What is correlation coefficients in Statistics?

Correlation coefficients are used to calculate how vital a connection is between two variables. There are different types of correlation coefficients, one of the most popular is Pearson’s correlation (also known as Pearson’s R)which is commonly used in linear regression.

Correlation coefficient Formula

The correlation coefficient procedure is used to determine how strong a relationship is between the data. The correlation coefficient procedure yields a value between 1 and -1. In which,

-1 indicates a strong negative relationship
1 indicates strong positive relationships
And an outcome of zero implies no connection at all

A correlation coefficient of -1 means there is a negative decrease of a fixed proportion, for every positive increase in one variable.
A correlation coefficient of 1 means there is a positive increase of a fixed proportion of others, for every positive increase in one variable.
Zero means that for every increase, there is neither a positive nor a negative increase. The two just aren’t related.

Types of Formulae

Pearson’s correlation coefficient formula
R = [n(xy) - (x)(y)]/ [√(nx - (x)).(ny-(y))]

Sample correlation coefficient formula
rxy = cov(x,y)/ (Sx.Sy)
Sxy is the sample Covariance, and Sx and Sy are the sample standard deviations

Population correlation coefficient formula
pxy = cov(X,Y)/xy
It uses σx and σy as the population standard deviation and, σxy as the population Covariance.