Correlation vs regression both of these terms of statistics that are used to measure and analyze the connections between two different variables and used to make the predictions. This method is commonly used in various industries; besides this, it is used in everyday lives.

For example, you might see that someone is wearing expensive attire; you automatically think that he/she might be financially successful. Another example of it is that you think to lose weight by working out in the morning, and then you start running from the next morning.

The above-mentioned examples are the real-life examples of **correlation vs regression**, as one variable, i.e., expensive attires, is directly related to other variables, i.e., being wealthy. Therefore, we have provided you the list of similarities and differences of **correlation vs regression**.

**What is the correlation**?

As correlation itself give you the meaning of the word that is ‘co’ means together, and ‘relation’ means a connection or the link between two quantities. Or we can say that if a variable change, then another variable will automatically change whether it could be directly or indirectly.

For instance, assume that we have two different variables x and y. The changes in these two variables are taken as positive or negative. Whenever the two variables are changed in the same direction. Or we can say that if a single variable is increasing, then the second variable will also increase then the change is considered to be positive.

**The formula of correlation**

The correlation coefficient is used to indicate the data of the relationship between two variables by using the following formula:

Where

**rxy**– the correlation coefficient of the variables x and y.**xi**– the values of the x-variable is a representation.**x̅**– the mean of the values of the x-variable.**yi**– the values of the y-variable in a representation.**ȳ**– the mean of the values of the y-variable.

**What is the regression?**

Regression represents how the single variable affects the other variable, or a single variable can be responsible for the changes in another variable. It implies that the results are dependent on a single or more variable.

For example, correlation is used to define the relationship between the two variables, Whereas regression is used to represent the effect of each other. The example of it is, because of heavy rainfall, several crops can be damaged. And it could lead to floods also.

**The formula of regression**

The regression is used to represent the relationship between a variable and an independent variable. So it can be represented as:

Where:

**Y**– Dependent variable.**X**– Independent variable.**a**– Intercept.**b**– Slope.**ϵ**– error (Residual).

Now before proceeding to the differences of both **correlation vs regression**, let’s find out the similarities of both.

**Similarities of both correlation vs regression **

- Both terminologies are used to quantify the strength and direction of the relationship between two variables.
- There is a certain point when correlation and regression slope both are negative individually.
- Again both correlation and regression slope can be positive.

**Differences between correlation vs regression **

Besides the similarities, there are some differences that are listed below:

Parameter | Correlation | Regression |

Definition | It is used to measure statistics that determine the connection between two variables. | It is used to represent the connection between the independent and dependent variables. |

Usages | To show the linear connection between two variables. | To get the best data and to estimate a single variable on the basis of other variables. |

Independent and dependent variables | There is no difference between both variables. | In this, both of the variables are different from each other. |

Indicate | The coefficient of correlation signifies the extent to which the two variables values that move together. | It signifies the effect of changes in the units that are known as a variable (X) on the estimated variable (Y). |

Aim | To get the numeric values expressions’ relation between variables. | To determine the values of selected variables on the basis of the fixed variables. |

Data representation | It represents a single point. | It can represent the data with a line. |

Use mathematical equations | No, there is no direct connection between mathematical equations. | Yes, there is a direct connection between mathematical equations. |

**Conclusion**

The above discussion on **correlation vs regression** shows that there are similarities and dissimilarities between the two mathematical concepts, even though both are studied together. The correlation is used by the researchers when they want to know the variable under the study are correlated or not if this is so. Then what is the strength of the association. Whereas, the regression analysis is used to get function relationship between the two variables to make the further projections of the events.

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