Consider the following model: Y i = 1 + 2 D i + u i Where D i = 0 for the first

Consider the following model:

Y_i = β₁ + β₂D_i + u_i

Where

D_i = 0 for the first 20 observations and D_i = 1 for the remaining 30 observations. You are also told that var (u²_i) = 300.

a. How would you interpret β₁ and β₂?

b. What are the mean values of the two groups?

c. How would you compute the variance of (β̂₁ + β̂₂)? You are given that the cov (β̂₁, β̂₂) = −15.