Question

Short Answer Question We have a dataset with n = 10 pairs of observations (Li, Yi), and n n Xi = 683 Yi = 813, i=1 n n n x= 47, 405, Xiyi = 56,089, Ly? = 66, 731. i=1 i=1 i=1 What is the coefficient of correlation for this data?

Answer 1

Answer:

Correlation coefficient = 0.8103

Solution:

We know the formula for the correlation coefficient r between the two variables is given as below:

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

We are given

n = 10

∑x = 683

∑y = 813

∑x^2 = 47405

∑xy = 56089

∑y^2 = 66731

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 = 0.810348

This coefficient indicate that there is strong positive association exists between two variables.