Question

Calculate the correlation coefficient of the following data: x 45 46 46 47 48 49 50 y 44 48 45 48 52 51 49

Answer 1

$x̄ = \frac{45+46+46+47+48+49+50}{7} = 47.2857 \\ȳ = \frac{44+48+45+48+52+51+49}{7} = 48.1429$

Now, creating a table

Coefficient of correlation

$(r) =\frac{Σ(x_i - x̄)(y_i - ȳ)}{\sqrt{(Σ( x_i - x̄)^2Σ(y_i - ȳ)^2 ) }} \\=\frac{23.7143}{\sqrt{(19.4286*50.8571)}} \\=0.7544$