Question

Let x be the average number of employees in a group health insurance plan, and let y be the average administrative cost as a percentage of claims.

x	3	7	15	40	71
y	40	35	30	28	19

(c) Use a calculator to verify that Σx = 136, Σx² = 6924, Σy = 152, Σy² = 4870, and Σxy = 3284. Compute r. (Round your answer to three decimal places.)

r =

Answer 1

Correlation coefficient = r = [n∑xy - ∑x∑y]/sqrt[(n∑x^2 – (∑x)^2)*(n∑y^2 – (∑y)^2)]

So, by using given values, we have

r = [n∑xy - ∑x∑y]/sqrt[(n∑x^2 – (∑x)^2)*(n∑y^2 – (∑y)^2)]

r = [5*3284 - 136*152]/sqrt[(5*6924 – (136)^2)*(5*4870– (152)^2)]

r = -4252/4482.243

r = -0.94863

r = -0.949