Tests: The Linear Regression Model (Studentized Residuals)

Ivan Jacob Agaloos Pesigan

2020-12-31

# The Linear Regression Model: Studentized Residuals {#linreg-estimation-tepsilonhat-example}

Data

See jeksterslabRdatarepo::wages.matrix() for the data set used in this example.

X <- jeksterslabRdatarepo::wages.matrix[["X"]]
# age is removed
X <- X[, -ncol(X)]
y <- jeksterslabRdatarepo::wages.matrix[["y"]]
head(X)
#>      constant gender race union education experience
#> [1,]        1      1    0     0        12         20
#> [2,]        1      0    0     0         9          9
#> [3,]        1      0    0     0        16         15
#> [4,]        1      0    1     1        14         38
#> [5,]        1      1    1     0        16         19
#> [6,]        1      1    0     0        12          4
head(y)
#>      wages
#> [1,] 11.55
#> [2,]  5.00
#> [3,] 12.00
#> [4,]  7.00
#> [5,] 21.15
#> [6,]  6.92

Studentized Residuals

h <- h(X = X)
sigma2hatepsilonhat <- sigma2hatepsilonhat(
  X = X,
  y = y
)
epsilonhat <- epsilonhat(
  X = X,
  y = y
)
result_tepsilonhat1 <- as.vector(
  .tepsilonhat(
    sigma2hatepsilonhat = sigma2hatepsilonhat,
    h = h,
    epsilonhat = epsilonhat
  )
)
result_tepsilonhat2 <- as.vector(
  tepsilonhat(
    X = X,
    y = y
  )
)

lm() function

lmobj <- lm(
  wages ~ gender + race + union + education + experience,
  data = jeksterslabRdatarepo::wages
)
lm_tepsilonhat <- as.vector(rstudent(lmobj))

context("Test linreg-estimation-tepsilonhat")
test_that("result_tepsilonhat1.", {
  expect_equivalent(
    length(result_tepsilonhat1),
    length(lm_tepsilonhat)
  )
  for (i in seq_along(result_tepsilonhat1)) {
    expect_equivalent(
      round(result_tepsilonhat1[i], digits = 0),
      round(lm_tepsilonhat[i], digits = 0)
    )
  }
})
#> Test passed 🥇
test_that("result_tepsilonhat2.", {
  expect_equivalent(
    length(result_tepsilonhat2),
    length(lm_tepsilonhat)
  )
  for (i in seq_along(result_tepsilonhat2)) {
    expect_equivalent(
      round(result_tepsilonhat2[i], digits = 0),
      round(lm_tepsilonhat[i], digits = 0)
    )
  }
})
#> Test passed 😀