Question

Proof:

Prove that adding more nodes to a regression tree reduces SSE

Answer 1

answer-

introduction of regression decision tree mean you need to follow the material-

1-Replication Requirements- What you’ll need to reproduce the analysis in this tutorial.

2-The idea- A quick overview of how regression trees work.

3-Basic implementation- Implementing regression trees in R.

4-Tuning- Understanding the hyperparameters we can tune.

5-Bagging- Improving performance by fitting many trees.

Basic implementation by adding more nodes to a regression tree reduces SSE

1-We can fit a regression tree using rpart and then visualize it using rpart.plot by the tree.,

2-The fitting process and the visual output of regression trees and classification trees are very similar. Both use the formula method for expressing the model (similar to lm).

3- when fitting a regression tree, we need to set method = "new node". By default, rpart will make an intelligent guess as to what the method value should be based on the data type of your response column, but it’s recommened that you explictly set the method for reproducibility reasons

reduces SSE-

Step 1: you replace the original data with new data. The new data usually have a fraction of the original data's columns and rows, which then can be used as hyper-parameters in the bagging model.and when add new nodes.

Step 2: You build classifiers on each dataset.clasify the nodes when decision tree use, Generally, you can use the same classifier for making models and predictions.

Step 3: you use an average value to combine the predictions of all the classifiers, depending on the problem. Generally, these combined values are more robust than a single model.

Step 4: and you can redeues to SSE bty the add new nodes by Regression tree,