I would like to know how to interpret the coefficient on an interaction term as a percentage change when the dependent variable is logged. I provide an example below using the
mtcars data set in
am is binary and
wt is continuous.
$\ln(mpg)= \beta_0 + \beta_1\cdot wt + \beta_2\cdot am + \beta_3\cdot wt\cdot am$
In this case, I would interpret the main effect on
am to mean that when
mpg increases by 47.7% when
am moves from 0 to 1, where
47.7 = exp(0.38981)-1)*100.
I would like to know if coefficient on the interaction can also be interpreted as a percentage change. For example, exponentiating the coefficient for the interaction yields
(exp(-0.15391)-1)*100 = -14.3%. My interpretation is that for a one unit increase in
mpg decreases by 14.3% more for
I've already plotted the interaction effects, but because the y-scale is in logged mpg the substantive interpretation isn't obvious even though the plot illustrates the interaction quite clearly.
data(mtcars) summary(mtcars[,c("mpg", "wt", "am")]) m1 <- lm(log(mpg) ~ wt + am + wt*am, data=mtcars) summary(m1) Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 3.72680 0.15145 24.607 < 2e-16 *** wt -0.24148 0.03940 -6.129 1.29e-06 *** am 0.38981 0.21383 1.823 0.0790 . wt:am -0.15391 0.07245 -2.124 0.0426 *