Linear Regression
Synopsis
This operator calculates a linear regression model from the input ExampleSet.
Description
Regression is a technique used for numerical prediction. Regression is a statistical measure that attempts to determine the strength of the relationship between one dependent variable ( i.e. the label attribute) and a series of other changing variables known as independent variables (regular attributes). Just like Classification is used for predicting categorical labels, Regression is used for predicting a continuous value. For example, we may wish to predict the salary of university graduates with 5 years of work experience, or the potential sales of a new product given its price. Regression is often used to determine how much specific factors such as the price of a commodity, interest rates, particular industries or sectors influence the price movement of an asset.
Linear regression attempts to model the relationship between a scalar variable and one or more explanatory variables by fitting a linear equation to observed data. For example, one might want to relate the weights of individuals to their heights using a linear regression model.
This operator calculates a linear regression model. It uses the Akaike criterion for model selection. The Akaike information criterion is a measure of the relative goodness of a fit of a statistical model. It is grounded in the concept of information entropy, in effect offering a relative measure of the information lost when a given model is used to describe reality. It can be said to describe the tradeoff between bias and variance in model construction, or loosely speaking between accuracy and complexity of the model.
Differentiation
Polynomial Regression
Polynomial regression is a form of linear regression in which the relationship between the independent variable x and the dependent variable y is modeled as an nth order polynomial.
Input
training set
This input port expects an ExampleSet. This operator cannot handle nominal attributes; it can be applied on data sets with numeric attributes. Thus often you may have to use the Nominal to Numerical operator before application of this operator.
Output
model
The regression model is delivered from this output port. This model can now be applied on unseen data sets.
example set
The ExampleSet that was given as input is passed without changing to the output through this port. This is usually used to reuse the same ExampleSet in further operators or to view the ExampleSet in the Results Workspace.
weights
This port delivers the attribute weights.
Parameters
feature selection
This is an expert parameter. It indicates the feature selection method to be used during regression. Following options are available: none, M5 prime, greedy, T-Test, iterative T-Test
alpha
This parameter is available only when the feature selection parameter is set to 'T-Test'. It specifies the value of alpha to be used in the T-Test feature selection.
max iterations
This parameter is only available when the feature selection parameter is set to 'iterative T-Test'. It specifies the maximum number of iterations of the iterative T-Test for feature selection.
forward alpha
This parameter is only available when the feature selection parameter is set to 'iterative T-Test'. It specifies the value of forward alpha to be used in the T-Test feature selection.
backward alpha
This parameter is only available when the feature selection parameter is set to 'iterative T-Test'. It specifies the value of backward alpha to be used in the T-Test feature selection.
eliminate colinear features
This parameter indicates if the algorithm should try to delete collinear features during the regression or not.
min tolerance
This parameter is only available when the eliminate colinear features parameter is set to true. It specifies the minimum tolerance for eliminating collinear features.
use bias
This parameter indicates if an intercept value should be calculated or not.
ridge
This parameter specifies the ridge parameter for using in ridge regression.