The ReturnResiduals Option

The residuals of a fit are the differences between the fitted values and the experimental values of the dependent variable. The least-squares technique used by LinearFit attempts to minimise the residuals.

As part of the graphical output of the fit the residuals of the fit are graphed, usually as a small insert in the main graph. The ReturnResiduals option allows you to see the actual numeric values of those residuals. The relevant part of the Fit Options screen looks like this when we set the option to True:

After setting this option, say we fit some student-taken data from a constant volume gas thermometer to a straight line. The results of the fit are:

A0 = -263. ± 18. A1 = 3.71 ± 0.21. Sum of Squares = 133.9 for 3 degrees of freedom. (Assumed statistical error in the dependent variable: 6.68082)

In a separate window the residuals will look like this:

Each datapoint in the dataset is represented by three numbers:
{ ind , { residual , error in residual }}.
where:

• ind: the value of the independent variable for this datapoint.
• residual: the value of the residual for this datapoint.
• error in residual: the assumed error in the value of the residual. This is just the assumed error in the dependent variable for that datapoint. This may be a bit of an oversimplification, since the errors in the fitted parameters effect the error in the residual also.

In some circumstances, there may not be any assumed error in the value of the dependent variable. In this case, ReturnResiduals will return a list with each datapoint represented by only two numbers:
{ ind , residual }.

Authors

This help document is Copyright © 1999 David M. Harrison. The sample screens are Copyright © 1999 Solomon R.C. Douglas and David M. Harrison. This is version 1.1 of the help document, date (m/d/y) 11/25/99.