Practical Data Analysis with JMP®

Residual Analysis

Several of the conditions just cited refer directly to the random error term in the model, ε_i. Because we cannot know the precise location of the theoretical regression line, we cannot know the precise values of the ε_is. 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 Y_i and the fitted line to approximate the ε_i 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 ...