Question

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

Answer 1

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.