L. The data BGSall in the alr4 package contains information on n 136 children in the Berkeley Guidance study, including heights at ages 2 and 18 (HT2 and HT18), and gender (Sex). Consider the regression of HT18 on HT2 and the grouping factor Sex. (a) Draw the scatterplot of HT18 versus HT2, using a different color for males and females. Add the two parallel estimated regression lines to the scatterplot. Comment on the infor- mation in the graph about an appropriate mean function for these data. (b) Obtain the appropriate test for a parallel regression model (c) Assuming the parallel regression model is adequate, estimate a 95% confidence interval for the difference between males and females. For the parallel regression model, this is the difference in the intercepts of the two groups. L. The data BGSall in the alr4 package contains information on n 136 children in the Berkeley Guidance study, including heights at ages 2 and 18 (HT2 and HT18), and gender (Sex). Consider the regression of HT18 on HT2 and the grouping factor Sex. (a) Draw the scatterplot of HT18 versus HT2, using a different color for males and females. Add the two parallel estimated regression lines to the scatterplot. Comment on the infor- mation in the graph about an appropriate mean function for these data. (b) Obtain the appropriate test for a parallel regression model (c) Assuming the parallel regression model is adequate, estimate a 95% confidence interval for the difference between males and females. For the parallel regression model, this is the difference in the intercepts of the two groups