Residuals vs Predicted Plot

This is a plot of the residuals versus the ascending predicted response values. It is a visual check for the assumption of constant variance. The plot should be a random scatter having a consistent top to bottom range of residuals across the predictions on the X1 axis.

An expanding variance (“megaphone pattern <”), along with smiles and frowns on this plot indicates the need for a transformation.

This plot is also used to examine outliers. Outliers are runs with residuals outside the red lines on the plot. An outlier is an observation that is not fit well by the model. This can mean the observation has a problem, the wrong model has been used, or some combination of both.

The limits are computed as Student’s t-values,

\(\pm\,{\large t}\left(\frac{\alpha}{2n},\, n-p-1\right)\)

where n is the number of runs and p is the number of coefficients in the model including the intercept.

The n is used as both a basis for the degrees of freedom, and the Bonferroni correction to a family-wise alpha-risk for all the runs.