Question

Calculate the correlation coefficient between the corresponding values of X and Y in the following table:

X	2	4	5	6	8	11
Y	18	12	10	8	7	5

• A. $-0.65$
• B. $-0.82$
• C. $-0.92$
• D. $-0.48$

Answer 1

Answer: (C)

$-0.92$

$X2456811\_\_\_\_\_\_\_\_\_\sum x=36$ $Y181210080705\_\_\_\_\_\_\_\sum y=60$ $x=x-\overline{x}-4-2-1025\_\_\_\_\_\_0$ $Y=y-\overline{y}820-2-3-5\_\_\_\_\_0$ $XY-32-400-6-25\_\_\_\_\_\_-67$ $X^{2}16410425\_\_\_\_\_50$ $Y^{2}64404925\_\_\_\_\_\_\_\_\_\_\sum Y^2=106$

Therefore, $\overline{a}=\frac{36}{6}=6$

$\overline{y}=\frac{60}{6}=10$

Therefore, $=\frac{\sum XY}{\sqrt{\sum X^2\sum Y^2}}=\frac{-67}{\sqrt{50\ast 106}}=-0.92$