In the following regression model: Y i = 1 + 2 D i + u i Y represents hourly wage in dollars and

In the following regression model:

Y_i = β₁ + β₂D_i + u_i

Y represents hourly wage in dollars and D is the dummy variable, taking a value of 1 for a college graduate and a value of 0 for a high-school graduate. Using the OLS formulas given in Chapter 3, show that β̂₁ = Y̅_hg and β̂₂ = Y̅_cg – Y̅_hg, where the subscripts have the following meanings: hg = high-school graduate, cg = college graduate. In all, there are n1 high-school graduates and n₂ college graduates, for a total sample of n = n₁ + n₂.