Last Update: February 21, 2022
Linear Regression: Residual Standard Error in R can be estimated using stats package lm, summary.lm functions and sigma value for evaluating linear regression goodness of fit. Main parameters within lm function are formula with y ~ x1 + … + xp model description and data with data.frame object including model variables. Main parameter within summary.lm function is object with previously fitted lm model.
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 AER package HousePrices object [1].
First, we load package AER for data [2].
In [1]:
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 data.frame structure.
In [2]:
data(HousePrices)
head(HousePrices[,1:3])
Out [2]:
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 [3]:
mlr <- lm(formula = price ~ lotsize + bedrooms, data = HousePrices)
Fourth, we can print mlr model summary results which include estimated residual standard error using summary.lm function.
In [4]:
summary.lm(mlr)
Out [4]:
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 [5]:
smlr <- summary.lm(mlr)
smlr$sigma
Out [5]:
[1] 21229.05
Sixth, we can additionally print mlr model estimated residual standard error using sqrt, sum functions and its residuals, df.residual values.
In [6]:
sqrt(sum(mlr$residuals^2)/mlr$df.residual)
Out [6]:
[1] 21229.05
Courses
My online courses are hosted at Teachable website.
For more details on this concept, you can view my Linear Regression in R Course.
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.
[2] AER R Package. Christian Kleiber and Achim Zeileis. (2008). Applied Econometrics with R. Springer-Verlag, New York.