# "LinearRegression"(Machine Learning Method)

• Method for Predict.
• Predict values using a linear combination of features.

# Details & Suboptions

• The linear regression predicts the numerical output y using a linear combination of numerical features . The conditional probability is modeled according to , with .
• The estimation of the parameter vector θ is done by minimizing the loss function , where m is the number of examples and n is the number of numerical features.
• The following suboptions can be given:
•  "L1Regularization" 0 value of in the loss function "L2Regularization" Automatic value of iin the loss function "OptimizationMethod" Automatic what optimization method to use
• Possible settings for the "OptimizationMethod" option include:
•  "NormalEquation" linear algebra method "StochasticGradientDescent" stochastic gradient method "OrthantWiseQuasiNewton" orthant-wise quasi-Newton method
• For this method, Information[PredictorFunction[],"Function"] gives a simple expression to compute the predicted value from the features.

# Examples

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## Basic Examples(2)

Train a predictor on labeled examples:

Look at the Information:

Predict a new example:

Generate two-dimensional data:

Train a predictor function on it:

Compare the data with the predicted values and look at the standard deviation:

## Options(5)

### "L1Regularization"(2)

Use the "L1Regularization" option to train a predictor:

Generate a training set and visualize it:

Train two predictors by using different values of the "L1Regularization" option:

Look at the predictor function to see how the larger L1 regularization has forced one parameter to be zero:

### "L2Regularization"(2)

Use the "L2Regularization" option to train a predictor:

Generate a training set and visualize it:

Train two predictors by using different values of the "L2Regularization" option:

Look at the predictor functions to see how the L2 regularization has reduced the norm of the parameter vector:

### "OptimizationMethod"(1)

Generate a large training set:

Train predictors with different optimization methods and compare their training times: