2. For students at Walden University, the relationship between college GPA (with range 040) and X1 high school GPA (range 0-4.0) and X2 = college board score (range 200-800) satisfies E(Y) = .20+.50%, + 002X2.

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

b) Show that the relationship between Y and X, for those students with X2 = 500 is = E(Y) 1.25x1.

c) Show that when X = 600. E(Y) = 1.4+,5X. Thus, increasing X by 100 slufts the line elating Y to X1 upward by 1002.2 units.

d) Show that setting X at a variety of values yields a collection of parallel lines, each having slope .002. relating the mean of Y to X2.

e) Since B = 50 is larger than f=002, docs this imply that X, has the greater partial eflect on Y? Explain.

Transcribed Image Text:

50+ 1 Partial Regression Residual Plot -+------+------+------+------+--- 20 + ++ 1 1 40+ 1 30+ 1 11 1 1 1 1 1 1 1 2 CRIME 1 2 10 + 1 1 1 1 1 1 1 1 0 T 1 1 1 1 1 1 1 1 -10+ 12 1 1 11 11 1 1 1 1 11 1 1 1 1 1 2 -20+ 2 1 1 -30+ 1 1 1 -40+ -6 -4 -2 0 2 4 Figure 11.13 INCOME 6 8 10