Question

An outbreak of the deadly Ebola virus in 2002 and 2003 killed 91 of the 95 gorillas in 7 home ranges in the Congo. To study the spread of the virus, measure distance by the number of home ranges separating a group of gorillas from the first group infected. Here are data on distance and number of days until deaths began in each later group:
Distance x 1 4 6 6 6 7
Days y 2 20 29 38 44 50
Find the correlation r between x and y.

r = ?

Answer 1

Answer:

Correlation between x and y is 0.9508          

Step-by-step explanation:

We are given the following in the question:

Distance(x):   1     4       6     6       6       7

      Days(y):  2    20    29    38     44     50

We have to find the correlation between x and y.

$\sum y = 183\\\sum x=30\\\bar{x} = \displaystyle\frac{\sum x}{n} = \frac{30}{6} = 5\\\\\bar{y} = \displaystyle\frac{\sum y}{n} = \frac{183}{6} = 30.5\\\\(x-\bar{x}) = -4,-1,+1,+1,+1,+2\\(y-\bar{y}) = -28.5,-10.5,-1.5,7.5,13.5,19.5\\\sum (x-\bar{x}) (y-\bar{y}) = 183\\\sum(x-\bar{x})^2 = 24\\\sum(y-\bar{y})^2= 1543.5$

Formula:

$r = \dfrac{\sum(x-\bar{x})(y - \bar{y})}{\sqrt{\sum(x-\bar{x})^2\sum(y-\bar{y})^2}}$

Putting values, we get,

$r = \dfrac{183}{\sqrt{24\times 1543.5}} = 0.9508$

Thus, correlation between x and y is 0.9508