Week 3 Group By and Probabilities
Roshan R Naidu (02/02/2026)
Importing Libraries
# Load tidyverse as a collection of data science packages (Practically not needed to import any other packages mostly after importing this package)
library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.6
## ✔ forcats 1.0.1 ✔ stringr 1.6.0
## ✔ ggplot2 4.0.1 ✔ tibble 3.3.1
## ✔ lubridate 1.9.4 ✔ tidyr 1.3.2
## ✔ purrr 1.2.1
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors# Load dplyr for data manipulation
library(dplyr)
# Load ggplot2 for data visualisation
library(ggplot2)Loading and Exploring The Dataset
# Load the dataset
bike_data <- read.csv("/Users/roshannaidu/Desktop/IU Sem 2/Stats 1/bike+sharing+dataset/hour.csv")
# View structure and data types of variables
str(bike_data)## 'data.frame': 17379 obs. of 17 variables:
## $ instant : int 1 2 3 4 5 6 7 8 9 10 ...
## $ dteday : chr "2011-01-01" "2011-01-01" "2011-01-01" "2011-01-01" ...
## $ season : int 1 1 1 1 1 1 1 1 1 1 ...
## $ yr : int 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth : int 1 1 1 1 1 1 1 1 1 1 ...
## $ hr : int 0 1 2 3 4 5 6 7 8 9 ...
## $ holiday : int 0 0 0 0 0 0 0 0 0 0 ...
## $ weekday : int 6 6 6 6 6 6 6 6 6 6 ...
## $ workingday: int 0 0 0 0 0 0 0 0 0 0 ...
## $ weathersit: int 1 1 1 1 1 2 1 1 1 1 ...
## $ temp : num 0.24 0.22 0.22 0.24 0.24 0.24 0.22 0.2 0.24 0.32 ...
## $ atemp : num 0.288 0.273 0.273 0.288 0.288 ...
## $ hum : num 0.81 0.8 0.8 0.75 0.75 0.75 0.8 0.86 0.75 0.76 ...
## $ windspeed : num 0 0 0 0 0 0.0896 0 0 0 0 ...
## $ casual : int 3 8 5 3 0 0 2 1 1 8 ...
## $ registered: int 13 32 27 10 1 1 0 2 7 6 ...
## $ cnt : int 16 40 32 13 1 1 2 3 8 14 ...# View first few rows of the dataset
head(bike_data)# View summary statistics for all variables
summary(bike_data)## instant dteday season yr
## Min. : 1 Length:17379 Min. :1.000 Min. :0.0000
## 1st Qu.: 4346 Class :character 1st Qu.:2.000 1st Qu.:0.0000
## Median : 8690 Mode :character Median :3.000 Median :1.0000
## Mean : 8690 Mean :2.502 Mean :0.5026
## 3rd Qu.:13034 3rd Qu.:3.000 3rd Qu.:1.0000
## Max. :17379 Max. :4.000 Max. :1.0000
## mnth hr holiday weekday
## Min. : 1.000 Min. : 0.00 Min. :0.00000 Min. :0.000
## 1st Qu.: 4.000 1st Qu.: 6.00 1st Qu.:0.00000 1st Qu.:1.000
## Median : 7.000 Median :12.00 Median :0.00000 Median :3.000
## Mean : 6.538 Mean :11.55 Mean :0.02877 Mean :3.004
## 3rd Qu.:10.000 3rd Qu.:18.00 3rd Qu.:0.00000 3rd Qu.:5.000
## Max. :12.000 Max. :23.00 Max. :1.00000 Max. :6.000
## workingday weathersit temp atemp
## Min. :0.0000 Min. :1.000 Min. :0.020 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:1.000 1st Qu.:0.340 1st Qu.:0.3333
## Median :1.0000 Median :1.000 Median :0.500 Median :0.4848
## Mean :0.6827 Mean :1.425 Mean :0.497 Mean :0.4758
## 3rd Qu.:1.0000 3rd Qu.:2.000 3rd Qu.:0.660 3rd Qu.:0.6212
## Max. :1.0000 Max. :4.000 Max. :1.000 Max. :1.0000
## hum windspeed casual registered
## Min. :0.0000 Min. :0.0000 Min. : 0.00 Min. : 0.0
## 1st Qu.:0.4800 1st Qu.:0.1045 1st Qu.: 4.00 1st Qu.: 34.0
## Median :0.6300 Median :0.1940 Median : 17.00 Median :115.0
## Mean :0.6272 Mean :0.1901 Mean : 35.68 Mean :153.8
## 3rd Qu.:0.7800 3rd Qu.:0.2537 3rd Qu.: 48.00 3rd Qu.:220.0
## Max. :1.0000 Max. :0.8507 Max. :367.00 Max. :886.0
## cnt
## Min. : 1.0
## 1st Qu.: 40.0
## Median :142.0
## Mean :189.5
## 3rd Qu.:281.0
## Max. :977.0# Check number of rows and columns
dim(bike_data)## [1] 17379 17# Display all variable names
names(bike_data)## [1] "instant" "dteday" "season" "yr" "mnth"
## [6] "hr" "holiday" "weekday" "workingday" "weathersit"
## [11] "temp" "atemp" "hum" "windspeed" "casual"
## [16] "registered" "cnt"# Check for missing values in each column
colSums(is.na(bike_data))## instant dteday season yr mnth hr holiday
## 0 0 0 0 0 0 0
## weekday workingday weathersit temp atemp hum windspeed
## 0 0 0 0 0 0 0
## casual registered cnt
## 0 0 0Grouping 1: Rentals by Season
# Group by season and summarize total rentals
season_group <- bike_data %>%
group_by(season) %>%
summarise(total_rentals = sum(cnt), avg_temp = mean(temp))
season_group# Calculate probabilities for each season group
season_group <- season_group %>%
mutate(probability = total_rentals / sum(total_rentals))
season_groupGrouping 1 Visualisation
# Create a bar chart to visualize total rentals by season
ggplot(season_group, aes(x = as.factor(season), y = total_rentals, fill = as.factor(season))) +
geom_bar(stat = "identity") +
labs(title = "Total Rentals by Season", x = "Season", y = "Total Rentals") +
theme_minimal(base_size = 14) +
theme(
plot.title = element_text(face = "bold", hjust = 0.5),
legend.position = "top"
)
Insight and Hypothesis
From the Visual analysis of Group 1, we observe that summer has the highest probability of bike rentals, while winter has the lowest. This suggests that cold weather significantly affects bike rental behavior.
