# Seemingly Unrelated Regression (AI Studio Core)

## Synopsis

This operator performs regressions on coherent ExampleSets with different labels and will take into account the correlation of residuals to build the model. It creates a composite regression model optimized for predicting all label attributes at the same time.## Description

This operator creates a model that consists of multiple
regressions targeting different label attributes for the same set of
examples. Once each single linear regression is built for each input
ExampleSet (delivered at
*unrelated example sets*
ports),
the covariance of the residuals is used to improve the quality of
predictions that are influenced by effects not captured by the attributes.

The first port is dedicated for the original ExampleSet, which
must contain the union of all attributes delivered at
*unrelated
example sets*
input ports. Moreover, all input ExampleSets must
have the same number of examples.

Practically, all
*seemingly unrelated*
input
ExampleSets should have the same examples as the original one, but only
contain a subset of its attributes and its own dedicated label.

Please note that whenever a Seemingly Unrelated Regression model
is applied, the prediction attributes will not have
*prediction
*
roles, as only one attribute can have this role at a time. You
can add
*prediction*
role to a single attribute by using
*Set Role*
operator.

## Input

- training set (IOObject)
- unrelated example sets (IOObject)

## Output

- model (Model)
- example set (Data Table)
This is an example set output port

## Parameters

- feature selectionThe feature selection method used during regression.
- alphaThis is the significance level of the t-test.
- max iterationsThe maximal number of rounds for iterative selection.
- forward alphaThis is the alpha level for the used t-test for selecting attributes.
- backward alphaThis is the alpha level for the used t-test for deselecting attributes.
- eliminate colinear featuresIndicates if the algorithm should try to delete colinear features during the regression.
- min toleranceThe minimum tolerance for the removal of colinear features.
- use biasIndicates if an intercept value should be calculated.
- ridgeThe ridge parameter used for ridge regression. A value of zero switches to ordinary least squares estimate.