# Interpretation regression coefficients predictors and dummy variables

I have to run a regression predicting the DV (continuous) from an equation with: Y = X1(dichotomous factor, coded 0-1)+X2(dichotomous factor, coded 0-1)+X1X2+M1+M2+M3+...+Mn, where M1...Mn - continuous predictors

My question is: Given that I have two dichotomous variables in the equation, how do I interpret the value of the regression coefficients of the other predictors in the equation? I found different resources suggesting that the other predictors' coefficients should be interpreted as the value of that predictor when all other terms and predictors in the equation are held constant. For me this suggests two things: 1.) They represent the value of M1...Mn when X1=X2=0 or 2.) They represent the value of M1...Mn when X1=X2=mean (?). I'd appreciate it when someone could suggest an interpretation for these terms!

• Please, next time use $\TeX$ – stochazesthai Mar 4 '15 at 6:55

## 1 Answer

In a regression setting like the one you have presented, the value of an estimated coefficient indicates the effect on the dependent variable of a unit increases of the predictor associated with the coefficient, keeping all the others predictors fixed. Thus, in the interpretation you are focusing on the marginal effect (your estimated coefficient) of one predictor on the dependent variable, and the values assumed by the others estimated coefficients or predictors do not affect your interpretation.