1. Consider the regression of perceptions of hospital care quality (Y) on age (X1) and geographical region, where the latter is a qualitative variable with four classes (N, S, E, W).

Define indicator variables as follows: X2 = 1 if region is S, 0 otherwise; X3 = 1 region is E, 0 otherwise; X4 = 1 regions is W, 0 otherwise. Assume the first-order response model

E(Y) = ?+ ?₁ X1 + ? ₂ X2 + ? ₃ X3 + ? ₄ X4

is appropriate

On the axis below, draw response functions for the four geographical regions that are consistent with all of the following statements and the assumed first-order model.

Take care to label each of your lines with parameter values (slope and intercept).

(i.) For a fixed age, being in the South increases the expected quality perceptions as compared to being in the North.

(ii.) For a fixed age, expected quality perception is the same for Eastern and Western regions, but both have lower expected quality perceptions than the Northern region.

(iii.) Regardless of region, average quality perception decreases with age.