Section 13.3 Summary
- Multiple regression describes the linear relationship between one response variable and more than one predictor variable, . The multiple regression equation is an extension of the regression equation: where represents the number of variables in the equation, and represent the multiple regression coefficients.
- The multiple coefficient of determination represents the proportion of the variability in the response that is explained by the multiple regression equation. The adjusted coefficient of determination adjusts the value of as a penalty for having too many unhelpful variables in the equation.
- The multiple regression model is an extension of the regression model from Section 13.1. The population multiple regression equation is . The test is performed to assess the significance of the overall model.
- To determine whether a particular variable has a significant linear relationship with the response variable , we perform the test for the significance of that variable. One may perform as many such tests as there are variables in the model, which is assuming the overall test is significant.
- Dummy variables are 0/1 variables that allow, via recoding, categorical variables to be included in the multiple regression model.
- The Strategy for Building a Multiple Regression Model brings together all we have learned about multiple regression modeling.