Measure of Dispersion (Multi Variable)

Covariance shows how 2 random variables vary together with respect to their respective mean. On the other side, Variance tells us  how one variable is varying against the mean.

Cov(X,Y) = Σ E((X – μ) E(Y – ν)) / n-1 

  • X = 1st Variable
  • Y = 2nd Variable
  • μ = Mean of X
  • ν = Mean of Y
  • n = Number of items in the data set

We take “n-1” as that’s the degree of freedom in a sample

Sample Correlation Coefficient

Correlation Coefficient shows how strongly two variables are related to each other

Strong Positive Correlation => If one variable goes up, other also goes up

  • Example: Show Size and Foot Length

Strong Negative Correlation => If one variable goes up, other goes down

  • Example: Pace of vehicle and Time taken to cover a distance

Pearson Correlation Coefficient

Pearson Coefficient is described as per above formula

Its used widely in regression analysis of real life situations 

However, we must understand that correlation doesn’t not differentiate between dependent and independent variables

A researcher has to be aware of the data holistically before arriving at any conclusion after finding correlation

Correlation Examples

Correlation is Not Causation

Causation is implying that two events A and B have a cause-and-effect relationship with one another.

Causation is also known as causality. It means that either event A causes event B or event B causes event A.

  • Firstly, causation means that two events appear at the same time or one after the other.
  • Secondly, it means these two variables not only appear together, the existence of one causes the other to manifest.

Remember, Correlation does not imply Causation. Correlation may sometimes be a Coincidence.