Linear regression with product of factor and independent variable

Question

I am try to estimate a demand model:

d_t^k = a_t - b^k p_t^k + e_t^k

The indices t are for week number, k are for pro

Answer 1

After doing some experimentation, it seems that

lm(demand ~ factor(week) + factor(product) * price, data = df)

does work.

I don't know why I hadn't thought it would work earlier.