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 
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.
| Value of (r) | Type of correlation |
| +1 | Perfect positive correlation |
| -1 | Perfect negative correlation |
| 0.25 | Weak positive correlation |
| 0.75 | Strong positive correlation |
| -0.25 | Weak negative correlation |
| -0.75 | Strong negative correlation |
| 0 | No correlation |
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.
| Hours | 1 | 3 | 5 | 7 | 8 | 10 |
| marks | 8 | 12 | 15 | 17 | 18 | 20 |
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