What are the differences between ANOVA and regression?

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Accepted Answer

ANOVA (Analysis of Variance) and regression are two very similar types of statistical models with only a few differences between them.

Basis of Differentiation
ANOVA
Regression

Definition
Is a statistical technique used to determine if there are any statistical differences between the means of three or more independent groups
Is a statistical technique used to determine the relationship between one dependent variable and two or more independent variables

What the test is based on
Is based on one or more categorical predictor variables
Is based on one or more continuous predictor variables

What the test focuses on
Focuses on random variables
Focuses on fixed or independent or continuous variables

When the test is used
Is used when the predictor variables are categorical
Is used when the predictor variables are continuous

Order of performing the test
Is the initial test for identifying factors that can influence a data test
ANOVA test results are used in F-test on the relevance of the regression formula

Waht the test is used for
Is mainly used to determine whether or not data from various groups have a common mean
Is mainly used for making estimates or predictions based on the dependent variable

Number of models
Has three models: Fixed effect; Random Effect; Mixed Effect
Has two models: Linear regression；Multiple regression

Error terms associated with the test
Can have several error terms
Has only one error term

Basis of Differentiation	ANOVA	Regression
Definition	Is a statistical technique used to determine if there are any statistical differences between the means of three or more independent groups	Is a statistical technique used to determine the relationship between one dependent variable and two or more independent variables
What the test is based on	Is based on one or more categorical predictor variables	Is based on one or more continuous predictor variables
What the test focuses on	Focuses on random variables	Focuses on fixed or independent or continuous variables
When the test is used	Is used when the predictor variables are categorical	Is used when the predictor variables are continuous
Order of performing the test	Is the initial test for identifying factors that can influence a data test	ANOVA test results are used in F-test on the relevance of the regression formula
Waht the test is used for	Is mainly used to determine whether or not data from various groups have a common mean	Is mainly used for making estimates or predictions based on the dependent variable
Number of models	Has three models: Fixed effect; Random Effect; Mixed Effect	Has two models: Linear regression；Multiple regression
Error terms associated with the test	Can have several error terms	Has only one error term

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