predicting-bikes-rental-demand.Rmd

---
title: "Predicting Bike Shares Demand with Ridge and Lasso"
date: "`r Sys.Date()`"
output: html_document
author: "Jehangeer!"
message: false
warning: false
---

# About Data Analysis Report

This RMarkdown file contains the report of the data analysis done for the project on forecasting daily bike rental demand using time series models in R. It contains analysis such as data exploration, summary statistics and building the time series models. The final report was completed on `r date()`. 

**Data Description:**

This dataset contains the daily count of rental bike transactions between years 2011 and 2012 in Capital bikeshare system with the corresponding weather and seasonal information.

**Data Source:** https://www.kaggle.com/datasets/marklvl/bike-sharing-dataset

**Relevant Paper:** 

Fanaee-T, Hadi, and Gama, Joao, 'Event labeling combining ensemble detectors and background knowledge', Progress in Artificial Intelligence (2013): pp. 1-15, Springer Berlin Heidelberg



# Load and explore the data

## Load data and install packages

```{r}


## Importing required packages

# install.packages("tidyverse")
# install.packages("tidymodels")

library(tidyverse)
library(tidymodels)

bikes_hours <- read_csv("bike-sharing-dataset/hour.csv")

glimpse(bikes_hours)


# theme set

theme_set(theme_minimal(base_size = 12, base_family = "Open Sans"))

```

## Which factors contribute to bike rental demand?

Here are the objectives of doing the advanced analysis on bike rental demand: 

Attain superior accuracy in predicting bike rental demand.

Investigate whether a noteworthy correlation exists between the season and the bike rental demand.

Gain insights into how bike rental demand varies across different time segments within a day.

Determine the relationship between bike rental demand and prevailing weather conditions.


## Describe and explore the data

```{r}
# first six observations of the datasets

head(bikes_hours)

# checking missing values
sum(is.na(bikes_hours))

# summary statistics
summary(bikes_hours)

```

Here, a distinct dataframe is established to maintain data integrity, enabling easy adjustments without reloading the original dataset. This new dataframe excludes 'instant' and 'dteday' variables, as they hold no predictive value.

```{r}
# Constructing a 'bike_data' dataframe with organized data attributes

bike_data <-  data.frame(count = bikes_hours$cnt,
                         season = as.factor(bikes_hours$season), 
                         year = as.factor(bikes_hours$yr),
                         month = as.factor(bikes_hours$mnth),
                         hour = as.factor(bikes_hours$hr),
                         holi = as.factor(bikes_hours$holiday),
                         week = as.factor(bikes_hours$weekday),
                         work = as.factor(bikes_hours$workingday),
                         weather = as.factor(bikes_hours$weathersit),
                         env.temp = bikes_hours$temp,
                         feel.temp = bikes_hours$atemp,
                         humidity = bikes_hours$hum,
                         windspeed = bikes_hours$windspeed,
                         registered = bikes_hours$registered,
                         casual = bikes_hours$casual)

# Column names
names(bike_data)

# Glimpse of new data
glimpse(bike_data)

# Distribution of response variable.

bike_data |> 
  ggplot(aes(x = count)) +
  geom_histogram() +
  labs(title = "Distriution of Count")

```

We are considering the use of a Poisson regression model because our response variable consists of discrete numeric values, although they are no any non-negative integers, and response variable follows poisson distribution.

```{r}
# Fit a Poisson regression model
poisson_model <- glm(count ~ ., 
             data = bike_data, 
             family = "poisson")

summary(poisson_model)

# Checking over dispersion

# install.packages("AER")

library(AER)

dispersion_test <- dispersiontest(poisson_model)
print(dispersion_test)


```

The p-value is very close to zero (p-value < 2.2e-16), indicating that the true dispersion is significantly greater than 1.

Based on these results, we should consider using an alternative modeling approach that can account for over dispersion.

Negative Binomial Regression: This model is suitable for count data with overdispersion and can be a good choice in this situation.

```{r}
# install.packages("MASS")

library(MASS)

model_nb <- glm.nb(count ~ ., data = bike_data)

summary(model_nb)

```

This Negative Binomial regression model provides insights into the factors that influence bike rentals. Predictor variables as season, year, month, hour, weather conditions, and environmental factors all play a significant role in determining the number of bike rentals. Variables, like hour and temperature, have a particularly strong impact, while others, like holidays, have a less pronounced effect.


```{r}
# Calculating the AIC
aic_value <- AIC(model_nb)

# AIC value
aic_value
```

The model's AIC value of approximately 179,577.1 indicates a reasonable trade-off between goodness of fit and model complexity, suggesting its suitability for predicting bike rentals. However, further model refinement and evaluation against alternative models may be necessary to optimize performance.