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Example of Regression Analysis with Quadratic Terms and Corresponding
Joint Significance Tests
SYSTAT commands:
use asa9103
select v3$<>'GBON', v3$<>'PKST'
model u20smp=constant+sec70+natincr+sdug+v285+lv119d+lv119d*lv119d,
+pdem65d+pdem65d*pdem65d
estimate
hypothesis
effect=lv119d & lv119d*lv119d
test
hypothesis
effect=pdem65d & pdem65d*pdem65d
test
Regression output:
97 CASES DELETED DUE TO MISSING DATA.
DEP VAR: U20SMP N: 56 MULTIPLE R: 0.904 SQUARED MULTIPLE R: 0.818
ADJUSTED SQUARED MULTIPLE R: .787 STANDARD ERROR OF ESTIMATE: 3.783
VARIABLE COEFFICIENT STD ERROR STD COEF TOLERANCE T P(2 TAIL)
CONSTANT 55.667 4.493 0.000 . 12.390 0.000
SEC70 -0.120 0.054 -0.393 0.124 -2.219 0.031
NATINCR 0.454 0.106 0.553 0.232 4.276 0.000
SDUG 0.419 0.112 0.774 0.090 3.729 0.001
V285 -0.377 0.109 -1.185 0.033 -3.450 0.001
LV119D -3.888 2.888 -0.298 0.079 -1.346 0.185
LV119D
*LV119D -0.855 1.709 -0.038 0.658 -0.500 0.619
PDEM65D -0.035 0.043 -0.112 0.207 -0.816 0.419
PDEM65D
*PDEM65D -0.002 0.001 -0.173 0.352 -1.649 0.106
ANALYSIS OF VARIANCE
SOURCE SUM-OF-SQUARES DF MEAN-SQUARE F-RATIO P
REGRESSION 3018.653 8 377.332 26.373 0.000
RESIDUAL 672.463 47 14.308
TEST FOR EFFECT CALLED: LV119D
AND
TEST FOR EFFECT CALLED: LV119D*LV119D
A MATRIX
1 2 3 4 5
1 0.000 0.000 0.000 0.000 0.000
2 0.000 0.000 0.000 0.000 0.000
6 7 8 9
1 1.000 0.000 0.000 0.000
2 0.000 1.000 0.000 0.000
TEST OF HYPOTHESIS
SOURCE SS DF MS F P
HYPOTHESIS 40.886 2 20.443 1.429 0.250
ERROR 672.463 47 14.308
TEST FOR EFFECT CALLED: PDEM65D
AND
TEST FOR EFFECT CALLED: PDEM65D*PDEM65D
A MATRIX
1 2 3 4 5
1 0.000 0.000 0.000 0.000 0.000
2 0.000 0.000 0.000 0.000 0.000
6 7 8 9
1 0.000 0.000 1.000 0.000
2 0.000 0.000 0.000 1.000
TEST OF HYPOTHESIS
SOURCE SS DF MS F P
HYPOTHESIS 46.939 2 23.470 1.640 0.205
ERROR 672.463 47 14.308
Last modified 15 February 1999