Question

Calculate the value of r using the computation formula (6.1) for the following data. X Y 2 8 4 6 5 2 3 3 1 4 7 1 2 4

quan stat

Answer 1

Here we need to determine the correlation coefficient (r) for the given data set,

No.	X	Y
1	2	8
2	4	6
3	5	2
4	3	3
5	1	4
6	7	1
7	2	4

Now what is a correlation coefficient?

Correlation Coefficient (r)

The correlation coefficient gives us the degree of linear relationship between two variables X and Y. It is given by,

r=1, High correlation between X and Y

r=0, No correlation between X and Y

r=-1, Negative correlation between X and Y

The correlation coefficient always lies between,

Coming back to our problem,

Here we need to determine the correlation coefficient (r).

The table of calculations is provided below,

No.	xi	yi	(xi-x̄)^2	(yi-ȳ)^2	(xi-x̄)*(yi-ȳ)
1	2	8	2.0408	16	-6.5306
2	4	6	0.3265	4	1.4694
3	5	2	2.4694	4	-2.2449
4	3	3	0.1837	1	0.1837
5	1	4	5.898	0	-1.3878
6	7	1	12.7551	9	-8.6735
7	2	4	2.0408	0	-0.8163
Total	24	28	25.7143	34	-18

Now,

Hence the correlation coefficient r=-0.6088