Homework: HW CH25 Question 6, 25.1.46-T HW Score: 14.06%, 1.13 of 8 points Part 1 of 11 Points: 0.5 of 1 Save The cases that make up this data set are types of vehicles. For each of the 29 types of vehicles sold in a certain region during the last model year; we have the combined mileage and the horsepower of the engine (HP). A model for the association of mileage and horsepower required taking logs of both variables. The column Vehicle Type denotes whether the vehicle is a car, truck, or SUV. Complete parts (a) through (f) below. Click the icon to view the data set. (a) Plot the log 10 of mileage on the log 10 of horsepower for vehicles of all three types in one scatterplot. Does the relationship between the response and the explanatory variable appear to be similar for the different groups? Use color-coding or different symbols to distinguish the data of the two types of property. Use blue circles for cars, green diamonds for trucks, and red squares for SUVs. Choose the correct graph below. O A. O B. O C. OD. 1.5 2.8- 1.5 2.81 log(MPG) log (MPG) log (MPG) log(MPG) 2.2+ 1.1+ 2.2+ 2.2 28 1.1 1.5 2.2 28 1.1 1.5 log (HP) log (HP) log (HP) log(HP)X Data table .......: Full data set Vehicle Combined Type MPG Horsepower log (MPG) log (HP) TruckDummy SUVDummy TruckLog(HP) SUVLog(HP) suv 24 200 1.380 2.301 2.301 car 25 211 1.398 2.324 0 0 truck 15 310 1.176 2.491 2.491 car 28 211 1.447 2.324 SUV 18 234 1.255 2.369 2.369 car 16 430 1.204 2.633 car 14 430 1.146 2.633 O truck 14 525 1.146 2.720 2.72 car 21 333 1.322 2.522 car 17 354 1.230 2.549 SUV 21 200 1.322 2.301 2.301 car 24 265 1.380 2.423 car 13 470 1.114 2.672 car 15 470 1.176 2.672 car 13 510 1.114 2.708 o o o o o o o o o - 0 0 0 - o o o o o o o - 0 0 0 0 - 0 0 truck 18 315 1.255 2.498 2.498 car 15 470 1.176 2.672 car 16 430 1.204 2.633 car 16 420 1.204 2.623 truck 20 190 1.301 2.279 2.2 79 car 15 475 1.176 2.677 car 13 505 1.114 2.703 suv 19 300 1.279 2.477 OOOOO OOO O NOOO 2.477 SUV 14 555 1.146 2.744 2.744 SUV 19 300 1.279 2.477 2. 77 SUV 14 555 1.146 2.744 2.744 car 17 415 1.230 2.618 car 17 400 1.230 2.602 car 20 400 1.301 2.602(b) Fit the multiple regression of log 10 of mileage versus five explanatory variables: the explanatory variable graphed in (a), dummy variables that identify the vehicle type (one for trucks and one for SUVs), and the two associated interactions. Summarize the estimated regression. Let Y be log (MPG), X, be log (HP), X2 be TruckDummy, and X3 be SUVDummy. Identify the multiple regression line. Y = +()X, +(X2+(X3+()X1X2+ ()X1X3 (Round to three decimal places as needed.)(d) Assume that the model meets the conditions for the MRM. Use the incremental F-test to assess the size of the change in R produced when the dummy variables and interactions are added to the model. (The value of Ky| for the model with dummy variables and interactions is 5. You will need to fit the simple regression of log 10 of mileage on log 10 of horsepower to get its R" statistic.) An appropriate critical value for the incremental F-test is 4. Does the test agree with your visual impression from (a)? Identify the hypotheses. Ho: The slope(s) of the is/are O. He: The slope(s) of the is/are O