Clay et al. (2014) state that "The amount of lead in the drinking water depends on the chemical properties of the water [..] more acidic water (lower PH) leaches lead faster". We should thus expect that the relationship between lead pipes on infant mortality also depends on the water PH. To assess this hypothesis, we want first to graph a crossplot of the relationship between infant mortality and PH for cities with and without lead pipes. Hint : the plot command can be used. Add the line col = factor (groupname). So you should have something like: plot(Xvar, Yvar, col = factor(groupname) ) Don't forget to make the graph more informative by adding title, axis legend. You may also change the colors and symbols used. Copy the graph into your answer and comment. Question 5 (30 points) 1. Conduct a linear regression of infant mortality rate on the indicator for lead pipes and the water PH. Report those results (you might want to produce a table of results, as more regressions will also need to be reported). Comment on the coefficients, their statistical significance, and the effects that the independent variables have on child mortality. (10 points) 2. The relationship between lead leaching and PH might not be linear. Include a quadratic term in PH, and re-run the regression. Report those results in your table of results and comment. Does the introduction of a quadratic term improve the fit of the model? (10 points) 3. Include a cubic term in PH, and add it to the previous specification. Conduct an F-test on whether the cubic model offers a better fit than a linear model. Report your test results and comment. (10 points)