Question

A regression model to predict the price of diamonds included the following predictor variables: the weight of the stone (in carats where 1 carat = 0.2 gram), the color rating (D, E, F, G, H, or I), and the clarity rating (IF, VVS1, VVS2, VS1, or VS2).

How many indicator variables would be included in the model in order to prevent the least squares estimation from failing?

Answer 1

To avoid multicollinearity in the regression model for predicting diamond prices with categorical predictors, 9 indicator variables are used: 5 for color ratings and 4 for clarity ratings.

Step-by-step explanation:

To predict the price of diamonds using a regression model with three predictor variables – the weight of the stone in carats, the color rating, and the clarity rating – we need to use indicator (or dummy) variables for the categorical predictors (color and clarity ratings). Each categorical variable with N categories must be represented by N-1 dummy variables to ensure the model can estimate parameters without falling into the 'dummy variable trap' that would lead to perfect multicollinearity.

For the color rating with 6 possible categories (D, E, F, G, H, I), we would use 5 dummy variables (one less than the total number of categories). For the clarity rating with 5 categories (IF, VVS1, VVS2, VS1, VS2), we would use 4 dummy variables. The weight of the stone, being a continuous variable, does not need a dummy variable.Therefore, the total number of indicator variables included in the model would be 5 (color) + 4 (clarity) = 9 indicator variables.