Tests: The Linear Regression Model (Predicted)

Ivan Jacob Agaloos Pesigan

2020-12-31

# The Linear Regression Model: Predicted Values {#linreg-estimation-predicted-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

\(\mathrm{Py}\)

Pmatrix <- P(X = X)
betahat <- betahat(
  X = X,
  y = y
)
result_Py1 <- .Py(
  y = y,
  P = Pmatrix
)
result_Py2 <- .Py(
  y = y,
  X = X
)
result_Py3 <- Py(
  X = X,
  y = y
)

\(\mathrm{X} \hat{\boldsymbol{\beta}}\)

result_Xbetahat1 <- .Xbetahat(
  X = X,
  y = y
)
result_Xbetahat2 <- .Xbetahat(
  X = X,
  betahat = betahat
)
result_Xbetahat3 <- Xbetahat(
  X = X,
  y = y
)

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

result_yhat <- yhat(
  X = X,
  y = y
)

lm() function

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

context("Test linreg-estimation-projection")
test_that("Py = yhat.", {
  expect_equivalent(
    length(result_Py1),
    length(result_Py2),
    length(result_Py3),
    length(result_Xbetahat1),
    length(result_Xbetahat2),
    length(result_Xbetahat3),
    length(result_yhat),
    length(lm_yhat)
  )
  for (i in seq_along(result_Py1)) {
    expect_equivalent(
      result_Py1[i],
      lm_yhat[i]
    )
  }
  for (i in seq_along(result_Py2)) {
    expect_equivalent(
      result_Py2[i],
      lm_yhat[i]
    )
  }
  for (i in seq_along(result_Py3)) {
    expect_equivalent(
      result_Py3[i],
      lm_yhat[i]
    )
  }
  for (i in seq_along(result_Xbetahat1)) {
    expect_equivalent(
      result_Xbetahat1[i],
      lm_yhat[i]
    )
  }
  for (i in seq_along(result_Xbetahat2)) {
    expect_equivalent(
      result_Xbetahat2[i],
      lm_yhat[i]
    )
  }
  for (i in seq_along(result_Xbetahat3)) {
    expect_equivalent(
      result_Xbetahat3[i],
      lm_yhat[i]
    )
  }
  for (i in seq_along(result_yhat)) {
    expect_equivalent(
      result_yhat[i],
      lm_yhat[i]
    )
  }
})
#> Test passed 🌈
test_that("error.", {
  expect_error(
    .Py(
      y = y
    )
  )
  expect_error(
    .Xbetahat(
      X = X
    )
  )
})
#> Test passed 🌈