Question

A multiple regression equation to predict a student's score in College Algebra (hat{y}) based on their high school GPA

Upper level algebra
ANSWERED
asked 2021-03-07

A multiple regression equation to predict a student's score in College Algebra \((\hat{y})\) based on their high school GPA (\(x_1x_1\)), their high school Algebra II grade (\(x_2x_2\)), and their placement test score (\(x_3x_3\)) is given by the equation below.
\(\hat{y}=-9+5x_1x_1+6x_2x_2+0.3x_3x_3\)
a) According to this equation, what is the predicted value of the student's College Algebra score if their high school GPA was a 3.9, their high school Algebra II grade was a 2 and their placement test score was a 40? Round to 1 decimal place.
b) According to this equation, what does the student's placement test score need to be if their high school GPA was a 3.9, their high school Algebra II grade was a 2, and their predicted College Algebra score was a 67? Round to 1 decimal place.

Answers (1)

2021-03-08
Step 1
Given,
A multiple regression equation to predict a student's score in College Algebra \((\hat{y})\) based on their high school GPA (x1), their high school Algebra II grade (x2), and their placement test score (x3) is given by the equation below.
\(\hat{y}=-9+5x_{1}+6x_{2}+0.3x_{3}\)
Step 2
a)
The predicted value of the student's College Algebra score if their high school GPA was a 3.9, their high school Algebra II grade was a 2 and their placement test score was a 40 is calculated as follows:
\(\hat{y}=-9+5x_{1}+6x_{2}+0.3x_{3}\)
\(=-9+5(3.9)+6(2)+0.3(40)\)
\(=-9+43.5=34.5\)
The predicted value of the student's College Algebra score is 34.5.
b)
The student's placement test score need to be if their high school GPA was a 3.9, their high school Algebra II grade was a 2, and their predicted College Algebra score was a 67 is calculated as follows:
\(\hat{y}=-9+5x_{1}+6x_{2}+0.3x_{3}\)
\(67=-9+5(3.9)+6(2)+0.3x_{3}\)
\(67=22.5+0.3x_{3}\)
\(44.5=0.3x_{3}\)
\(x_{3}=\frac{44.5}{0.3}=148.3\)
The student's placement test score need to be 148.3
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