For students at Walden University, the relationship between y = college GPA (with range 0–4.0) and x1 =

high school GPA (range 0–4.0) and x2 = verbal college board score (range 200–800) satisfies E(y) = 0.20 +

0.50x1 + 0.002x2.

(a) Find the mean college GPA for students having (i)

high school GPA = 4.0 and college board score = 800,

(ii) x1 = 3.0 and x2 = 300.

(b) Show that the relationship between y and x1 for those students with x2 = 500 is E(y) = 1.2 + 0.5x1.

(c) Show that when x2 = 600, E(y) = 1.4 + 0.5x1. Thus, increasing x2 by 100 shifts the line relating y to x1 upward by 100β2 = 0.2 units.

(d) Show that setting x1 at a variety of values yields a collection of parallel lines, each having slope 0.002, relating the mean of y to x2.