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

Haven 2021-03-07 Answered

A multiple regression equation to predict a student's score in College Algebra (y^) based on their high school GPA (x1x1), their high school Algebra II grade (x2x2), and their placement test score (x3x3) is given by the equation below.
y^=9+5x1x1+6x2x2+0.3x3x3
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.

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Expert Answer

firmablogF
Answered 2021-03-08 Author has 92 answers

Step 1
Given,
A multiple regression equation to predict a student's score in College Algebra (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.
y^=9+5x1+6x2+0.3x3
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:
y^=9+5x1+6x2+0.3x3
=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:
y^=9+5x1+6x2+0.3x3
67=9+5(3.9)+6(2)+0.3x3
67=22.5+0.3x3
44.5=0.3x3
x3=44.50.3=148.3
The student's placement test score need to be 148.3

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Jeffrey Jordon
Answered 2021-11-17 Author has 2047 answers

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