---
title: "Carseats: Categorical predictors"
author: "Trevor Hastie and Robert Tibshirani"
output:
  pdf_document: default
---

Here, I am adapting the lab associated with Chapter 3 of the textbook. 

## Qualitative Predictors

We will now examine the **simulated** `Carseats` data, which is part of the `ISLR2` library. We will  attempt to predict `Sales` (child car seat sales) in $400$ locations based on a number of predictors.

```{r chunk25}
library(ISLR2)
head(Carseats)
```

**What about a spreadsheet array?**

```{r}
plot(Carseats)
```

**While we do not get much out of the array, we can easily identify the categorical predictors.**

The `Carseats` data includes qualitative predictors such as `shelveloc`, an indicator of the quality of the shelving location---that is, the  space within a store in which the car seat is displayed---at each location. The predictor `shelveloc` takes on three possible values:  *Bad*, *Medium*, and *Good*. Given a qualitative variable such as `shelveloc`, `R` generates dummy variables automatically. Below we fit a multiple regression model that includes some interaction terms.

```{r chunk26}
lm.fit <- lm(Sales ~ . + Income:Advertising + Price:Age, 
    data = Carseats)
summary(lm.fit)
```

The `contrasts()` function returns the coding that `R` uses for the dummy variables.

```{r chunk27}
attach(Carseats)
contrasts(ShelveLoc)
```

You should use `?contrasts` to learn about other contrasts, and how to set them.

`R` has created a `ShelveLocGood` dummy variable that takes on a value of 1 if the shelving location is good, and 0 otherwise. It has also created a `ShelveLocMedium` dummy variable that equals 1 if the shelving location is medium, and 0 otherwise.
A bad shelving location corresponds to a zero for each of the two dummy variables.
The fact that the coefficient for `ShelveLocGood` in the regression output is positive indicates that a good shelving location is associated with high sales (relative to a bad location). And `ShelveLocMedium` has a smaller positive coefficient, indicating that a medium shelving location is associated with higher sales than a bad shelving location but lower sales than a good shelving location.