Consider a dummy-variable regression model for the annual salary of school teachers in three different counties in southern California: Orange county (OC), LA county (LAC), and San Diego county (SDC). Let annual salaries of school teachers in these counties depend on years of experience and years of education.

Assume that Y_i is annual salary, X_i is years of years of experience, and Z is the years of higher education, D_1i = 1 for LAC and D_1i=0 for SDC and OC, while D_2i=1 for SDC and D_2i=0 for LAC and OC.

Y_i = b₁ + b₂X_i + b₃Z_i + b₄D_1i + b₅D_2i +e_i

Assume that school teachers in SDC have the highest salary while teacher in OC have the second highest and teachers in LAC have the lowest salary when years of experience and years of higher education are zero.

Question: Extend the above model so that you can investigate whether school teachers in other counties can catch up school teachers in SDC with the increase in years of experience and years of education. Please show work.