Question

Here is a bivariate data set.

x	y
97	45.2
33.2	95.3
58.3	59.5
58.3	84.2
61.9	41.8
50.1	73.2
47.5	97.5
24.8	70.7
9.5	115.9
52.1	68.1
52.4	84.6
18	93.6
65.8	76.5
60.4	40.4

Find the correlation coefficient and report it accurate to three decimal places.
r =

What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place.
r² = %

Answer 1

ΣX = 689.3
ΣY = 1046.5
ΣX * Y = 46806.18
ΣX2 = 40374.15
ΣY2 = 84838.19

$r = ( ( N * \Sigma XY) - \Sigma X \Sigma Y) / (\sqrt{ (N \Sigma (X^{2}) - (\Sigma X)^{2} )(N \Sigma (Y^{2}) - (\Sigma Y)^{2} })$
$r = ( ( 14 * 46806.18 ) - 689.3 * 1046.5 ) / ( \sqrt{ ( 14 * 40374.15 ) - ( 689.3 )^{2} )( 14 * 84838.19 ) - ( 1046.5 )^{2} })$
r = - 0.723

Coefficient of Determination
= 0.523

R2 =

Explained variation = 0.523* 100 = 52.3%

Unexplained variation = 1 - 0.523* 100 = 47.7%