How to interpret the beta coefficients of the categorical predictors?

How to interpret the beta coefficients of the categorical predictors?

I have coded the categorical predictor (with three levels) into three dummy variables, and entered the two dummy variables into the regression along with the continuous predictors. My question is: How do I interpret the beta coefficients of the categorical predictors?

How to use categorical predictors in regression analysis?

Dummy coding provides a way of using categorical predictor variables in regression or other statistical analysis. Dummy coding uses only ones and zeros to convey all of the necessary information on categories or groups. In general, a categorical variable with k k levels / categories will be transformed into k − 1 k − 1 dummy variables.

What are continuous predictors in a regression model?

Your interpretation of the continuous predictors you have entered in the regression model seems to be somewhat mistaken. A more appropriate way to understand it would be “the expected increase/decrease in the dependent variable for one unit change in the independent variable”.

How to do regression with categorical variables in R?

In the residual plot (which should now be a box plot instead of a scatter plot) we should see no obvious trends as well as roughly equal variance (spreads) as a function of the explanatory variable. The required plots should still be formed by using the diagRegressionPlots command in my R package.

When to use the intercept of the betas?

You are right about the interpretation of the betas when there is a single categorical variable with k levels. If there were multiple categorical variables (and there were no interaction term), the intercept ( β ^ 0) is the mean of the group that constitutes the reference level for both (all) categorical variables.

When are there multiple categorical variables with k levels?

You are right about the interpretation of the betas when there is a single categorical variable with k levels. If there were multiple categorical variables (and there were no interaction term), the intercept ( ˆβ0) is the mean of the group that constitutes the reference level for both (all) categorical variables.

What is the intercept of a categorical variable?

If there were multiple categorical variables (and there were no interaction term), the intercept ( ˆβ0) is the mean of the group that constitutes the reference level for both (all) categorical variables. Using your example scenario, consider the case where there is no interaction, then the betas are: