Use the table of values to calculate the linear correlation coefficient r.

X Y

4 - 5

53 - 1

86 13

162 16

Given the data

X, ... rankX ... Y ... rankY ... d=rx-ry ... d²

4 ... 4 ... - 5 ... 4 ... 0 ... 0

53 ... 3 ... - 1 ... 3 ... 0 ... 0

86 ... 2 ... 13 ... 2 ... 0 ... 0

162 ... 1 ... 16 ... 1 ... 0 ... 0

Then, using the rank correlation formula

p = 1 - 6•Σd² / n (n²-1)

p = 1 - 6• 0 / 4 (4²-1)

p = 1 - 0

p = 1

So, the rank correlation is 1, this means that the two variables being compared are monotonically related, even if their relationship is not linear.