The file CommunityCrime. csv is a dataset containing 319 observations on 123 variables. The observations are communities within the United States. The data combines socio-economic data from the 1990 US Census, law enforcement data from the 1990 US LEMAS survey, and crime data from the 1995 FBI Uniform Crime Reporting program. A detailed description of all variables is available at http://archive. ics. uci. edu/ml/machine-learning-databases/c ommunities/communities. names. We seek to predict the variable ViolentCrimesPerPop, the total number of violent crimes per 100,000 people.

Note: when asked to perform cross validation to select a tuning parameter, be sure to conduct this cross validation on the training data only, then see how well your cross validated tuning parameter does on the test data.

(a). Set a seed of 1 and split the data into a 90% training set, and a 10% test set.

(b). Fit a linear model using least squares on the training set. Report the test error obtained.

(c). Fit a ridge regression model on the training set with λ chosen by cross-validation. Report
the test error obtained.

(d). Fit a lasso model on the training set with λ chosen by cross-validation. Report the test error obtained, along with the number of non-zero coefficient estimates.

(e). Fit a PCR model on the training set with M chosen by crossvalidation. Report the test error obtained along with the value of M selected by cross-validation.

(f). Fit a PLS model on the training set with M chosen by cross-validation. Report the test error obtained, along with the value of M selected by cross-validation.

(g). Comment on the above parts and how well you believe we can predict violent crime rate using these methods.