This article throws light on two analyses finding a base in multivariate distribution - correlation and regression. A distribution comprising of multiple variables is called a multivariate distribution. Therefore, it is essential to understand their significance and gain a clear understanding of the terms correlation and regression before moving ahead with the differences between them.

## Correlation vs. Regression

**The comparison between correlation and regression can be studied through a tabular format as given below:**

Basis of Difference |
Correlation |
Regression |
---|---|---|

Meaning |
Correlation refers to a statistical measure that determines the association or co-relationship between two variables. | Regression depicts how an independent variable serves to be numerically related to any dependent variable. |

Utility |
Used for representing the linear relationship existing between two variables. | It is used for fitting the best line and estimating the value of one variable based on its relationship with the other. |

Dependent /Independent variables |
There is no difference between the two. Both variables are mutually dependent. | Both variables serve to be different in terms of regression analysis. One variable is independent, while the other is dependent. |

Indicator of |
It indicates the extent and way in which two variables make their movements together. | Regression depicts the impact of any unit change in the value of the known variable (x) on the value of the estimated variable (y). |

Objective |
To find the numerical value that defines and shows the relationship between variables. | To estimate the values of random variables based on the values shown by fixed variables. |

Purpose |
The primary purpose is to predict the most dependable forecasts. | The primary purpose is to predict/ estimate the value of any unknown variable by taking the help of the known variable. |

Scope |
Correlation analysis offers limited applications. | Regression analysis provides a broader scope of applications. |

Range |
Coefficients may range from -1.00 to +1.00. | If byx > 1, then bxy < 1 in regression analysis. |

Responding Nature |
The correlation coefficient serves to be independent of any change of Scale or shift in Origin. | The regression coefficient shows dependency on the change of Scale but is independent of its shift in Origin. |

Nature of Coefficient |
The correlation coefficient is mutual and symmetrical. | Regression coefficient fails to be symmetrical. |

Exceptional Cases |
Non-sense correlation may find a place in some correlation analyses. | Non-sense regression is non-existent in regression analysis. |

Mathematical treatment. |
Not very useful for advanced mathematical treatment. | It is widely used for advanced mathematical treatment. |

Measures |
This type of analysis measures the degree/extent to which any two variables make their movements in unison. | It depicts the fundamental level as well as the nature of existing linear relationships between two variables. Regression describes one variable in the form of a linear function of the other variable. |

Relationship |
It is confined to the linear relationships existing between variables only. Correlation does not depict the cause of the effect of the variables. | It encompasses both linear as well as non-linear relationships. The cause and effect relationship between the two is indicated, and a functional link is established. |

Variables |
Both variables x and y are random variables. | In regression, x is a random variable while y is a fixed variable. At times, both variables may be like random variables. |

Coefficient |
The coefficient correlation serves to be a relative measure. |
The regression coefficient is generally an absolute figure. |

## Definition of Correlation

Correlation is described as the analysis that informs users about the association or the absence of any relationship between any two variables **‘x’ and ‘y.’** The word correlation combines **‘Co’ (together) **and relation (interaction/connection) in context to any two quantities. Correlation between two given variables exists when a unit change in any one variable gains a retaliation (in response) in the form of an equivalent change in the other variable. The answer can be either direct or indirect. Conversely, the two variables are said to be uncorrelated in case the movement in any one variable fails to generate any flow in the other variable, be it directly or indirectly. Correlation is, therefore, a statistical technique representing the strength of the connection between any given pairs of variables.

**Given below are the measures of correlation:**

- The correlation coefficient of Karl Pearson’s Product-moment
- Scatter diagram
- Coefficient of concurrent deviations
- Coefficient of Spearman’s rank correlation

### Types of Correlation

**The three types of relationship to their nature are:**

**1. Positive Correlation: **When two variables are seen moving in the same direction, wherein an increase in the value of one variable results in an increase in other, and vice versa, then they are said to be positively correlated, e.g., profit and investment.

**2. Negative Correlation:** On the other hand, when two variables are seen moving in different directions, and in a manner that any increase in one variable results in a decrease in value of the other, and vice versa, then the variables are said to be negatively correlated; e.g., price and demand of any product.

**3. Zero Correlation: **If any given change in a variable is not dependent on the other, then the variables are said to have Zero Correlation, e.g., marks and height of students in a class.

Correlation can be either positive or negative.

## Definition of Regression

Regression analysis is useful for predicting the value of a dependent variable based on the known value of any independent variable. It is assumed that an average mathematical relationship exists between the two variables. Regression refers to the statistical technique for assessing the changes occurring in the metric dependent -variable caused due to the transition occurring in one/more independent variables. The incurring analysis is based on the average mathematical relationship existing between the two/more variables. Regression is known to play an essential role in terms of several human activities. Overall, it serves to be a powerful and flexible instrument in the hands of analysts. Regression is used for forecasting any event based on past or present events; e.g., a business’s annual profit may be ascertained based on records with the help of regression.

There exist two variables x and y in any simple linear regression. Herein, y depends on x, or in other words. It is influenced by x. While x is referred to as the predictor or independent variable, y is termed as the criterion or dependent variable.

### Types of Regression

**Based on their functionality, the different types of regression are as follows:**

**1.Simple linear Regression: **It is a statistical method used for summarizing and studying the relationships between any two continuous variables – an independent variable and a dependent variable.

**2. Multiple Linear Regression: **This type of regression examines the linear relationship existing between a dependent variable and more than one independent variable.

**Conclusion:**

The difference between correlation and regression, the two crucial mathematical concepts, cannot be studied independently of each other. Correlation analysis is best used when a researcher has to assess whether the variables under study are directly/ indirectly correlated or not. In case they are correlated, then this type of analysis showcases the strength of their association. The most popular measure of correlation is Pearson’s correlation coefficient.

In regression analysis, it is possible to establish a functional relationship between any pair of given variables with the intent of making future projections concerning events.