Residual Analysis - Probability Plots Tab

Multiple Regression - Computational Approach

Select the Probability plots tab of the Residual Analysis dialog to access options to review probability plots. All residual plots and spreadsheets are unlimited/user-limited as defined by the Maximum number of rows (cases) in a single results Spreadsheet or Graph box on the Residual Analysis - Advanced tab. Note that when Pairwise deletion is selected in the MD deletion group box in the Startup Panel, the program will substitute any missing values with the respective means in the computations for predicted and residual values (and related statistics).

Normal plot of residuals

Click the Normal plot of residuals button to produce a normal probability plot of the residuals. Multiple regression assumes that the residual values (observed minus predicted values) are normally distributed, and that the regression function (the relationship between the independent and dependent variables) is linear in nature. If any of these assumptions is grossly violated, then the regression coefficients (B coefficients) may be affected (inflated or deflated), and the statistical significance tests inflated or deflated. If "all is well," one can expect the residual values to be normally distributed. Normal probability plots provide a quick way to visually inspect to what extent the pattern of residuals follows a normal distribution. If the residuals are not normally distributed, they will deviate from the line. Outliers may also become evident in this plot. If there is a general lack of fit, and the data seem to form a clear pattern (e.g., an S shape) around the line, then the dependent variable may have to be transformed in some way (e.g., a log transformation to "pull in" the tail of the distribution, etc.; refer to the manual for additional details). For more information on how the standard normal probability plot is constructed, see Normal probability plots.

Half-normal plot

Click the Half-normal plot button to produce a half-normal probability plot of the residuals. The half-normal probability plot is constructed in the same way as the standard normal probability plot, except that only the positive half of the normal curve is considered. Consequently, only positive normal values will be plotted on the y-axis.

Detrended normal plot

Click the Detrended normal plot button to produce a detrended normal probability plot of the residuals. The detrended normal probability plot is constructed in the same way as the standard normal probability plot, except that, before the plot is produced, the linear trend is removed. This often "spreads out" the plot, thereby allowing you to detect patterns of deviations more easily.