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A car enthusiast is interested in the relationship between the miles per gallon (M PG) and the horsepower of cars. He takes a sample of 24 ditTerent models and makes of cars and records each ca r's MPG {"M PG"} as stated by the manufacturer and horsepower ("hp"). This data is shown in the two vectors below. To use the data, copy and paste the following lines into your R or Rstudio console. hp=c(93,110,52,1 09,91,215,180,130,911T5,335,93,52,335,105, 11 0,245,93,56,335,150,180,110,1t5); MPG=c(22_B,2130.4.21426,104,1?.3,15_2,21_5,19.2,15,22_8,3l)_4,15,181,21,13_3,22_B,27.3,15,15.5,113,21,191); a. Compute the correlation between MPG and horsepower. Answer: Round to at least ve decimals it necessary b. State the regression equation used to express the MPG (Y) as a linear function of horsepower (X). Repon all decimals printed by R. K: t Ill \\3 ( 31 c. Which is the correct interpretation of 31 in the above regression equation? 0 A. As horsepower increases by 1 unit, MPG decreases by 31 units O B. The horsepower for a carwith U MPG is, on average, 31 O 0. As horsepower increases by Lil units, the MPG decreases on average by 1 unit 0 D. The miles per gallon for a car with a horsepower of D is, on average, 51 O E. As horsepower increases by '51 units, the MPG decreases by 1 unit 0 F. A5 horsepower increases by 1 unit, MPG decreases on average by 51 units d. The coeicient of determination tells us that % of the variation in ? V is explained by its linear relationship with '? V _ Round to at least five decimals it necessary e. Consider the tenth car in the dataset, which is a car that has a horsepower of 175 and a MPG of 19.2. Compute the residual for this car. Round to at least five decimals it necessary