Question

A multiple regression equation to predict a student's score in College Algebra (\hat{y}) based on their high school GPA (x_{1}), their high school Alg

Upper level algebra
ANSWERED
asked 2021-01-27
A multiple regression equation to predict a student's score in College Algebra \(\displaystyle{\left(\hat{{{y}}}\right)}\) based on their high school GPA \(\displaystyle{\left({x}_{{{1}}}\right)}\), their high school Algebra II grade \(\displaystyle{\left({x}_{{{2}}}\right)}\), and their placement test score \(\displaystyle{\left({x}_{{{3}}}\right)}\) is given by the equation below.
\(\displaystyle\hat{{{y}}}=-{9}+{5}{x}_{{{1}}}+{6}{x}_{{{2}}}+{0.3}{x}_{{{3}}}\)
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)

2021-01-28
Step 1
Given,
A multiple regression equation to predict a student's score in College Algebra \(\displaystyle{\left(\hat{{{y}}}\right)}\) based on their high school GPA \(\displaystyle{\left({x}_{{{1}}}\right)}\), their high school Algebra II grade \(\displaystyle{\left({x}_{{{2}}}\right)}\), and their placement test score \(\displaystyle{\left({x}_{{{3}}}\right)}\) is given by the equation below.
\(\displaystyle\hat{{{y}}}=-{9}+{5}{x}_{{{1}}}+{6}{x}_{{{2}}}+{0.3}{x}_{{{3}}}\)
Step 2
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:
\(\displaystyle\hat{{{y}}}=-{9}+{5}{x}_{{{1}}}+{6}{x}_{{{2}}}+{0.3}{x}_{{{3}}}\)
\(\displaystyle{67}=-{9}+{5}{\left({3.9}\right)}+{6}{\left({2}\right)}+{0.3}{x}_{{{3}}}\)
\(\displaystyle{67}={22.5}+{0.3}{x}_{{{3}}}\)
\(\displaystyle{44.5}={0.3}{x}_{{{3}}}\)
\(\displaystyle{x}_{{{3}}}={\frac{{{44.5}}}{{{0.3}}}}={148.3}\)
The student's placement test score need to be 148.3.
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