Least Squares Fitting

Hello,

It is often said that the square of the correlation coefficient, $r^2$ , is the fraction of the variation in y that is explained by its relationship with x. I seek assistance with determining how this translates to the following:

1- $r^2$ = (deviations from trendline)/(standard deviation of y data)

i.e. standard deviation of the data's deviation from the trendline divided by the the standard deviation of the y data is 1- $r^2$ .

Look forward to your advise.

Best regards,
wirefree