Tests: The Linear Regression Model (Residuals)

Ivan Jacob Agaloos Pesigan

2020-12-31

# The Linear Regression Model: Residuals {#linreg-estimation-residuals-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

\(\mathrm{My}\)

Pmatrix <- P(X = X)
Mmatrix <- M(X = X)
betahat <- betahat(
  X = X,
  y = y
)
yhat <- yhat(
  X = X,
  y = y
)
result_My1 <- .My(
  y = y,
  M = Mmatrix
)
result_My2 <- .My(
  y = y,
  X = X,
  P = Pmatrix
)
result_My3 <- My(
  X = X,
  y = y
)

\(\mathrm{y} - \mathrm{\hat{y}}\)

result_yminusyhat1 <- .yminusyhat(
  y = y,
  yhat = yhat
)
result_yminusyhat2 <- .yminusyhat(
  y = y,
  X = X
)

result_yminusyhat3 <- yminusyhat(
  X = X,
  y = y
)

\(\boldsymbol{\hat{\varepsilon}}\)

result_epsilonhat <- epsilonhat(
  X = X,
  y = y
)

lm() function

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

context("Test linreg-estimation-projection")
test_that("Py = yhat.", {
  expect_equivalent(
    length(result_My1),
    length(result_My2),
    length(result_My3),
    length(result_yminusyhat1),
    length(result_yminusyhat2),
    length(result_yminusyhat3),
    length(result_epsilonhat)
  )
  for (i in seq_along(result_My1)) {
    expect_equivalent(
      result_My1[i],
      lm_epsilonhat[i]
    )
  }
  for (i in seq_along(result_My2)) {
    expect_equivalent(
      result_My2[i],
      lm_epsilonhat[i]
    )
  }
  for (i in seq_along(result_My3)) {
    expect_equivalent(
      result_My3[i],
      lm_epsilonhat[i]
    )
  }
  for (i in seq_along(result_yminusyhat1)) {
    expect_equivalent(
      result_yminusyhat1[i],
      lm_epsilonhat[i]
    )
  }
  for (i in seq_along(result_yminusyhat2)) {
    expect_equivalent(
      result_yminusyhat2[i],
      lm_epsilonhat[i]
    )
  }
  for (i in seq_along(result_yminusyhat3)) {
    expect_equivalent(
      result_yminusyhat3[i],
      lm_epsilonhat[i]
    )
  }
  for (i in seq_along(result_epsilonhat)) {
    expect_equivalent(
      result_epsilonhat[i],
      lm_epsilonhat[i]
    )
  }
})
#> Test passed 😸
test_that("error.", {
  expect_error(
    .My(
      y = y
    )
  )
  expect_error(
    .yminusyhat(
      y = y
    )
  )
})
#> Test passed 🥳