Partial Least Squares

Residual Analysis Plots - Residual versus Leverage

  

The residual versus leverage plot is a scatterplot of the standardized residuals versus the leverage of each observation. When examining this plot, look for:

·    Outliers - Observations with standardized residuals greater than +/- 2, which lie outside the horizontal reference lines on the plot.

·    Leverage points - Observations with leverage values greater than 2m / n, where m = the number of components and n = the number of observations, which are considered extreme. They have x-scores far from zero and are to the right of the vertical reference line, which is located at the value 2m / n on the x-axis. If 2m / n is greater than one, the reference line doesn't appear on your plot because leverage values are always between 0 and 1.

Example Output

image\plsr_16n.gif

 

image\plsr_17n.gif

Interpretation

This example has two residual versus leverage plots, one for moisture and one for fat. Brushing the graph identifies points that may be outliers or have high leverage.

·    In the plot for moisture, soybean samples 41 and 42 are to the right of the vertical line, which indicates they have extreme leverage values. Soybean samples 22 and 36 are above the top horizontal line, indicating they are outliers. These points are also outliers on the residual versus fit plot.

·    In the plot for fat, soybean samples 41 and 42 are again leverage points, indicated by their position to the right of the vertical line. Soybean samples 27, 18, and 39 are outliers, indicated by their position above and below the horizontal reference lines. Sample 39 is also an outlier on the residual versus fit plot.