Question

We have a dataset with n = 10 pairs of observations (xi; yi), and Xn i=1 xi = 683; Xn i=1 yi = 813; Xn i=1 x2i = 47; 405; Xn i=1 xiyi = 56; 089; Xn i=1 y2 i = 66; 731: What is the coefficient of correlation for this data?

We have a dataset with n= 10 pairs of observations (li, yi), and n n Σ ti = 683, Σ9: = 813, i=1 η α? = 47, 405, Iiyi - 56, 089, Συ? = 66, 731. Σ - 1=1 What is the coefficient of correlation for this data?

Answer 1

The formula for correlation coefficient r is given as below:

Correlation coefficient = r = [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