Re: interpreting significant interactions in Multiple Regression

The following data came from a slightly
distorted 2-level factorial design. The fact
that the variables V1 and V2 are somewhat
correlated doesn't change the lesson to be
learned from this.

In the following I set the centering constant
for V2 to -24. The centering constant for
V1 has been set to -5, -6, -7, and -8.

Notice that the t-ratio for V2 varies with the
centering constant for V1.

Yes, if all terms are included in the model
then the predicted values are the same
no matter what centering constants are
used. But if the choice of constant (using
no centering constant at all is the same
as using zero) then the t-ratio for V2 may
be so low as to cause us to eliminate
that term from the model. In which case
the game changes dramatically.


Example of the effects of centering constants
//
V1, V2, Prod
//
V1 = V1 - 5 <--- centering constant
V2 = V2 - 24 <--- centering constant
V12 = V1*V2 <--- interaction
//
V1, Var1
V2, Var2
V12, V1V2
Prod, Production Rate as K-lbs
//
5 18 188
12 20 218
6 28 180
10 29 228
4 22 173
10 22 212
6 32 167
9 33 223

NOTE: There are 8 rows of data.

Centering constants are -5, -24
VARIABLES COEFFICIENTS SE OF COEFF T-RATIO
0 Intercept 173.94
1 Var1 8.70013 0.38242 22.75
2 Var2 -2.53918 0.29317 8.66 <---
3 V1V2 0.98692 0.08617 11.45
RESSUMSQ STDDEV OF RES DF R-SQ
30.34294 2.75422 4 0.9926

Centering constants are -6, -24
VARIABLES COEFFICIENTS SE OF COEFF T-RATIO
0 Intercept 182.64
1 Var1 8.70013 0.38242 22.75
2 Var2 -1.55226 0.23202 6.69 <---
3 V1V2 0.98692 0.08617 11.45
RESSUMSQ STDDEV OF RES DF R-SQ
30.34205 2.75418 4 0.9926

Centering constants are -7, -24
VARIABLES COEFFICIENTS SE OF COEFF T-RATIO
0 Intercept 191.34
1 Var1 8.70013 0.38242 22.75
2 Var2 -0.56534 0.19123 2.96 <---
3 V1V2 0.98692 0.08617 11.45
RESSUMSQ STDDEV OF RES DF R-SQ
30.34205 2.75418 4 0.9926

Centering constants are -8, -24
VARIABLES COEFFICIENTS SE OF COEFF T-RATIO
0 Intercept 200.04
1 Var1 8.70013 0.38241 22.75
2 Var2 0.42158 0.18481 2.28 <---
3 V1V2 0.98692 0.08617 11.45
RESSUMSQ STDDEV OF RES DF R-SQ
30.34175 2.75417 4 0.9926

.

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