Question

Find the value of the correlation coefficient for the data shown in the table. Round to the nearest hundredths.

A) r = 0.85
B) r = 0.75
C) r = −0.75
D) r = −0.85

Answer 1

The answer is D.

r= -0.85

Hope this helps

Answer 2

`r=(6(702000)-(29000)(152))/(√([6(150000000) -(29000)^2][6(4000) -(152)^2]))=-0.852`

So then the correlation coefficient would be r =-0.852

D) r = −0.85

Explanation:

We have the follwoing dataset:

X: 3000, 5500, 6500, 6000,4500, 3500

Y: 34,22,18,26,24,28

n=6

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

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 = 29000, \sum y = 152, \sum xy = 702000, \sum x^2 =150000000, \sum y^2 =4000`

And if we replace we got:

`r=(6(702000)-(29000)(152))/(√([6(150000000) -(29000)^2][6(4000) -(152)^2]))=-0.852`

So then the correlation coefficient would be r =-0.852

So then the correct option would be:

D) r = −0.85