Question

Given : n = 6, ∑(x − 18.5) = −3, ∑(y − 50) = 20, ∑(x − 18.5)(y − 50) = −120,

∑(x − 18.5)

2 = 19, ∑(y − 50)

2 = 850 . Calculate coefficient of correlation.

Answer 1

Given

$$n=6, \bar{x}=18.5, \bar{y}=50$$

$$S_{xx}=\sum(x-\bar{x})^2=19$$

$$S_{yy}=\sum(y-\bar{y})^2=850$$

$$S_{xy}=\sum(x-\bar{x})(y-\bar{y})=-120$$

Coefficient of correlation

$$r=\dfrac{S_{xy}}{\sqrt{S_{xx}}\sqrt{S_{yy}}}$$

$$=\dfrac{-120}{\sqrt{19}\sqrt{850}}\approx-0.944267$$

$$r<0, 0.7<|r|\leq1$$

Strong negative correlation.