Correlation

Need for correlation

For comparing two bivariate datasets, mean, median, mode, standard deviation and other measures of central tendencies could not be used as it was possible to have two sets of numbers with the same measures of central tendency and while calculating median and mode, we have to sort the dataset which leads to the violation of parity as after sorting, different values of x may be mapped to different values of y

Intuition behind correlation

Let there be two data series named x and y

  1. It cancels the effect of units of each column in the bivariate data series and hence makes correlation independent of units so that we can compare any series
  2. It brings the correlation to the range of -1 to 1 which provides a universal scale for comparison of bivariate data series
  3. Since standard deviation is always positive, it does not change the sign of any term in the formula of covariance

Properties of correlation

  1. It is symmetric which means that correlation between x and y is same as the correlation between y and x
  2. It is always between -1 and 1
  3. Correlation coefficient is independent of scale change and origin change which means that correlation does not change when you multiply or divide each element of the series with a particular number or you add or subtract each element of the series by a particular number

Inference of correlation

  1. If the correlation coefficient is close to -1 it means that the value of x decreases with increase in value of y. This implies strong negative correlation
  2. If the correlation coefficient is close to 0 it means that the value of x is independent of value of y. This implies no correlation
  3. If the correlation coefficient is close to 1 it means that the value of x increases with increase in value of y. This implies strong positive correlation

Demerits of correlation

Correlation can only determine the linear relation between two variables and cannot determine polynomial relation between two variables.

--

--

Get the Medium app

A button that says 'Download on the App Store', and if clicked it will lead you to the iOS App store
A button that says 'Get it on, Google Play', and if clicked it will lead you to the Google Play store
Aayushmaan Jain

Aayushmaan Jain

122 Followers

A data science enthusiast currently pursuing a bachelor's degree in data science