Question

Could you please explain in detail the differences and similarities between the one-way ANOVA model and the linear regression model given that you have a quantitative predictor variable?

Answer 1

Similarities :

1)Both the Regression and ANOVA are the statistical models which are used in order to predict the continuous outcome

2)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.

Differences :

• 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.