# Linear Regression component

Use this component to create a linear regression model for use in a pipeline. Linear regression attempts to establish a linear relationship between one or more independent variables and a numeric outcome, or dependent variable.

You use this component to define a linear regression method, and then train a model using a labeled dataset. The trained model can then be used to make predictions.

Linear regression is a common statistical method, which has been adopted in machine learning and enhanced with many new methods for fitting the line and measuring error. Simply put, regression refers to prediction of a numeric target. Linear regression is still a good choice when you want a simple model for a basic predictive task. Linear regression also tends to work well on high-dimensional, sparse data sets lacking complexity.

Azure Machine Learning supports a variety of regression models, in addition to linear regression. However, the term "regression" can be interpreted loosely, and some types of regression provided in other tools are not supported.

• The classic regression problem involves a single independent variable and a dependent variable. This is called simple regression. This component supports simple regression.

• Multiple linear regression involves two or more independent variables that contribute to a single dependent variable. Problems in which multiple inputs are used to predict a single numeric outcome are also called multivariate linear regression.

The Linear Regression component can solve these problems, as can most of the other regression components.

• Multi-label regression is the task of predicting multiple dependent variables within a single model. For example, in multi-label logistic regression, a sample can be assigned to multiple different labels. (This is different from the task of predicting multiple levels within a single class variable.)

This type of regression is not supported in Azure Machine Learning. To predict multiple variables, create a separate learner for each output that you wish to predict.

For years statisticians have been developing increasingly advanced methods for regression. This is true even for linear regression. This component supports two methods to measure error and fit the regression line: ordinary least squares method, and gradient descent.

• Gradient descent is a method that minimizes the amount of error at each step of the model training process. There are many variations on gradient descent and its optimization for various learning problems has been extensively studied. If you choose this option for Solution method, you can set a variety of parameters to control the step size, learning rate, and so forth. This option also supports use of an integrated parameter sweep.

• Ordinary least squares is one of the most commonly used techniques in linear regression. For example, least squares is the method that is used in the Analysis Toolpak for Microsoft Excel.

Ordinary least squares refers to the loss function, which computes error as the sum of the square of distance from the actual value to the predicted line, and fits the model by minimizing the squared error. This method assumes a strong linear relationship between the inputs and the dependent variable.

## Configure Linear Regression

This component supports two methods for fitting a regression model, with different options:

### Create a regression model using ordinary least squares

1. Add the Linear Regression Model component to your pipeline in the designer.

You can find this component in the Machine Learning category. Expand Initialize Model, expand Regression, and then drag the Linear Regression Model component to your pipeline.

2. In the Properties pane, in the Solution method dropdown list, select Ordinary Least Squares. This option specifies the computation method used to find the regression line.

3. In L2 regularization weight, type the value to use as the weight for L2 regularization. We recommend that you use a non-zero value to avoid overfitting.

4. Select the option, Include intercept term, if you want to view the term for the intercept.

Deselect this option if you don't need to review the regression formula.

5. For Random number seed, you can optionally type a value to seed the random number generator used by the model.

Using a seed value is useful if you want to maintain the same results across different runs of the same pipeline. Otherwise, the default is to use a value from the system clock.

6. Add the Train Model component to your pipeline, and connect a labeled dataset.

7. Submit the pipeline.

### Results for ordinary least squares model

After training is complete:

• To make predictions, connect the trained model to the Score Model component, along with a dataset of new values.

### Create a regression model using online gradient descent

1. Add the Linear Regression Model component to your pipeline in the designer.

You can find this component in the Machine Learning category. Expand Initialize Model, expand Regression, and drag the Linear Regression Model component to your pipeline

2. In the Properties pane, in the Solution method dropdown list, choose Online Gradient Descent as the computation method used to find the regression line.

3. For Create trainer mode, indicate whether you want to train the model with a predefined set of parameters, or if you want to optimize the model by using a parameter sweep.

• Single Parameter: If you know how you want to configure the linear regression network, you can provide a specific set of values as arguments.

• Parameter Range: Select this option if you are not sure of the best parameters, and want to run a parameter sweep. Select a range of values to iterate over, and the Tune Model Hyperparameters iterates over all possible combinations of the settings you provided to determine the hyperparameters that produce the optimal results.

4. For Learning rate, specify the initial learning rate for the stochastic gradient descent optimizer.

5. For Number of training epochs, type a value that indicates how many times the algorithm should iterate through examples. For datasets with a small number of examples, this number should be large to reach convergence.

6. Normalize features: If you have already normalized the numeric data used to train the model, you can deselect this option. By default, the component normalizes all numeric inputs to a range between 0 and 1.

Note

Remember to apply the same normalization method to new data used for scoring.

7. In L2 regularization weight, type the value to use as the weight for L2 regularization. We recommend that you use a non-zero value to avoid overfitting.

8. Select the option, Decrease learning rate, if you want the learning rate to decrease as iterations progress.

9. For Random number seed, you can optionally type a value to seed the random number generator used by the model. Using a seed value is useful if you want to maintain the same results across different runs of the same pipeline.

10. Train the model:

• If you set Create trainer mode to Single Parameter, connect a tagged dataset and the Train Model component.

• If you set Create trainer mode to Parameter Range, connect a tagged dataset and train the model by using Tune Model Hyperparameters.

Note

If you pass a parameter range to Train Model, it uses only the default value in the single parameter list.

If you pass a single set of parameter values to the Tune Model Hyperparameters component, when it expects a range of settings for each parameter, it ignores the values, and uses the default values for the learner.

If you select the Parameter Range option and enter a single value for any parameter, that single value you specified is used throughout the sweep, even if other parameters change across a range of values.

11. Submit the pipeline.

### Results for online gradient descent

After training is complete:

• To make predictions, connect the trained model to the Score Model component, together with new input data.

## Next steps

See the set of components available to Azure Machine Learning.