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• The improvements in technology and connectivity have been changing all types of business, bikes rental also experienced these transitions.
• Bike-sharing systems are a new generation of traditional bike rentals where the whole process from membership, rental and return has become automatic.
• In other words, bike-sharing systems consists of strong and durable bikes that are available into a network of docking stations throughout some region.

• The bike-sharing systems can be unlocked from any station and returned to any station in the system, making them ideal for one-way trips.

• Capital Bikeshare is metro DC’s bike-share company, with more than 4,300 bikes available at 500 stations across six USA jurisdictions.
• Opened in September 2010, Capital Bikeshare was the largest bike sharing service in the United States until New York City’s Citi Bike began operations in May 2013.

• The dependet variable the problem is the number of bicicles rented per day.
• Find out which are the most relevant variables to define the number of bike rentals using Capital Bikeshare.
• Use data visualization and statistical measures to analysize the dataset variables relationship.
• Create a multilinear regression model to exam the variables importance.

• The dataset contains the daily count of rental bikes between years 2011 and 2012 in Capital Bikeshare system with the corresponding weather and seasonal informatio.
• There are a total of 16 columns in the dataset and 731 rows.
• Let´s read the dataset and check it´s structure:

# Read dataset
day <- read.csv('day.csv')

# Check dataset structure
str(day)

## 'data.frame':    731 obs. of  16 variables:
##  $ instant   : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ dteday    : chr  "2011-01-01" "2011-01-02" "2011-01-03" "2011-01-04" ...
##  $ 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 ...
##  $ holiday   : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ weekday   : int  6 0 1 2 3 4 5 6 0 1 ...
##  $ workingday: int  0 0 1 1 1 1 1 0 0 1 ...
##  $ weathersit: int  2 2 1 1 1 1 2 2 1 1 ...
##  $ temp      : num  0.344 0.363 0.196 0.2 0.227 ...
##  $ atemp     : num  0.364 0.354 0.189 0.212 0.229 ...
##  $ hum       : num  0.806 0.696 0.437 0.59 0.437 ...
##  $ windspeed : num  0.16 0.249 0.248 0.16 0.187 ...
##  $ casual    : int  331 131 120 108 82 88 148 68 54 41 ...
##  $ registered: int  654 670 1229 1454 1518 1518 1362 891 768 1280 ...
##  $ cnt       : int  985 801 1349 1562 1600 1606 1510 959 822 1321 ...

• All variables of the dataset are numerical, except for the variable dteday that is character.
• Let´s check the definition of the variables:

• To begin, let´s check if there are any missingg values on the dataset.
• Secondly, let´s refine the dataset folowing variables in order to produce the data visualization:
  • dteday transform into date
  • season transform into factor
  • weathersit transform into factor

# Check missing values
any(is.na(data))

## [1] FALSE

# Transform variable dteday as date
day$dteday <- as.Date(day$dteday, format = '%Y-%m-%d')

# Refine variable season
day$season <- factor(day$season, levels = 1:4, labels = c("winter","spring","summer","fall"))

# Refine variable weathersit
day$weathersit <- factor(day$weathersit, levels = 1:4, labels = c(
        "clear_sky",
        "cloudy",
        "ligth_snow_rain",
        "heavy_snow_rain"))

• Let´s plot a time series graph of the variable cnt.

# Plot graph
ggplot(day, aes(x = dteday, y = cnt)) + 
    geom_line() + theme_minimal() + labs(x = 'Date', y = 'Number of Bikes Rented') +
    theme(axis.text = element_text(size=14), axis.title = element_text(size=14))

• We can notice with the time-series graph that the number of bike rents increases significantly from 2011 to 2012.
• Furthermore, the graph also shows a seasonal influence and a high fluctuation over the value of bike rents.

• Let´s plot a boxplot graph of cnt according to weathersit.

ggplot(day, aes(y=cnt, fill = weathersit, x = weathersit)) +
    geom_boxplot() + theme_minimal() + labs(x = '', fill = '', y = 'Number of Bikes Rented') +
    theme(axis.title.x = element_blank(), axis.text.x = element_blank(), 
    legend.text = element_text(size=14), axis.title = element_text(size=14),
    axis.text = element_text(size=14))

• We can notice with the boxplot graph that the weather influences the number of bikes rented.
• As expected, the number of bikes rented during clear sky weather tends to be higher comparing to the other weather conditions.

