Question

a. Using the provided information below,

x=33.2, x2=131.67, y=30.78 , y2=116.52 , xy=119.8 , and n=10

i. Find the sample correlation coefficient r

ii. Find the co-efficient of determination

Answer 1

i.

$r=\frac{n∑xy-∑x∑y}{\sqrt{[n∑x^2-(∑x)^2][[n∑y^2-(∑y)^2]}}$

$=\frac{10(119.8)-33.2(30.78)}{\sqrt{[10(131.667)-33.2^2][10(116.52)-30.78^2}}$

$=\frac{1198-1024.884}{\sqrt{(214.46)(217.7916)}}$

$=\frac{173.116}{\sqrt{46707.58654}}$

$=\frac{173.116}{216.1194}$

$=0.801$

ii. $r^2=0.6416$