Answer

Solved Step By Step with Explanation - Alpha hat equals alpha

Taking the derivative of SSR(α) with respect to α and setting it to zero, we can find the value of α that minimizes SSR(α):

d(SSR(α))/dα = -2Σ(yi - α) = 0

Therefore, the estimated value of α, denoted as α^, is:

α^ = (1/n)Σyi

(1/n)Σyi = (1/n)Σ(α^ + εi)

Since (1/n)Σyi is equal to α^, we can rewrite the equation as:

Therefore, we can conclude that α^ = α if the assumption that the average error is zero is satisfied.