This question involves the use of multiple linear regression on the Auto data set.

Questions

Some of the exercises are not tested by Dodona (for example the plots), but it is still useful to try them.

• Produce a scatterplot matrix which includes all of the variables in the data set.

• Compute the matrix of correlations between the variables using the function cor() and store it in Auto.cor. You will need to exclude the name variable, which is qualitative.

• Use the lm() function to perform a multiple linear regression with mpg as the response and all other variables except name as the predictors. Store the model in lm.fit1. Use the summary() function to print the results.

• MC1:
  A) There is a statistically significant relationship between the predictors and the response.
  B) Based on the coefficient of year we can conclude that more recent cars are more fuel efficient (higher mpg).
  • 1) Both statements are true.
  • 2) Both statements are false.
  • 3) A is true and B is false.
  • 4) A is false and B is true.

• Use the plot() function to produce diagnostic plots of the linear regression fit. Comment on any problems you see with the fit. Do the residual plots suggest any unusually large outliers? Does the leverage plot identify any observations with unusually high leverage?

• Build the following model and store it in lm.fit2 (\(h\) stands for horsepower and \(d\) for displacement:

\[ln(mpg) = \beta_0 + \beta_1 d + \beta_2 h + \beta_3 h^2 + \\ \beta_4 d^2 + \beta_5 h d\]

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Assume that:

• The ISLR2 library has been loaded
• The Auto dataset has been loaded and attached