Using the Motor Trend Car Road Tests dataset mtcars, in faraway R package, fit a model...

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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The Motor Trend Car Road Tests dataset (mtcars.csv) contains the data extracted from the 1974 Motor...

The Motor Trend Car Road Tests dataset (mtcars.csv) contains the data extracted from the 1974 Motor Trend US magazine and comprises fuel consumption and 10 aspects of automobile design and performance for 32 automobiles (1973–74 models). The dataset contains 32 observations on 11 variables. Analyze the dataset according to the following steps: 1. Calculate sample mean and sample variance of each variable. 2. Calculate the sample variance-covariance matrix and the sample correlation matrix. What can you say about the variance-covariance...

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R has a number of datasets built in. One such dataset is called mtcars. This data...

R has a number of datasets built in. One such dataset is called mtcars. This data set contains fuel consumption and 10 aspects of automobile design and performance for 32 automobiles (1973-74 models) as reported in a 1974 issue of Motor Trend Magazine. We do not have to read in these built-in datasets. We can just attach the variables by using the code attach(mtcars) We can just type in mtcars and see the entire dataset. We can see the variable...

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