Robust Linear Models

Use lm_robust() to calculate heteroskedasticity-robust standard error values of housing prices

Learning Goals

Use estimatr to explore how lm_robust() can be used as a heteroskedasticity-robust estimator

Set up

• load packages
• import housing price data
• visualize some of the data in a table

show

library(estimatr)
library(kableExtra)
library(tidyverse)
library(modelsummary)

HPRICE2 <- read.csv("HPRICE2.csv")

kbl(head(HPRICE2)) %>%
  kable_classic(full_width = F, html_font = "Cambria")

price	nox	rooms	stratio
24000	5	7	15
21599	5	6	18
34700	5	7	18
33400	5	7	19
36199	5	7	19
28701	5	6	19

Use lm_robust() to run a bivariate regression with heteroskedasticity-robust standard errors

show

model1 <- lm_robust(formula = price ~ nox , data = HPRICE2)
summary(model1)

Call:
lm_robust(formula = price ~ nox, data = HPRICE2)

Standard error type:  HC2 

Coefficients:
            Estimate Std. Error t value   Pr(>|t|) CI Lower CI Upper
(Intercept)    39232     1451.2   27.03 3.858e-100    36381    42083
nox            -3060      260.5  -11.75  2.536e-28    -3572    -2548
             DF
(Intercept) 504
nox         504

Multiple R-squared:  0.1731 ,   Adjusted R-squared:  0.1715 
F-statistic: 137.9 on 1 and 504 DF,  p-value: < 2.2e-16

Predict the housing price when nox = 7

• derive the standard error and 95% confidence interval

show

predicted_price <- data.frame(nox=c(7)) 
output <- predict(model1, newdata=predicted_price, se.fit=TRUE, interval='confidence')

avg_price <- round(output$fit[1], digits = 2)
ci_upper <- round(output$fit[3], digits = 2)
ci_lower <- round(output$fit[2], digits = 2)
se <- round(output$se.fit[1], digits = 2)

If NO_x = 7, we predict the average housing price to be approximately $17812.74 with a 95% confidence interval of 16709.01 to 18916.48 and a standard error of 561.79.

Use lm_robust() to run a multiple regression with heteroskedasticity-robust standard errors

show

model2 <- lm_robust(formula = price ~ nox + rooms, data = HPRICE2)
summary(model2)

Call:
lm_robust(formula = price ~ nox + rooms, data = HPRICE2)

Standard error type:  HC2 

Coefficients:
            Estimate Std. Error t value  Pr(>|t|) CI Lower CI Upper
(Intercept)   -16343     4809.5  -3.398 7.327e-04   -25792    -6893
nox            -1646      265.1  -6.207 1.133e-09    -2166    -1125
rooms           7635      650.4  11.738 2.749e-28     6357     8913
             DF
(Intercept) 503
nox         503
rooms       503

Multiple R-squared:  0.5023 ,   Adjusted R-squared:  0.5003 
F-statistic: 150.4 on 2 and 503 DF,  p-value: < 2.2e-16

Predict the housing price when nox = 5 and rooms = 6

• derive the standard error and 95% confidence interval

show

predicted_price=data.frame(nox=c(5), rooms=c(6))
output <- predict(model2, newdata=predicted_price, se.fit=TRUE, interval='confidence')

avg_price <- round(output$fit[1], digits = 2)
ci_upper <- round(output$fit[3], digits = 2)
ci_lower <- round(output$fit[2], digits = 2)
se <- round(output$se.fit[1], digits = 2)

If NO_x = 5 and the house has 6 rooms, we predict the average housing price to be approximately $21238.77 with a 95% confidence interval of 20648.73 to 21828.81 and a standard error of 300.32.