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The residuals of a model are the actual values minus the predicted values. Many statistical models make assumptions about the error, which is estimated by the residuals.

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The difference between total error, prediction error and fitted error via residual

Consider a regression model $Y=E(Y|X)+Prediction \ Error$ i.e $Prediction \ error = Y-E(Y|X)$. Now, define an estimate of the regression function $E(Y|X)=\hat{Y}+ Fitted \ error$ i.e. Fitted error = $ …
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