Questions: A model uses average household income as the dependent variable and county as the independent variable. All 120 Kentucky counties are included and modeled using dummy variables. How many dummy variables will be necessary? 119 120 121 122

Solution Steps

To determine the number of dummy variables needed for a categorical variable with \( n \) categories, we use \( n-1 \) dummy variables. Since there are 120 counties in Kentucky, we will need \( 120 - 1 = 119 \) dummy variables.

We are given that there are \( n = 120 \) counties in Kentucky.

To model a categorical variable with \( n \) categories using dummy variables, we need \( n - 1 \) dummy variables. Therefore, the number of dummy variables required is calculated as follows: \[ n_{\text{dummy}} = n - 1 = 120 - 1 = 119 \]

Final Answer