Partial Least Squares

Model Selection and Validation Tables - Components and X-Variance

  

Minitab displays a model selection and validation table for each response in your model. The column labeled components lists the models that Minitab calculates. The first model has one component, the second model two components, the third model three components, and so on. Each row contains information on the models Minitab calculates. The column labeled X Variance indicates how much of the variance in the predictors is explained by the model.

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, the scientists used cross-validation, which selected 10 components for the PLS model. Because they did not specify the number of components to cross-validate, by default, Minitab validated 10 components.

The x-variance value for the model with 10 components is 0.99, which indicates that the model explains virtually all of the variance in the predictors.