Question

Using the provided information below,

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

Find the sample correlation coefficient rimage.png (4mks)

Find the co-efficient of determination

Answer 1

Correlation coefficient:

$r=\frac{n\Sigma xy-\Sigma x\Sigma y}{\sqrt{(n\Sigma x^2-(\Sigma x)^2)(n\Sigma y^2-(\Sigma y)^2)}}= \frac{10*119.8-33.2*30.78}{\sqrt{(10*131.67-33.2^2)(10*116.52-30.78^2)}}=0.8148.$

Coefficient of determination:

$r^2=0.8148^2=0.6639.$