We know that, in the simple linear regression case, the coefficient of determination is equal to Pearson's correlation coefficient squared; R2 = (r)2. Now, what is the relationship between the non-parametric regression and spearman correlation coefficient?.
There is no straightforward relation.
Simple linear regression is a special case of linear regression: the regression method where you aim to minimise the sum of squared vertical distances. For other types of linear regression (e.g. minimising the orthogonal distances or WLS), the relation r^2 = R^2 doesn't hold anymore.
There is not one method that can call itself the default non-parametric regression method. There are many different methods - penalised least squares, lowess curve fitting, kernel estimation, etc. - all of them are (obviously) different; and for none of them a simple relation with the Spearman rho holds.
Hi, Good Afternoon,
Kindly see the link:
http://influentialpoints.com/Training/Nonparametric_correlation_and_regression_use_and_misuse.htm
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