Partial Least Squares

Model Selection and Validation Tables - R-Sq

  

The R-Sq value provides the proportion of variation in each response that is explained by the predictors, indicating how well each model fits your data. Minitab displays the Rimage\squared.gif values for all the calculated models. The Rimage\squared.gif for the selected model is based on the sum of squares in the analysis of variance table.

If you do not use cross-validation, SS and Rimage\squared.gif are the only columns that appear in the model selection and validation table.

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 Rimage\squared.gif for the selected model is located in the row with 10 components. The Rimage\squared.gif for moisture is 93.5% and for fat, 89.6%, indicating that the model fits the data extremely well.