(Deviations from Averages) Let X be full-column rank and x = 1 for all n. (a) Show that the OLS fit of y

(Deviations from Averages) Let X be full-column rank and xₙₖ = 1 for all n.

(a) Show that the OLS fit of yₙ − ȳ on xₙₖ − x̄ₖ (k = 1, …, K − 1) gives the same fitted coefficients for these explanatory variables as the OLS fit of yₙ on xₙₖ (k = 1, …, K) gives for coefficients β̂ₖ (k = 1, …, K − 1).

(b) Given the β̂ₖ (k

X-1