(Data Set campuscrime.csv is in the comments )

Solve Using R / R studio

The data set campuscrime.csv contains the number of burglaries reported at a collection of 4? U.S. public universities with over 10,000 students in the year 2009. In addition, covariates are included which may explain differences in crime rates, including total number of students, percentage of men, average SAT and ACT test scores, and tuition. a. Perform an exploratory data analysis. Support your analysis with plots and summary statistics. i. Analyze whether number of burglaries could be reasonably modeled with a Poisson distribution. ii. Analyze which covariates you expect to be the best predictors of burglaries. b. Consider a model with 4 predictors: act.comp + tuition + pct.male + total. Try fitting a linear regression with burg09 as the response. Are there any concerns with this linear regression model? c. Run a Poisson regression model with the 4 predictors from {b}. Interpret the coefficients for tuition and pct.male. d. Replace tuition with tuition in thousands in your model from {c) i.e., tuition.thous=tuition1'1000. How does your new model compare to your model in (c}? Interpret the coefficient for tuition.thous. e. We will consider the possibility of including the total number of students at a university as an offset. i. Explain why we might consider total as an offset. ii. Refit your model from {d) with total (actually, logltotall] as an offset rather than as a predictor. Does this new model appear to fit better or worse than the model from {d}? iii. Refit your model from {d) with logltotal} rather than total so logltotal) is a predictor and not an offset. If total were a good candidate for an offset, what would we expect the coefficient of logltotal) to be? Does a 95% confidence interval for that coefficient contain the value you expected? f. Run the following model, then interpret the coefficients for tuition.thous and the interaction between tuition.thous and act.comp