Question

Calculate Pearson's coefficient of correlation between the values of $X$ and $Y$.

X	1	2	3	4	5
Y	7	6	5	4	3

• A. $-0.3$
• B. $0.3$
• C. $1$
• D. $-1$

Answer 1

The correct option is D $-1$

$X12345\_\_\_\_\_\_\_\_\_\overline{x}\frac{15}{5}=3$ $Y76543\_\_\_\_\_\_\_\_\_\_\_\overline{y}=\frac{25}{5}=5$ $Y=y-\overline{y}020100-1-1\_\_\_\_\_\_0$ $XY-4-10-1-4\_\_\_\_\_\_\_\_\_\_\_\sum XY=-10$ $X^{2}41014\_\_\_\_\_\_\_\sum X^2=10$

$Y^{2}41014\_\_\_\_\_\_\_\_\_\_\sum Y^2=10$

Therefore, $r=\frac{\sum XY}{\sqrt{\sum X^2\sum Y^2}}=\frac{-10}{\sqrt{10\ast 10}}=\frac{-10}{10}=-1.$