Vladyka Cvičenie4

#Import údajov Cieľom tejto analýzy je preskúmať pit stopy vo Formule 1 z hľadiska ich dĺžky, načasovania a frekvencie. Pit stopy predstavujú kľúčový prvok pretekovej stratégie, keďže ovplyvňujú celkový čas jazdca aj jeho pozíciu na trati. Analýza sa zameriava na identifikáciu typických hodnôt a odchýlok, ktoré môžu naznačovať rôzne strategické prístupy alebo neštandardné situácie počas pretekov.

library(dplyr)
library(tidyr)
library(ggplot2)
library(knitr)
library(kableExtra)
library(stats)

# Načítanie dát
pit_stops <- read.csv(
  "C:/Users/vlady/Documents/pit_stops.csv",
  header = TRUE,
  sep = ",",
  dec = ".",
  stringsAsFactors = FALSE
)

# Premenovanie stĺpcov
pit_stops <- pit_stops %>%
  rename(
    race_id = raceId,
    driver_id = driverId,
    stop_number = stop,
    duration_text = duration,
    duration_ms = milliseconds
  )
# Kontrola chýbajúcich hodnôt
print("Počet chýbajúcich údajov v jednotlivých premenných:")

[1] "Počet chýbajúcich údajov v jednotlivých premenných:"

colSums(is.na(pit_stops))

      race_id     driver_id   stop_number           lap          time duration_text   duration_ms 
            0             0             0             0             0             0             0 

Tabuľky, grafy, jednoduché štatistiky

Boxplot

# ------------------------
# Boxplot pit stopov
# ------------------------
limit_95 <- quantile(pit_stops$duration_ms, 0.95, na.rm = TRUE)

ggplot(dplyr::filter(pit_stops, duration_ms <= limit_95), aes(x = duration_ms)) +
  geom_histogram(binwidth = 200, fill = "lightblue", color = "darkblue") +
  labs(
    title = "Rozdelenie trvania pitstopov F1",
    x = "Dĺžka pit stopu (ms)",
    y = "Počet pit stopov"
  ) +
  theme_minimal()

ggplot(pit_stops, aes(x = lap)) +
  geom_histogram(binwidth = 2, boundary = 0, fill = "lightblue", color = "darkblue") +
  labs(
    title = "Rozdelenie pit stopov podľa kola",
    x = "Kolo",
    y = "Počet pit stopov"
  ) +
  theme_minimal()

limit_95 <- quantile(pit_stops$duration_ms, 0.95, na.rm = TRUE)

ggplot(
  dplyr::filter(pit_stops, stop_number %in% 1:4, duration_ms <= limit_95),
  aes(x = factor(stop_number), y = duration_ms)
) +
  geom_boxplot(fill = "lightblue", color = "darkblue") +
  labs(
    title = "Dĺžka pit stopov podľa poradia (bez extrémov)",
    x = "Poradie pit stopu",
    y = "Trvanie (ms)"
  ) +
  theme_minimal()

# ------------------------
# Základné štatistiky do tabuľky
# ------------------------
pit_stats <- pit_stops %>%
  group_by(stop_number) %>%
  summarise(
    n = n(),
    mean = mean(duration_ms, na.rm = TRUE),
    sd = sd(duration_ms, na.rm = TRUE),
    min = min(duration_ms, na.rm = TRUE),
    q25 = quantile(duration_ms, 0.25, na.rm = TRUE),
    median = median(duration_ms, na.rm = TRUE),
    q75 = quantile(duration_ms, 0.75, na.rm = TRUE),
    max = max(duration_ms, na.rm = TRUE),
    .groups = "drop"
  )

pit_stats %>%
  kable(
    digits = 2,
    caption = "Základné štatistiky dĺžky pit stopov podľa poradia zastávky"
  ) %>%
  kable_styling(
    full_width = FALSE,
    bootstrap_options = c("striped", "hover", "condensed")
  ) %>%
  column_spec(1, bold = TRUE) %>%
  row_spec(0, bold = TRUE, background = "#f2f2f2") %>%
  add_header_above(c(" " = 1, "Štatistiky dĺžky pit stopu" = 8))

