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# What is correlation?

## Overview

Basically correlation is the measurement of the strength of a linear relationship between two variables say x and y.

In other words, we define the it as- if the change in one variable affects a change in other variable, then these two variables are said to be correlated.

For example:

1.     The correlation between a person’s income and expenditures.

2.     As the temperature goes up, the demand of ice cream also go up.

## Types of correlation

Positive correlation- When both variables move in the same direction, or if the increase in one variable results in a corresponding increase in the other one is called positive correlation.

Negative correlation- When one variable increases and other decreases or vise-versa, then the variables said to be negatively correlated.

No correlation- When two variables are independent and do not affect each other then there will be no correlation between the two and said to be un-correlated.

Note- (Perfect correlation)- When a variable changes constantly with the other variable, then these two variables are said to be perfectly correlated.

## Scatter plots or dot diagrams

Scatter or dot diagram is used to check the correlation between the two variables.

It is the simplest method to represent a bivariate data.

When the dots in diagram are very close to each other, then we can say that there is a fairly good correlation.

If the dots are scattered then we get a poor correlation.

## Karl Pearson’s coefficient of correlation

Karl Person’s coefficient of correlation is also called product moment correlation coefficient.

It is denoted by ‘r’, and defined as-

Here and are the standard deviations of these series.

Alternate formula-

Note-

• Correlation coefficient always lies between -1 and +1.
• Correlation coefficient is independent of change of origin and scale.
• If the two variables are independent then correlation coefficient between them is zero.

## Solved example

Example: The data given below is about the marks obtained by a student and hours she studied.

Find the correlation coefficient between hours and marks obtained.

Solution:

Let hours = x and marks = y

Karl Person’s coefficient of correlation is given by-

The correlation coefficient between hours and marks obtained is-

r = 0.98