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# Correlation matrix and R^2 of GPA and salary

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How important is GPA in determining the starting salary of recent business school graduates? Does graduating from a business school increase the starting salary?
The Director of Undergraduate Studies at a major university wanted to study these questions. She gathered the following sample information on 15 graduates
last spring to investigate these questions.

1 \$31.50 3.245 0
2 33 3.278 0
3 34.1 3.52 1
4 35.4 3.74 1
5 34.2 3.52 1
6 34 3.421 1
7 34.5 3.41 1
8 35 3.63 1
9 34.7 3.355 1
10 32.5 3.08 0
11 31.5 3.025 0
12 32.2 3.146 0
13 34 3.465 1
14 32.8 3.245 0
15 31.8 3.025 0

The salary is reported in \$000, GPA on the traditional 4-point scale. A 1 indicates the student graduated from a school of business;
a 0 indicates that the student graduated from one of the other schools.

a. Develop a correlation matrix. Do you see any problems with multicollinearity?
b. Determine the regression equation. Discuss the regression equation. How much does graduating from a college of business add to a starting salary? What starting salary would you estimate for a student with a GPA of 3.00. Who graduated from a college of business?
c. What is the value of R2? Can we conclude that this value is greater than 0?
d. Would you consider deleting either of the independent variables?
e. Plot the residuals in a histogram. Is there any problem with the normality assumption?
f.Plot the fitted values against the residuals. Does this plot indicate any problems with homoscedasticity
a. Develop a correlation matrix. Do you see any problems with multicollinearity?