# Total effect of X on Y under presence of interaction effects

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## Total effect of X on Y under presence of interaction effects

 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         [[alternative HTML version deleted]] ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: Total effect of X on Y under presence of interaction effects

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## Re: Total effect of X on Y under presence of interaction effects

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## Re: Total effect of X on Y under presence of interaction effects

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