For all students at Walden University, the prediction equation for y = college GPA

QUESTION:

For all students at Walden University, the prediction equation for y = college GPA (range 0–4.0) and x1 = high school GPA (range 0–4.0) and x2 = college board score (range 200–800) is ŷ = 0.20 + 0.50x1 + 0.002x2.

(a) Find the predicted college GPA for students having (i) high school GPA = 4.0 and college board score = 800 and (ii) x1 = 2.0 and x2 = 200.

(b) For those students with x2 = 500, show that ŷ = 1.20 + 0.50x1.

(c) For those students with x2 = 600, show that ŷ = 1.40 + 0.50x1. Thus, compared to part b, the slope for x1 is still 0.50, and increasing x2 by 100 (from 500 to 600) shifts the intercept upward by 100  (slope for x2) = 100(0.002) = 0.20 units.


ANSWER:

(a) (i)  ŷ = 0.20 + 0.50 x1 + 0.002 x2  = 0.20 + 0.50(4.0) + 0.002(800) = 3.80

(ii) ŷ = 0.20 + 0.50 x1 + 0.002 x2 = 0.20 + 0.50(2.0) + 0.002(200) = 1.60

(b) ŷ = 0.20 + 0.50 x1 + 0.002(500) = 0.20 + 0.50 x1 + 1 = 1.20 + 0.50 x1

(c) ŷ = 0.20 + 0.50 x1 + 0.002(600) = 0.20 + 0.50 x1 + 1.2 = 1.40 + 0.50 x1

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