
  library(AER)
  library(MASS)


  # generate the binary variable `old` and append it to the dataset
  
  
  # conduct the regression and assign it to `mod_bb`
  
  
  # print a robust summary to the console


  # generate the binary variable `old` and append it to the dataset
  Boston$old <- as.numeric(Boston$age >= 95)
  
  # conduct the regression and assign it to `mod_bb`
  mod_bb <- lm(medv ~ chas*old, data = Boston)
  
  # print a robust summary to the console
  coeftest(mod_bb, vcov. = vcovHC)


  ex() %>% check_object("Boston") %>% check_column("old", col_missing_msg = "Have you added the column `old` to `Boston`?") %>%
  check_equal(incorrect_msg = "Have you correctly calculated the column `old` based on `age`?")
  test_or({
    test_object("mod_bb")
  },{
    f <- ex() %>% override_solution("lm(medv ~ old*chas, data = Boston)") %>% check_function("lm")
    f %>% check_arg("formula") %>% check_equal()
  },{
    f <- ex() %>% override_solution("lm(Boston$medv ~ Boston$chas*Boston$old)") %>% check_function("lm")
    f %>% check_arg("formula") %>% check_equal()
  },{
    f <- ex() %>% override_solution("lm(Boston$medv ~ Boston$old*Boston$chas)") %>% check_function("lm")
    f %>% check_arg("formula") %>% check_equal()
  },{
    f <- ex() %>% override_solution("attach(Boston);lm(medv ~ chas*old)") %>% check_function("lm")
    f %>% check_arg("formula") %>% check_equal()
  },{
    f <- ex() %>% override_solution("attach(Boston);lm(medv ~ old*chas)") %>% check_function("lm")
    f %>% check_arg("formula") %>% check_equal()
  },{
    f <- ex() %>% override_solution("lm(medv ~ chas + old + chas:old, data = Boston)") %>% check_function("lm")
    f %>% check_arg("formula") %>% check_equal()
  },{
    f <- ex() %>% override_solution("lm(medv ~ old + chas + old:chas, data = Boston)") %>% check_function("lm")
    f %>% check_arg("formula") %>% check_equal()
  },{
    f <- ex() %>% override_solution("lm(Boston$medv ~ Boston$chas + Boston$old + Boston$chas:Boston$old)") %>% check_function("lm")
    f %>% check_arg("formula") %>% check_equal()
  },{
    f <- ex() %>% override_solution("lm(Boston$medv ~ Boston$old + Boston$chas + Boston$old:Boston$chas)") %>% check_function("lm")
    f %>% check_arg("formula") %>% check_equal()
  },{
    f <- ex() %>% override_solution("attach(Boston);lm(medv ~ chas + old + chas:old)") %>% check_function("lm")
    f %>% check_arg("formula") %>% check_equal()
  },{
    f <- ex() %>% override_solution("attach(Boston);lm(medv ~ old + chas + old:chas)") %>% check_function("lm")
    f %>% check_arg("formula") %>% check_equal()
  })
  
ex() %>% check_function("coeftest") %>% {
    check_arg(., "x") %>% check_equal()
    check_arg(., "vcov.") %>% check_equal()
  }
  success_msg("Correct! The estimated effect of moving from a suburb with a low proportion of old buildings to a one with a high proportion is -7.13 + 10.55 * chas. So depending on the passing of the Charles River through a suburb, the effect is positive or negative.")