Hypothesis: Rentals are lower in winter due to unfavorable biking conditions (e.g., cold, snow). We can test this hypothesis by analyzing rental behavior during different weather conditions in winter.
Grouping 2: Rentals by Weather Condition and Holiday
# Group by weather condition and holiday
weather_holiday_group <- bike_data %>%
group_by(weathersit, holiday) %>%
summarise(total_rentals = sum(cnt), avg_humidity = mean(hum))## `summarise()` has grouped output by 'weathersit'. You can override using the
## `.groups` argument.weather_holiday_group# Calculate probabilities for each weather-holiday group
weather_holiday_group <- weather_holiday_group %>%
mutate(probability = total_rentals / sum(total_rentals))
weather_holiday_groupGrouping 2 Visualisation
# Create a bar chart to visualize rentals by weather condition and holiday
ggplot(weather_holiday_group, aes(x = as.factor(weathersit), y = total_rentals, fill = as.factor(holiday))) +
geom_bar(stat = "identity", position = "dodge") +
labs(title = "Total Rentals by Weather Condition and Holiday", x = "Weather Condition", y = "Total Rentals") +
theme_minimal(base_size = 14) +
theme(
plot.title = element_text(face = "bold", hjust = 0.5),
legend.position = "top"
)
Insight and Hypothesis
Bike rentals are lower on holidays during bad weather. This suggests that holidays may reduce the need for commuting, and bad weather further discourages biking.
Hypothesis: On holidays with bad weather (e.g., rainy or snowy days), rentals drop significantly because leisure biking is less attractive in poor weather conditions. This can be tested by analyzing rentals across more specific weather patterns during holidays.
Grouping 3: Rentals by Weekday and Working Day
# Group by weekday and working day
weekday_workday_group <- bike_data %>%
group_by(weekday, workingday) %>%
summarise(total_rentals = sum(cnt), avg_windspeed = mean(windspeed))## `summarise()` has grouped output by 'weekday'. You can override using the
## `.groups` argument.weekday_workday_group# Calculate probabilities for weekday-working day groups
weekday_workday_group <- weekday_workday_group %>%
mutate(probability = total_rentals / sum(total_rentals))
weekday_workday_groupGrouping 3 Visualisation
# Create a line plot to visualize total rentals by weekday and working day
ggplot(weekday_workday_group, aes(x = weekday, y = total_rentals, color = as.factor(workingday), group = workingday)) +
geom_line() +
labs(title = "Total Rentals by Weekday and Working Day", x = "Weekday", y = "Total Rentals") +
theme_minimal(base_size = 14) +
theme(
plot.title = element_text(face = "bold", hjust = 0.5),
legend.position = "top"
)
Insight and Hypothesis
The highest number of rentals occurs on working weekdays, likely due to commuters using bikes for transport. Conversely, weekends and non-working days show a lower number of rentals.
Hypothesis: Rentals are concentrated on weekdays due to commuting demand. On weekends, people use bikes more for leisure, leading to fewer rentals on average.
Investigating Combinations: Season and Holiday
# Create unique combinations of season and holiday
season_holiday_combinations <- bike_data %>%
group_by(season, holiday) %>%
summarise(total_rentals = sum(cnt)) %>%
ungroup()## `summarise()` has grouped output by 'season'. You can override using the
## `.groups` argument.season_holiday_combinations# Check for missing combinations
all_combinations <- expand.grid(season = unique(bike_data$season),
holiday = unique(bike_data$holiday))
missing_combinations <- anti_join(all_combinations, season_holiday_combinations, by = c("season", "holiday"))
missing_combinationsVisualization for Season and Holiday Combinations
# Visualize the combinations of season and holiday
ggplot(season_holiday_combinations, aes(x = as.factor(season), y = total_rentals, fill = as.factor(holiday))) +
geom_bar(stat = "identity", position = "dodge") +
labs(title = "Bike Rentals by Season and Holiday", x = "Season", y = "Total Rentals") +
theme_minimal(base_size = 14) +
theme(
plot.title = element_text(face = "bold", hjust = 0.5),
legend.position = "top"
)
From the combinations of season and holiday, we find that rentals during holidays in winter are among the least common. This is consistent with the earlier hypothesis that colder weather discourages bike use, especially during holiday periods when fewer people are commuting.
Summary and Conclusion
In this analysis of the UCI Bike Sharing dataset, I derived the following observations:
Groupings based on season, weather conditions, holidays, weekdays, and working days, with insights into how these factors affect bike rental probabilities.
Probability analysis helped me detect the lowest-probability groups (such as rentals on holidays during bad weather) and identify potential anomalies.
Visualizations illustrated the distribution of bike rentals across different conditions, providing a clear understanding of how external factors like weather and time influence bike usage.
Some further questions that I would like to investigate:
How does temperature variability within each season affect bike rentals?
Do registered users rent bikes more consistently across weather conditions compared to casual users?
Are there any unusual spikes in rentals during extreme weather conditions that could be tied to special events?