ANOVA for Regression – Learn It 1

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ANOVA for Regression – Learn It 1

Understand what is measured by SSRegression, SSResiduals, and SSTotal in a regression context
Discuss the factors that affect the value of F-statistics in a regression context

Previously, you learned how to conduct a one-way ANOVA for scenarios that involve comparing more than two groups. Now, let’s extend what you learned about ANOVA to a regression context.

ANOVA Table

In an ANOVA table, the calculation illustrating the total variation within the groups of interest is known as the error sum of squares (SSError). The calculation illustrating the total variation between the groups is known as the group sum of squares (SSGroup).

Source	Degrees of Freedom (df)	Sum of Squares	Mean Square	F-Statistic
Group	[latex]k-1[/latex] (The number of groups minus 1)	SSGroup	[latex]\dfrac{\text{SSGroup}}{k-1}[/latex]	[latex]\dfrac{\text{MSGroup}}{\text{MSError}}[/latex]
Error	[latex]N-k[/latex] (The total number of data points minus the number of groups)	SSError	[latex]\dfrac{\text{SSError}}{N-k}[/latex]
Total	[latex]N-1[/latex] (The total number of data points minus 1)	SSGroup + SSError