Question

Calculate correlation coefficient between X, the number of rainy days per month and Y, the number of rain coats sold in that month in a certain shop for 12 months. Interpret the results.

X	:	14	8	18	10	22	9	3	5	6	11	13	13
Y	:	15	11	20	12	15	7	3	4	7	10	11	29

Answer 1

X	Y	$\left(\mathit{X}\mathit{-}\overline{X}\right)$ (x)	x2	$\left(\mathit{Y}\mathit{-}\overline{\mathit{Y}}\right)$ (y)	y2	xy
14	15	3	9	3	9	9
8	11	−3	9	−1	1	3
18	20	7	49	8	64	56
10	12	−1	1	0	0	0
22	15	11	121	3	9	33
9	7	−2	4	−5	25	10
3	3	−8	64	−9	81	72
5	4	−6	36	−8	64	48
6	7	−5	25	−5	25	25
11	10	0	0	−2	4	0
13	11	2	4	−1	1	−2
13	29	2	4	17	289	34
ƩX =132	ƩY =144		Ʃx2 =326		Ʃy2 =572	Ʃxy =288

N = 12

$$\begin{gathered} \overline{X}=\frac{\mathrm{\Sigma }X}{N}=\frac{132}{12}=11 \\ \overline{Y}=\frac{\mathrm{\Sigma }Y}{N}=\frac{144}{12}=12 \\ r=\frac{\mathrm{\Sigma }xy}{\sqrt{\mathrm{\Sigma }{x}^2\times \mathrm{\Sigma }{y}^2}}=\frac{288}{\sqrt{326\times 572}}=\frac{288}{18.05\times 23.91} \\ =\frac{288}{431.82} \\ =0.6669=0.67(\mathrm{approx}.) \end{gathered}$$

There is a moderate degree of (+) correlation between the number of rainy days and the number of rain coats sold. In other words, as the number of rainy days increases in a month, the number of rain coats sold in that month increases moderately.

Note: As per the textbook, coefficient of correlation is $-$0.67. However, as per the above solution coefficient of correlation should be +0.67.