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Practical Data Analysis with JMP® by Robert Carver

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Residual Analysis

Several of the conditions just cited refer directly to the random error term in the model, εi. Because we cannot know the precise location of the theoretical regression line, we cannot know the precise values of the εis. The random error term values are the difference between the observed values of Y and the position of the theoretical line. Although we don't know where the theoretical line is, we do have a fitted line and we'll use the differences between each observed Yi and the fitted line to approximate the εi values.

These differences are called residuals. Again, a residual is the difference between an observed value of Y and the fitted value of Y corresponding to the observed value of X. Visually, it is the vertical distance ...

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