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 [1].

Courses
My online courses are hosted at Teachable website.
For more details on this concept, you can view my Linear Regression Courses.
References
[1] 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.