Question

complete the table and use the formula to calculate pearson r. (round off to two decimal places after each operation.)
correlation table

x	y	(x - \\(\overline{x}\\))	(y - \\(\overline{y}\\))	(x - \\(\overline{x}\\))(y - \\(\overline{y}\\))	(x - \\(\overline{x}\\))²	(y - \\(\overline{y}\\))²
45	30
30	40
35	30
50	25
\\(\overline{x}=\\)	\\(\overline{y}=\\)		\\(\sum =\\)		\\(\sum =\\)	\\(\sum =\\)

r = \\(\frac{\sum((x - \overline{x})(y - \overline{y}))}{\sqrt{\sum(x - \overline{x})²\times\sum(y - \overline{y})²}}\\)
what is the correlation of the two groups?
-0.9
-0.85
-0.7
-0.65

Explanation:

Step1: Calculate the means of x and y

$\bar{x}=\frac{25 + 45+30+35+50}{5}=\frac{185}{5}=37$
$\bar{y}=\frac{50 + 30+40+30+25}{5}=\frac{175}{5}=35$

Step2: Fill in the table values

x	y	$(x - \bar{x})$	$(y - \bar{y})$	$(x - \bar{x})(y - \bar{y})$	$(x - \bar{x})^2$	$(y - \bar{y})^2$
45	30	$45-37 = 8$	$30-35=-5$	$8\times(-5)=-40$	$8^2 = 64$	$(-5)^2 = 25$
30	40	$30 - 37=-7$	$40-35 = 5$	$(-7)\times5=-35$	$(-7)^2=49$	$5^2 = 25$
35	30	$35-37=-2$	$30 - 35=-5$	$(-2)\times(-5)=10$	$(-2)^2 = 4$	$(-5)^2 = 25$
50	25	$50-37 = 13$	$25-35=-10$	$13\times(-10)=-130$	$13^2 = 169$	$(-10)^2 = 100$
$\bar{x}=37$	$\bar{y}=35$			$\sum=-375$	$\sum=430$	$\sum=400$

Step3: Calculate Pearson r

$r=\frac{\sum((x - \bar{x})(y - \bar{y}))}{\sqrt{\sum(x - \bar{x})^2\times\sum(y - \bar{y})^2}}=\frac{-375}{\sqrt{430\times400}}=\frac{-375}{\sqrt{172000}}\approx\frac{-375}{414.73}\approx - 0.90$

Answer:

-0.9