Robust Fitting Tool

R2026b

Interactive robust regression

expand all in page

Description

The Robust Fitting tool fits an ordinary least-squares regression model and a robust regression model to data with a single predictor.

The tool displays a scatter plot of the data and the regression fit lines. Right-click any data point to see its least-squares leverage and robust weight. You can drag any data point to a new location and the tool updates the regression fits automatically.

Required Products

  • MATLAB®

  • Statistics and Machine Learning Toolbox™

Robust Fitting tool

Open the Robust Fitting Tool

  • MATLAB command prompt: Enter robustdemo.

Examples

expand all

This example shows how to start an interactive fitting session with robustdemo.

Generate data from a linear function with added noise.

rng(0,"twister") % for reproducibility
x = -5:5;
y = x + 2*randn(size(x));

Change the value at x = 10 to make it an outlier.

y(10)=30;

Fit an ordinary least-squares regression model and a robust regression model to the data.

robustdemo(x,y)

Plot of an ordinary least-squares regression (in red) and a robust regression (in green) fit to sample data points

The tool displays a scatter plot with two fitted lines. The red line is the fit using ordinary least-squares regression. The green line is the fit using robust regression. Below the plot, the tool displays the equations for the fitted lines, as well as the estimated root mean squared errors for each fit.

Right-click any data point to see its least-squares leverage and robust weight.

Least-squares leverage and robust weight for the point at approximately (10,6)

The right-most point has a relatively high leverage of 0.32. The point exerts a large influence on the least-squares fit, but its small robust weight indicates that it is effectively excluded from the robust fit.

To see how a change in the data affects the fits, click and drag any data point to a new location. The tool displays the updated fits, and you can right-click the point to see the updated leverage and weight.

Least-squares leverage and robust weight for the point moved to approximately (9.5,9.5)

Moving the right-most data point closer to the least-squares line makes the two fitted lines nearly identical. The adjusted data point has significant weight in the robust fit.

Programmatic Use

robustdemo opens the Robust Fitting tool with a plot showing a sample of roughly linear data with one outlier. Below the plot, the tool displays equations of the lines fitted to the data using ordinary least-squares regression and robust regression, as well as estimates of the root mean squared errors.

robustdemo(x,y) fits lines to the data x and responses y using ordinary least-squares regression and robust regression. x and y are numeric vectors.

Version History

Introduced before R2006a

See Also

|