The histogram of the residuals shows the distribution of the residuals for all observations.
Use the histogram of the residuals to determine whether the data are skewed or include outliers. The patterns in the following table may indicate that the model does not meet the model assumptions.
What the pattern may indicate
A long tail in one direction
A bar that is far away from the other bars
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.
Normal probability plot of residuals
The normal probability plot of the residuals displays the residuals versus their expected values when the distribution is normal.
If the batch factor is random, use the conditional residuals to evaluate normality.
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.
The following patterns violate the assumption that the residuals are normally distributed.
If you see a nonnormal pattern, use the other residual plots to check for other problems with the model, such as non-constant variance or a time order effect. If the residuals do not follow a normal distribution and the data have fewer than 15 observations, then confidence intervals for predictions, confidence intervals for coefficients, and p-values for coefficients can be inaccurate.
Residuals versus fits
The following graphs show an outlier and a violation of the assumption that the variance of the residuals is constant.
If you identify any patterns or outliers in your residual versus fits plot, consider the following solutions:
Verify that the observation is not a measurement error or data-entry error.
Consider performing the analysis without this observation to determine how it impacts your results.
Residuals versus order
The residuals versus order plot displays the residuals in the order that the data were collected.
Use the residuals versus order plot to verify the assumption that the residuals are independent from one another. Independent residuals show no trends or patterns when displayed in time order. Patterns in the points may indicate that residuals near each other may be correlated, and thus, not independent. Ideally, the residuals on the plot should fall randomly around the center line:
If you see a pattern, investigate the cause. The following types of patterns may indicate that the residuals are dependent.
Residuals versus the variables
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.