Regression Tree/Decision Tree for Regression  Python for Integrated Circuits   An Online Book  

Python for Integrated Circuits http://www.globalsino.com/ICs/  


Chapter/Index: Introduction  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z  Appendix  
================================================================================= A regression tree, also known as a decision tree for regression, is a machine learning algorithm used for solving regression problems. It is a type of supervised learning technique that is primarily employed for predicting a continuous numeric output variable, as opposed to a classification tree, which is used for predicting categorical labels. Here's how a regression tree works:
Regression trees are easy to interpret and visualize, making them useful for gaining insights into the relationships between input features and the target variable. However, they are prone to overfitting the training data, especially when the tree becomes too deep and complex. To mitigate this issue, techniques like pruning (removing or simplifying branches of the tree) and using ensemble methods like Random Forests are often employed. JMP (pronounced "jump") is a powerful statistical software package primarily used for data analysis, visualization, and exploration. It offers a wide range of statistical and data mining tools, including decision trees, which can be used for both classification and regression tasks. In JMP, you can create regression trees using the "Fit Model" platform or the "Partition" platform, depending on the version and edition of JMP you are using. Here's how you can create a regression tree in JMP:
Once you've created the regression tree in JMP, you can visualize and interpret the results. JMP provides various graphical and tabular representations of the tree, making it easy to understand the relationships between the predictor variables and the response variable. Keep in mind that the specific steps and features available in JMP may vary slightly depending on the version of the software you are using, so it's a good idea to consult the documentation or help resources provided with your version of JMP for more detailed instructions. The key difference between classification trees and regression trees lies in the nature of the response variable they are designed to predict:
The predicted value for a regression tree node can be given by, [4003a] where,
Therefore, is calculated as the average of the target values for all the data points in the region R_{m}. Then, we have the mean squared error (MSE) for the regression tree node , given by, [4003b] where, The numerator on the right side is the sum of the squared differences between the actual target values ) and the predicted values (y^_{m}) for all data points in the region .The mean squared error is a commonly used metric to assess the performance of regression models. Figure 4003a plots month and latitude which are suitable for ski around the world. Figure 4003a. Month and latitude which are suitable for ski around the world. (Code) Figure 4003b plots the regression tree with the month and latitude, which are suitable for ski around the world, described in Figure 4003a.
Note that decision trees can be used for both classification and regression tasks, and they are capable of handling both categorical and numerical variables. Furthermore, decision trees are fairly high variance models. (see page4313) Table 4003. Applications and related concepts of decision tree.
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