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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