4. (16 Points) Truck and SUV Safety Ratings A few years ago, The Wall Street Journal reported safety scores on 33 models of SUV's and trucks. Safety scores {response variable) were reported, as well as the vehicle's weight (pounds) and an indicator of whether the yehicle has side air bags (1 if it does, 0 if not). Data-set: carsafety.csy a) Write a model equation relating safety scores to weight, presence of side airbags, and an interaction term that allows the effect of weight to depend on whether side airbags are present. b) Fit the model above using R. Write the tted model equation for vehicles with and without airbags. c) Find 95% condence intervals for each beta parameter. Write your conclusions. d) Test for the hypothesis that the interaction term can be dropped. Write conclusions in context. A B C D E Model Safety Weight Airbag N TOYOTA-AVALON 111.34 3437 W CHEVROLET-IMPALA 119.22 3454 4 FORD-RANGER 113.39 3543 BUICK-LESABRE 124.6 3610 6 MAZDA-MPV 117.13 3660 7 PLYMOUTH-VOYAGER 117.29 3665 8 VOLVO-580 136.66 3698 9 AUDI-A8 138.62 3751 10 DODGE-DAKOTA 120.49 3765 11 ACURA-RL 113.05 3824 12 PONTIAC-TRANSPORT 118.83 3857 13 CHRYSLER-TOWN&COUNTRY 122.62 3918 14 FORD-F-150 118.7 3926 15 TOYOTA-4RUNNER 130.96 3945 16 MERCURY-GRAND-MARQUIS 136.37 3951 17 ISUZU-RODEO 126.92 3966 18 TOYOTA-SIENNA 138.54 3973 P I O P O O P O P O O B B O B O O O O O O O K K O K B O K KOPP 19 MERCURY-VILLAGER 123.07 4041 20 LINCOLN-TOWN-CAR 120.83 4087 21 FORD-F-150X 132.01 4125 22 FORD-WINDSTAR 152.48 4126 23 NISSAN-PATHFINDER 137.67 4147 24 OLDSMOBILE-BRAVADO 117.61 4164 25 HONDA-ODYSSEY 156.84 4244 26 MERCURY-MOUNTAINEER 136.27 4258 27 TOYOTA-TUNDRA 118.27 4356 28 MERCEDES-BENZ-ML320 140.57 4396 29 FORD-ECONOLINE 140.72 4760 30 DODGE-RAM 120.08 4884 31 LINCOLN-NAVIGATOR 144.57 4890 32 DODGE-RAM 144.75 4896 33 CADILLAC-ESCALANTE 158.82 5372 34 CHEVROLET-SUBURBAN 170.26 5759 35 36