Using the Motor Trend Car Road Tests dataset mtcars, in farawayR package, fit a model with mpg: Miles/(US) gallon as the responseand the other variables as predictors. (a) Which variables arestatistically significant at the 5% level? For each and every testprovide the null and alternative hypotheses, critical region (orrejection region), test statistics and your conclusions. (30) (b)What interpretation should be given to the coefficient for vs:Engine? (3) (c) Compute 90 and 95% confidence intervals for theparameter associated with hp: Gross horsepower and interpret theresults. (6) (d) Compute and display a 95% joint confidence regionfor the parameters associated with wt: Weight (1000 lbs) and hp:Gross horsepower. Plot the origin on this display. The location ofthe origin on the display tells us the outcome of a certainhypothesis test. State that test and its outcome. (5) (e) Fit amodel with just mpg: Miles/(US) gallon; cyl: Number of cylinders;and disp: Displacement (cu.in.) as predictors and use an F-test tocompare it to the full model. For this test provide the null andalternative hypotheses, critical region (or rejection region), teststatistics and your conclusions. Please use R, Datasetmtcars(faraway)
