11.1. For students at Waiden University, the relationship between y = college CPA (with range 0-4.0)

and xi - high school CPA (range 0-4.0) and X2 = college board score (range 200-800) satisfies E(y) = 0.20 + O.SO.ri + 0.002x2.

(a) Find the mean college GPA for students having (i) high school GPA = 4.0 and college board score = 800, (ii)xi = 3.0 and X2 = 300.

(b) Show that the relationship between y and xj for those students with X2 = 500 is E(y) = 1.2 + 0.5xi.

(c) Show that when X2 = 600, E(y) = 1.4 +

0.5x|. Thus, increasingX2 by 100 shifts the line relating y to xi upward by 100/32 =

0.2 units.

(d) Show thatscttingxi at a variety ofvaluesyields a collection of parallel lines, each having slope 0.002, relating the mean ofy to X2.