.5 -1 1
2 15.7 5.30 8.5 -1 1
2 14.9 9.85 6.0 -1 1
2 19.7 3.60 2.9 -1 1
2 17.2 4.05 0.2 -1 1
2 16.0 4.40 2.6 -1 1
2 12.8 7.15 7.0 -1 1
2 13.6 7.25 3.2 -1 1
2 14.2 5.30 6.2 -1 1
2 13.1 3.10 5.5 -1 1
2 16.5 2.40 6.6 -1 1
3 16.0 4.55 2.9 0 -2
3 12.5 2.65 0.7 0 -2
3 18.5 6.50 5.3 0 -2
3 19.2 4.85 8.3 0 -2
3 12.0 8.75 9.0 0 -2
3 13.0 5.20 10.3 0 -2
3 11.9 4.75 8.5 0 -2
3 12.0 5.85 9.5 0 -2
3 19.8 2.85 2.3 0 -2
3 16.5 6.55 3.3 0 -2
3 17.4 6.60 1.9 0 -2
;
proc reg;
model y1 y2 y3 = x1 x2;
mtest;
run;
-------------------------------------------------------------------------------
The SAS System
Model: MODEL1
Dependent Variable: Y1
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 2 52.92424 26.46212 2.701 0.0835
Error 30 293.96545 9.79885
C Total 32 346.88970
Root MSE 3.13031 R-square 0.1526
Dep Mean 16.33030 Adj R-sq 0.0961
C.V. 19.16873
Parameter Estimate
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 16.330303 0.54491724 29.968 0.0001
X1 1 1.295455 0.66738460 1.941 0.0617
X2 1 0.492424 0.38531468 1.278 0.2111
-------------------------------------------------------------------------------
Dependent Variable: Y2
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 2 3.97515 1.98758 0.472 0.6282
Error 30 126.28727 4.20958
C Total 32 130.26242
Root MSE 2.05173 R-square 0.0305
Dep Mean 5.71515 Adj R-sq -0.0341
C.V. 35.89975
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 5.715152 0.35715949 16.002 0.0001
X1 1 0.304545 0.43742925 0.696 0.4917
X2 1 0.171212 0.25254990 0.678 0.5030
-------------------------------------------------------------------------------
Dependent Variable: Y3
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 2 81.82970 40.91485 2.879 0.0718
Error 30 426.37091 14.21236
C Total 32 508.20061
Root MSE 3.76993 R-square 0.1610
Dep Mean 6.47576 Adj R-sq 0.1051
C.V. 58.21603
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 6.475758 0.65626038 9.868 0.0001
X1 1 1.786364 0.80375153 2.223 0.0339
X2 1 0.419697 0.46404616 0.904 0.3730
-------------------------------------------------------------------------------
Multivariate Test:
Multivariate Statistics and F Approximations
S=2 M=0 N=13
Statistic Value F Num DF Den DF Pr > F
Wilks' Lambda 0.52578837 3.5382 6 56 0.0049
Pillai's Trace 0.47667015 3.0248 6 58 0.0122
Hotelling-Lawley Trace 0.89723004 4.0375 6 54 0.0021
Roy's Greatest Root 0.89198797 8.6226 3 29 0.0003
NOTE: F Statistic for Roy's Greatest Root is an upper bound.
NOTE: F Statistic for Wilks' Lambda is exact.