5.4 Residuals

Calculate the differences between the observed and predicted values.

• A residual is the difference between the observed response value and the predicted response value for the given value of the explanatory variable: residual =-y y or (residual =-observed pyy redicted .)

Interpret the differences between the observed and predicted values.

• If the residual is positive, the model underpredicts (underestimates) the value of the response variable. If the residual is negative, the model overpredicts (overestimates) the value of the response variable.

Describe the form of association of bivariate data using residual plots.

• A residual plot is a scatterplot of the residuals versus the predicted response values (or the explanatory variable values).
• Residual plots can be used to investigate the appropriateness of the linear regression model for the observed data.
• The linear regression model should only be fit to the data if the data exhibit a linear trend. Apparent randomness in a residual plot for a linear regression model is confirmation of a linear form in the association between the two variables and indicates that the simple linear regression model is an appropriate model for the data.
• Curvature in the residual plot for a linear regression model suggests that the linear model is not the most appropriate model for the data.