Main Content


Interactive robust regression




robustdemo shows the difference between ordinary least squares and robust regression for data with a single predictor. With no input arguments, robustdemo displays a scatter plot of a sample of roughly linear data with one outlier. The bottom of the figure displays equations of lines fitted to the data using ordinary least squares and robust methods, together with estimates of the root mean squared errors.

Use the right mouse button to click on a point and view its least-squares leverage and robust weight.

Use the left mouse button to click-and-drag a point. The displays will update.

robustdemo(x,y) uses x and y data vectors you supply, in place of the sample data supplied with the function.


The following steps show you how to use robustdemo.

  1. Start the example. To begin using robustdemo with the built-in data, simply type the function name:


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

    The resulting figure shows 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. At the bottom of the figure are the equations for the fitted lines, together with the estimated root mean squared errors for each fit.

  2. View leverages and robust weights. Right-click on 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)

    In the built-in data, the right-most point has a relatively high leverage of 0.35. The point exerts a large influence on the least-squares fit, but its small robust weight shows that it is effectively excluded from the robust fit.

  3. See how changes in the data affect the fits. With the left mouse button, click and hold on any data point and drag it to a new location. When you release the mouse button, the displays update:

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

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

Version History

Introduced before R2006a