Question

The director of an alumni association wants to determine whether there is any type of relationship between the amount of an alumni's contribution (in dollars) and the number of years the alumnus has been out of school. Based on the data below, compute the value of the correlation coefficient between the number of years and the amount of the contribution. Years x 1​ 3​ 4​ 10​ 9​ 7​ Contribution y 630​ 180​ 210​ 30​ 90​ 90​

Answer 1

`r=(6(3750)-(34)(1230))/(√([6(256) -(34)^2][6(490500) -(1230)^2]))=-0.8287`

So then the correlation coefficient would be r =-0.8287

Explanation:

Information provided

Years x 1​ 3​ 4​ 10​ 9​ 7​

Contribution y 630​ 180​ 210​ 30​ 90​ 90​

And in order to calculate the correlation coefficient we can use this formula:

`r=(n(\sum xy)-(\sum x)(\sum y))/(√([n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]))`

For our case we have this:

n=6
`\sum x = 34, \sum y =1230, \sum xy = 3750, \sum x^2 =256, \sum y^2 =490500`

Replacing into the formula we got:

`r=(6(3750)-(34)(1230))/(√([6(256) -(34)^2][6(490500) -(1230)^2]))=-0.8287`

So then the correlation coefficient would be r =-0.8287