Derek York, in his paper "Least squares fitting of a straight line with correlated errors", from 1968, uses the correlation coefficient ri (equation 1). However, he does not present its definition or I was not able to get it. I also checked his other paper from 1966 ("Least-squares fitting of a straight line"), but there he presents a coefficient of correlation for all data (page 1079), not for single pairs. Am I getting it wrong and I should use the r definition from York (1966) to calculate the MSWD? Or, as I thought, what I am looking for is a definition for the error correlation between the errors of Xs and Ys pairs?
The correlation coefficient r of two variables X and Y is defined by r = SIGMA[(Xi-meanX)*(Yi-meanY)]/(sdX*sdY) where sdX is the standard deviation of X. If it the correlation between the errors of X and Y that you are interested in, you replace the Xs and the Ys above with their respective errors in the definition given above.
Please give either the original paper or the equation 1 to increase the odds that someone recognize that is the ri in this context even is the notation is not standard.
@Ette Etuk: your formula is lacking a 1/n or 1/(n-1) term, according to the definition of sd you use.
Dear Felipe,
I am sending you an article in order to try clarifying any doubt related to least squares regression with in both variables.
Best regards,
Elcio Oliveira
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