In short: In some important uses of statistical model building, traditional regression analysis doesn't work or fit very well. One of the reasons to use regre

In short: In some important uses of statistical model building, traditional regression analysis doesn't work or fit very well. One of the reasons to use regression was to look at the regression coefficients as guides to the importance of the corresponding variables. Well, that was always a bit fishy anyway for more than just a differential, i.e., partial derivative, view. In some important applications, e.g., with some really complicated biomedical data, instead of so much emphasis on the coefficients, what is really needed is a model with some accurate predictions. So to get such predictions, we can drop the emphasis on just traditional regression analysis and interpreting its coefficients and, instead, use much more general means of model building. Relevant old approaches have been Fourier methods for band limited smoothing and interpolation, multivariate least squares spline interpolation, and categorical data analysis, e.g., logistic regression with log-linear going way back in the math for the social sciences. Then Breiman and others did Classification and Regression Trees -- a.k.a., CART for which there is software. In short, build a tree: Start at the root node. Take the input data and partition it into two collections, put each collection in a node that is a child of the root node, and fit each collection separately. Then split those two nodes similarly. Then maybe have a good fit to the data and good predicted values. However, have lost the considerable advantages of traditional regression analysis, but also didn't have or use the sometimes severe assumptions of that old analysis. With traditional regression, had a lot in statistical hypothesis tests, etc., to evaluate the quality of the work, but with the tree, etc. don't have such things. So, for the tree, evaluate the quality by seeing how accurate the model is on a second collection of data, test data, statistically similar to the first collection used to find the tree. If the model is accurate on the test data, then maybe have some good work. Else try again and then do some more statistical work to avoid a case of just getting a spurious fit from just trying until got lucky. Since I have a lot of respect for Breiman, I'm willing to take seriously whatever he wrote.