MANOVA CRF-32 Example Using PROC REG
Same data as Assignment 8
data crf32;
input a b y1 y2 x1 x2 x3;
x4 = x1*x3; output;
x5 = x2*x3; output;
cards;
1 1 10 21 1 1 1
1 1 12 22 1 1 1
1 1 9 19 1 1 1
1 1 10 21 1 1 1
1 1 14 23 1 1 1
1 2 9 14 1 1 -1
1 2 8 15 1 1 -1
1 2 11 16 1 1 -1
1 2 9 17 1 1 -1
1 2 9 17 1 1 -1
2 1 11 23 -1 1 1
2 1 14 27 -1 1 1
2 1 13 24 -1 1 1
2 1 15 26 -1 1 1
2 1 14 24 -1 1 1
2 2 11 15 -1 1 -1
2 2 12 18 -1 1 -1
2 2 10 16 -1 1 -1
2 2 9 17 -1 1 -1
2 2 9 18 -1 1 -1
3 1 8 17 0 -2 1
3 1 7 15 0 -2 1
3 1 10 18 0 -2 1
3 1 8 17 0 -2 1
3 1 7 19 0 -2 1
3 2 9 22 0 -2 -1
3 2 8 18 0 -2 -1
3 2 10 17 0 -2 -1
3 2 9 19 0 -2 -1
3 2 8 19 0 -2 -1
;
proc reg;
model y1 y2 = x1 x2 x3 x4 x5;
a:mtest x1, x2;
b:mtest x3;
axb:mtest x4, x5;
run;
----------------------------------------------------------------------------
Model: MODEL1
Dependent Variable: Y1
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 5 93.10000 18.62000 9.800 0.0001
Error 24 45.60000 1.90000
C Total 29 138.70000
Root MSE 1.37840 R-square 0.6712
Dep Mean 10.10000 Adj R-sq 0.6027
C.V. 13.64757
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 10.100000 0.25166115 40.133 0.0001
X1 1 -0.850000 0.30822070 -2.758 0.0109
X2 1 0.850000 0.17795130 4.777 0.0001
X3 1 0.700000 0.25166115 2.782 0.0104
X4 1 -0.350000 0.30822070 -1.136 0.2674
X5 1 0.550000 0.17795130 3.091 0.0050
Dependent Variable: Y2
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 5 283.46667 56.69333 24.297 0.0001
Error 24 56.00000 2.33333
C Total 29 339.46667
Root MSE 1.52753 R-square 0.8350
Dep Mean 19.13333 Adj R-sq 0.8007
C.V. 7.98358
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 19.133333 0.27888668 68.606 0.0001
X1 1 -1.150000 0.34156503 -3.367 0.0026
X2 1 0.516667 0.19720266 2.620 0.0150
X3 1 1.933333 0.27888668 6.932 0.0001
X4 1 -0.650000 0.34156503 -1.903 0.0691
X5 1 1.416667 0.19720266 7.184 0.0001
Multivariate Test: A
Multivariate Statistics and F Approximations
S=2 M=-0.5 N=10.5
Statistic Value F Num DF Den DF Pr > F
Wilks' Lambda 0.36855473 7.4429 4 46 0.0001
Pillai's Trace 0.69074032 6.3310 4 48 0.0004
Hotelling-Lawley Trace 1.55241585 8.5383 4 44 0.0001
Roy's Greatest Root 1.44074791 17.2890 2 24 0.0001
NOTE: F Statistic for Roy's Greatest Root is an upper bound.
NOTE: F Statistic for Wilks' Lambda is exact.
Multivariate Test: B
Multivariate Statistics and Exact F Statistics
S=1 M=0 N=10.5
Statistic Value F Num DF Den DF Pr > F
Wilks' Lambda 0.33304572 23.0298 2 23 0.0001
Pillai's Trace 0.66695428 23.0298 2 23 0.0001
Hotelling-Lawley Trace 2.00259072 23.0298 2 23 0.0001
Roy's Greatest Root 2.00259072 23.0298 2 23 0.0001
Multivariate Test: AXB
Multivariate Statistics and F Approximations
S=2 M=-0.5 N=10.5
Statistic Value F Num DF Den DF Pr > F
Wilks' Lambda 0.30092873 9.4636 4 46 0.0001
Pillai's Trace 0.70226819 6.4938 4 48 0.0003
Hotelling-Lawley Trace 2.31242251 12.7183 4 44 0.0001
Roy's Greatest Root 2.30781925 27.6938 2 24 0.0001
NOTE: F Statistic for Roy's Greatest Root is an upper bound.
NOTE: F Statistic for Wilks' Lambda is exact.