(9 marks) The weight (in kg) and height (in m) of 33 men from population A and 41 men from population B are measured. A scatterplot of the data is below. Let Y and @1 be the weight and height, respectively, of the ith man. Let X2i be 1 if the ith man is from population A and 0 otherwise. A model for these data is Yi = Bo + Billi + Bzizi + B3xlizzi + Gi. You may assume that weights are independent and normally distributed. Some output is below. Population We ght (kg> fit=with (df, 1m(Weight-Height*Population)) > summary (fit) Call: 1m(formula = Weight ~ Height * Population) Residuals: Min 1Q Median 3Q Max -44 . 047 -8.168 -0. 366 6. 272 56. 769 Coefficients : Estimate Std. Error t value Pr(>|t/) (Intercept) -637 . 53 91.59 -6. 961 1.47e-09 * *# Height 455.55 53. 18 8. 566 1. 66e-12 "* * PopulationB -100 .25 112 . 87 -0. 888 0. 377 Height : Populations 62. 20 66 . 05 0. 942 0. 350 Signif. codes: 0 '**#' 0.001 " ' 0. 01 = ' 0. 05 . . ' 0.1 . ' 1 Residual standard error: 18.9 on 70 degrees of freedom Multiple R-squared: 0. 786, Adjusted R-squared: 0.7768 F-statistic: 85.71 on 3 and 70 DF, p-value: