Question

Calculate coefficient of correlation, from the given data:

X 2 3 4 5 6 7 8

Y 4 7 8 9 10 14 18​

Answer 1

Given:

X 2 3 4 5 6 7 8

Y 4 7 8 9 10 14 18

To find:

​Calculate the coefficient of correlation

Solution:

We need to find the coefficient of correlation of the given data.

For that first, we will make a table of required values.

Table:  

X      Y      $X^{2}$     $Y^{2}$       XY

2      4       4      16         8

3      7       9      49        21

4      8      16      64       32

5      9      25     81        45

6     10     36     100      60

7     14     49      196      98

8     18     64     324      144

Here N = 7

∑X = 35;   ∑Y = 70;   ∑XY = 409;   ∑$X^{2}$ = 203;   ∑$Y^2$ = 830

Now, the coefficient of correlation can be obtained by using the formula

r = N x ∑XY - (∑X  ∑Y ) / √[N x  ∑$X^{2}$ - (∑X$)^2$][N x  ∑$Y^2$ - ( ∑Y$)^2$]

putting all the values

r = 7 x 490 - (35 x 70) / √[7 x 203 - $(35)^2$][7 x 830 - $(70)^2$]

r = 980 / 422.32

r = 2.32

Therefore the coefficient of correlation will be 2.32