Problem 3. The purpose of this problem is to perform a regression analysis of the 35 Scotish hill races data contained in the data set hills in Rsafd library. 1. Produce the scatterplot of the variable time against climb, and superimpose the polynomial regression line of time against climb (use order p=8 for the polynomial regression). Repeat the same thing for time against dist. For each of these regressions, compute the raw residuals and produce their normal QQ plot. Comment. 2. Using the result of the regression of time against dist, compute the prediction of the recorded time for the marathon (i.e. the value of 26.2 for the variable dist). Problem 3. The purpose of this problem is to perform a regression analysis of the 35 Scotish hill races data contained in the data set hills in Rsafd library. 1. Produce the scatterplot of the variable time against climb, and superimpose the polynomial regression line of time against climb (use order p=8 for the polynomial regression). Repeat the same thing for time against dist. For each of these regressions, compute the raw residuals and produce their normal QQ plot. Comment. 2. Using the result of the regression of time against dist, compute the prediction of the recorded time for the marathon (i.e. the value of 26.2 for the variable dist)