The learning objectives for this week are as follows: Perform model diagnostics for MLR to identify possible violations of model assumptions and utilize advanced regression models to deal with challenges such as non-constant variance, influential outliers, and multicollinearity; Implement bootstrapping methods to enhance the alignment of results with data that does not meet underlying assumptions. Problems 1-5 use the life expectancy dataset. Problem 1 (24 pts) For the life expectancy data, Consider the MLR model given by Y ~ X_1 X_2 X_3. (a) [6 pts] Obtain a partial regression plot for X_1, X_2, and X_3 and discuss whether the regression relationships in the fitted regression function are inappropriate for any of the predictor variables. (b) [10 pts] Check for influential points by calculating DFFITS, DFBETAS and Cook's distance values. (c) [8 pts] Determine whether there is multicollinearity present based on VIF. Problem 2 (3 pts) Use R to summarize the OLS model. Then compute the confidence interval for the linear impact of X_1, X_2 and X_3