# overfitting of regression tree from the beginning

I am trying to build a regression tree to model insurance claim frequencies. I have 36000 observations and 9 covariates.

My model overfits right from the beginning!, ie as the cost complexity goes down, the relative validation error goes up. I am using this command in R:

rpart_model <-rpart(cbind(Duration,Nbclaims) ~ Gender + DriverAge +
CarAge + Area + Leasing + Power + Fract + Contract, data = motor,    method="poisson",parms=list(shrink=1), control=rpart.control(cp=0))


and obtain these results:

        CP nsplit rel error xerror     xstd
1   1.9019e-03        0     1.00000   1.0002   0.022911

2   1.3854e-03        1     0.99810   1.0004   0.022973

3   1.1587e-03        2     0.99671   1.0057   0.023185

4   9.1009e-04        5     0.99324   1.0069   0.023269

5   9.0852e-04        6     0.99233   1.0134   0.023526

6   8.8781e-04        7     0.99142   1.0134   0.023531

7   8.5397e-04       10     0.98872   1.0150   0.023603

8   8.5119e-04       11     0.98786   1.0153   0.023621


I have done my research to try and figure this issue out but am completely stuck for the moment, could anyone help with this?

Complexity Parameter CP describes a threshold $$T$$. If branch provides improvement less than $$T$$ it is deleted from the tree. You are using cp=0 so you told the algorithm to DO NOT prune any branches independly on their results! CP tested by printcp are very small also.
model_pruned <- prune(rpart_model, cp=0.01)

You can compare your trees' structures using rpart.plot(tree_object) method. I think the original tree is way too complex and that is why it overfitts at start.