Residual

A residual is defined as the difference between the observed and predicted value, that is:

Additionally, studentized residuals are computed. The formula for the studentized residuals is given by:

A normal probability plot of the (studentized) residuals is constructed as follows. First, the (studentized) residuals are rank ordered. From these ranks, Statistica® computes z values (that is, standardized values of the normal distribution) based on the assumption that the data come from a normal distribution.

These z values are plotted on the y-axis in the plot. If the observed (studentized) residuals (plotted on the x-axis) are normally distributed, all values should fall onto a straight line. If the residuals are not normally distributed, they deviate from the line. Outliers can also become evident in this plot. If there is a general lack of fit and the data seem to form a clear pattern (example, an S shape) around the line, the variable has to be transformed in some way (example, a log transformation to "pull-in" the tail of the distribution, etc.)