Output for Centering Example
Gerard E. Dallal, Ph.D.
Independent Variables: X1
DEP VAR: Y N: 5 MULTIPLE R: 0.822 SQUARED MULTIPLE R: 0.676
ADJUSTED SQUARED MULTIPLE R: .568 STANDARD ERROR OF ESTIMATE: 3.795
VARIABLE COEFFICIENT STD ERROR STD COEF TOLERANCE T P(2 TAIL)
CONSTANT 20.400 3.980 0.000 . 5.126 0.014
X1 -3.000 1.200 -0.822 1.000 -2.500 0.088
ANALYSIS OF VARIANCE
SOURCE SUM-OF-SQUARES DF MEAN-SQUARE F-RATIO P
REGRESSION 90.000 1 90.000 6.250 0.088
RESIDUAL 43.200 3 14.400
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Independent Variables: Z1
DEP VAR: Y N: 5 MULTIPLE R: 0.822 SQUARED MULTIPLE R: 0.676
ADJUSTED SQUARED MULTIPLE R: .568 STANDARD ERROR OF ESTIMATE: 3.795
VARIABLE COEFFICIENT STD ERROR STD COEF TOLERANCE T P(2 TAIL)
CONSTANT 11.400 1.697 0.000 . 6.718 0.007
Z1 -3.000 1.200 -0.822 1.000 -2.500 0.088
ANALYSIS OF VARIANCE
SOURCE SUM-OF-SQUARES DF MEAN-SQUARE F-RATIO P
REGRESSION 90.000 1 90.000 6.250 0.088
RESIDUAL 43.200 3 14.400
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Independent Variables: X2
DEP VAR: Y N: 5 MULTIPLE R: 0.753 SQUARED MULTIPLE R: 0.567
ADJUSTED SQUARED MULTIPLE R: .422 STANDARD ERROR OF ESTIMATE: 4.387
VARIABLE COEFFICIENT STD ERROR STD COEF TOLERANCE T P(2 TAIL)
CONSTANT 16.341 3.174 0.000 . 5.148 0.014
X2 -0.449 0.227 -0.753 1.000 -1.980 0.142
ANALYSIS OF VARIANCE
SOURCE SUM-OF-SQUARES DF MEAN-SQUARE F-RATIO P
REGRESSION 75.465 1 75.465 3.921 0.142
RESIDUAL 57.735 3 19.245
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Independent Variables: Z2
DEP VAR: Y N: 5 MULTIPLE R: 0.278 SQUARED MULTIPLE R: 0.077
ADJUSTED SQUARED MULTIPLE R: .000 STANDARD ERROR OF ESTIMATE: 6.401
VARIABLE COEFFICIENT STD ERROR STD COEF TOLERANCE T P(2 TAIL)
CONSTANT 9.686 4.461 0.000 . 2.171 0.118
Z2 0.857 1.711 0.278 1.000 0.501 0.651
ANALYSIS OF VARIANCE
SOURCE SUM-OF-SQUARES DF MEAN-SQUARE F-RATIO P
REGRESSION 10.286 1 10.286 0.251 0.651
RESIDUAL 122.914 3 40.971
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Independent Variables: X1, X2
DEP VAR: Y N: 5 MULTIPLE R: 0.868 SQUARED MULTIPLE R: 0.753
ADJUSTED SQUARED MULTIPLE R: .506 STANDARD ERROR OF ESTIMATE: 4.057
VARIABLE COEFFICIENT STD ERROR STD COEF TOLERANCE T P(2 TAIL)
CONSTANT 26.400 8.701 0.000 . 3.034 0.094
X1 -8.143 6.631 -2.231 0.037 -1.228 0.344
X2 0.857 1.084 1.436 0.037 0.791 0.512
ANALYSIS OF VARIANCE
SOURCE SUM-OF-SQUARES DF MEAN-SQUARE F-RATIO P
REGRESSION 100.286 2 50.143 3.047 0.247
RESIDUAL 32.914 2 16.457
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Independent Variables: Z1, Z2
DEP VAR: Y N: 5 MULTIPLE R: 0.868 SQUARED MULTIPLE R: 0.753
ADJUSTED SQUARED MULTIPLE R: .506 STANDARD ERROR OF ESTIMATE: 4.057
VARIABLE COEFFICIENT STD ERROR STD COEF TOLERANCE T P(2 TAIL)
CONSTANT 9.686 2.827 0.000 . 3.426 0.076
Z1 -3.000 1.283 -0.822 1.000 -2.339 0.144
Z2 0.857 1.084 0.278 1.000 0.791 0.512
ANALYSIS OF VARIANCE
SOURCE SUM-OF-SQUARES DF MEAN-SQUARE F-RATIO P
REGRESSION 100.286 2 50.143 3.047 0.247
RESIDUAL 32.914 2 16.457
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