Percent of error statistics due to largest residuals for CART^® Regression

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 tree is more sensitive to the selection of splitting the nodes with least squared error or least absolute deviation.

When you use a validation technique, Minitab calculates separate statistics for the training data and for the test data. You can compare the statistics to examine the relative performance of the tree on the training data and on new data. The test statistics are usually a better measure of how the tree 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 4500. From the perspective of the MSE, that indicates that 1% of the data account for about 12% of the error. In such a case, the 45 cases that contribute most of the error to the tree can represent the most natural opportunity to improve the tree. Finding a way to improve the fits for those cases leads to a relatively large increase in the overall performance of the tree.

This condition can also indicate that you can have greater confidence in nodes of the tree 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.