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