Question

Find the product moment correlation between sales and expenses of the following 10 firms.

Firms	:	1	2	3	4	5	6	7	8	9	10
Sales	:	50	50	55	60	65	65	65	60	60	50
Expenses	:	11	13	14	16	16	15	15	14	13	13

Answer 1

Sales (X)	Expenses (Y)	$\left(\mathit{X}\mathbf{-}\overline{\mathit{X}}\right)$ x	x2	$\left(\mathit{Y}\mathbf{-}\overline{\mathit{Y}}\right)$ y	y2	xy
50	11	−8	64	−3	9	24
50	13	−8	64	−1	1	8
55	14	−3	9	0	0	0
60	16	2	4	2	4	4
65	16	7	49	2	4	14
65	15	7	49	1	1	7
65	15	7	49	1	1	7
60	14	2	4	0	0	0
60	13	2	4	−1	1	−2
50	13	−8	64	−1	1	8
ƩX = 580	ƩX = 140		Ʃx2 = 360		Ʃy2 = 22	Ʃxy = 70

N = 10

$$\begin{gathered} \overline{X}=\frac{\mathrm{\Sigma }X}{N}=\frac{580}{10}=58 \\ \overline{Y}=\frac{\mathrm{\Sigma }Y}{N}=\frac{140}{10}=14 \\ r=\frac{\mathrm{\Sigma }xy}{\sqrt{\mathrm{\Sigma }{x}^2}\times \sqrt{\mathrm{\Sigma }{y}^2}} \\ =\frac{70}{\sqrt{360}\times \sqrt{22}} \\ =\frac{70}{18.97\times 4.69} \\ =\frac{70}{88.9693} \\ =0.7867\mathrm{or}0.787(\mathrm{approx}.) \end{gathered}$$

Thus, there exists high positive correlation between sales of firm and expenses.