Interpreting dummy variable interaction terms

Question

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

When adding these interaction terms to the regression, I omitted one dummy variable interaction term (Jan_dum_temp) to avoid the dummy variable trap.

The resulting model is:

y(hat) = b1 + b2Feb_dum_temp + ... + b12Dec_dum_temp + other explanatory variables

How do I estimate/interpret the effects of January's seasonality and temperature (Jan_dum_temp)?

Answer 1

It is generally inappropriate to leave out the components of an interaction term in a regression.

At the very least you should include a plain "temperature" term in your model. Whichever dummy variable you leave out is your reference category. So b2 should be the effect of temperature in February relative to January. But without the uninteracted temperature term, your model does not allow temperature to have any effect in January.