Standard Error of Forecast in Multiple Regression

Proof of a Useful Result

by Joseph S. DeSalvo

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Proof that the standard error of forecasting the dependent variable and the expected value of the dependent variable in a multiple regression reduce to very simple formulas when evaluated at the sample means of the independent variables. These simple formulas involve only knowledge of sample size and the standard error of estimate, the latter of which is typically printed out in computer regression routines. By using these results, one avoids the necessity of calculating the more complicated general formulas for the standard error, in those cases for which evaluation at the mean will suffice. Although the results are not surprising, the author has been unable to find a published proof.

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