Question

We have a dataset with n= 10 pairs of observations (Li, Yi), and n n Σ I i = 683, Yi = 813, i=1 i=1 n n n mm = 47, 405, Xiyi 56,089, y = 66, 731. i=1 i=1 i=1 What is the coefficient of correlation for this data?

Answer 1

Solution:

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

From given information, we have

n = 10

∑x = 683

∑y = 813

∑x^2 = 47405

∑y^2 = 66731

∑xy = 56089

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

r = [10*56089 - 683*813]/sqrt((10*47405 - 683^2)*(10*66731 - 813^2))

r = 5611 / 6924.182

r = 0.810348

Correlation coefficient = r = 0.810348

This correlation coefficient indicates that there is a strong positive association exists between two variables.