Correlation and Regression analysis are used in statistical research and analysis where they use multi-variable distribution. A multi-variable distribution is nothing but a distribution of multiple variables. So, this article talks about the difference between Correlation and Regression regarding establishing a relation between two or more variables.

So, first of all, let us understand the difference between Correlation and Regression in the next paragraph.

**Correlation and Regression** **Differences –**

The Correlation and Regression differences have been described in the table below:

Points of Difference |
Regression |
Correlation |

Purpose |
It is used to fit the appropriate line and calculate the value of one variable based on the relation with another. | It is used to represent the linear relationship between two existing variables. |

Definition |
Regression helps to find out how an independent variable can numerically be related to another dependent variable. | Correlation is a statistical measure that determines the association between two variables. |

What does it indicate? |
Regression helps find any unit change in the value of the known variable (m) against the value of the estimated variable (n). | Correlation indicates the extent to which two variables changes in coordination with each other. |

Dependent or Independent variables |
In regression analysis, both the variables are different, i.e. one variable is independent and the other dependent. | In Correlation analysis, there is no difference between the two variables, i.e. both variables are mutually dependent. |

What is the Purpose? |
The primary purpose of regression analysis is to estimate the value of the unknown variable with the established variable. | The primary purpose of Correlation analysis is to predict dependable forecasts. |

What is the Objective |
Regression analysis helps in estimating the values of random variables about the values of fixed variables. | Correlation analysis helps to find the numerical value that depicts the relationship between the two variables. |

What is the Range? |
In regression analysis, if bnm > 1, then bmn < 1 is the range. | In correlation analysis, coefficients may range between -1.00 and 1.00. |

What is the Scope? |
Regression analysis helps in providing a broader range of applications. | Correlation analysis helps in providing limited applications. |

Nature of the Coefficient |
The regression coefficient doesn’t have to be symmetrical. | The correlation coefficient is always mutual and is symmetrical too. |

What is the Response Nature? |
The regression coefficient is dependent on the change of scale. However, it is independent of its change in origin. | The correlation coefficient is independent of any change of scale or any shift in its origin. |

Mathematical Interpretation? |
Regression analysis is widely used in advanced mathematical research works. | Correlation analysis is not very useful in advanced mathematical research works. |

Relation |
The regression includes both linear and non-linear relationships. The cause and effect relationship and the functional link are established. | Correlation analysis is confined to the linear relationships between the variables. It does not depict the cause and effect relationship of the variables. |

What does it Measure? |
Regression depicts the fundamental nature of the existing relationship between variables. It depicts one variable in the form of a linear function with respect to the other. | Correlation analysis measures the extent to which two variables change in unison with each other. |

What is the Coefficient? |
The regression coefficient is an absolute value. | The coefficient correlation gives a relative measure. |

What are the variables involved? |
In regression, when ‘m’ is the random variable, ‘n’ is the fixed variable. | Here, ‘m’ and ‘n’ are random variables. |

**What is Correlation?**

Correlation analysis helps analyse and find out the association or dissociation of the relationship between two different variables. Correlation denotes ‘togetherness’ and ‘interaction’ between any two random variables. If such a relationship is established between the two, there is a response from one variable to another when a unit change is initiated in one.

Also, there is a possibility of failing to generate any movement in any of the variables if they are uncorrelated. In short, we can say that correlation tries to represent the relative strength of interaction between two variables directly or indirectly.

**What are the Measures of Correlation?**

There are several measures of correlation which are listed below-

- Scatter diagram
- Concurrent deviations Co-efficient
- Karl Pearson’s Correlation Coefficient of Product-Moment
- Spearman’s Rank Correlation Co-efficient

**What are the Different Types of Correlation?**

There are three types of Correlation. They are positive correlation, negative correlation, and zero correlation. Each gives an idea about the kind of relationship each has with the other variable.

**1) Positive Correlation – **

Two variables are said to be in positive correlation if an increase or decrease in the value of the variable results in an increase or decrease in the value of the other variable. These two variables can also be said to be moving in a similar direction. For Example – Input cost and cost price of a commodity.

**2) Negative Correlation – **

Two variables are said to be negatively correlated if the increase or decrease in the value of particular variable results in the decline or increase in the value of the other variable. These two variables can be said to be moving in the opposite direction. For example – The cost, price and demand of a commodity.

**3) Zero Correlation –**

Two variables are said to be in zero correlation if a variable is not dependent on the other and are not in relation to each other. For example – Marks are scored by an individual and his weight.

**What is Regression?**

Regression is used to analyse the value of a dependent variable based on the known value of another independent variable. This shows that there is a statistical relationship between the two variables.

So, regression analysis is used to assess the change in the dependent variable by decoding the changes associated with the independent variable. This analysis is based on the assumption of a mathematical relationship between the two variables.

Regression analysis is used in several activities and plays an essential role in establishing statistical models. It acts as a convenient and flexible tool in the hands of statistical analysts to deduce meaningful conclusions to real-life problems.

**What are the Different Types of Regression Analysis?**

There are different types of regression based on their function. Some of them are listed below.

**1) Multiple Linear Regression Model –**

If there is more than one independent variable while trying to establish a relation between a dependent variable, this type of analysis is called multiple linear regression.

**2) Simple Linear Regression Model –**

Simple linear regression analysis is used to examine the association between an independent variable and a dependent variable.

**Conclusion**

Now that we have understood the concepts of regression and correlation analysis, we need to keep in mind that this statistical concept cannot be studied in isolation. To derive meaningful conclusions to statistical research, both have to be studied together.

Correlation is used to find out whether the variables under observation are related or not. If they are related, the analysis shows their strength of association. Regression analysis is used by researchers when they want to establish a forecast by establishing an association with the variables involved.