Alfisol, Item 003:

LMMpro, version 2.0 The Langmuir Optimization Program plus The Michaelis-Menten Optimization Program

What does LMMpro do? List of Published Articles Using LMMpro History of Linear Regression Methods Linear Regressions Deriving Linear Regression Methods

NLLS Regressions v-NLLS Optimization n-NLLS Optimization Axes Conversion Factor (ACF) Types of Errors

Correlation Coefficient (r2) Correlation Coefficient (η2) Correlation Coefficient (η*2) Do's & Don't's References Cited

Correlation Coefficient (η²)

The correlation coefficient η² coincides with r² in the linear regression setup. The eta-square term is used here for the correlation coefficient value of the untransformed data.

The η² assumes that a vertical minimum for the error terms corresponds to a better curve fit of the data collected. It is defined as:

η2 =1 - Σ (yi - yp)2 Σ (yi - ya)2 where, yp = the predicted value when x = xi, ya = arithmetic mean value of y for all values of x, and yi = the experimental value measured when x = xi.

A perfect fit by a curve will have η² = 1.00, whereas a poor fit by a curve will have a low value. If η² = 0, then the predicted curve is no better than a simple average of the data collected. With all regressions, η² < 1, always.

This is not easy to do by hand. Computers are needed to perform these calculations easily and quickly.