13.1 Introduction to Multiple Regression

Previously, we studied simple linear regression, which allowed us to build a model of the linear relationship between one independent variable and one dependent variable.  Then we could use the model to make predictions about the value of the dependent variable. For example, a simple linear regression model can be used to predict a person’s salary (the dependent variable) from the person’s age (the independent variable).

But, what if more than one independent variable impacts the value of the dependent variable?  For example, a person’s salary depends on more factors than just the person’s age.  A person’s salary can also be related to their experience, their education, and their profession.  We want to build a model that allows us to incorporate more than one independent variable.  Because more information can be used in the model, additional independent variables can make regression models more accurate in predicting the dependent variable.  A multiple regression model allows us to use two or more independent variables to predict one dependent variable.

As we saw with simple linear regression, in addition to building the model, we need ways to assess how good the multiple regression model fits the data and how good the model is at predicting values of the dependent variable.