# 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 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. 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