Bike Data

Email: anshul.nograiya@gmail.com

COLLEGE: Penn State University

1. Introduction

Bike sharing platforms are on a boom and opening up in many cities across the world. They have automated the complete the process of membership, renting and return. In 2017, there were 55 systems in place across US with 42,000 bikes in the network. Similarly across the world, there are 1000 similar programs in operation. With the passage of time, these programs are gaining popularity because of increasing awareness in public regarding traffic, environmental issues, and health issues. The picture below depicts the increasing trips using bike sharing in US alone. As opposed to other transport services such bus or subway, the duration of travel, departure, and arrival location are not controlled by an organization. These programs are also affected by changing weather conditions and calamities. Currently, a lot of programs are springing across universities throughout the states, which are encouraging younger people to develop and follow a healthier lifestyle. This research is being conducted with the intent of studying effect of calender days and various weather factors on the demand of bicycles.

image

2. Overview of the Study

More and more people prefer to rent bikes because it is a cheap, convenient, healthy and environment friendly method for short trips (Shaheen, Guzman, & Zhang, 2010). This increase in user-base increases the complexities in handling them. A lot of research today is towards forecasting bike demand and rebalancing stations according to meet the anticipated demand. (Raviv, Tzur, and Forma 2013) tackles the problem of finding truck routes and plans for how many bikes to move between stations. The paper minimizes an objective function tied to both the operating cost of the vehicles as well as penalty functions relating to station imbalance. Similarly, (Rainer-Harbach et al. 2013) takes a local search approach to finding a similar solution.

image

CBS New York: (August 24, 2015)

“Just the mismatch between docks and bikes”, “Sometimes these racks are empty; sometimes they’re packed, and that forces me to fend, when I’ve got to ditch a bike or I need to be somewhere fast.”

Abc7NY: (December 12, 2014)

“And another daily biker says he has trouble finding bikes in some spots, like near the Port Authority, you have to walk up 10 blocks or so.”

3. Data Description

The bike share demand data is recorded by Capital Bikeshare platform that operates in Washington DC. The data consists of entries for a period of 2 years with daily weather and general conditions. The data has 731 entries with 16 attributes. A brief description of the attributes is provided below:

instant: record index
dteday : date
season : season (1:springer, 2:summer, 3:fall, 4:winter)
yr : year (0: 2011, 1:2012)
mnth : month ( 1 to 12)
holiday : weather day is holiday or not (extracted from [Web Link])
weekday : day of the week
workingday : if day is neither weekend nor holiday is 1, otherwise is 0.
- weathersit : i: Clear, Few clouds, Partly cloudy, Partly cloudy

ii: Mist + Cloudy, Mist + Broken clouds, Mist + Few clouds, Mist

iii: Light Snow, Light Rain + Thunderstorm + Scattered clouds, Light Rain + Scattered clouds

iv: Heavy Rain + Ice Pallets + Thunderstorm + Mist, Snow + Fog

temp : Normalized temperature in Celsius. The values are derived via (t-t_min)/(t_max-t_min), t_min=-8, t_max=+39 (only in hourly scale)
atemp: Normalized feeling temperature in Celsius. The values are derived via (t-t_min)/(t_max-t_min), t_min=-16, t_max=+50 (only in hourly scale)
hum: Normalized humidity. The values are divided to 100 (max)
windspeed: Normalized wind speed. The values are divided to 67 (max)
casual: count of casual users
registered: count of registered users
cnt: count of total rental bikes including both casual and registered

From the above list of attributes, we remove the first two attributes as they are not required for our analysis. The data is provided by UCI machine learning repository:https://archive.ics.uci.edu/ml/datasets/bike+sharing+dataset

4. Model Analysis:

The model we develop here is a linear regression model of the form:

\[Count= \alpha_0 + \alpha_1(i)*AttributesRegardingDay + \alpha_2(j)* AttributeRegardingWeather + \epsilon\]

bike <- read.csv("day.csv")
model <-lm(bike$cnt~bike$season+bike$yr+bike$mnth+bike$weekday+bike$weathersit+bike$windspeed)
summary(model)

## 
## Call:
## lm(formula = bike$cnt ~ bike$season + bike$yr + bike$mnth + bike$weekday + 
##     bike$weathersit + bike$windspeed)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5014.4  -915.3   134.9   923.4  3362.8 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      3511.98     225.75  15.557  < 2e-16 ***
## bike$season       916.71      74.59  12.290  < 2e-16 ***
## bike$yr          2141.37      91.58  23.383  < 2e-16 ***
## bike$mnth         -97.04      23.91  -4.059 5.47e-05 ***
## bike$weekday       81.21      22.84   3.555 0.000403 ***
## bike$weathersit  -961.08      84.33 -11.397  < 2e-16 ***
## bike$windspeed  -3349.88     607.68  -5.513 4.92e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1236 on 724 degrees of freedom
## Multiple R-squared:  0.596,  Adjusted R-squared:  0.5926 
## F-statistic:   178 on 6 and 724 DF,  p-value: < 2.2e-16

From the analysis we have conducted, that we are able to develop a model that is able to account for 59.60% of the variation associated with Count. Using the above model we can predict the usage of shared bikes every day. The model above accounts for both the calender and the weather data.

