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The admissions officer for Clearwater College developed the following estimated regression equation relating the final college GPA to the student’s SAT mathematics score and highschool GPA. ŷ = −1.41 + .0235 x 1 + .00486 x 2 where x 1 = high-school grade point average x 2 = SAT mathematics score y = final college grade point average a. Interpret the coefficients in this estimated regression equation. b. Predict the final college GPA for a student who has a high-school average of 84 and a score of 540 on the SAT mathematics test.

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Essentials Of Statistics For Busin...

9th Edition
David R. Anderson + 4 others
Publisher: South-Western College Pub
ISBN: 9780357045435

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Chapter
Section
BuyFindarrow_forward

Essentials Of Statistics For Busin...

9th Edition
David R. Anderson + 4 others
Publisher: South-Western College Pub
ISBN: 9780357045435
Chapter 15, Problem 49SE
Textbook Problem
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The admissions officer for Clearwater College developed the following estimated regression equation relating the final college GPA to the student’s SAT mathematics score and highschool GPA.

ŷ = −1.41 + .0235x1 + .00486x2

where

x1 = high-school grade point average

x2 = SAT mathematics score

y = final college grade point average

  1. a. Interpret the coefficients in this estimated regression equation.
  2. b. Predict the final college GPA for a student who has a high-school average of 84 and a score of 540 on the SAT mathematics test.

a.

To determine

Interpret the coefficients in the estimated regression equation.

Explanation of Solution

Calculation:

The estimated regression equation relating the final GPA to the student’s SAT mathematics score and high school is GPA is y^=1.41+0.0235x1+0.00486x2, where x1 denotes the high school grade point average, x2 denotes the SAT mathematics score and y denotes the final college grade point average.

Multiple linear regression model:

A multiple linear regression model is given as y^=b0+b1x1+...+bpxp where y^ is the predicted value of response or dependent variable, and x1,x2,...,xp are the k predictor variables. The quantities b1,b2,...,bp are the estimated slopes corresponding to x1,x2,...,xp respectively and b0 is the estimated intercept of the line, from the sample data.

Slope in a multiple regression equation:

The slope bi in a multiple regression equation is the amount of change in the response variable, y^, due to unit increase in the corresponding predictor variable, xi.

The ‘Coefficient’ column of the regression analysis output gives the slopes corresponding to the respective variables stored in the column ‘Variable’.

The coefficient or slope of x1 in the regression model is b1=0.0235.

The interpretation of the coefficient b1 in the regression model is that the value of final college grade point average (y)increases by 0.0235unit for one unit increase in high school grade point average(x1), provided the effect of SAT mathematical score (x2 ) is constant.

The coefficient or slope of x2 in the regression model is b2=0.00486.

The interpretation of the coefficient b2 in the regression model is that the value of final college grade point average (y)increases by 0.00486unit for one unit increase in SAT mathematical score (x2 ), provided the effect of high school grade point average(x1) is constant.

b.

To determine

Predict final college GPA for a student who has a high-school average of 84 and a score of 540 on the SAT mathematical test.

Answer to Problem 49SE

The predicted final college GPA for a student who has a high-school average of 84 and a score of 540 on the SAT mathematical test is 3.19.

Explanation of Solution

Calculation:

The high school average of 84 implies that, x1=84 and SAT mathematical score 540 implies that x2=540.

The regression equation is y^=1.41+0.0235x1+0.00486x2.

For x1=84 and x2=540, predicted value of y is,

y^=1.41+0.0235(84)+0.00486(540)=1.41+1.974+2.62443.19

Thus, the predictedfinal college GPA for a student who has a high-school average of 84 and a score of 540 on the SAT mathematical test is 3.19.

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Chapter 15 Solutions

Essentials Of Statistics For Business & Economics
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