The two most common terms used in the world of statistics are Correlation followed by Regression. The two terms are described as ‘Analysis’ as they are based on the dissemination of numerous variables.

This phenomenon is commonly known as multivariate distribution. They are most commonly used when the association between two quantitative variables needs to be examined.

Interviewees are most likely to be quizzed on the distinguishing characteristics of Correlation and Regression. However, many people suffer doubtfulness in understanding the two above phrases.

## Key Takeaways

- Correlation measures the strength and direction of the relationship between two variables, while regression is used to predict the value of one variable based on the value of another.
- Correlation does not imply causation, while regression can help identify causal relationships.
- Correlation can be calculated using a simple formula, while regression requires more complex mathematical models.

**Correlation vs Regression**

Correlation refers to the degree of association between two variables. Regression is used to model the relationship between two variables. Correlation measures the degree of association between two variables, while regression is used for modeling the relationship between two variables.

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The relationship between the two different variables was initially assessed. Regression has countless instinctive applications in the day to day life. Here is a thorough comparison table that can successfully explain the differences between the two terms.

**Comparison Table**

Parameter of Comparison | Correlation | Regression |
---|---|---|

Meaning | It determines the co-relationship, which is the association between two variables. It largely depends on statistics-based procedures. | Justifying the arithmetic relation between the two, an autonomous and dependent value. |

Objective | It enables the identification of the numerical value that expresses the relationship between two or more variables. | In Regression, the values of a fixed variable help us pinpoint and approximate the values of the random variable. |

Usage | The linear association between the two variables is shown. | Mostly based on an estimation based on one variable to predict the value of the other variable. |

Independent Variable & Dependent variable | Both dependent as well as independent variables are similar to each other. | Independent and dependent variables are not the same. |

Indication | It measures the degree to which the two variables change simultaneously. | Regression signifies how the switch in the value of a variable (x) is determined by the variable (y). |

**What is the Correlation?**

Correlation is derived from two words, ‘Co’, which means together, and ‘relation,’ meaning link or a connection between a couple of quantities.

It merely means the degree of change occurring in one of the variables and is reacted by a corresponding change in the other variable. This could be an explicit change or an implicit one.

**It successfully depicts the degree of association between two **variables taken into consideration; it is based on the principles of statistics. The value determined can either be a positive one or a negative one.

When both variables move in an identical direction, it is a positive correlation, and the results correspond to one another, leading to investment and gain.

Contrarily, a negative correlation occurs when the variables are moving in opposite directions; this results in a decline in the other variable. For instance, the value and requirement of an item are interrelated.

An example where correlation can be successfully implemented is when a company wishes to compare the cumulative number of sales made to the number of salespersons employed.

**What is Regression?**

**Regression attempts **to determine the relationship between one variable and **other significant variables.**

The two types of variables used are a dependent one and an independent one. Regression makes one step ahead of correlation as it adds the prediction capabilities.

Regression is applied on an intuitive level by people daily.

It holds a significant place in human actions, as it is a potent tool used to predict the events that occurred before these times, in the present and future, based on previous or current events and occurrences.

For instance, past business records can estimate future profits. It can be explained with a simple example of how we wake up in the morning. If you go to bed early, you can wake up early in the morning more easily.

We can understand linear regression using two variables, ‘x’ and ‘y’. Here, the variables ‘x’ and ‘y’ depend on one another, i.e., ‘y’ depends or is affected by ‘x,’ which is an independent variable.

The mentioned factors are indicated on a statistical graph, which is a mathematical representation.

Quantitative Regression is more accurate as it creates an arithmetic interpretation of an equation. This equation or formulae can be used for analyzing and predicting in the future.

For instance, a doctor estimates a patient’s appropriate drug dosage (independent variable) based on their body weight, which is a dependent variable.

**Main Differences Between Correlation and Regression**

- Only a single piece of data or statistics is considered in Correlation. However, Regression provides a complete mathematical equation.
- Correlation pinpoints the degree to which two variables are associated with each other. On the other hand, Regression reflects the impression of a unit change in the independent variable due to the changes in the dependent variable.
- Correlation can give a crisp value describing the relationship between the two variables. Regression is beneficial as it thoroughly examines and further predicts values for a variable using mathematical equations.
- In Correlation, the variables ‘x’ and ‘y’ are arbitrary. They can weigh blood pressure or cholesterol level instead of Regression, which assumes ‘x’ as a fixed variable with no error, such as temperature setting.
- The correlation was derived during the 16th century from Medieval Latin, meaning a mutual relationship or connection between two or more things.
- On the other side, Francis Galton coined Regression in the 19
^{th}century. He used it to illustrate a biological occurrence. In Particular, regression means reverting to a primitive state.

**References**

- https://psycnet.apa.org/record/1960-06763-000
- https://link.springer.com/content/pdf/10.3758/BRM.41.4.1149.pdf
- https://psycnet.apa.org/record/1995-97110-002

Piyush Yadav has spent the past 25 years working as a physicist in the local community. He is a physicist passionate about making science more accessible to our readers. He holds a BSc in Natural Sciences and Post Graduate Diploma in Environmental Science. You can read more about him on his bio page.