Last Update: February 21, 2022
Linear Regression: Residual Standard Error is used to evaluate linear regression goodness of fit by estimating its residual standard deviation.
As example, we can fit a three-variable multiple linear regression with formula . Then, we can estimate its residual standard error with formula . Residual mean squared error with formula is estimated as residual sum of squares divided by residual degrees of freedom . Residual sum of squares with formula is estimated as the sum of squared regression residuals . Regression residuals with formula are estimated as differences between actual and fitted values. Residual degrees of freedom with formula are the number of observations minus number of independent variables minus constant term.
Below, we find an example of estimated residual standard error from multiple linear regression of house price explained by its lot size and number of bedrooms .
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 Data Description: Sales prices of houses sold in the city of Windsor, Canada, during July, August and September, 1987.
Original Source: Anglin, P., and Gencay, R. (1996). Semiparametric Estimation of a Hedonic Price Function. Journal of Applied Econometrics, 11, 633–648.
Source: AER R Package HousePrices Object. Christian Kleiber and Achim Zeileis. (2008). Applied Econometrics with R. Springer-Verlag, New York.