In this assignment we will be using probability and distributions concepts. Go through section 3.6 in ISLR as preparation for this exercise. Familiarize yourself with the College dataset. You can learn more about the dataset and variables here: https://cran.r-project.org/web/packages/ISLR/ISLR.pdf.

1. Produce some numerical and graphical summaries of the College dataset. Pick variables that you feel are interesting based on questions 2 and 3 below. Comment on the relationships explored in question 2 based on these summaries.

2. Explore the following relationships using simple linear regression:

a. Amount charged for room and board as a function of the number of accepted students

b. Number enrolled expressed as a function of number of accepted students

c. Instructional expenditure per student as a function of number of new students enrolled

d. Graduation rate as a function of number of applications accepted

Provide the model summary in each case. Give the confidence and prediction intervals for the response variables. Comment on the fit in each case. Plot the predictor and response variables along with the least squares regression line in each case.

3. Fit a multiple linear regression model to explain percent of alumni who donate as a function of 4 or 5 other variables from the dataset. Be sure to include Private as one of the variables. Explain and justify your choice of the other predictor variables. Provide the model summary. Interpret the coefficient for the Private variable. Comment on the fit of the model. Briefly list a few things you would try next to improve the fit.