The histogram of the residuals shows the distribution of the residuals for all observations.
Pattern | What the pattern may indicate |
---|---|
A long tail in one direction | Skewness |
A bar that is far away from the other bars | An outlier |
Because the appearance of a histogram depends on the number of intervals used to group the data, don't use a histogram to assess the normality of the residuals. Instead, use a normal probability plot.
A histogram is most effective when you have approximately 20 or more data points. If the sample is too small, then each bar on the histogram does not contain enough data points to reliably show skewness or outliers.
The normal probability plot of the residuals displays the residuals versus their expected values when the distribution is normal.
Use the normal probability plot of the residuals to verify the assumption that the residuals are normally distributed. The normal probability plot of the residuals should approximately follow a straight line.
If you see a nonnormal pattern, use the other residual plots to check for other problems with the model, such as missing terms or a time order effect. If the residuals do not follow a normal distribution, the confidence intervals and p-values can be inaccurate.
The residuals versus fits graph plots the residuals on the y-axis and the fitted values on the x-axis.
Use the residuals versus fits plot to verify the assumption that the residuals are randomly distributed and have constant variance. Ideally, the points should fall randomly on both sides of 0, with no recognizable patterns in the points.
Pattern | What the pattern may indicate |
---|---|
Fanning or uneven spreading of residuals across fitted values | Nonconstant variance |
Curvilinear | A missing higher-order term |
A point that is far away from zero | An outlier |
A point that is far away from the other points in the x-direction | An influential point |
If you identify any patterns or outliers in your residual versus fits plot, consider the following solutions:
Issue | Possible solution |
---|---|
Nonconstant variance | Consider using Fit General Linear Model with a Box-Cox transformation. |
An outlier or influential point |
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The residuals versus order plot displays the residuals in the order that the data were collected.
The residual versus variables plot displays the residuals versus another variable. The variable could already be included in your model. Or, the variable may not be in the model, but you suspect it affects the response.
If you see a non-random pattern in the residuals, it indicates that the variable affects the response in a systematic way. Consider including this variable in an analysis.