Consider the correlation matrix below showing the correlations between the poten
ID: 3154854 • Letter: C
Question
Consider the correlation matrix below showing the correlations between the potential predictors.
Correlation: PPS, T/S Ratio, Avg. Salary, %Takers
PPS T/S Ratio Avg. Salary
T/S Ratio -0.371
Avg. Salary 0.870 -0.001
%Takers 0.593 -0.213 0.617
Cell Contents: Pearson correlation
1. Based on this correlation matrix, what criticism can be made about the following multiple regression model?
Regression Analysis: Avg. Tot. Score versus Avg. Salary, %Takers, PPS
Model Summary
S R-sq R-sq(adj) R-sq(pred)
32.7980 81.96% 80.78% 78.76%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 998.0 31.5 31.69 0.000
Avg. Salary -0.31 1.65 -0.19 0.853 4.39
%Takers -2.840 0.225 -12.64 0.000 1.65
PPS 13.33 7.04 1.89 0.065 4.20
2. Consider the model output below. Which model do we consider better, the model from Question 1 or this model? Why?
Regression Analysis: Avg. Tot. Score versus PPS, %Takers
Model Summary
S R-sq R-sq(adj) R-sq(pred)
32.4595 81.95% 81.18% 79.59%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 993.8 21.8 45.52 0.000
PPS 12.29 4.22 2.91 0.006 1.54
%Takers -2.851 0.215 -13.25 0.000 1.54
Explanation / Answer
1. Based on the correlation matrix, it is observed that PPS and Average Salary have a high value of correlation coefficient, so is the case with Average Salary and % Takers.
This will lead to the problem of multicollinearity in the regression model, which will make the estimators inefficient.
2. Model 2 has a higher R-Squared Adjusted (81.18%) than Model 1 (80.78%).
So Model 2 is better. This is because, on dropping Average Salary variable from Model 1, model's explanatory power per degree of freedom improves as the variable dropped was insiginificant (P-value = 0.853)