Does anybody know how to calculate a correlation coefficient?

Question

I have a table of units of advertising and revenue:

Rev: 20 | 50 | 30 | 100 | 50 | 90 | 80
Ads: 1 | 2 | 3 | 4 | 5 | 6 | 7

I have drawn the graph (first part of the questio), but now I have to calculate the correlation coefficient between advertising and revenues.

Does anybody know the formula (in really simple terms) for this please? I will be very very grateful for any help! Sorry to be a nuisence, I'm just really stuck.

Answer 1

Variables Xj and Xk

Deviations are computed as the difference between the case's magnitude xij on one variable (Xj), and the location xij of the case on the line if Xj and Xk were perfectly correlated.

Equation of the straight line is Xj = a + bXk,

Deviation = di or gi

The sum of the squared deviations of gi is sum(g^2i)

h = 1 - sum(d^2i) / sum(g^2i)

g^i = xij - j,
sum(g^2i) = (xij - j)^2,
sum(g^2i) / n = (xij - j)^2 / n = 2j.
h = 1 - sum(d^2i) / sum(g^2i)
h = (sum(g^2i) - sum(d^2i)) / sum(g^2i)
h = (total variance - independent variance) / total variance
h = (variance in common) / total variance.
h = r^2 = correlation coefficient

Answer 2

add 3 more columns to your table, squares of ads (x's), squares of rev (y's), and products (x times y). you'll need sum of x's: Σx, sum of y's: Σy, sum of x²'s: Σx², sum of y²'s: Σy², sum of products: Σxy, and squares of sums: (Σx)² and (Σy)². put them all together according to the 2nd formula for r(sub xy) in the link article. I'd use Excel, frankly, since the needed formula is built in.