Tests: The Linear Regression Model (ANOVA Table)

Ivan Jacob Agaloos Pesigan

2020-12-31

# The Linear Regression Model: ANOVA Table {#linreg-estimation-anovatable-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

ANOVA Table

n <- nrow(X)
k <- ncol(X)
RSS <- RSS(
  X = X,
  y = y
)
ESS <- ESS(
  X = X,
  y = y
)
result1 <- .anovatable(
  RSS = RSS,
  ESS = ESS,
  n = n,
  k = k
)
result2 <- .anovatable(
  ESS = ESS,
  n = n,
  k = k,
  X = X,
  y = y
)
result3 <- .anovatable(
  RSS = RSS,
  n = n,
  k = k,
  X = X,
  y = y
)
result4 <- .anovatable(
  n = n,
  k = k,
  X = X,
  y = y
)
result5 <- anovatable(
  X = X,
  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
lm_F <- summary(lmobj)$fstatistic
lm_df1 <- lm_F[[2]]
lm_df2 <- lm_F[[3]]
lm_df3 <- lm_df1 + lm_df2
lm_F <- lm_F[[1]]
lm_p <- pf(lm_F, df1 = lm_df1, df2 = lm_df2, lower.tail = FALSE)
lm_MS_model <- lm_ESS / lm_df1
lm_MS_error <- lm_RSS / lm_df2

result_df1 <- c(
  result1["Model", "df"],
  result2["Model", "df"],
  result3["Model", "df"],
  result4["Model", "df"],
  result5["Model", "df"]
)
result_df2 <- c(
  result1["Error", "df"],
  result2["Error", "df"],
  result3["Error", "df"],
  result4["Error", "df"],
  result5["Error", "df"]
)
result_df3 <- c(
  result1["Total", "df"],
  result2["Total", "df"],
  result3["Total", "df"],
  result4["Total", "df"],
  result5["Total", "df"]
)
result_SS1 <- c(
  result1["Model", "SS"],
  result2["Model", "SS"],
  result3["Model", "SS"],
  result4["Model", "SS"],
  result5["Model", "SS"]
)
result_SS2 <- c(
  result1["Error", "SS"],
  result2["Error", "SS"],
  result3["Error", "SS"],
  result4["Error", "SS"],
  result5["Error", "SS"]
)
result_SS3 <- c(
  result1["Total", "SS"],
  result2["Total", "SS"],
  result3["Total", "SS"],
  result4["Total", "SS"],
  result5["Total", "SS"]
)
result_MS1 <- c(
  result1["Model", "MS"],
  result2["Model", "MS"],
  result3["Model", "MS"],
  result4["Model", "MS"],
  result5["Model", "MS"]
)
result_MS2 <- c(
  result1["Error", "MS"],
  result2["Error", "MS"],
  result3["Error", "MS"],
  result4["Error", "MS"],
  result5["Error", "MS"]
)
result_F <- c(
  result1["Model", "F"],
  result2["Model", "F"],
  result3["Model", "F"],
  result4["Model", "F"],
  result5["Model", "F"]
)
result_p <- c(
  result1["Model", "p"],
  result2["Model", "p"],
  result3["Model", "p"],
  result4["Model", "p"],
  result5["Model", "p"]
)
context("Test linreg-estimation-anovatable.")
test_that("df1", {
  for (i in seq_along(result_df1)) {
    expect_equivalent(
      lm_df1,
      result_df1[i]
    )
  }
})
#> Test passed 🎊
test_that("df2", {
  for (i in seq_along(result_df2)) {
    expect_equivalent(
      lm_df2,
      result_df2[i]
    )
  }
})
#> Test passed 🎊
test_that("df3", {
  for (i in seq_along(result_df3)) {
    expect_equivalent(
      lm_df3,
      result_df3[i]
    )
  }
})
#> Test passed 🌈
test_that("ss1", {
  for (i in seq_along(result_SS1)) {
    expect_equivalent(
      lm_ESS,
      result_SS1[i]
    )
  }
})
#> Test passed 🌈
test_that("ss2", {
  for (i in seq_along(result_SS2)) {
    expect_equivalent(
      lm_RSS,
      result_SS2[i]
    )
  }
})
#> Test passed 😀
test_that("ss3", {
  for (i in seq_along(result_SS3)) {
    expect_equivalent(
      lm_TSS,
      result_SS3[i]
    )
  }
})
#> Test passed 🎊
test_that("ms1", {
  for (i in seq_along(result_MS1)) {
    expect_equivalent(
      lm_MS_model,
      result_MS1[i]
    )
  }
})
#> Test passed 🥳
test_that("ms2", {
  for (i in seq_along(result_MS2)) {
    expect_equivalent(
      lm_MS_error,
      result_MS2[i]
    )
  }
})
#> Test passed 😀
test_that("f", {
  for (i in seq_along(result_F)) {
    expect_equivalent(
      lm_F,
      result_F[i]
    )
  }
})
#> Test passed 🥇
test_that("p", {
  for (i in seq_along(result_p)) {
    expect_equivalent(
      lm_p,
      result_p[i]
    )
  }
})
#> Test passed 🥳