Data analysis Part 12: Correlation and its application

Correlation and its application

In previous articles we have seen that,  

• Variance is a parameter in statistics that measures variation of a single random variable. 

•  In comparison, covariance (co-variance) measures how two independent random variables vary together. 

• Covariance measures directional relationship between two independent random variables. 

In this article we shall discuss about 'Correlation' 

                                                           Two jute ropes with different strengths 

• Unlike Covariance, Correlation represents not only direction but also Strength of the relationship between two independent random variables.
  

Formula

Correlation (ρ) 

`ρ(X,Y)=\frac{Cov(X,Y)}{\sigma_x.\sigma_Y}`

σ = Standard deviation of variable x

Since we are dividing covariance by Standard deviation, correlation represent both direction as well as strength of relationship between two independent variables.

Range of value

-1 ≤ Correlation coefficient (r) ≤ +1

r = Pearson's correlation coefficient 

Table 1: Interpretation of Pearson correlation coefficient value (r). 

Correlation Coefficient Value (r)	Direction and Strength of Correlation
0	No association
±0.2	Weak
±0.5	Moderate
±0.8	Strong
±1	Perfect

Example 1: Effect of temperature on ice cream sale

Table.2

Temperature (oC)	Ice cream sale/ day
35	520
37	600
45	760
49	850
43	650
39	610
46	830

Correlation coefficient =  0.962

As it can be seen from above Correlation coefficient that, sales of ice cream and temperature of a place are strongly linked to each other (Table.1). 

Example 2:  Effect of USA stock market on Indian stock market

Table.3

Year	Dow Jones	Sensex
2011	2.74	-15.67
2012	3.73	12.99
2013	19.6	6.41
2014	13.53	34.05
2015	1.52	-10.5
2016	20.02	7.06
2017	24.44	23.14
2018	-10.79	0.29
2019	14.16	13.78
2020	6.7	12.14

Correlation coefficient =  0.532

As it can be seen from above Correlation coefficient that, US Dow Jones and Indian Sensex are not strongly linked, rather the relationship is pretty moderate/ weak (Table.1).  

Correlation coefficient of of 0.532 means 53.2% of the variance in one variable (US Dow Jones) is accounted for by the second variable and vice versa (Indian Sensex). 

Reference

All references are hyperlinked in the text.