# CORRELATION COEFFICIENT

We have seen that relationship between two variable is denoted by correlation and how it can be determined using graph but sometimes it becomes difficult to tell the value of r by just seeing the graph so now I am going to show you how to calculate these correlation mathematically. It is quiet easy. This correlation can be calculated using different methods.

**Pearson’s Correlation coefficient :**

Only the name sounds tricky but it is actually quiet simple, lets see what it is. So what is Pearson Correlation?

Correlation between sets of data is a measure of how well they are related. The most common measure of correlation in stats is the Pearson Correlation. It shows the linear relationship between two sets of data. In simple terms, it answers the question, Can I draw a line graph to represent the data? Two letters are used to represent the Pearson correlation: Greek letter rho (ρ) for a population and the letter “r” for a sample.

The formula for Pearson’s correlation coefficient is as follow:-

**Spearman’s Rank Correlation coefficient :**

This is also as simple as Pearson’s, let me show you what it is.

So what does Spearman’s rank correlation coefficient do ?

Spearman’s rank correlation coefficient rs measures the strength of monotonic (but not

necessarily linear) relationship between two variables.

So we are measuring how much they move together but the changes are not necessarily at a

constant rate.

How is it related to Pearson’s correlation coefficient ?

The Spearman correlation between two variables is equal to the Pearson correlation between the rank values of those two variables; while Pearson's correlation assesses linear relationships, Spearman's correlation assesses monotonic relationships.

The formula for Spearman’s rank correlation coefficient is as follow:-

Now let us test what we have learned so far :

Written by Pratyaksh ( Pursuing graduation from St.Xaviers Calcutta and has cleared 2 actuarial papers )