Regression vs ANOVA

Difference Between Regression and ANOVA

Both the Regression and ANOVA are the statistical models which are used in order to predict the continuous outcome but in case of the regression, continuous outcome is predicted on basis of the one or more than one continuous predictor variables whereas in case of ANOVA continuous outcome is predicted on basis of the one or more than one categorical predictor variables.

Regression is a statistical method to establish the relationship between sets of variables in order to make predictions of the dependent variable with the help of independent variables, ANOVA, on the other hand, is a statistical tool applied on unrelated groups to find out whether they have a common mean.

What is Regression?

Regression is a very effective statistical method to establish the relationship between sets of variables. The variables for which the regression analysis is done are the dependent variable and one or more independent variables. It is a method to understand the effect on a dependent variable of one or more than one independent variable.

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Suppose for example a paint company uses one of the derivatives of crude solvent & monomers as its raw material, we can run a regression analysis between the price of that raw material and the price of Brent crude prices.
In this example, the price of the raw material is the dependent variable and the price of Brent prices is the independent variable.
As the price of solvents and monomers increases and decreases in price with the rise and fall of Brent prices, the price of the raw material is the dependent variable.
Similarly for any business decision in order to validate a hypothesis that a particular action will lead to the increase in the profitability of a division can be validated based on the result of the regression between the dependant and independent variables.

What is Anova?

ANOVA is the short form of analysis of variance. ANOVA is a statistical tool that is generally used on random variables. It involves group not directly related to each other in order to find out whether there exist any common means.

A simple example to understand this point is to run ANOVA for the series of marks of students from different colleges in order to try to find out whether one student from one school is better than the other.
Another example can be if two separate research team is researching different products not related to each other. ANOVA will help to find which one is providing better results. The three popular techniques of ANOVA are a random effect, fixed effect, and mixed effect.

Regression vs ANOVA Infographics

Key Differences Between Regression and ANOVA

Regression is applied to variables that are mostly fixed or independent in nature and ANOVA is applied to random variables.
Regression is mainly used in two forms they are linear regression and multiple regression, tough other forms of regression are also present in theory those types are most widely used in practice, on the other hand, there are three popular types of ANOVA they are a random effect, fixed effect, and mixed effect.
Regression is mainly used in order to make estimates or predictions for the dependent variable with the help of single or multiple independent variables and ANOVA is used to find a common mean between variables of different groups.
In the case of regression, the number of the error term is one but in the case of ANOVA, the number of the error term is more than one.

Comparative Table

Basis	Regression	ANOVA
Definition	Regression is a very effective statistical method to establish the relationship between sets of variables.	ANOVA is the short form of analysis of variance. It is applied to unrelated groups to find out whether they have a common mean
Nature of Variable	Regression is applied on independent variables or fixed variables.	ANOVA is applied to variables which are random in nature
Types	Regression is mainly used in two forms they are linear regression and multiple regression, the later is when the number of independent variables is more than one.	The three popular types of ANOVA are a random effect, fixed effect, and mixed effect.
Examples	A paint company uses solvent & monomers as its raw material which is a derivative of crude; we can run a regression analysis between the price of that raw material and the price of Brent crude prices.	If two separate research teams are researching different products not related to each other. ANOVA will help to find which one is providing better results.
Variables Used	Regression is applied to two sets of variables, one of them is the dependent variable and the other one is the independent variable. The number of independent variables in regression can be one or more than one.	ANOVA is applied to variables from different which not necessarily related to each other.
Use of the Test	Regression is mainly used by the practitioners or industry experts in order to make estimates or predictions for the dependent variable.	ANOVA is used to find a common mean between variables of different groups.
Errors	The predictions made by the regression analysis are not always desirable that’s because of the error term in a regression, this error term is also known as residual. In the case of regression, the number of the error term is one.	The number of errors in case ANOVA, unlike regression, is more than one.

Conclusion

Both regressions and ANOVA are powerful statistical tools that are applied to multiple variables. Regression is used in order to make predictions of the dependent variable with the help of independent variables that have some relations. It is helpful to validate a hypothesis of whether the hypothesis made is correct or not.

Regression is used on variables that are fixed or independent in nature and can be done with the use of a single independent variable or multiple independent variables. ANOVA is used to find a common between variables of different groups that are not related to each other. It is not used to make a prediction or estimate but to understand the relations between the set of variables.