Práca s údajmi2

# Načítanie balíkov
library(dplyr)
library(ggplot2)
library(broom)
library(gt)
library(corrplot)

# Načítanie dát
data("USArrests")
head(USArrests)

#  Príprava dát 
USArrests$UrbanGroup <- ifelse(USArrests$UrbanPop > median(USArrests$UrbanPop),
                               "HighUrban", "LowUrban")

# Korelačná tabuľka 
cor_matrix <- round(cor(USArrests[,1:4]), 2)

# Korelačná tabuľka (bielo-červený štýl)
cor_matrix %>%
  as.data.frame() %>%
  tibble::rownames_to_column("Variable") %>%
  gt() %>%
  tab_header(title = "Korelačná matica datasetu USArrests") %>%
  data_color(
    columns = -Variable,
    colors = scales::col_numeric(
      palette = c("white", "red"),
      domain = c(0, 1)
    )
  ) %>%
  tab_style(style = cell_text(weight = "bold"), locations = cells_column_labels())

Korelačná matica datasetu USArrests
Variable	Murder	Assault	UrbanPop	Rape
Murder	1.00	0.80	0.07	0.56
Assault	0.80	1.00	0.26	0.67
UrbanPop	0.07	0.26	1.00	0.41
Rape	0.56	0.67	0.41	1.00

# Voliteľná vizualizácia
corrplot(cor_matrix, method = "color", addCoef.col = "black",
         tl.col = "black", tl.srt = 45,
         col = colorRampPalette(c("white","red"))(200),
         title = "Korelácie medzi premennými",
         mar = c(0,0,2,0))

#  T-test: Murder ~ UrbanGroup
t_test_result <- t.test(Murder ~ UrbanGroup, data = USArrests)
t_table <- broom::tidy(t_test_result)

t_table %>%
  gt() %>%
  tab_header(title = "T-test: Porovnanie vrážd podľa urbanizácie") %>%
  fmt_number(columns = where(is.numeric), decimals = 3) %>%
  data_color(
    columns = c(statistic, estimate1, estimate2),
    colors = scales::col_numeric(
      palette = c("white", "red"),
      domain = range(t_table$statistic, na.rm = TRUE)
    )
  )

T-test: Porovnanie vrážd podľa urbanizácie
estimate	estimate1	estimate2	statistic	p.value	parameter	conf.low	conf.high	method	alternative
0.456	8.025	7.569	0.372	0.712	44.071	−2.013	2.925	Welch Two Sample t-test	two.sided

# ANOVA: Rape ~ UrbanGroup
anova_result <- aov(Rape ~ UrbanGroup, data = USArrests)
anova_table <- broom::tidy(anova_result)

anova_table %>%
  gt() %>%
  tab_header(title = "ANOVA: Porovnanie miery znásilnení podľa urbanizácie") %>%
  fmt_number(columns = where(is.numeric), decimals = 3) %>%
  data_color(
    columns = c(sumsq, meansq, statistic),
    colors = scales::col_numeric(
      palette = c("white", "red"),
      domain = range(anova_table$statistic, na.rm = TRUE)
    )
  )

ANOVA: Porovnanie miery znásilnení podľa urbanizácie
term	df	sumsq	meansq	statistic	p.value
UrbanGroup	1.000	844.017	844.017	11.727	0.001
Residuals	48.000	3,454.712	71.973	NA	NA

#  Lineárna regresia
lm_result <- lm(Murder ~ UrbanPop + Assault + Rape, data = USArrests)
lm_table <- broom::tidy(lm_result)

lm_table %>%
  gt() %>%
  tab_header(title = "Lineárna regresia: Predikcia miery vrážd") %>%
  fmt_number(columns = where(is.numeric), decimals = 3) %>%
  data_color(
    columns = c(estimate, statistic),
    colors = scales::col_numeric(
      palette = c("white", "red"),
      domain = range(lm_table$statistic, na.rm = TRUE)
    )
  )

Lineárna regresia: Predikcia miery vrážd
term	estimate	std.error	statistic	p.value
(Intercept)	3.277	1.738	1.885	0.066
UrbanPop	−0.055	0.028	−1.962	0.056
Assault	0.040	0.006	6.729	0.000
Rape	0.061	0.056	1.102	0.276

summary_info <- broom::glance(lm_result)
summary_info %>%
  gt() %>%
  tab_header(title = "Zhrnutie regresného modelu") %>%
  fmt_number(columns = where(is.numeric), decimals = 3) %>%
  data_color(
    columns = everything(),
    colors = scales::col_numeric(
      palette = c("white", "red"),
      domain = range(summary_info$r.squared, na.rm = TRUE)
    )
  )

Zhrnutie regresného modelu
r.squared	adj.r.squared	sigma	statistic	p.value	df	logLik	AIC	BIC	deviance	df.residual	nobs
0.672	0.651	2.574	31.424	0.000	3.000	−116.140	242.281	251.841	304.832	46.000	50.000

# Boxplot pre ANOVA
ggplot(USArrests, aes(x = UrbanGroup, y = Rape, fill = UrbanGroup)) +
  geom_boxplot(color = "black") +
  scale_fill_manual(values = c("white", "red")) +
  theme_minimal(base_size = 14) +
  labs(title = "Boxplot: Miera znásilnení podľa urbanizácie",
       x = "Urbanizačná skupina", y = "Rape")

# Scatterplot pre regresiu
ggplot(USArrests, aes(x = Assault, y = Murder, color = UrbanPop)) +
  geom_point(size = 3) +
  scale_color_gradient(low = "white", high = "red") +
  theme_minimal(base_size = 14) +
  labs(title = "Scatterplot: Vzťah medzi lúpežami, vraždami a urbanizáciou",
       x = "Assault", y = "Murder")

Závery testov z datasetu:

Korelácie Murder ↔︎ Assault = 0.8 Silná väzba medzi lúpežami a vraždami

T-test p = 0.712 Urbanizácia nemá významný vplyv na vraždy

ANOVA p = 0.001 Urbanizácia má vplyv na mieru znásilnení

Regresia p(modelu) = 0.000, R² = 0.67 Model je silný, hlavný faktor: Assault

Vizualizácie Murder ~ Assault lineárny trend Potvrdzuje závery testov