STAT 4385 Applied Regression Analysis Computer Project III (Due on 05/07/2021 Friday before 11:59pm, Upload your report in OneNote ) (Model Diagnostics) The crime data contain the crime rate, and...

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STAT 4385 Applied Regression Analysis Computer Project III (Due on 05/07/2021 Friday before 11:59pm, Upload your report in OneNote ) (Model Diagnostics) The crime data contain the crime rate, and other information for each of fifty (n = 50) cities (Reference: Life In America’s Small Cities, by G.S. Thomas). One objective of the study is to model the crime rate (Y ) based on other predictor variables (X1–X5). A short variable description is given below. Variable Name Meaning Y crimerate total overall reported crime rate per 1 million residents X1 police.funding annual police funding in $/resident X2 high % of people 25 years+ with 4 yrs. of high school X3 middle % of 16 to 19 year-olds not in highschool and not highschool graduates. X4 in.college % of 18 to 24 year-olds in college X5 graduate % of people 25 years+ with at least 4 years of college First download the dataset and read the data in to R. The objective of this project is to find the best linear model and conduct model diagnostics. Make sure that you interpret the results appropriately. 1. Use the all subset(or best subset) selection procedure with AIC to find your best linear regres- sion model. 2. Output the Table of Parameter Estimates and the ANOVA table for your best model. Interpret the R2. 3. Take the following specific steps to check model assumptions. (a) (Check Normality) Obtain the studentized jackknife residuals and check if they follow the standard normal distribution using histogram and Q-Q plot graphically and referring to the Shapiro-Wilk test for normality. (b) (Check Homoscedasticity) Plot Absolute Jackknife Residuals vs. Fitted values using the R function spreadLevelPlot() in Package {car}. Apply the Breusch-Pagan test or bptest() function in the R Package {lmtest} to test for non-constant error variance. (c) (Check Independence) Apply the Durbin-Watson test to check for auto-correlated errors. 1 (d) (Check Linearity) Use partial residual plots (Function crPlots in the car package) to check on linearity or functional form for each continuous predictor that you have included in your best linear model. 4. (Outlier Detection) Identify outliers that are outlying in terms of predictors, response, and being influential by using the leverage hii, the studentized jackknife residuals ri, and Cook’s distance di. Make a bubble plot of these three measures using Function influencePlot in the car package. 5. (Multicollinearity) Assess multicollinearity by obtaining the variance inflation factor (VIF) measures. You don’t have to consider the intercept term. Use 10 for VIF to determine presence of severe multicollinearity. Some helpful tips for computer projects are listed below: ˆ Start early and don’t wait till the last day/minute; ˆ Use copy-and-paste appropriately to include necessary R output into your final report; ˆ Remember to interpret every result and graphs that you present; ˆ Place your R codes in an appendix. 2