How can I determine the r-squared value for regression trees?

I am using regression trees and I know that there is a way to determine an R^2 value for the tree, but I am not sure how to do it. I am using the function RegressionTree.fit with Matlab 2013a, but just downloaded 2014a on another computer. So I could use either version.

Answer 1

[the cyclist]

I don't think this is an output property of the model, but it is easy to calculate. Here is an example based on the one in the documentation for RegressionTree.fit:

load carsmall
tree = RegressionTree.fit([Weight, Cylinders],MPG,'MinParent',20,'PredictorNames',{'W','C'})

mpg_predicted = predict(tree,[Weight,Cylinders]);

RMSE = sqrt(nanmean((mpg_predicted-MPG).^2))

RMSE0 = nanstd(MPG-nanmean(MPG));

r_sq = 1 - (RMSE/RMSE0)

I would double-check all that, but you should be in the right direction.

[Janet Reimer]

I do not have a value that I would use as the MPG in this example. I have a 15,000 x 3 matrix of predictors and a vector for the response. so tree = RegressionTree.fit(X,y). How do I deal with the extra variable in the example?

[the cyclist]

You might want to look at the example I mentioned. In that case, MPG is the response variable. So, I think in your case you are going to do

y_predicted = predict(tree,X);

RMSE = sqrt(nanmean((y_predicted-y).^2))
RMSE0 = nanstd(y-nanmean(y));
r_sq = 1 - (RMSE/RMSE0)