Correlation in Statistics

Correlation in Statistics

If we could see grammatically the word correlation generally describes the association,   in simple words, if we explain correlation statistically it is the statistical tool to analyze the level of relationship that exists between two variables. 
Making it further easier when two variables move together we can say them to be correlated.

Mathematical Statement and Values

  • The measure of correlation is usually expressed as correlation coefficient.
  • The range or the degree of relationship usually lies between -1 to +1 (-1 ≤ r ≥  +1).
  • The direction of change is usually represented by a sign.

Purpose of Correlation 

The correlation study enables us to gain knowledge about the degree and the range of relationship that lies between two variables.

Methods to Study Correlation

  • Scatter Diagram
  • Correlation Graph
  • Correlation Co-efficient

Types of Correlation

  • Positive Correlation
  • Negative Correlation

Case 1: Positive Correlation: values of the two variables changes in the same direction.
Example: Height and Weight
Further,  if X and Y are the two variables, if X is increasing Y also increases.
Case 2: Negative Correlation: values of the two variables changes in the opposite direction.
Example: Price & Quantity.

Analysis Based on the Value of Correlation Co-efficient

If the value of r = +1 then the correlation found to have between two variables are perfect and positive. 
When r = -1 then it is found to be perfect and negative.
But when r=0 then there is no correlation between them.

How does the correlation differ from the regression?

Correlation does not depend on the cause and effect relationships between the variables under study whereas the regression depends on it.
The formulae for calculating the correlation coefficient r is given by,


Simple Correlation

In the study of the relationship between variables, if we consider only two variables it is said to be a simple correlation.

Multiple Correlation

One variable is in one-side and all the other variables are on the other side.

Partial Correlation

Relationship between the one variable and the other is studied, if one of the other variables remains constant.


  • It helps to study the relationship between two variables.
  • It is very important in carrying out the research work.
  • It helps in analyzing the traits and the capacities of the pupils by giving them proper guidance and training.

Few examples,
If r = 0, no correlation
r=0.2, low positive correlation
r=0.9, high positive correlation
r=-0.2, low negative correlation

The graphical representation based on the value of r is below,



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