If we want to import a categorical variable with 5 different categories in a linear regression, we need to generate how many dummy variables?

## Answer<br /><br />When you want to include a categorical variable with 5 different categories in a linear regression model, you need to generate **4 dummy variables**.<br /><br />### Explanation<br /><br />In linear regression, categorical variables are typically represented using **dummy variables** (also known as indicator variables). A dummy variable is a binary variable that indicates whether a certain category of the categorical variable is present or not.<br /><br />The reason we need one less dummy variable than the number of categories is due to the **"dummy variable trap"**. This trap occurs when the dummy variables are multicollinear, i.e., one variable can be predicted perfectly from the others. This happens when we use a separate dummy variable for each category, because the sum of the dummy variables equals one. To avoid this trap, we typically use one less dummy variable than the number of categories, with one category serving as the "reference category".<br /><br />For example, if we have a categorical variable with categories A, B, C, D, and E, we could create dummy variables for categories A, B, C, and D. Then, if all of these dummy variables are 0, it means that the category is E.<br /><br />Here's a simple representation of how the categories could be encoded into dummy variables:<br /><br />| Original Category | Dummy A | Dummy B | Dummy C | Dummy D |<br />|-------------------|---------|---------|---------|---------|<br />| A | 1 | 0 | 0 | 0 |<br />| B | 0 | 1 | 0 | 0 |<br />| C | 0 | 0 | 1 | 0 |<br />| D | 0 | 0 | 0 | 1 |<br />| E | 0 | 0 | 0 | 0 |<br /><br />In this table, "1" indicates the presence of a category, and "0" indicates its absence. As you can see, category E is represented by the absence of all other categories (i.e., when all dummy variables are 0).