This problem uses the UN11 data in the alr4 package. (a) Plot fertility against ppgdp. Fit a linear model regressing fertility on ppgdp and add the fit on the plot. Comment on why this model is not good. (b) Use a "residuals vs fit" plot to check if there is any non-constant variance or non-linearity problem. State the main problem and explain why in one or two sentences. (c) Use a normal Q-Q probability plot to check if the normality assumption is met. State the main problem and explain why in one or two sentences. (d) Shapiro-Wilk test is a test of normality of a numeric variable. The null hypothesis for this test is that the variable is normally distributed. Use the R function shapiro. test() to test if the residuals of the linear fit in part (a) is normally distributed. State the p-value of this test and your conclusion given α = 0.05. Does the result support your conclusion in part (c)? (Use the code ?shapiro. test or help(shapiro. test) to understand how to use this function.)