In one of the common college guides, a variety of information on 147 major universities was… 1 answer below »

Problem 5 (37 points). In one of the common college guides, a variety of information on 147 major universities was provided. The data included the following variables (the variable names are in parentheses; these match the column headings in the fileAlumniGiving.csv. Data file:AlumniGiving.csv

1. average SAT score (SAT)

2. freshmen in the top 10% of their high school class, percentage (Top10)

3. acceptance rate, percentage (AccRate)

4. faculty with Ph.D., percentage (PhD)

5. student-faculty ratio (Ratio)

6. educational spending per full-time equivalent (FTE) student, in dollars (not the same as tuition; this is institutional education-related spending per FTE student) (Spend)

7. graduation rate, percentage (probably the percentage of entering students who graduate within 4 or 6 years) (GradRate)

8. alumni giving rate, percentage (Alumni)

An alumni office is particularly interested in trying to explain differences in alumni giving rates across the schools. For any hypothesis tests, use a 0.05 level of significance.

1. Run a regression which includes all the independent variables (“Full” model). Include the summary output from the model here.

1. Is the overall model significant? State the test, the hypotheses, the test statistic, the decision rule, the p-value, and the decision. Express the decision in the context of the problem.

1. Interpret the value of the Ratio coefficient in the context of the problem. Use a simple example to illustrate the meaning.

1. Find a 95% confidence interval of the Ratio coefficient, and interpret it in the context of the problem.

1. Interpret the value of R2 in the context of the problem.

1. Interpret the value of the standard error of the regression in the context of the problem.

1. Suppose UNH’s actual values for the variables are as follows: SAT=1040, Top10=26, AccRate=74, PhD=85, Ratio=15, Spend=\$7149, GradRate=69, Alumni=16. What does the model predict for the expected alumni giving rate for UNH? What is the value of the residual for UNH? Interpret the value of the residual in the context of the problem; i.e., in language that would be meaningful to UNH administrators.

1. For the UNH data in the previous part, compute a 95% confidence interval for alumni giving, and a 95% prediction interval for alumni giving, and interpret in the context of the problem.

1. Which of the variables are significant in the model? State the reason/logic by which you know this.

1. Using the same data, find a better model (“Final” model). The alumni office is most interested in determining a small number of key variables that have significant explanatory power. Briefly list/describe your changes from the initial model and the final model (i.e., what you changed, and why). Include the summary regression output and write out the regression equation. Also provide/highlightR2,Ra2,se, and the p-values for the slope coefficients.