Question

Given that $r=0.4\sum (x-\overline{x})(y-\overline{y})=108,{\sigma }_y=3$ and $\sum (x-\overline{x}{)}^2=900$. Find the number of pairs of observations.

Answer 1

${\sigma }_x^2=\frac{1}{n}\sum (x-\overline{x}{)}^2=\frac{900}{n}⟹{\sigma }_x=\frac{30}{\sqrt{n}}$

Given $r=0.4\sum (x-\overline{x})(y-\overline{y})=108=\frac{\frac{1}{n}\sum (x-\overline{x})(y-\overline{y})}{{\sigma }_x{\sigma }_y}$

$⟹n{\sigma }_x{\sigma }_y=2.5⟹\sqrt{n}\left(90\right)=2.5⟹n=\frac{6.25}{8100}=0.00077$