**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 and are the standard deviations of these series.

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