What is the purpose of residual analysis in regression?

To assess model fit and detect nonlinearity, heteroscedasticity, outliers, and influential points.

Residual analysis looks at the differences between what the model predicts and what is actually observed. This helps you judge how well the model fits and to spot problems: a residuals plot can reveal nonlinearity if you see a curved pattern, or heteroscedasticity if the spread of residuals grows or shrinks with the fitted values. Large residuals flag potential outliers, and points with high leverage that also have large residuals can be influential enough to distort the fit. Checking residuals also supports inference by checking that the error terms are approximately normal and independent. So, the main purpose is to assess model fit and detect nonlinearity, heteroscedasticity, outliers, and influential points.

To compute the mean of dependent variable.

To test for normality of the dependent variable.

To maximize R-squared.

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