Write a detailed note on Carl's Correlation Coefficient Algorithm. Justify the necessary of Algorithm by giving suitable example.

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Carl Pearson Coefficient of correlation is a measure of linear relationship between two variables. It lies between -1 and 1.

The closer it is to 1(or -1), the stronger the positive(or negative) linear relationship between the two variables. If it is close to 0, there is no linear relation.

Example :

X(height - cm)	Y(weight - kg)
174	61
175	65
176	67
177	68
178	72
182	74
183	80
186	87
189	92
193	95

Number of cases: n = 10

Sr. No.	X	Y	$X^2$	$Y^2$	XY
1	174	61	30276	3721	10614
2	175	65	30625	4225	11375
3	176	67	30976	4489	11792
4	177	68	31329	4624	12036
5	178	72	31684	5184	12816
6	182	74	33124	5476	13468
7	183	80	33489	6400	14640
8	186	87	34596	7569	16182
9	189	92	35721	8464	17388
10	193	95	37249	9025	18335
∑	1813	761	329069	59177	138646

∑ X = 1813

∑ Y = 761

∑ $X^2$= 329069

∑ $Y^2$ = 59177

∑ XY = 138646

∑ X ∑ Y = 138646

$r=\dfrac{n(∑xy)-(∑x)(∑y)}{\sqrt{[n∑x^2 -(∑x)^2 ][n∑y^2 - (∑y)^2 ]} }$

$\therefore$ Correlation coefficient: r = 0.9864

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