This question should be answered using the `Carseats`

data set from the ISLR2 package.

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

- Fit a multiple regression model to predict
`Sales`

using`Price`

,`Urban`

, and`US`

. Store the model in`lm.fit1`

. - Provide an interpretation of each coefficient in the model. Be carefulâ€”some of the variables in the model are qualitative!
- Write out the model in equation form on paper, being careful to handle the qualitative variables properly.
- For which of the predictors can you reject the null hypothesis
\(H_0 : \beta_j = 0\)? On the basis of your response, fit a
smaller model that only uses the predictors for which there is
evidence of association with the outcome. Store the model in
`lm.fit2`

- How well do the models in 1. and 5. fit the data?
Store the \(R^2\) of both models in
`r.squared1`

and`r.squared2`

, respectively. - Using the model from 4., obtain 95 % confidence intervals for
the coefficient(s). Store the confidence interval in
`conf.int.95`

. - Is there evidence of outliers or high leverage observations in the model from 4.?

Assume that:

- The ISLR2 library has been loaded
- The Carseats dataset has been loaded and attached