Tests: The Linear Regression Model (Descriptives - Simple Regression)

Ivan Jacob Agaloos Pesigan

2020-12-31

# The Linear Regression Model: Descriptives - Simple Regression {#linreg-estimation-descriptives-simple-example}

Data

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

X <- jeksterslabRdatarepo::wages.matrix[["X"]]
# age is removed
X <- X[, "education"]
X <- unname(
  cbind(
    1,
    X
  )
)
y <- unname(
  jeksterslabRdatarepo::wages.matrix[["y"]]
)
head(X)
#>      [,1] [,2]
#> [1,]    1   12
#> [2,]    1    9
#> [3,]    1   16
#> [4,]    1   14
#> [5,]    1   16
#> [6,]    1   12
head(y)
#>       [,1]
#> [1,] 11.55
#> [2,]  5.00
#> [3,] 12.00
#> [4,]  7.00
#> [5,] 21.15
#> [6,]  6.92

data <- X[, -1]
data <- cbind(
  y,
  data
)
n <- nrow(X)
k <- ncol(X)
df1 <- k - 1
df2 <- n - k
muhatX <- as.vector(colMeans(X))
muhatX <- muhatX[-1]
muhaty <- mean(y)
muhat <- c(muhaty, muhatX)
Rhat <- as.vector(cor(data))
RXhat <- 1
ryXhat <- cor(data)
ryXhat <- ryXhat[1, 2]
Sigmahat <- as.vector(cov(data))
SigmaXhat <- as.vector(var(X[, -1]))
sigmayXhat <- cov(data)
sigmayXhat <- sigmayXhat[1, 2]
sigma2Xhat <- var(X[, -1])
sigma2yhat <- var(y)
sigma2hat <- c(sigma2yhat, sigma2Xhat)
sigmahat <- sqrt(sigma2hat)

Descriptive Statistics

output <- descriptives(
  X = X,
  y = y,
)
#> 
#> Central Moments:
#>        Mean       SD   Skewness Kurtosis
#> y  12.36585 7.896350  1.8502679 4.860048
#> X2 13.14507 2.813823 -0.2907198 2.993715
#> 
#> Mardia's Estimate of Multivariate Skewness and Kurtosis:
#>                 b1           b1.chisq      b1.correction b1.chisq.corrected 
#>       3.925195e+00       8.432628e+02       1.002329e+00       8.452264e+02 
#>              b1.df               b1.p     b1.p.corrected                 b2 
#>       4.000000e+00      3.264144e-181      1.225698e-181       1.735584e+01 
#>               b2.z               b2.p 
#>       4.198742e+01       0.000000e+00 
#> 
#> Correlations:
#>           y       X2
#> y  1.000000 0.456518
#> X2 0.456518 1.000000

result_X <- as.vector(output[["X"]])
result_y <- as.vector(output[["y"]])
result_data <- as.vector(output[["data"]])
result_n <- as.vector(output[["n"]])
result_k <- as.vector(output[["k"]])
result_df1 <- as.vector(output[["df1"]])
result_df2 <- as.vector(output[["df2"]])
result_muhatX <- as.vector(output[["muhatX"]])
result_muhaty <- as.vector(output[["muhaty"]])
result_muhat <- as.vector(output[["muhat"]])
result_Rhat <- as.vector(output[["Rhat"]])
result_RXhat <- as.vector(output[["RXhat"]])
result_ryXhat <- as.vector(output[["ryXhat"]])
result_Sigmahat <- as.vector(output[["Sigmahat"]])
result_SigmaXhat <- as.vector(output[["SigmaXhat"]])
result_sigmayXhat <- as.vector(output[["sigmayXhat"]])
result_sigma2Xhat <- as.vector(output[["sigma2Xhat"]])
result_sigma2yhat <- as.vector(output[["sigma2yhat"]])
result_sigma2hat <- as.vector(output[["sigma2hat"]])
result_sigmahat <- as.vector(output[["sigmahat"]])

context("Test linreg-estimation-descriptives")
test_that("X", {
  X_vector <- as.vector(X)
  for (i in 1:length(result_X)) {
    expect_equivalent(
      result_X[i],
      X_vector[i]
    )
  }
})
#> Test passed 🎊
test_that("y", {
  y_vector <- as.vector(y)
  for (i in 1:length(result_y)) {
    expect_equivalent(
      result_y[i],
      y_vector[i]
    )
  }
})
#> Test passed 😀
test_that("data", {
  data_vector <- as.vector(data)
  for (i in 1:length(result_data)) {
    expect_equivalent(
      result_data[i],
      data_vector[i]
    )
  }
})
#> Test passed 🌈
test_that("n", {
  expect_equivalent(
    n,
    result_n
  )
})
#> Test passed 😀
test_that("k", {
  expect_equivalent(
    k,
    result_k
  )
})
#> Test passed 🎊
test_that("df1", {
  expect_equivalent(
    df1,
    result_df1
  )
})
#> Test passed 😀
test_that("df2", {
  expect_equivalent(
    df2,
    result_df2
  )
})
#> Test passed 🎉
test_that("muhatX", {
  for (i in 1:length(result_muhatX)) {
    expect_equivalent(
      muhatX[i],
      result_muhatX[i]
    )
  }
})
#> Test passed 🥳
test_that("muhaty", {
  expect_equivalent(
    muhaty,
    result_muhaty
  )
})
#> Test passed 😸
test_that("muhat", {
  for (i in 1:length(result_muhat)) {
    expect_equivalent(
      muhat[i],
      result_muhat[i]
    )
  }
})
#> Test passed 🎉
test_that("Rhat", {
  for (i in 1:length(result_Rhat)) {
    expect_equivalent(
      Rhat[i],
      result_Rhat[i]
    )
  }
})
#> Test passed 😸
test_that("RXhat", {
  expect_equivalent(
    RXhat,
    result_RXhat
  )
})
#> Test passed 😸
test_that("ryXhat", {
  for (i in 1:length(result_ryXhat)) {
    expect_equivalent(
      ryXhat[i],
      result_ryXhat[i]
    )
  }
})
#> Test passed 😸
test_that("Sigmahat", {
  for (i in 1:length(result_Sigmahat)) {
    expect_equivalent(
      Sigmahat[i],
      result_Sigmahat[i]
    )
  }
})
#> Test passed 🥇
test_that("SigmaXhat", {
  for (i in 1:length(result_SigmaXhat)) {
    expect_equivalent(
      SigmaXhat[i],
      result_SigmaXhat[i]
    )
  }
})
#> Test passed 🌈
test_that("sigmayXhat", {
  for (i in 1:length(result_sigmayXhat)) {
    expect_equivalent(
      sigmayXhat[i],
      result_sigmayXhat[i]
    )
  }
})
#> Test passed 🎉
test_that("sigma2Xhat", {
  for (i in 1:length(result_sigma2Xhat)) {
    expect_equivalent(
      sigma2Xhat[i],
      result_sigma2Xhat[i]
    )
  }
})
#> Test passed 🎊
test_that("sigma2yhat", {
  expect_equivalent(
    sigma2yhat,
    result_sigma2yhat
  )
})
#> Test passed 🌈
test_that("sigma2hat", {
  for (i in 1:length(result_sigma2hat)) {
    expect_equivalent(
      sigma2hat[i],
      result_sigma2hat[i]
    )
  }
})
#> Test passed 😸
test_that("sigmahat", {
  for (i in 1:length(result_sigmahat)) {
    expect_equivalent(
      sigmahat[i],
      result_sigmahat[i]
    )
  }
})
#> Test passed 😀