Lecture 7/ 3rd Stage /Covariance and Correlation/ 2nd Course /2018-2019

Definition of Covariance
Covariance is a statistical term, defined as a systematic relationship between a pair of random variables wherein a change in one variable reciprocated by an equivalent change in another variable.

Covariance can take any value between -? to +?, wherein the negative value is an indicator of negative relationship whereas a positive value represents the positive relationship. Further, it ascertains the linear relationship between variables. Therefore, when the value is zero, it indicates no relationship. In addition to this, when all the observations of the either variable are same, the covariance will be zero.

In Covariance, when we change the unit of observation on any or both the two variables, then there is no change in the strength of the relationship between two variables but the value of covariance is changed.

Definition of Correlation
Correlation is described as a measure in statistics, which determines the degree to which two or more random variables move in tandem. During the study of two variables, if it has been observed that the movement in one variable, is reciprocated by an equivalent movement another variable, in some way or the other, then the variables are said to be correlated.

Correlation is of two types, i.e. positive correlation or negative correlation. The variables are said to be positively or directly correlated when the two variables move in the same direction. On the contrary, when the two variables move in opposite direction, the correlation is negative or inverse.



The value of correlation lies between -1 to +1, wherein values close to +1 represents strong positive correlation and values close to -1 is an indicator of strong negative correlation. There are four measures of correlation:

Scatter diagram
Product-moment correlation coefficient
Rank correlation coefficient
Coefficient of concurrent deviations

Key Differences Between Covariance and Correlation
The following points are noteworthy so far as the difference between covariance and correlation is concerned:

A measure used to indicate the extent to which two random variables change in tandem is known as covariance. A measure used to represent how strongly two random variables are related known as correlation.
Covariance is nothing but a measure of correlation. On the contrary, correlation refers to the scaled form of covariance.
The value of correlation takes place between -1 and +1. Conversely, the value of covariance lies between -? and +?.
Covariance is affected by the change in scale, i.e. if all the value of one variable is multiplied by a constant and all the value of another variable are multiplied, by a similar or different constant, then the covariance is changed. As against this, correlation is not influenced by the change in scale.
Correlation is dimensionless, i.e. it is a unit-free measure of the relationship between variables. Unlike covariance, where the value is obtained by the product of the units of the two variables.

Similarities
Both measures only linear relationship between two variables, i.e. when the correlation coefficient is zero, covariance is also zero. Further, the two measures are unaffected by the change in location.