Alfisol, Item 003:  LMMpro, version 2.0 The Langmuir Optimization Program 

The correlation coefficient η^{2} coincides with r^{2} in the linear regression setup. The etasquare term is used here for the correlation coefficient value of the untransformed data.
The η^{2} assumes that a vertical minimum for the error terms corresponds to a better curve fit of the data collected. It is defined as:

A perfect fit by a curve will have η^{2} = 1.00, whereas a poor fit by a curve will have a low value. If η^{2} = 0, then the predicted curve is no better than a simple average of the data collected. With all regressions, η^{2} < 1, always.
This is not easy to do by hand. Computers are needed to perform these calculations easily and quickly.