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
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.

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.