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# Regression vs ANOVA

Updated on April 17, 2024
Article byWallstreetmojo Team
Edited byAshish Kumar Srivastav
Reviewed byDheeraj Vaidya, CFA, FRM

## Difference Between Regression and ANOVA

Both regression and ANOVA are the statistical models used to predict the continuous outcome. Still, in the case of regression, the continuous outcome is predicted based on one or more than one continuous predictor variable. Whereas, in the case of ANOVA, a continuous outcome is predicted based on one or more than one categorical predictor variable.

Regression is a statistical method to establish the relationship between sets of variables to make predictions of the dependent variable with the help of independent variables. On the other hand, ANOVA is a statistical tool applied to unrelated groups to determine whether they have a common meaning.

### What is Regression?

Regression is a very effective statistical method for establishing the relationship between 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 of one or more independent variables on a dependent variable.

• 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 that raw material’s price and the Brent crude prices.
• In this example, the raw material price is the dependent variable, and the price of Brent is the independent variable.
• As the price of solvents and monomers increases and decreases with the rise and fall of Brent prices, the raw material price is the dependent variable.
• Similarly, one can validate any business decision to validate a hypothesis that a particular action will increase a division’s profitability based on the regression between the dependent and independent variables.

For eg:
Source: Regression vs ANOVA (wallstreetmojo.com)

### What is Anova?

ANOVA is the short form of analysis of variance. ANOVA is a statistical tool generally used on random variables. It involves groups not directly related to each other to determine whether any common means exist.

• A simple example to understand this point is to run ANOVA for the series of marks of students from different colleges to try to find out whether one student from one school is better than the other.
• Another example can be if two research teams are researching different products unrelated 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.
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### Regression vs ANOVA Infographics

For eg:
Source: Regression vs ANOVA (wallstreetmojo.com)

### Key Differences Between Regression and ANOVA

• Regression applies to mostly fixed or independent variables, and ANOVA applies to random variables.
• Regression is used in two forms: linear regression and multiple regression. Tough other forms of regression are also present in theory. Those types are used in practice. On the other hand, there are three popular types of ANOVA: random effect, fixed effect, and mixed effect.
• Regression is used to make estimates or predictions for the dependent variable with the help of single or multiple independent variables. ANOVA is used to find a common mean between variables of different groups.
• In the case of regression, the error term is one, but in the case of ANOVA, the number of the error term is more than one.

### Conclusion

Both regressions and ANOVA are powerful statistical tools applied to multiple variables. For example, one may use regression to make predictions of the dependent variable with the help of independent variables with some relations. In addition, it is helpful to validate a hypothesis, whether the hypothesis made is correct or not.

Regression is used on fixed or independent variables and done with a single independent variable or multiple independent variables. ANOVA is used to find a common between variables of different unrelated groups. It is not used to make a prediction or estimate but to understand the relations between the set of variables.

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