Question

$n=10,\sum x=55,\sum x^2=385,\sum y=40,\sum y^2=192,\sum (x+y{)}^2=947$. The correlation coefficient is

• A. $0.68$
• B. $-0.68$
• C. $0.9$
• D. $-0.5$

Answer 1

Answer: (B)

$-0.68$

$n=10,\sum x=55,\sum x^2=385,\sum {(x+y)}^2=947$ $\sum y=40,\sum y^2=192,$

$\sum (x^2+y^2+2xy)=947$

$(\sum x^2+\sum y^2+2\sum xy)=947$

$385+192+2\sum xy)=947$

$\sum xy=185$

$r=\frac{n\sum xy-(\sum x\times \sum y)}{\sqrt{(n\sum x^2-\sum x^2)(n\sum y^2-\sum y^2)}}=\frac{10\times 185-55\times 40}{\sqrt{(10\times 385-{55}^2)(10\times 192-{40}^2)}}=-0.68$