Percent of error statistics due to largest residuals for MARS® Regression


This command is available with the Predictive Analytics Module. Click here for more information about how to activate the module.

Use the percent of error statistics to examine the amount of error in the model fits from the worst fits. When the analysis uses a validation technique, you can also compare the statistics of the model for the training and test data.

Each row of the table shows the error statistics for the given percentage of residuals. The percent of the Mean Squared Error (MSE) that comes from the largest residuals is usually higher than the percent for the other two statistics. MSE uses the squares of the errors in the calculations, so the most extreme observations typically have the greatest influence on the statistic. Large differences between the percent of error for MSE and the other two measures can indicate that the model is more sensitive to the selection of the basis functions with the R-squared criterion or the mean absolute deviation criterion.

When you use a validation technique, the results include separate statistics for the training data and for the test data. You can compare the statistics to examine the relative performance of the model on the training data and on new data. The test statistics are usually a better measure of how the model will perform for new data.

A possible pattern is that a small percentage of the residuals account for a large portion of the error in the data. For example, in the following table, the total size of the data set is about 4400. From the perspective of the MSE, that indicates that 1% of the data account for about 13% of the error. In such a case, the 31 cases that contribute most of the error to the model can represent the most natural opportunity to improve the model. Finding a way to improve the fits for those cases leads to a relatively large increase in the overall performance of the model.

This condition can also indicate that you can have greater confidence in regions of the model that do not have cases with the largest errors. Because most of the error comes from a small number of cases, the fits for the other cases are relatively more accurate.

Percent of Error Statistics Due to Largest Residuals

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