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

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