[R] Total effect of X on Y under presence of interaction effects

From: Michael Haenlein <haenlein_at_escpeurope.eu>
Date: Wed, 11 May 2011 10:26:07 +0200


Dear all,

this is probably more a statistics question than an R question but probably there is somebody who can help me nevertheless.

I'm running a regression with four predictors (a, b, c, d) and all their interaction effects using lm. Based on theory I assume that a influences y positively. In my output (see below) I see, however, a negative regression coefficient for a. But several of the interaction effects of a with b, c and d have positive signs. I don't really understand this. Do I have to add up the coefficient for the main effect and the ones of all interaction effects to get a total effect of a on y? Or am I doing something wrong here?

Thanks very much for your answer in advance,

Regards,

Michael

Michael Haenlein
Associate Professor of Marketing
ESCP Europe
Paris, France

Call:
lm(formula = y ~ a * b * c * d)

Residuals:

    Min 1Q Median 3Q Max
-44.919 -5.184 0.294 5.232 115.984

Coefficients:

            Estimate Std. Error t value Pr(>|t|)
(Intercept)  27.3067     0.8181  33.379  < 2e-16 ***
a           -11.0524     2.0602  -5.365 8.25e-08 ***
b            -2.5950     0.4287  -6.053 1.47e-09 ***
c           -22.0025     2.8833  -7.631 2.50e-14 ***
d            20.5037     0.3189  64.292  < 2e-16 ***
a:b          15.1411     1.1862  12.764  < 2e-16 ***
a:c          26.8415     7.2484   3.703 0.000214 ***
b:c           8.3127     1.5080   5.512 3.61e-08 ***
a:d           6.6221     0.8061   8.215 2.33e-16 ***
b:d          -2.0449     0.1629 -12.550  < 2e-16 ***
c:d          10.0454     1.1506   8.731  < 2e-16 ***
a:b:c         1.4137     4.1579   0.340 0.733862
a:b:d        -6.1547     0.4572 -13.463  < 2e-16 ***
a:c:d       -20.6848     2.8832  -7.174 7.69e-13 ***
b:c:d        -3.4864     0.6041  -5.772 8.05e-09 ***
a:b:c:d       5.6184     1.6539   3.397 0.000683 ***

---

Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1

Residual standard error: 7.913 on 12272 degrees of freedom Multiple R-squared: 0.8845, Adjusted R-squared: 0.8844 F-statistic: 6267 on 15 and 12272 DF, p-value: < 2.2e-16

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