Multiple Regression

Introduction And Definitions Page 3

(Speaker)

One way to check for more meaningful relationships between data is to add more variables to the model, or in other words, use multiple regression. In a multiple regression, we infer a linear relationship between one response variable and a set of two or more explanatory variables. If your data have three variables (X, Y, and Z), then multiple regression will produce a model of the form:

Z equals A, plus B₁ times X, plus B₂ times Y.

The constant term, A, gives the intercept of the regression equation, and it will have the same units as Z. The slope B₁, for example, is the expected difference in Z between two subjects with the same value of Y but a one-unit difference in X. This concept is referred to as controlling for a variable.

Controlling for a variable is a key concept to keep in mind when performing regression diagnostics to both assess the validity of the model and isolate the impact of a single variable. This interactive will cover two types of regression diagnostics: partial residual plots, and partial regression plots.