.. _model.lr:

Linear Regression
=================

.. figure:: icons/linear-regression.png

A linear regression algorithm with optional L1 (LASSO), L2 (ridge) or L1L2 (elastic net) regularization.

Signals
-------

**Inputs**:

-  **Data**

   A data set

-  **Preprocessor**

   A preprocessed data set.

**Outputs**:

-  **Learner**

   A linear regression learning algorithm with settings as specified in the
   dialog.

-  **Predictor**

   A trained regressor. Output signal sent only if input *Data* is present.

Description
-----------

The **Linear Regression** widget constructs a learner/predictor that learns a `linear function <https://en.wikipedia.org/wiki/Linear_regression>`_ from its input data. The model can identify the relationship between a predictor xi and the response variable y. Additionally, `Lasso <https://en.wikipedia.org/wiki/Least_squares#Lasso_method>`_ and `Ridge <https://en.wikipedia.org/wiki/Least_squares#Lasso_method>`_ regularization parameters can be specified. Lasso regression minimizes a penalized version of the least squares loss function with L1-norm penalty and Ridge regularization with L2-norm penalty.

Linear regreesion works only on regression tasks.

.. figure:: images/LinearRegression-stamped.png
   :scale: 50 %

1. The learner/predictor name
2. Choose a model to train:

   -  no regularization 
   -  a `Ridge <https://en.wikipedia.org/wiki/Least_squares#Lasso_method>`_
      regularization (L2-norm penalty)
   -  a `Lasso <https://en.wikipedia.org/wiki/Least_squares#Lasso_method>`_
      bound (L1-norm penalty)
   -  an `Elastic net <https://en.wikipedia.org/wiki/Elastic_net_regularization>`_
      regularization

3. Produce a report.
4. Press *Apply* to commit changes. If *Apply Automatically* is ticked, changes are committed automatically. 

Example
-------

Below, is a simple workflow with *housing* data set. We trained **Linear Regression** and :doc:`Random Forest <../model/randomforest>` and evaluated their performance in :doc:`Test&Score <../evaluation/testandscore>`.

.. figure:: images/LinearRegression-regression.png