Please use excel format

A business website decided to use publicly available information to determine how well starting

salaries of graduates of a university or college predict mid-career salaries. The website compiled

a sample of 320 universities and colleges which are shown in the table including the following variables:

Undergraduate school

Region

Median starting salary

California region

Western region

Midwestern region

Southern region

Median mid-career salary

Note that Northeastern region is the baseline, and so is not included among the regional

dummy variables.

a. Determine the sample correlation coefficient, r, between Median starting salary and

Median mid-career salary. Test the alternative hypothesis that the correlation between

Median starting salary and Median mid-career salary ? 0. Specifically, what are the test

statistic and the p-value for that test statistic? For ? = .05, what do you conclude about the

relationship between the variables?

b. Now estimate a simple linear regression to predict the Median mid-career salary using only

Median starting salary. Write the estimated regression equation.

c. How well does the model fit the dependent variable? Cite the appropriate statistic from the

regression output, and interpret that statistic.

d. What is the fitted slope coefficient? Interpret that slope coefficient. Is there a linear relationship

between the independent and dependent variables at ? = .05? Report the relevant test statistic

and p-value for that test statistic.

e. Now estimate a multiple linear regression to predict Median mid-career salary using

Median starting salary and the four region dummy variables. Write the estimated regression

equation.

f. Is the model estimated in part (e) statistically significant at the ? = .05 level? Write the null

and alternative hypotheses for this test, the appropriate test statistic, the p-value for that test

statistic, as well as your conclusion.

g. Using the model estimated in part (e), which independent variables (if any) are related to the

dependent variable Median mid-career salary at the ? = .05 level, in this model? Include

relevant values from the Excel output to support your conclusions.

h. An aspiring college student wants to know, if she chooses to attend a southern college which

has a median starting salary of $50,000, what salary she can expect to earn mid-career.

Using the regression equation from parts (e) to (g) to compute the expected mid-career

salary, develop an approximate 90% prediction interval for that mid-career salary. Can she be confident of earning a mid-career salary above $75,000?

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