Given the regression of advertising expenditures (y) on, type of firm (incorporated, not incorporated). Define

x1= 1 if firm incorporated

x1 = 0 otherwise

The first-order regression model then would be:

yi =0+1xi1+i

1. Obtain (X^T)( X) matrix for this special case of a single qualitative predictor variable, for i = 1, . . . , n when n1 firms are not incorporated, and n2 firms are incorporated (n1 + n2 = n).
2. Find (X^T)( X)1 and b.