Chapter 8 examined regression modeling for the simple linear regression case of a single predictor and a single response. Clearly, however, data miners and predictive analysts are usually interested in the relationship between the target variable and a set of (two or more) predictor variables. Most data mining applications enjoy a wealth of data, with some data sets including hundreds or thousands of variables, many of which may have a linear relationship with the target (response) variable. *Multiple regression modeling* provides an elegant method of describing such relationships. Compared to simple linear regression, multiple regression models provide improved precision for estimation and prediction, analogous to the improved precision of regression estimates over univariate estimates. A *multiple regression model* uses a linear surface, such as a plane or hyperplane, to approximate the relationship between a continuous response (target) variable, and a set of predictor variables. While the predictor variables are typically continuous, categorical predictor variables may be included as well, through the use of indicator (dummy) variables.

In simple linear regression, we used a straight line (of dimension 1) to approximate the relationship between the response and one predictor. Now, suppose we would like to approximate the relationship between a response and two continuous predictors. In this ...

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