When you fit a model to data with nonlinear regression, it is often useful to weight the data. This is most often done when the amount of variation is proportional to the Y value, so there is more scatter with large values. 

Prism performs weighted nonlinear regression. But it doesn't report a weighed R². Instead, until Prism 5.02 and 5.0b,  it reports the unweighted R² for the fit determined by weighted nonlinear regression (and labels it 'unweighted'). 

Why? In versions 1-4 of Prism, the weighted nonlinear regression was weighted by the Y values of the data. With this scheme, a weighted R² would make no sense.  With Prism 5, we switched to weighting by the Y values of the curve (and adjusting those weights as the nonlinear regression progresses). With weighting by the Y values of the curve, it makes perfect sense to compute a weighted R², but we didn't realize this when we created Prism 5, so Prism 5.00 and 5.01 and 5.0a continued to report the unweighted R2.

Prism 5.02 and Prism 5.0b calculate the R² of a weighted fit as detailed below:

1. Fit the model using relative (1/Y²) or Poisson (1/Y) weighting to compute the weighted sum-of-squares (wSSmodel)
2. Fit the data to a horizontal line model (Y=Mean + )*X) using the same weighting to compute the weighted sum-of-squares (wSShorizontal). 
3. The weighted R² is:

                1.0 - (wSSmodel/wSShorizontal)

Notes:

• This method will only work with Prism 5, as Prism 4 and earlier did the weighting differently. 
• This method will work with weighting by 1/Y or 1/Y2, but not the other weighting methods (which would result in different weights for different points in the horizontal fit case).