Partial Least Squares

Residual Analysis Plots - Residual Normal Probability Plot

  

This graph plots the standardized residuals versus their expected values when the distribution is normal. The residuals from the analysis should be normally distributed. In practice, for data with a large number of observations, moderate departures from normality do not seriously affect the results.

The normal probability plot of the residuals should roughly follow a straight line. Use this plot to look for the following:

This pattern...

Indicates...

Not a straight line

Nonnormality

Curve in the tails

Skewness

A point far away from the line

An outlier

Changing slope

An unidentified variable

If your data have fewer than 50 observations, the plot may display curvature in the tails even if the residuals are normally distributed. As the number of observations decreases, the probability plot may show even greater variation and nonlinearity. Use the normal probability plot and goodness-of-fit tests to assess the normality of residuals in small data sets.

Example Output

image\plsr_12n.gif

 

image\plsr_13n.gif

Interpretation

For the soybean data, the residuals for the plot of fat appear to follow a straight line. No evidence of nonnormality, skewness, outliers, or unidentified variables exists. The residuals for the moisture plot do not appear to follow a straight line. Several points fall outside the 95% confidence interval, indicating problems with normality. This could result from observations with unusually large residuals.