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Question: using the motor trend car road tests dataset mtcars in...

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Using the Motor Trend Car Road Tests dataset mtcars, in faraway R package, fit a model with mpg: Miles/(US) gallon as the response and the other variables as predictors. (a) Which variables are statistically significant at the 5% level? For each and every test provide the null and alternative hypotheses, critical region (or rejection 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 the parameter associated with hp: Gross horsepower and interpret the results. (6) (d) Compute and display a 95% joint confidence region for the parameters associated with wt: Weight (1000 lbs) and hp: Gross horsepower. Plot the origin on this display. The location of the origin on the display tells us the outcome of a certain hypothesis test. State that test and its outcome. (5) (e) Fit a model with just mpg: Miles/(US) gallon; cyl: Number of cylinders; and disp: Displacement (cu.in.) as predictors and use an F-test to compare it to the full model. For this test provide the null and alternative hypotheses, critical region (or rejection region), test statistics and your conclusions. Please use R, Dataset mtcars(faraway)

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