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]]
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