Multiple Regression

Introduction And Definitions Page 4

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A partial residual plot is useful for identifying outliers, as well as determining whether a linear model is the correct type of model to use, as opposed to nonlinear.

A residual is the difference between an actual observed value of y and the predicted value, or y-hat, for a given x value, based on the regression model.

A scatter plot of residuals can reveal whether a linear model is appropriate based on whether there is a discernible pattern in the residuals. If there is no pattern, then a linear model is preferred. If there is a pattern, a linear relationship is likely not the correct choice for the plotted variable.

Residual plots are also useful in identifying outliers. An outlier will have a residual value either well above or well below the others since the actual value of an outlier is much different than the value predicted by the model. Outliers should be evaluated, and if they are due to a collection or calculation error, they should be removed from the study.