Multiple lineare Regression: Ein vertiefter Einblick in die statistische Modellierung

Read in path and auxiliary functions

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source(file = file.path("Source", "functions.R"))

Load packages

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source(file = file.path("Source", "rpackages.R"))

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noise <- list()
anz <- 25
set.seed(272024)#
for (i in 1:anz){
  noise[[i]] <- 20-rtruncnorm(200, a=0,b=20, mean = 10, sd = 2)
}
df.noise<-as.data.frame(noise)
names(df.noise) <- c("V1","V2","V3","V4","V5","V6","V7","V8","V9","V10",
                     "V11","V12","V13","V14","V15","V16","V17","V18","V19",
                     "V20","V21","V22","V23","V24","V25")

group<- c(rep(0,100),rep(1,100))

data <- cbind(df.noise,group)
View(data)

candidate_models <- list(length=anz)
for(i in 1:anz){
  candidate_models[[i]] <- formula(paste0(names(df.noise)[i],"~ group"))
}
# candidate_models[[5]] 

summary_models <- list(length=anz)
for(i in 1:anz){
  summary_models[[i]] <- summary(glm(candidate_models[[i]], data = data))
}
# summary_models[[9]]
# summary_models[[12]]
# library("broom")
tidy_model9 <- tidy(glm(candidate_models[[9]], data = data)) 
tidy_model9

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tidy_model12 <- tidy(glm(candidate_models[[12]], data = data)) 
tidy_model12

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## t-test ist äquivalent


# T-Test für Modell 9
test_9 <- t.test(candidate_models[[9]], var.equal = TRUE, alternative = "two.sided", data = data)
result_9 <- tibble(
  Modell = "Modell 9",
  t_Wert = round(test_9$statistic, 3),
  df = round(test_9$parameter, 1),
  p_Wert = round(test_9$p.value, 4),
  Mittelwert_Gruppe1 = round(test_9$estimate[1], 2),
  Mittelwert_Gruppe2 = round(test_9$estimate[2], 2)
)

# T-Test für Modell 12
test_12 <- t.test(candidate_models[[12]], var.equal = TRUE, alternative = "two.sided", data = data)
result_12 <- tibble(
  Modell = "Modell 12",
  t_Wert = round(test_12$statistic, 3),
  df = round(test_12$parameter, 1),
  p_Wert = round(test_12$p.value, 4),
  Mittelwert_Gruppe1 = round(test_12$estimate[1], 2),
  Mittelwert_Gruppe2 = round(test_12$estimate[2], 2)
)

# Ausgabe als separate Tabellen
kable(result_9, caption = "T-Test Ergebnis für Modell 9")

T-Test Ergebnis für Modell 9
Modell	t_Wert	df	p_Wert	Mittelwert_Gruppe1	Mittelwert_Gruppe2
Modell 9	3.323	198	0.0011	10.49	9.6

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kable(result_12, caption = "T-Test Ergebnis für Modell 12")

T-Test Ergebnis für Modell 12
Modell	t_Wert	df	p_Wert	Mittelwert_Gruppe1	Mittelwert_Gruppe2
Modell 12	2.048	198	0.0419	10.12	9.55