# How to | Perform a Linear Regression

One of the most common statistical models is the linear regression model. A linear model predicts the value of a response variable by the linear combination of predictor variables or functions of predictor variables. In the Wolfram Language, LinearModelFit returns an object that contains fitting information for a linear regression model and allows for easy extraction of results and diagnostics.

Simulate a dataset:

Use LinearModelFit to construct a linear model for the data:

Extract the functional form of the model:

Plot the functional form of the model:

Show the data and the line of best fit:

Obtain information about the parameter estimates:

Extract and plot the standardized residuals and fit residuals:

Plot the Cook distances by observation number:

Alternatively, plot the Cook distances versus predictor value:

The previous examples demonstrated a selection of properties supported by LinearModelFit; many more are available:

• Basic Statistics
• Descriptive Statistics
• Continuous Distributions
• Discrete Distributions
• Curve Fitting
• Convolutions and Correlations
• How to: Do Statistical Analysis
• How to: Work with Tables
• Statistics
• Functions Used in Statistics
• Descriptive Statistics
• Statistical Model Analysis
• Statistical Plots Package
• "How to" Topics