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)?