Question: Consider the dataset SAT12, which is studied in the Chapter 13 reading materials.Below is an excerpt of this dataset. PPST/S-RAvg.$ % Takers Verbal Math Total

Consider the dataset SAT12, which is studied in the Chapter 13 reading materials.Below is an excerpt of this dataset.

PPST/S-RAvg.$ % Takers Verbal Math Total

Alabama4.40517.2 31.14484915381029

Alaska8.96317.6 47.95147445489934

Arizona4.77819.3 32.17527448496944

Arkansas4.45917.1 28.93464825231005

Wisconsin6.9315.9 37.74695015721073

Wyoming6.1614.9 31.285104765251001

We are interested in constructing and analyzing multiple regression models to predict Avg. Total SAT Score (ATS).

a.Consider the correlation matrix below showing the correlations between the potential predictors.

Correlation: PPS, T/S Ratio, Avg. Salary, %Takers

PPST/S RatioAvg. Salary

T/S Ratio-0.371

Avg. Salary0.870-0.001

%Takers0.593-0.2130.617

Cell Contents: Pearson correlation

Based on this correlation matrix, what criticism can be made about the following multiple regression model (ModelA)? (Hint:Note the correlation between PPS and Avg. Salary.)

A.Regression Analysis: Avg. Tot. Score versus Avg. Salary, %Takers, PPS

Model Summary

SR-sqR-sq(adj)R-sq(pred)

32.798081.96%80.78%78.76%

Coefficients

TermCoefSE CoefT-ValueP-ValueVIF

Constant998.031.531.690.000

Avg. Salary-0.311.65-0.190.8534.39

%Takers-2.8400.225-12.640.0001.65

PPS13.337.041.890.0654.20

b.Write the regression equation for Model A.

c.TRUE or FALSE: If Avg. Salary is removed from Model A, adj. R-squared will decrease.Briefly explain your answer.

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