Partial Least Squares

Predicted Response Tables - Test R-Sq

Minitab displays a test R-sq only when you have response values for the observations in your test set. Use the test R $image\squared.gif$ to judge the accuracy of cross-validation in estimating your model's predictive ability. If you use cross-validation, compare the test R $image\squared.gif$ to the predicted R-squared. Ideally, these values should be similar. A test R $image\squared.gif$ that is significantly smaller than the predicted R $image\squared.gif$ indicates that cross-validation is overly optimistic about the model's predictive ability or that the two data samples are from different populations.

Example Output

Predicted Response for New Observations Using Model for Moisture

Row Fit SE Fit 95% CI 95% PI

1 14.5184 0.388841 (13.7343, 15.3026) (12.5910, 16.4459)

2 9.3049 0.372712 ( 8.5532, 10.0565) ( 7.3904, 11.2193)

3 14.1790 0.504606 (13.1614, 15.1966) (12.1454, 16.2127)

4 16.4477 0.559704 (15.3189, 17.5764) (14.3562, 18.5391)

5 15.1872 0.358044 (14.4652, 15.9093) (13.2842, 17.0903)

6 9.4639 0.485613 ( 8.4846, 10.4433) ( 7.4492, 11.4787)

Test R-sq: 0.906451

Predicted Response for New Observations Using Model for Fat

Row Fit SE Fit 95% CI 95% PI

1 18.7372 0.378459 (17.9740, 19.5004) (16.8612, 20.6132)

2 15.3782 0.362762 (14.6466, 16.1098) (13.5149, 17.2415)

3 20.7838 0.491134 (19.7933, 21.7743) (18.8044, 22.7632)

4 14.3684 0.544761 (13.2698, 15.4670) (12.3328, 16.4040)

5 16.6016 0.348485 (15.8988, 17.3044) (14.7494, 18.4538)

6 20.7471 0.472648 (19.7939, 21.7003) (18.7861, 22.7080)

Test R-sq: 0.762701

Interpretation

In this example, the scientists had response data for the new flour samples.

· For moisture, the test R $image\squared.gif$ is 90.6%. The predicted R $image\squared.gif$ for moisture using the 10-component model (located in the model selection and validation table) is 89.4%.

· For fat, the test R $image\squared.gif$ is 76.3%. The predicted R $image\squared.gif$ for fat using the 10-component model (located in the model selection and validation table) is 78.1%.

Because the test R $image\squared.gif$ values are very similar to the predicted R $image\squared.gif$ values for both moisture and fat, the scientists conclude that prediction and cross-validation accurately estimated the model's predictive ability.