This question involves the use of simple linear regression on the Auto data set. Make sure that you omit rows with missing values.

Questions

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

• Use the lm() function to perform a simple linear regression with mpg as the response and horsepower as the predictor. Store the model in lm.fit. Use the summary() function to print the results.

• What is the predicted mpg associated with a horsepower of 102? (store answer in pred)

• What are the associated 95 % confidence and prediction intervals of the prediction with a horsepower of 102? (store answers in conf.int.95 and pred.int.95)

• MC1:
  A) Out of the F-statistic we can conclude that there is a relationship between the predictor and the response.
  B) A confidence interval is always wider than the prediction interval.
  • 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.
• MC2:
  A) The low p-value of horsepower hints at a weak relationship between horsepower and mpg.
  B) Since the coefficient of horsepower is negative, we can conclude that the more horsepower a car has, the lower the mpg will be (on average).
  • 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.

• Plot the response and the predictor. Use the abline() function to display the least squares regression line.

• Use the plot() function to produce diagnostic plots of the least squares regression fit. Comment on any problems you see with the fit.

Use the code below as a starting point.

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Assume that:

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