I have a data set expressed as in the figure here.
'y' is some measured quantity with known error and 'fit' is some attempt to fit a function with zero error.
In order to evaluate the quality of the fit (and thereby rank different fits) it is possible to calculate a Pearson Correlation Coefficient, in this case approx 0.8.
My question is that although I can calculate a correlation coefficient is it possible to also calculate an error for the Pearson's correlation coefficient? i.e. 0.8+/-0.05??
If a Pearson Correlation Coefficient is not the best way to score the fit I would also be interested in alternatives.