a. Begin with the data from \(n=185\) countries throughout the world that have valid (nonmissing) life expectancies. Plot the life expectancy versus the gross domestic product and private expenditures on health. From these plots, describe why it is desirable to use logarithmic transforms, InGDP and lnHEALTH, respectively. Also plot life expectancy versus lnGDP and lnHEALTH to confirm your intuition.

b. Use a stepwise regression algorithm to help you select a model. Do not consider the variables RESEARCHERS, SMOKING, and FEMALEBOSS, as these have many missing values. For the remaining variables, use only the observations without any missing values. Do this twice, with and without the categorical variable REGION.

c. Return to the full dataset of \(n=185\) countries and run a regression model using FERTILITY, PUBLICEDUCATION, and lnHEALTH as explanatory variables.

c(i). Provide histograms of standardized residuals and leverages.

c(ii). Identify the standardized residual and leverage associated with Lesotho, formerly Basutoland, a kingdom surrounded by South Africa. Is this observation an outlier, a high leverage point, or both?

c(iii). Rerun the regression without Lesotho. Cite any differences in the statistical coefficients between this model and the one in part c(i).