Základné štatistiky dĺžky pit stopov podľa poradia zastávky

	Štatistiky dĺžky pit stopu
stop_number	n	mean	sd	min	q25	median	q75	max
1	5573	74778.35	300436.67	14160	22087.00	23744.0	26879.00	3069017
2	3716	81413.58	270539.34	12897	21892.75	23467.5	25788.50	2048175
3	1496	96718.27	325293.53	12959	21472.00	23350.0	26238.25	2485913
4	427	106832.92	374243.56	13925	21041.00	23132.0	27150.50	2434653
5	120	391127.17	757595.35	14493	22481.25	25681.5	42762.25	2461612
6	29	426872.79	822788.18	13173	22979.00	31494.0	74200.00	2483382
7	3	29079.33	5910.42	22379	26842.50	31306.0	32429.50	33553
15	1	24239.00	NA	24239	24239.00	24239.0	24239.00	24239
42	1	24132.00	NA	24132	24132.00	24132.0	24132.00	24132
48	1	28211.00	NA	28211	28211.00	28211.0	28211.00	28211
51	1	24232.00	NA	24232	24232.00	24232.0	24232.00	24232
52	1	23813.00	NA	23813	23813.00	23813.0	23813.00	23813
57	1	24384.00	NA	24384	24384.00	24384.0	24384.00	24384
70	1	24367.00	NA	24367	24367.00	24367.0	24367.00	24367

lap_stats <- pit_stops %>%
  group_by(stop_number) %>%
  summarise(
    n = n(),
    mean_lap = mean(lap, na.rm = TRUE),
    median_lap = median(lap, na.rm = TRUE),
    min_lap = min(lap, na.rm = TRUE),
    max_lap = max(lap, na.rm = TRUE),
    .groups = "drop"
  )

lap_stats %>%
  kable(
    digits = 2,
    caption = "Základné štatistiky kola pit stopu podľa poradia zastávky"
  ) %>%
  kable_styling(
    full_width = FALSE,
    bootstrap_options = c("striped", "hover", "condensed")
  ) %>%
  column_spec(1, bold = TRUE) %>%
  row_spec(0, bold = TRUE, background = "#f2f2f2")

Základné štatistiky kola pit stopu podľa poradia zastávky

stop_number	n	mean_lap	median_lap	min_lap	max_lap
1	5573	16.39	15	1	64
2	3716	30.95	31	2	74
3	1496	37.99	39	3	73
4	427	42.34	44	6	78
5	120	47.41	46	20	70
6	29	52.21	54	31	64
7	3	65.00	64	64	67
15	1	2.00	2	2	2
42	1	2.00	2	2	2
48	1	3.00	3	3	3
51	1	2.00	2	2	2
52	1	2.00	2	2	2
57	1	2.00	2	2	2
70	1	2.00	2	2	2

stops_per_race <- pit_stops %>%
  group_by(race_id) %>%
  summarise(total_stops = n(),
            drivers = n_distinct(driver_id),
            avg_stops = total_stops / drivers)

ggplot(stops_per_race, aes(x = avg_stops)) +
  geom_histogram(binwidth = 0.2, fill = "lightblue", color = "darkblue") +
  labs(
    title = "Priemerný počet pit stopov na jazdca v pretekoch",
    x = "Pit stopy na jazdca",
    y = "Počet pretekov"
  ) +
  theme_minimal()

# ------------------------
# t-test: Porovnanie priemerov medzi prvým a druhým pit stopom
# ------------------------
t_test_result <- t.test(
  pit_stops$duration_ms[pit_stops$stop_number == 1],
  pit_stops$duration_ms[pit_stops$stop_number == 2]
)
t_test_result

    Welch Two Sample t-test

data:  pit_stops$duration_ms[pit_stops$stop_number == 1] and pit_stops$duration_ms[pit_stops$stop_number == 2]
t = -1.1075, df = 8503.2, p-value = 0.2681
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -18379.140   5108.681
sample estimates:
mean of x mean of y 
 74778.35  81413.58 

# ------------------------
# ANOVA: Porovnanie medzi všetkými pit stopmi
# ------------------------
anova_result <- aov(duration_ms ~ factor(stop_number), data = pit_stops)
summary(anova_result)

                       Df    Sum Sq   Mean Sq F value Pr(>F)    
factor(stop_number)    13 1.571e+13 1.208e+12   12.71 <2e-16 ***
Residuals           11357 1.080e+15 9.509e+10                   
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

# ------------------------
# Lineárna regresia: Predpoveď času pit stopu podľa lap a čísla stopu
# ------------------------
model <- lm(duration_ms ~ lap + stop_number, data = pit_stops)
summary(model)

Call:
lm(formula = duration_ms ~ lap + stop_number, data = pit_stops)

Residuals:
     Min       1Q   Median       3Q      Max 
-1125645   -74757   -59495   -42449  2948258 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 107753.5     6026.5  17.880  < 2e-16 ***
lap          -1939.7      207.9  -9.331  < 2e-16 ***
stop_number  14944.8     2026.5   7.375 1.76e-13 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 309000 on 11368 degrees of freedom
Multiple R-squared:  0.009317,  Adjusted R-squared:  0.009143 
F-statistic: 53.46 on 2 and 11368 DF,  p-value: < 2.2e-16