PLease Use R

Use the data `Carseats` in the package `ISLR`. More information about the data can be found using `help(Carseats)`.

```{r}

library(ISLR)

data(Carseats)

str(Carseats)

```

## Part (a)

Fit a multiple linear regression to predict `Sales`, using the variables `Price`, `Urban`, `US`, and `Income`.

## Part (b)

Provide an explanation of each coefficient in the model, in terms of the model; be careful -some of these are qualitative/categorical variables.

## Part (c)

At significance level of $\alpha = 0.01$, for which of these variables can you reject the null hypothesis of $H_0: \beta_0 = 0$?

What about at significance level of $\alpha = 0.05$?

## Part (d)

On the basis of your response to the previous question, fit a smaller model that only uses the predictors for which there is statistically significant evidence of association with the outcome, for signifance level $\alpha = 0.05$. (*Note: This is for testing purposes, this is __not__ how you should select variables*.)

## Part (e)

Assess and discuss how well the two models in (a) and (d) fit the data. Use any of the tools we learned in class, consider both *signifiance* and *validity*, and limit your response to a few sentences.

## Part (f)

Add an interaction term between `Price` and `US` to your reduced model from part (d). Does the model fit improve?

## Part (g)

Interpret the coefficients of `USYes` and`Price:USYes`, in terms of the model. Do not consider the improvement or lack of improvement from the last part.