Which assumptions should be checked for regression tree to validated model? I am working with regression tree. I have four predictors. There is a exponential relationship between predictor and dependent variable. But after building predictive model I cannot understand whether my model is a right one or not. Which tests can assure that my model is a good one?. For regression tree, is it necessary to test all the assumptions which is applied to linear regression.
I have checked and found that residuals are homoscedastic but in q-q plot residuals does not lies along the diagonal line. Here I attached the q-q plot please check it and suggests me whether residuals are normally distributed or not.
 A: With tree regression, you can be a little more relaxed about assumptions.  In particular, you simply give up on the "linearity" (or more precisely, the correct functional specification) assumption, because the natural process obviously does not follow the piecewise flat segmentation that is assumed by the tree model. Instead, you simply acknowledge that the model is wrong with regard to the "linearity" assumption, but proceed anyway, hoping that the flexibility and ease of interpretation of the model overcome this glaringly incorrect assumption.
The normality and constant variance assumptions have at least two useful aspects as regards tree regression.  (1)  The within-node prediction bounds $\hat y \pm 2 rmse$ make sense under these conditions; (2) The least squares estimation criteria also makes sense under these conditions.  Absent these conditions, alternate estimation procedures and prediction bounds are better.
In your case, it is clear from the outlier-prone character of the q-q plot that you could do better my using something other than least squares. Perhaps mean absolute deviations.
It is also clear that your model will miss observations occasionally by many more standard deviations (eg, 5) than you might expect had the distributions been normal. This is not necessarily a problem; it's just good to know how your model works.
A: Regression trees (recursive partitioning) make these main assumptions:

*

*Sample size is huge (say > 100,000, depending on the number of candidate features) so that the tree structure has some stability

*Relationships between continuous predictors and outcome are piecewise flat (as stated earler)

Assumption 2. is never seen in nature so you know already that regression trees have poor fit to the data, especially if there are any strong continuous predictors.  Assumption 1 is something you already know.
The failure of individual trees to be competitive at prediction and explanation is why random forests, bagging, and boosting exist.
Here is a paper on sample sizes needed for trees: https://bmcmedresmethodol.biomedcentral.com/articles/10.1186/1471-2288-14-137
