**Correlation: **

In statistics , correlation is a statistics relationship between two random variable. The word Correlation is made of Co- (together), and Relation.

For example; Your IQ and wealth in relation with your parents. Correlation among predictors and predictors and target variables.

**Types of correlation: **

**1. Positive Relation: ** When **high values of random variable X** go with **high values of random variable Y** and **low values of random variable X** go with** low values of random variable Y.** Known as positive relation between variables.

For example; see the table below

Distance (X) Km | Time (Y) minute |

0.5 | 5 |

1 | 10 |

1.5 | 15 |

2.0 | 20 |

In the table you can see that relatively high values of distance (X) go with relatively high values of time (Y) meaning it is a positive relation.

**Negative Relation: **** **If high values of X go with low values of Y, and vice versa, the variables are negatively correlated.

For example relation of speed and time ; As we know for fixed distance increasing in speed reduce time. Fixed distance -10 km

Speed km/minute | Time |

5 | 2 |

2 | 5 |

1 | 10 |

In the table you can see that relatively low values of distance (X) go with relatively high values of time (Y) meaning it is a positive relation.

**Little and No Relation: **** **When there is regularity in relation in two variables or it provide little information about relation of variables. Known as little and no relation.

**Scatterplot: **** **A plot where x-axis represent one variable and y-axis represent another. And graph contains cluster of dots that represents relation of variable pairs.

See the diagram below to understand scatterplot and correlation

In the above diagram ;

In **first case** weight increased with Height which is true in practical life. In **second case** people who smokes more , life expectancy of these people is low compare to people who don't smokes or do less smoking which is also true. These two relation is kind of **relation relation** of variables. For this let's assume that a** dot cluster approximates a ****straight ****line **and, therefore, reflects a **linear relationship. **And if a **dot cluster approximates a bent or curved line, **and therefore reflects a **curvilinear relationship. **

In** third case;** it does not represent any relation between variables as we know the height of a person doesn't matter with his life expectancy.

**Correlation Coefficient (r): **

A correlation coefficient is a numerical value between -1 to +1 which describe the relationship of variables.

You don't have to worry about formula in programming we can directly calculate correlation coefficient using** numpy.** You just have to import correlation coefficient (whichever you want ).

There are many types of correlation coefficient , one of which is pearson correlation coefficient.

The sign of r indicates the type of linear relation. means positive (+) ; **positive linear relation**

**negative (-) ; negative relation** and **neutral (0); no correlation.**

And the **value of r indicate how strong relation** is (without regard to sign).

**Covariance: **

In mathematics and statistics covariance is measure of the relationship between two random variables. Meaning a covariance matrix measure how much and at what extent two variables change together.

In other words

We know that a** variance** measures how a single variable deviates from its mean, **covariance** measures how two variables vary in tandem from their means.

**Note:** Note that covariance is measured with units unlike correlation.

**Positive Covariance:** means two variables tends to move in same direction.

**Negative Covariance: **means two variables tends to move in inverse direction.

This is the formula of covariance, like correlation you don't have to worry about formula; with** numpy **we can directly calculate covariance. In the formula X and Z are variables.

You can ask a question here that correlation and covariance both determine the relationship and measures the dependency between two random variables. **Then what is the difference between these two ? **

**Answer : Difference between correlation and covariance ? **