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

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

Learns a linear function of its input data.

Signals
-------

**Inputs**:

-  **Data**

   A data set

-  **Preprocessor**

   A preprocessed data set.

**Outputs**:

-  **Learner**

   A learning algorithm with the supplied parameters

-  **Predictor**

   A trained regressor. Signal *Predictor* sends the output signal only if
   signal *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/Tikhonov_regularization>`_
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.

.. figure:: images/linear-regression1-stamped.png

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 showing how to use both the *Predictor* and
the *Learner* output. We used the *Housing* data set. For the *Predictor*, we input the prediction model
into the :doc:`Predictions <../evaluation/predictions>` widget and view the results in the :doc:`Data Table <../data/datatable>`. For the 
*Learner*, we can compare different learners in the :doc:`Test&Score <../evaluation/testlearners>` widget.

.. figure:: images/linear-regression-example1.png