To calculate the correlation coefficient of the given data, we can use the following formula:
r = (Σxy - (Σx)(Σy) / √((Σx^2 - (Σx)^2)(Σy^2 - (Σy)^2))
Let's calculate step by step:
First, we need to calculate the sum of x, y, x^2, and y^2:
Σx = 1 + 4 + 8 + 6 + 2 = 21
Σy = 9 + 16 + 22 + 24 + 12 = 83
Σx^2 = 1^2 + 4^2 + 8^2 + 6^2 + 2^2 = 101
Σy^2 = 9^2 + 16^2 + 22^2 + 24^2 + 12^2 = 1385
Next, we calculate Σxy:
Σxy = (1 * 9) + (4 * 16) + (8 * 22) + (6 * 24) + (2 * 12) = 406
Now, we can substitute these values into the correlation coefficient formula:
r = (Σxy - (Σx)(Σy) / √((Σx^2 - (Σx)^2)(Σy^2 - (Σy)^2))
= (406 - (21 * 83)) / √((101 - (21)^2)(1385 - (83)^2))
= (406 - 1743) / √((101 - 441)(1385 - 6889))
= (-1337) / √((-340)(-5504))
= (-1337) / √(1873600)
= (-1337) / 1368.66
≈ -0.977
Therefore, the correlation coefficient of the given data is approximately -0.977.