<Li> This formula suggests a convenient single - pass algorithm for calculating sample correlations, but, depending on the numbers involved, it can sometimes be numerically unstable . </Li> <P> Rearranging again gives us this formula for r: </P> <Dl> <Dd> r = r x y = ∑ x i y i − n x _̄ y _̄ (∑ x i 2 − n x _̄ 2) (∑ y i 2 − n y _̄ 2). (\ displaystyle r = r_ (xy) = (\ frac (\ sum x_ (i) y_ (i) - n (\ bar (x)) (\ bar (y))) ((\ sqrt ((\ sum x_ (i) ^ (2) - n (\ bar (x)) ^ (2)))) ~ (\ sqrt ((\ sum y_ (i) ^ (2) - n (\ bar (y)) ^ (2)))))).) </Dd> </Dl> <Dd> r = r x y = ∑ x i y i − n x _̄ y _̄ (∑ x i 2 − n x _̄ 2) (∑ y i 2 − n y _̄ 2). (\ displaystyle r = r_ (xy) = (\ frac (\ sum x_ (i) y_ (i) - n (\ bar (x)) (\ bar (y))) ((\ sqrt ((\ sum x_ (i) ^ (2) - n (\ bar (x)) ^ (2)))) ~ (\ sqrt ((\ sum y_ (i) ^ (2) - n (\ bar (y)) ^ (2)))))).) </Dd>

For which data set is the sample correlation coefficient r equal to 1