PROBLEM 1 [16 pts] - to be answered by everyone The file bankingfull.txt attached to this assignment contains the full dataset. You analyzed a smaller set for a previous assignment. It provides data acquired from banking and census records for different zip codes in the bank's current market. Such information can be useful in targeting advertising for new customers or for choosing locations for branch offices. The data show median age of the population (AGE) median years of education (EDUCATION) median income (INCOME) in $ median home value (HOMEVAL) in $ median household wealth (WEALTH) in $ average bank balance (BALANCE) in $ The goal of this exercise is to define a regression model to predict the average bank balance as a function of the other variables. a ) Create scatterplots to visualize the associations between bank balance and the other five variables. Include the relevant output. Discuss the patterns displayed by the scatterplot. Also, explain if the associations appear to be linear? (you can create either scatterplots or a matrix plot) b) Compute correlation values of bank balance vs the other variables. Include the relevant output. Interpret the correlation values, and discuss which variables appear to be strongly associated. C) Fit a regression model of balance vs the other five variables (model M1). Compute the VIF statistics for each x-variable and analyze whether there is a problem of multicollinearity and take appropriate action. Include the relevant output. Discuss your answer. d) Apply your knowledge of regression analysis to define a better model M2. Include the SAS output for both models and answer the following questions : a. Analyze the adj-R2 values for both models M1 and M2. Which model has the largest adj-R2 value? b. Create residual plots (standardized residuals vs predicted; standardized residuals vs x- variables; and normal plot of residuals). Analyze the residual plots to check if the regression model assumptions are met by the data. Include the relevant output and discuss your analysis. Analyze if there are If so what a