Question

What is the value of the correlation coefficient r of the data set?

A. -0.84
B. 0.71
C. 0.84
D. 1

Answer 1

Answer: −0.28

Step-by-step explanation: i took the test, it's -0.28

Answer 2

The correct option will be: C) 0.84

Step-by-step explanation

Formula for Correlation coefficient :

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

First, for each point(x, y), we need to calculate x², y² and xy .

Then, we will find sum all x, y, x², y² and xy, which gives us Σx, Σy, Σx², ∑y² and Σxy

(Please refer to the attached image for the table )

Here we got, ∑x = 44 , ∑y = 183 , ∑x² = 362 , ∑y² = 6575 and ∑xy = 1480

'n' is the total number of data set, which is 7 here.

So, plugging those values into the above formula..........

`r= (n(\Sigma xy)-(\Sigma x)(\Sigma y))/(√([n\Sigma x^2-(\Sigma x)^2][n\Sigma y^2-(\Sigma y)^2]))\\ \\ r=(7(1480)-(44)(183))/(√([7(362)-(44)^2][7(6575)-(183)^2]))\\ \\ r=(10360-8052)/(√((598)(12536)))\\ \\ r=(2308)/(√(7496528))\\ \\ r=0.84`

So, the value of the correlation coefficient is 0.84