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If several of the observations that had large residual values are deleted and If the regression...

If several of the observations that had large residual values are deleted and If the regression equation is re-estimated using this reduced sample, what would likely happen to the R2 and the standard error of the estimate?

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Observations that are of large residual values are called OUTLIERS in the regression analysis. Due to the presence of these outliers, the regression line which tries to connect all the regression points would not be line of best fit. It is always recommended to remove the outliers from the model as they increase the noise (high standard errors) and reduce the coefficient of correlation (r) and coefficient of determination (r2).

So, if we remove such observations the re-estimate the equation using reduced sample, then the coefficient of determination (R2) will increase and the standard error of the estimate would fall as the sample observations would now be closer to the new regression line reducing the difference between actual and predicted errors

R2 will increase and Standard Error would fall.

**if you liked the explanation, then please upvote. Would be motivating for me. Thanks

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