• To start statistics analysis, let´s check some statistical measures of the values of bike rents for each seasson.

# Group data by seasson
table <- day %>% group_by(season) %>% summarise(min = min(cnt), lowerQuantile = quantile(cnt,probs = .25),
                                       median = median(cnt), upperQuantile = quantile(cnt,probs = .75),
                                       max = max(cnt), Mean = mean(cnt), standardDeviation = sd(cnt),
                                       count = n())

# Print table
knitr::kable(table)

• The descriptive statistics table show that there is a significant difference between the number of bikes rented depending on the season.

• Regression analysis is a statistical technique for estimating the relationships among variables.
• The objective of a regression model is to formulate a linear equation between the dependent and independent variable.
• Regression models with more than one independent variable are called multilinear regression.
• The multiple linear regression equation is formulated as the following:

\[y = \sum^n_{i = 1}B_0+B_i*x_i+E\]

\(y =\) dependent variable ; \(B_i =\) parameter

\(x_i =\) independent variable ; \(E =\) error

• Before fitting the regression model, it is necessary to remove the variables that can negatively influence the model.
• The following variables will be excluded from the dataset because:
  • dteday other variables (yr, mnth and weekday) already represents the date
  • instant only for identification
  • casual prevent overfitting the model
  • registered prevent overfitting the model

# Remove unwanted variables
day <- select(day, -c(dteday, instant, casual, registered))

# Create multiple linear regression model
model <- lm(cnt ~ ., data = day)

# Check model summary
model %>% summary()

## 
## Call:
## lm(formula = cnt ~ ., data = day)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3617.0  -370.3    72.4   473.0  3128.9 
## 
## Coefficients:
##                           Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                1307.97     241.26   5.421 8.09e-08 ***
## seasonspring               1158.76     114.67  10.105  < 2e-16 ***
## seasonsummer                921.46     165.16   5.579 3.43e-08 ***
## seasonfall                 1651.21     153.67  10.745  < 2e-16 ***
## yr                         2018.97      61.02  33.089  < 2e-16 ***
## mnth                        -15.24      16.15  -0.943  0.34574    
## holiday                    -531.53     187.34  -2.837  0.00468 ** 
## weekday                      67.51      15.17   4.449 1.00e-05 ***
## workingday                  116.17      67.10   1.731  0.08385 .  
## weathersitcloudy           -452.17      80.56  -5.613 2.85e-08 ***
## weathersitligth_snow_rain -1954.82     205.44  -9.515  < 2e-16 ***
## temp                       3941.82    1380.69   2.855  0.00443 ** 
## atemp                      1290.20    1507.55   0.856  0.39238    
## hum                       -1198.19     294.51  -4.068 5.26e-05 ***
## windspeed                 -2708.11     429.85  -6.300 5.19e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 812.2 on 716 degrees of freedom
## Multiple R-squared:  0.8276, Adjusted R-squared:  0.8242 
## F-statistic: 245.5 on 14 and 716 DF,  p-value: < 2.2e-16

• To conclude the hypothesis testing, let´s check the importance of the variables using the function varImp() from the R package caret.

# Create variables importance dataframe
varimport <- as.data.frame(varImp(model))
varimport$variable <- rownames(varimport)

# Print ordered variables importance dataframe
knitr::kable(varimport[order(varimport$Overall, decreasing = TRUE),])

• The multilinear regression model create had a good performance with an adjusted R-squared above 0.8.
• The most important variables that influence the number of bikes from Capital Bikeshare rented is year, followed by the season, weather and windspeed.
• Beyond that, as we can see by the model p-values, the season’s fall and spring are more important to the model comparing to the other seasons.
• To improve the data analysis, is recommended to transform the variable weekday into factor to check which weekday has more significance for the regression model.
• To conclude, we can highlight that the season and the weather are determinants when you are evaluating the daily number of bikes rented by costumer of Capital Bikeshare.

• Capital Bikeshare
• Wikipedia
• UCI Machine Learning Repository
• A Study on Multiple Linear Regression Analysis. Gülden Kaya Uyanık and Neşe Güler
• R packages:
  • tidyverse
  • caret
  • knitr