Calculate karl pearson's coefficient of correlation between expenditure and sales from given data.

Adevertising Expenses (000 Rs)	39	65	62	90	82	75	25	98	36	78
Sales (Lakhs of Rupees)	47	53	58	86	62	68	60	91	51	84

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written 6.8 years ago by

teamques10 ★ 70k

SR No.	Advertising (X-90)			Sales (Y-86)			Product
	X	dx	$dx^2$	y	dy	$dy^2$	dxdy
1	39	-51	2601	47	-39	1521	1989
2	65	-25	625	53	-33	1089	825
3	62	-28	784	58	-28	784	784
4	90	0	0	86	0	0	0
5	82	-8	64	62	-24	576	192
6	75	-15	225	68	-18	324	270
7	25	-65	4225	60	-26	676	1690
8	98	8	64	91	5	25	40
9	36	-54	2916	51	-35	1225	1890
10	78	-12	144	84	-2	4	24
N=10		$\sum{dx}= -250$	$\sum{dx^2}=11648$		$\sum{dy}=-200$	$\sum{dy^2}=6224$	$\sum{dxdy} = 7704$

$\begin{equation} r=\Bigg\{\frac{\sum{dxdy}-\frac{(\sum{dx})(\sum{dy})}{N}}{\sqrt{\sum{dx^2} -\frac{(\sum{dx^2})}{N}} \sqrt{\sum{dy^2} -\frac{(\sum{dy^2})}{N}}}\Bigg\} \\ r=\Bigg\{ \frac{7704- \frac{(-250)(-200)}{10}}{\sqrt{11648-\frac{(-250)^2}{10}} \sqrt{6224-\frac{(-200)^2}{10}}} \Bigg\} \\ r=\Bigg\{ \frac{7704- 5000}{\sqrt{11648-6250} \sqrt{6224-4000}} \Bigg\} \\ r=\Bigg\{ \frac{2704}{\sqrt{5398} \sqrt{2224}} \Bigg\} \\ r = 0.7804 \end{equation}$

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