Regression vs ANOVA

Last Updated : 27 Feb, 2024

ANOVA and Regression have distinct objectives. Whereas regression employs a binary response variable to predict the category, ANOVA generates a continuous response variable to anticipate its value. In this article, let’s understand the difference between regression and ANOVA.

What is Regression?

Regression is a statistical method that measures the association between several independent variables and a dependent variable. The objective of regression is to anticipate the dependent variable’s value by considering the independent variables. Regression models find widespread application in prediction, forecasting, and unraveling the inherent associations in datasets.

What is Anova?

ANOVA, known as Analysis of Variance, is also a statistical method that examine whether there are significant differences in the means among three or more groups. By evaluating the variance within and between groups, ANOVA helps determine if the observed distinctions likely stem from genuine group variations or mere chance. It’s frequently used in experimental studies to assess how independent variables impact a dependent variable, aiding researchers in pinpointing significant factors that affect the outcome being studied.

Key Differences Between Regression and ANOVA

Characteristic	Regression	ANOVA
Definition	A statistical technique to determine the relationship between a dependent variable and one or more independent variables.	A statistical technique to analyze the differences between group means in a sample.
Variable Usage	Used with fixed (independent) variables	Used with group (explanatory) variables that have a random component.
Types	Linear regression: One independent variable Multiple regression: Multiple independent variables	Fixed-effects ANOVA: All groups are of interest. Random-effects ANOVA: Groups represent a random sample from a larger population. Mixed-effects ANOVA: Combination of fixed and random effects
Purpose	Estimate or predict the dependent variable based on the independent variables. Understand the nature of the relationship between variables	Identify if the group means are statistically different from each other.
Assumptions	Linear relationship between independent and dependent variables. Normality of errors. Homoscedasticity (constant variance of errors)	Normality of errors Homoscedasticity (constant variance of errors)
Output	Regression equation: Shows the relationship between independent and dependent variables. Statistical significance: Indicates if the relationship is statistically noteworthy	F-statistic: Tests the overall null hypothesis of no difference between group means. Post-hoc tests: Identify specific groups that differ from each other (if necessary)
Strengths	Estimates and predicts the dependent variable. Understands the nature of the relationship between variables	Compares means across multiple groups.
Weaknesses	Assumes linear relationship, Sensitive to outliers	Limited to comparing means, not individual data points.

When to use Regression

Regression is useful for tracking model performance, deploying, iterating, and other machine-learning operations in addition to training. It is one of the most widely used machine learning techniques.
The categorical dependent variable is predicted using regression.
It is employed in cases when the forecast is binary, such as true or false, 0 or 1, yes or no.
When dealing with fixed or independent variables, regression is used.

When to use ANOVA

ANOVA is utilised when comparing the means of three or more groups.
One-way ANOVA may be used to determine the link between an independent variable and one quantitative dependent variable, which is useful for testing a specific hypothesis between groups. Analysing the effect of employee training on customer satisfaction scores is one example.
When analysing variables with a random component, ANOVA is used.