Question

Find the value of the linear correlation coefficient r. Round to 3 decimal places.

Table 2

x	17	20.6	21.4	34	47	25	26
y	12	19	10	17	18	17	16

Answer 1

Given is a table of values of variables x and y, here we need to find the linear correlation coefficient r.

No.	xi	yi
1	17	12
2	20.6	19
3	21.4	10
4	34	17
5	47	18
6	25	17
7	26	16

Correlation Coefficient

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

r=-1, there is high negative correlation between the variables x and y.

r=0, there is no correlation between the variables x and y.

r=1, there is high positive correlation between the variables x and y.

Coming back to our problem

The table of calculation is provided below,

No.	xi	yi	(xi-x̄)^2	(yi-ȳ)^2	(xi-x̄)*(yi-ȳ)
1	17	12	105.7959	12.7551	36.7347
2	20.6	19	44.6988	11.7551	-22.9224
3	21.4	10	34.6416	31.0408	32.7918
4	34	17	45.0816	2.0408	9.5918
5	47	18	388.6531	5.898	47.8776
6	25	17	5.2245	2.0408	-3.2653
7	26	16	1.6531	0.1837	-0.551
Total	191	109	625.7486	65.7143	100.2572

We know that,

Hence the value of the linear correlation coefficient,