Multiple Regression Model Assumptions

In Section 15.1 we introduced the following multiple regression model.

The assumptions about the error term e in the multiple regression model parallel those for the simple linear regression model.

To obtain more insight about the form of the relationship given by equation (15.11), consider the following two-independent-variable multiple regression equation.

The graph of this equation is a plane in three-dimensional space. Figure 15.5 provides an example of such a graph. Note that the value of e shown is the difference between the actual y value and the expected value of y, E( y), when x₁ = x* and x₂ = x*

In regression analysis, the term response variable is often used in place of the term dependent variable. Furthermore, since the multiple regression equation generates a plane or surface, its graph is called a response surface.

Source:  Anderson David R., Sweeney Dennis J., Williams Thomas A. (2019), Statistics for Business & Economics, Cengage Learning; 14th edition.