![]() We can also use statistical software to find that the residual standard error of the model is 4.44.Īnd, although it’s beyond the scope of this tutorial, we can use software to find the leverage statistic (h ii) for each observation: We can repeat this process to find the residual for every single observation: Residual = Observed value – Predicted value = 41 – 35.67 = 5.33 ![]() We can then calculate the residual for this observation as: For example, the predicted value of the first observation would be: Using this line, we can calculate the predicted value for each Y value based on the value of X. ![]() If we use some statistical software (like R, Excel, Python, Stata, etc.) to fit a linear regression line to this dataset, we’ll find that the line of best fit turns out to be: Suppose we have the following dataset with 12 total observations: Note: Sometimes standardized residuals are also referred to as “internally studentized residuals.” Example: How to Calculate Standardized Residuals This doesn’t necessarily mean that we’ll remove these observations from the model, but we should at least investigate them further to verify that they’re not a result of a data entry error or some other odd occurrence. In practice, we often consider any standardized residual with an absolute value greater than 3 to be an outlier. h ii: The leverage of the i th observation.RSE: The residual standard error of the model.One type of residual we often use to identify outliers in a regression model is known as a standardized residual. If we plot the observed values and overlay the fitted regression line, the residuals for each observation would be the vertical distance between the observation and the regression line: Residual = Observed value – Predicted value A residual is the difference between an observed value and a predicted value in a regression model. ![]()
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