# Linear Regression

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

**Inputs**

- Data: input dataset
- Preprocessor: preprocessing method(s)

**Outputs**

- Learner: linear regression learning algorithm
- Model: trained model
- Coefficients: linear regression coefficients

The **Linear Regression** widget constructs a learner/predictor that learns a linear function from its input data. The model can identify the relationship between a predictor xi and the response variable y. Additionally, Lasso and Ridge 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 regression works only on regression tasks.

- The learner/predictor name
- Parameters: Fit intercept. Unchecking the option forces the intercept to zero.
- Choose a model to train:
- no regularization
- a Ridge regularization (L2-norm penalty)
- a Lasso bound (L1-norm penalty)
- an Elastic net regularization

## Preprocessing

Linear Regression uses default preprocessing when no other preprocessors are given. It executes them in the following order:

- removes instances with unknown target values
- continuizes categorical variables (with one-hot-encoding)
- removes empty columns
- imputes missing values with mean values

To remove default preprocessing, connect an empty Preprocess widget to the learner.

## Feature Scoring

Linear Regression can be used with Rank for feature scoring. See Learners as Scorers for an example.

## Observing Coefficients

To observe coefficients of linear regression, first build a model, then pass the model to the Data Table. This will automatically connect the *Coefficients* output to the Data Table, where you can sort the table by coefficients and observe which variables positively and negatively correlate with the prediction.

## Example

Below, is a simple workflow with *housing* dataset. We trained **Linear Regression** and Random Forest and evaluated their performance in Test & Score.