Question

The deviations from their means of two series (X and Y) are given below:

X	:	−4	−3	−2	−1	0	+1	+2	+3	+4
Y	:	+3	−3	−4	0	+4	+1	+2	−2	−1

Calculate the Karl Pearson's coefficient of correlation and interpret the result .

Answer 1

x	y	x2	y2	xy
−4	3	16	9	−12
−3	−3	9	9	9
−2	−4	4	16	8
−1	0	1	0	0
0	4	0	16	0
1	1	1	1	1
2	2	4	4	4
3	−2	9	4	−6
4	−1	16	1	−4
		Ʃx2 =60	Ʃy2 =60	Ʃxy =0

$r=\frac{\mathrm{\Sigma }xy}{\sqrt{\mathrm{\Sigma }{x}^2\mathrm{\Sigma }{y}^2}}=\frac{0}{\sqrt{60\times 60}}=0$
Thus, there is no correlation between series X and series Y.