Multiple Linear Regression – Learn It 4

  • Write and describe a multiple linear regression model equation
  • Calculate and describe the unadjusted coefficient of determination
  • Assess the model assumptions with a residual or a predicted values plot

Residuals

We can assess whether or not it is reasonable to fit a linear regression model using residual plots, similar to simple linear regression. In multiple linear regression, the [latex]y[/latex]-axis has the residual values, and the [latex]x[/latex]-axis has the explanatory variables and/or the fitted values. For a multiple linear regression model, you create a residual plot for each continuous explanatory variable, as well as the fitted value.

We would expect to see the residual values appear randomly scattered across the [latex]x[/latex]-values with no clear patterns (e.g., residual plots that display a curvature violate the linearity condition). Residual plots that increase or decrease in magnitude (distance from zero) violate the constant variance condition.

The residual plot of the residuals vs. predicted values accounts for all the variables in the model. Residual plots of the residuals vs. individual exploratory variables allow us to identify a potential source of a violation. The normality condition is beyond the scope of this course.