Using Regression Tree to Solve Regression Problems

 Regression Tree options

Input attributes

inpnames

Drag and drop the input attributes which will be used to generate predictive rules in the decision tree.

Output attributes

outnames

Drag and drop the attributes which will contain the results of the predictive analysis.

Minimum number of patterns in a leaf

npattnode

The minimum number of patterns that a leaf can contain. If a node contains less than this threshold, tree growth is stopped and the node is considered a leaf.

Maximum impurity in a leaf

maximpur

Specify the threshold on the maximum impurity in a node. The impurity is calculated with the method selected in the Impurity measure option.

By default this value is zero, so trees grow until a pure node is obtained (if possible with training set data) and no ambiguities remain.

Pruning method

treepruning

The method used to prune redundant leaves after tree creation. The following choices are currently available:

• No pruning: leaves are not pruned and the tree is left unchanged.

• Cost-complexity pruning: according to this approach, implemented in CART the tree is pruned through a cost-complexity measure that creates a sequence of sub-trees and finds the best one through the application on a validation set. Each sub-tree is created from the previous one by minimizing a cost-complexity measure that takes into account both the mis-classification level in the training set and the number of leaves.

Method for handling missing data

treeusemissing

Missing data can be handled using one of the following methods:

• Replace with average: missing values are replaced with the value fixed by the user for the corresponding attribute (for example, by means of a Data Manager). If this value is not set, the average computed on the training set is employed.

• Remove from splits: patterns with missing value in the test attribute are removed from the subsequent nodes.

• Include in splits: patterns with missing values in the test attribute at a given node are sent to both the sub-nodes deriving from the split.

Select the attribute to split before the value

selattfirst

If selected, the QUEST method is used to select the best split. According to this approach, the best attribute to split is selected via a correlation measure, such as F-test or Chi-Square. After choosing the best attribute, the best value for splitting is selected.

Aggregate data before processing

aggregate

If selected, identical patterns are aggregated and considered as a single pattern during the training phase.

Initialize random generator with seed

initrandom, iseed

If selected, a seed, which defines the starting point in the sequence, is used during random generation operations. Consequently using the same seed each time will make each execution reproducible. Otherwise, each execution of the same task (with same options) may produce dissimilar results due to different random numbers being generated in some phases of the process.

Append results

append

If selected, the results of this computation are appended to the dataset, otherwise they replace the results of previous computations.

Import the adult dataset with the Import from Text File task, and specify that the second line defines the attribute type.

Add a Split Data task, and split the dataset into test (30%) and training (70%) sets.

Add a Regression Tree task to the process, and double click to open it.

As this is a regression task, we need an ordered output, so we define the hours-per-week attribute as the output attribute.

Drag and drop the following attributes onto the Input attributes pane:

• age

• workclass

• education

• occupation

• race

• sex

• native-country

• income

Click Compute process to start the analysis: the properties of the generated rules can be viewed in the Monitor tab of the RT task, in particular at the end of the process the number of conditions of the rules are distributed as follows : 

• there are 75 rules relative to different output intervals

• there are 33 rules with three conditions, 24 rules with 4 conditions and so on.

The total number of rules, and the minimum, maximum and average of the number of conditions is reported, too.

Analogous histograms can be viewed for covering and error, by clicking on the corresponding tabs.

The rule spreadsheet that can be viewed by adding a Rule Manager task to the process.

For example, rule 1 states that if material-status is in the set {Asian-Pac-Islander, Black, Other, White} then the corresponding hours-per-week is 40.

The total number of generated rules is 75.

We can check out the application of this set of rules to the training and test patterns by adding an Apply Model task, and computing it with the default options. Right-clicking the computed task, and selecting Take a look allows us to check out the results.

The application of the rules generated by the Regression Tree task has added four columns containing:

• the forecast for each pattern: pred(hours-per-week)

• the confidence relative to this forecast: conf(hours-per-week)

• the most important rule that determined the prediction: rule(hours-per-week)

• the classification error, i.e. 1 if misclassified and 0 if correctly classified: err(hours-per-week).

The content of the parentheses is the name of the variable the prediction refers to.

From the summary panel on the left we can see that the model scores a 12.35 of mean square error in the training set.

Selecting Test Set from the Displayed data drop down list shows how the rules behave on new data.

In the test set, the normalized mean square error is about 12.36.