Partial Least Squares

Model Selection and Validation Tables - R-Sq (Pred)

  

The predicted R-squared value tells you how well each calculated model predicts the response and is only calculated when you use cross-validation. Minitab selects the PLS model with the highest predicted Rimage\squared.gif.

Examine the Rimage\squared.gif and predicted Rimage\squared.gif values to determine if the model selected by cross-validation is most appropriate. In some cases, you may decide to use a different model than the one selected by cross-validation. Consider an example where adding two components to the model Minitab selects significantly increases Rimage\squared.gif and only slightly decreases the predicted Rimage\squared.gif. Because the predicted Rimage\squared.gif only decreased slightly, the model is not overfit and you may decide it better suits your data.

Example Output

Model Selection and Validation for Moisture

 

Components  X Variance    Error      R-Sq    PRESS  R-Sq (pred)

         1    0.984976  96.9288  0.806643  103.549     0.793436

         2    0.996400  88.9900  0.822479  105.650     0.789245

         3    0.997757  71.9304  0.856510   91.172     0.818127

         4    0.999427  58.3174  0.883666   75.778     0.848836

         5    0.999722  58.1261  0.884048   78.385     0.843634

         6    0.999853  48.5236  0.903203   69.024     0.862308

         7    0.999963  45.9824  0.908272   71.146     0.858076

         8    0.999976  33.1545  0.933862   51.386     0.897493

         9    0.999982  32.8074  0.934554   51.055     0.898154

        10    0.999986  32.7773  0.934615   53.299     0.893677

 

 

Model Selection and Validation for Fat

 

Components  X Variance    Error      R-Sq    PRESS  R-Sq (pred)

         1    0.984976  282.519  0.050127  308.628     0.000000

         2    0.996400  229.964  0.226824  267.199     0.101637

         3    0.997757  115.951  0.610155  143.986     0.515895

         4    0.999427   98.285  0.669550  127.389     0.571698

         5    0.999722   57.994  0.805015   76.435     0.743012

         6    0.999853   53.097  0.821480   72.109     0.757560

         7    0.999963   52.010  0.825133   72.412     0.756540

         8    0.999976   48.842  0.835784   76.432     0.743024

         9    0.999982   34.344  0.884529   67.884     0.771764

        10    0.999986   31.050  0.895604   65.116     0.781068

Interpretation

In this example, cross-validation selected 10 components for the PLS model because it produced the highest average predicted Rimage\squared.gif. The predicted Rimage\squared.gif for moisture is 89.4%; for fat, 78.1%. The scientists determine that the 10-component model is the best model for their data.