Tests: The Linear Regression Model (Sum of Squares)

Ivan Jacob Agaloos Pesigan

2020-12-31

# The Linear Regression Model: Sum of Squares {#linreg-estimation-SS-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

Residual Sum of Squares

epsilonhat <- epsilonhat(
  X = X,
  y = y
)
betahat <- betahat(
  X = X,
  y = y
)
result_RSS1 <- .RSS(
  epsilonhat = epsilonhat
)
result_RSS2 <- .RSS(
  X = X,
  y = y
)
result_RSS3 <- .RSS(
  X = X,
  y = y,
  betahat = betahat
)
result_RSS4 <- RSS(
  X = X,
  y = y
)

Explained Sum of Squares

yhat <- yhat(
  X = X,
  y = y
)
ybar <- mean(y)
result_ESS1 <- .ESS(
  yhat = yhat,
  ybar = ybar
)
result_ESS2 <- .ESS(
  yhat = yhat,
  y = y
)
result_ESS3 <- .ESS(
  ybar = ybar,
  X = X,
  y = y,
  betahat = NULL
)
result_ESS4 <- .ESS(
  ybar = ybar,
  X = X,
  y = y,
  betahat = betahat
)
result_ESS5 <- .ESS(
  X = X,
  y = y,
  betahat = betahat
)
result_ESS6 <- .ESS(
  X = X,
  y = y
)
result_ESS7 <- ESS(
  X = X,
  y = y
)

Total Sum of Squares

result_TSS <- TSS(
  y = y
)

lm() function

lmobj <- lm(
  wages ~ gender + race + union + education + experience,
  data = jeksterslabRdatarepo::wages
)
lm_anova <- anova(lmobj)
lm_RSS <- lm_anova["Residuals", "Sum Sq"]
lm_TSS <- sum(lm_anova[["Sum Sq"]])
lm_ESS <- lm_TSS - lm_RSS

result_RSS <- c(
  result_RSS1, result_RSS2, result_RSS3, result_RSS4
)
result_ESS <- c(
  result_ESS1, result_ESS2, result_ESS3, result_ESS4, result_ESS5, result_ESS6, result_ESS7
)
context("Test linreg-estimation-SS.")
test_that("RSS", {
  for (i in seq_along(result_RSS)) {
    expect_equivalent(
      lm_RSS,
      result_RSS[i]
    )
  }
})
#> Test passed 🥳
test_that("ESS", {
  for (i in seq_along(result_RSS)) {
    expect_equivalent(
      lm_ESS,
      result_ESS[i]
    )
  }
})
#> Test passed 🥇
test_that("TSS", {
  expect_equivalent(
    lm_TSS,
    result_TSS
  )
})
#> Test passed 🌈