Last Update: February 21, 2022
Linear Regression: Residual Standard Error in R can be estimated using
summary.lm functions and
sigma value for evaluating linear regression goodness of fit. Main parameters within
lm function are
y ~ x1 + … + xp model description and
data.frame object including model variables. Main parameter within
summary.lm function is
object with previously fitted
As example, we can estimate residual standard error from multiple linear regression of house price explained by its lot size and number of bedrooms using data included within
HousePrices object .
First, we load package
AER for data .
In : library(AER)
Second, we create
HousePrices data object from
AER package using
data function and print first six rows and three columns of data using
head function to view
In : data(HousePrices) head(HousePrices[,1:3])
Out : price lotsize bedrooms 1 42000 5850 3 2 38500 4000 2 3 49500 3060 3 4 60500 6650 3 5 61000 6360 2 6 66000 4160 3
Third, we fit model with
lm function using variables within
HousePrices data object and store outcome within
mlr object. Within
lm function, parameter
formula = price ~ lotsize + bedrooms fits model where house price is explained by its lot size and number of bedrooms.
In : mlr <- lm(formula = price ~ lotsize + bedrooms, data = HousePrices)
Fourth, we can print
mlr model summary results which include estimated residual standard error using
In : summary.lm(mlr)
Out : Call: lm(formula = price ~ lotsize + bedrooms, data = HousePrices) Residuals: Min 1Q Median 3Q Max -65665 -12498 -2075 8970 97205 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 5.613e+03 4.103e+03 1.368 0.172 lotsize 6.053e+00 4.243e-01 14.265 < 2e-16 *** bedrooms 1.057e+04 1.248e+03 8.470 2.31e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 21230 on 543 degrees of freedom Multiple R-squared: 0.3703, Adjusted R-squared: 0.3679 F-statistic: 159.6 on 2 and 543 DF, p-value: < 2.2e-16
Fifth, we can also store model summary results within
smlr object using
summary.lm function and print its
sigma value with estimated residual standard error.
In : smlr <- summary.lm(mlr) smlr$sigma
Out :  21229.05
Sixth, we can additionally print
mlr model estimated residual standard error using
sum functions and its
In : sqrt(sum(mlr$residuals^2)/mlr$df.residual)
Out :  21229.05
My online courses are hosted at Teachable website.
For more details on this concept, you can view my Linear Regression in R Course.
 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.
 AER R Package. Christian Kleiber and Achim Zeileis. (2008). Applied Econometrics with R. Springer-Verlag, New York.