Multivariate Regression Example -- Timm -- pg 314
data timm;
input apt ppvt rpmt n s ns na ss;
cards;
49 48 8 1 2 6 12 16
47 76 13 5 14 14 30 27
11 40 13 0 10 21 16 16
9 52 9 0 2 5 17 8
69 63 15 2 7 11 26 17
35 82 14 2 15 21 34 25
6 71 21 0 1 20 23 18
8 68 8 0 0 10 19 14
49 74 11 0 0 7 16 13
8 70 15 3 2 21 26 25
47 70 15 8 16 15 35 24
6 61 11 5 4 7 15 14
14 54 12 1 12 13 27 21
30 55 13 2 1 12 20 17
4 54 10 3 12 20 26 22
24 40 14 0 2 5 14 8
19 66 13 7 12 21 35 27
45 54 10 0 6 6 14 16
22 64 14 12 8 19 27 26
16 47 16 3 9 15 18 10
32 48 16 0 7 9 14 18
37 52 14 4 6 20 26 26
47 74 19 4 9 14 23 23
5 57 12 0 2 4 11 8
6 57 10 0 1 16 15 17
60 80 11 3 8 18 28 21
58 78 13 1 18 19 34 23
6 70 16 2 11 9 23 11
16 47 14 0 10 7 12 8
45 94 19 8 10 28 32 32
9 63 11 2 12 5 25 14
69 76 16 7 11 18 29 21
35 59 11 2 5 10 23 24
19 55 8 0 1 14 19 12
58 74 14 1 0 10 18 18
58 71 17 6 4 23 31 26
79 54 14 0 6 6 15 14
;
proc reg;
model apt ppvt rpmt = n s ns na ss;
mtest;
run;
-----------------------------------------------------------------------------
Model: MODEL1
Dependent Variable: APT
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 5 3653.77324 730.75465 1.626 0.1824
Error 31 13929.52406 449.33949
C Total 36 17583.29730
Root MSE 21.19763 R-square 0.2078
Dep Mean 31.27027 Adj R-sq 0.0800
C.V. 67.78844
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 4.151060 13.79833728 0.301 0.7655
N 1 -0.608872 1.67108493 -0.364 0.7181
S 1 -0.050156 0.94150677 -0.053 0.9579
NS 1 -1.732395 0.91046153 -1.903 0.0664
NA 1 0.494565 1.03689999 0.477 0.6367
SS 1 2.247721 1.10096010 2.042 0.0498
-----------------------------------------------------------------------------
Dependent Variable: PPVT
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 5 2883.67590 576.73518 6.467 0.0003
Error 31 2764.75653 89.18569
C Total 36 5648.43243
Root MSE 9.44382 R-square 0.5105
Dep Mean 62.64865 Adj R-sq 0.4316
C.V. 15.07426
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 33.005769 6.14733759 5.369 0.0001
N 1 -0.080567 0.74448994 -0.108 0.9145
S 1 -0.721050 0.41945344 -1.719 0.0956
NS 1 -0.298303 0.40562238 -0.735 0.4676
NA 1 1.470418 0.46195235 3.183 0.0033
SS 1 0.323965 0.49049195 0.660 0.5138
-----------------------------------------------------------------------------
Dependent Variable: RPMT
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 5 76.52860 15.30572 1.769 0.1486
Error 31 268.28221 8.65426
C Total 36 344.81081
Root MSE 2.94181 R-square 0.2219
Dep Mean 13.24324 Adj R-sq 0.0965
C.V. 22.21369
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 11.173378 1.91493727 5.835 0.0001
N 1 0.210995 0.23191365 0.910 0.3699
S 1 0.064567 0.13066258 0.494 0.6247
NS 1 0.213584 0.12635412 1.690 0.1010
NA 1 -0.037318 0.14390128 -0.259 0.7971
SS 1 -0.052143 0.15279156 -0.341 0.7352
-----------------------------------------------------------------------------
Multivariate Test:
Multivariate Statistics and F Approximations
S=3 M=0.5 N=13.5
Statistic Value F Num DF Den DF Pr > F
Wilks' Lambda 0.34316907 2.5381 15 80.45763 0.0039
Pillai's Trace 0.82528864 2.3529 15 93 0.0066
Hotelling-Lawley Trace 1.44875712 2.6722 15 83 0.0023
Roy's Greatest Root 1.05511542 6.5417 5 31 0.0003
NOTE: F Statistic for Roy's Greatest Root is an upper bound.