# Interactions terms and the dummy variables

I am attempting to model monthly retail electricity sales. To account for both the effects of seasonality and weather, I created an interaction term by multiplying 12 monthly dummy variables by the corresponding month's max temperature, such that:

Jan_dum_temp = Jan_dum * Jan_max_temp,
Feb_dum_temp = Feb_dum * Feb_max_temp,
.
.
.
Dec_dum_temp = Dec_dum * Dec_max_temp


The resulting model will be:

y(hat) = b1 + b2Jan_dum_temp + b3Feb_dum_temp + ... + b13Dec_dum_temp +
other explanatory variables


When adding these interaction terms to the regression, should I leave one interaction term out to avoid the dummy variable trap? If possible, please provide a source for your answer.

• What do you think? Does your regression allow a constant? If so, what might it mean? – Henry May 23 at 14:38
• Yes, there is a constant within my model. I do not think I should exclude one of the 12 monthly interaction terms because I have not run into the problem of perfect multicollinearity, especially after reviewing the table of 'Correlations of Parameter Estimates'. – Darlene May 23 at 14:54
• Yes, leave it out (or else your solver will semi-randomly omit one of the months). Think about the interprettaion of Feb_dum_temp: it is a difference in effect of temperature from February to January. – AdamO May 23 at 14:58
• My solver has not omitted one of the interaction terms when running the regression. However, when I manually omit the Jan_dum_temp interaction term and only include the following 11 monthly interaction terms, is the constant interpreted as the effect of January's interaction term? – Darlene May 23 at 15:06
• Or maybe better asked, when omitting January's interaction term, how do I interpret the effects of January's seasonality and weather? – Darlene May 23 at 15:16