The horizontal line is the simplest case of a regression line, so this makes sense.

In linear regression, R 2 compares the fits of the best fit regression line with a horizontal line (forcing the slope to be 0.0).

Minitab does not report R 2 with nonlinear regression because they think it is too misleading. Why do some suggest that R 2 not be reported with nonlinear regression? r 2 or R 2 ?īy tradition, statisticians use uppercase (R 2 ) for the results of nonlinear and multiple regression and lowercase (r 2 ) for the results of linear regression, but this is a distinction without a difference. This can only happen when an invalid equation is used so the result is simply wrong.

You may see references to R 2 possibly having a value greater than 1.0.

Yes that seems odd, but R 2 is not really the square of anything and it is possible.

When you choose a really inappropriate model or impose silly constraints (usually by mistake) the best-fit curve will fit worse than an horizontal line.

In this case, knowing X does not help you predict Y.

When R 2 equals 0.0, the best-fit curve fits the data no better than a horizontal line going through the mean of all Y values.

But if you have replicate Y values at the same X value, it is impossible for the curve to go through every point, so R 2 has to be less than 1.00. R 2 equals 1.00 when the curve goes through every point.The simple answer is that R 2 is usually a fraction between 0.0 and 1.0, and has no units. What is the range of values R 2 can have? Another way to think about R 2 is the square of the correlation coefficient between the actual and predicted Y values.With experimental data (and a sensible model) you will always obtain results between 0.0 and 1.0. You can think of R 2 as the fraction of the total variance of Y that is explained by the model (equation).

It compares the fit of your model to the fit of a horizontal line through the mean of all Y values. The value R 2 quantifies goodness of fit.

Curve fitting file deltagraph 7