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StatisticsEssentials Of Statistics For Business & EconomicsThe 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.BuyFind*arrow_forward*

9th Edition

David R. Anderson + 4 others

Publisher: South-Western College Pub

ISBN: 9780357045435

Chapter 15, Problem 49SE

Textbook Problem

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.

Expert Solution

**a.**

To determine

Interpret the coefficients in the estimated regression equation.

**Calculation:**

The estimated regression equation relating the final GPA to the student’s SAT mathematics score and high school is GPA is *y* denotes the final college grade point average.

*Multiple linear regression model:*

A multiple linear regression model is given as *k* predictor variables. The quantities

*Slope in a multiple regression equation*:

The slope

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

The interpretation of the coefficient *y*)increases by 0.0235unit for one unit increase in high school grade point average(

The coefficient or slope of

The interpretation of the coefficient *y*)increases by 0.00486unit for one unit increase in SAT mathematical score (

Expert Solution

**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.

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.

**Calculation:**

The high school average of 84 implies that,

The regression equation is

For *y* is,

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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