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When you want to include categorical variables in a regression model, you need to use indicator variables. These variables allow you to transform non-numeric data into a format that can be used within a regression analysis. In our example, the 'garage' variable is categorical with three levels: attached, detached, and no garage.
To incorporate this into your model, create specific indicators to represent these categories. For instance:

• 1 for 'attached'
• 0 for 'detached'
• n/a for 'no garage' (implied)

Indicator variables can take the value of 1 if the condition they represent is true and 0 otherwise. Defining them properly helps you understand the influence of different categories on the dependent variable, which in this case is the selling price of a home.

Dummy variables are a type of indicator variable that are especially useful when dealing with multivariate categorical data. In this scenario, since 'garage' can take three categories, we create two dummy variables. The reason for choosing two instead of three is to avoid multicollinearity, which can distort the regression results. For example:

• Dummy Variable 1 (X1): 1 if garage is attached, 0 otherwise
• Dummy Variable 2 (X2): 1 if garage is detached, 0 otherwise

Dummy variables replace categorical data with 1s and 0s, making it easier to include categorical information in a regression model. The values of 0 or 1 allow the regression model to factor in the presence or absence of a particular category. For the 'no garage' category, both dummy variables will be 0, serving as the reference category for the regression model.

Multicollinearity occurs when your independent variables are highly correlated. This condition can cause problems in your regression analysis, making it difficult to separate the individual effect of each variable. In the given example, if we used three dummy variables for 'garage' —one for each category— we would run into perfect multicollinearity because the total of all three dummy variables will always add up to 1. To avoid this, we use one less dummy variable than the number of categories.
Here’s why:

• If you include all three categories as separate dummy variables, you introduce redundancy, leading to an overfitting issue where the model cannot accurately estimate the coefficients.
• This redundancy implies that one dummy variable can always be predicted from the others (perfect collinearity), which invalidates the regression coefficients.

In our example, having two dummy variables for three categories ensures that the model is both simple and functional while avoiding multicollinearity. This way, each category is clearly represented in the model without redundancy.