Question

Calculate the correlation coefficient of (2,2), (5,3), (7,6), (9,7)

Answer 1

Count x y xy x^2 y^2
1 2 2 4 4 4
2 5 3 15 25 9
3 7 6 42 49 36
4 9 7 63 81 49
Sum 23 18 124 159 98

Correlation coefficient, r

`r = \frac{n[sum xy] - [sum x][sum y]}{ \sqrt{[n(sum x^(2) )- (sum x)^(2)][n( sum y^(2)) -( sum y)^(2) ] } }`

Substituting;

`r = \frac{4*124 - 23*18}{ \sqrt{[4*159 - 23^(2) ][4*98 - 18^(2)] } }` = 0.9613