# 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 x_{1} = high school GPA (range 0–4.0) and x_{2} = college board score (range 200–800) is ŷ = 0.20 + 0.50x_{1} + 0.002x_{2}.

(a) Find the predicted college GPA for students having (i) high school GPA = 4.0 and college board score = 800 and (ii) x_{1} = 2.0 and x_{2} = 200.

(b) For those students with x_{2} = 500, show that ŷ = 1.20 + 0.50x_{1}.

(c) For those students with x_{2} = 600, show that ŷ = 1.40 + 0.50x_{1}. Thus, compared to part b, the slope for x_{1} is still 0.50, and increasing x_{2} by 100 (from 500 to 600) shifts the intercept upward by 100 (slope for x_{2}) = 100(0.002) = 0.20 units.

__ANSWER:__

(a) (i) ŷ = 0.20 + 0.50 x_{1} + 0.002 x_{2} = 0.20 + 0.50(4.0) + 0.002(800) = 3.80

(ii) ŷ = 0.20 + 0.50 x_{1} + 0.002 x_{2} = 0.20 + 0.50(2.0) + 0.002(200) = 1.60

(b) ŷ = 0.20 + 0.50 x_{1} + 0.002(500) = 0.20 + 0.50 x_{1} + 1 = 1.20 + 0.50 x_{1 }

(c) ŷ = 0.20 + 0.50 x_{1} + 0.002(600) = 0.20 + 0.50 x_{1} + 1.2 = 1.40 + 0.50 x_{1}

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