5. Results

In the end, we are able to test association between variables present in the dataset, and present a model that can help a manager or decision maker better plan for the day ahead. USing this data, the problem of supply and demand of shared bikes can be balanced.

6. Conclusion

Variables season, yr, mnth, weekday, weathersit, and windspeed are associated to the number of bikes used everyday out of the 13 variables in consideration. The model above helps in forecasting the use of shared bikes everyday.

7. References

https://www.curbed.com/2017/3/21/15006248/bike-share-ridership-transit-safety

Raviv, T.; Tzur, M.; and Forma, I. 2013. Static repositioning in a bike-sharing system: models and solution approaches. EURO Journal on Transportation and Logistics 2(3):187- 229

Rainer-Harbach, M.; Papazek, P.; Hu, B.; and Raidl, G. R. 2013. Balancing bicycle sharing systems: A variable neighborhood search approach. In Middendorf, M., and Blum, C., eds., EvoCOP, volume 7832 of Lecture Notes in Computer Science, 121-132. Springer

Shaheen, S., Guzman, S., & Zhang, H. (2010). Bikesharing in Europe, the Americas, and Asia: past, present, and future. Transportation Research Record: Journal of the Transportation Research Board, (2143), 159-167

http://abc7ny.com/traffic/new-york-city-bike-share-audit-reveals-problems/433473/

http://newyork.cbslocal.com/2015/08/24/citi-bike-customers-seeing-red-over-broken-bikes/

8. Appendix: Describing data and visualizing Count vs related variables

Descriptive statistics

bike <- bike[-c(1,2)]
summary(bike)

##      season            yr              mnth          holiday       
##  Min.   :1.000   Min.   :0.0000   Min.   : 1.00   Min.   :0.00000  
##  1st Qu.:2.000   1st Qu.:0.0000   1st Qu.: 4.00   1st Qu.:0.00000  
##  Median :3.000   Median :1.0000   Median : 7.00   Median :0.00000  
##  Mean   :2.497   Mean   :0.5007   Mean   : 6.52   Mean   :0.02873  
##  3rd Qu.:3.000   3rd Qu.:1.0000   3rd Qu.:10.00   3rd Qu.:0.00000  
##  Max.   :4.000   Max.   :1.0000   Max.   :12.00   Max.   :1.00000  
##     weekday        workingday      weathersit         temp        
##  Min.   :0.000   Min.   :0.000   Min.   :1.000   Min.   :0.05913  
##  1st Qu.:1.000   1st Qu.:0.000   1st Qu.:1.000   1st Qu.:0.33708  
##  Median :3.000   Median :1.000   Median :1.000   Median :0.49833  
##  Mean   :2.997   Mean   :0.684   Mean   :1.395   Mean   :0.49538  
##  3rd Qu.:5.000   3rd Qu.:1.000   3rd Qu.:2.000   3rd Qu.:0.65542  
##  Max.   :6.000   Max.   :1.000   Max.   :3.000   Max.   :0.86167  
##      atemp              hum           windspeed           casual      
##  Min.   :0.07907   Min.   :0.0000   Min.   :0.02239   Min.   :   2.0  
##  1st Qu.:0.33784   1st Qu.:0.5200   1st Qu.:0.13495   1st Qu.: 315.5  
##  Median :0.48673   Median :0.6267   Median :0.18097   Median : 713.0  
##  Mean   :0.47435   Mean   :0.6279   Mean   :0.19049   Mean   : 848.2  
##  3rd Qu.:0.60860   3rd Qu.:0.7302   3rd Qu.:0.23321   3rd Qu.:1096.0  
##  Max.   :0.84090   Max.   :0.9725   Max.   :0.50746   Max.   :3410.0  
##    registered        cnt      
##  Min.   :  20   Min.   :  22  
##  1st Qu.:2497   1st Qu.:3152  
##  Median :3662   Median :4548  
##  Mean   :3656   Mean   :4504  
##  3rd Qu.:4776   3rd Qu.:5956  
##  Max.   :6946   Max.   :8714

Average bikes perday in both the years

aggregate(bike$cnt, by=list(Year=bike$yr), mean)

##   Year        x
## 1    0 3405.762
## 2    1 5599.934

Renting of bikes per season

print("1:spring, 2:summer, 3:fall, 4:winter")

## [1] "1:spring, 2:summer, 3:fall, 4:winter"

aggregate(bike$cnt, by=list(Season=bike$season), mean)

##   Season        x
## 1      1 2604.133
## 2      2 4992.332
## 3      3 5644.303
## 4      4 4728.163

plot(bike$season,bike$cnt, main = "renting of bikes per season")

Average daily bike trips per month

aggregate(bike$cnt, by=list(Month=bike$mnth), mean)

##    Month        x
## 1      1 2176.339
## 2      2 2655.298
## 3      3 3692.258
## 4      4 4484.900
## 5      5 5349.774
## 6      6 5772.367
## 7      7 5563.677
## 8      8 5664.419
## 9      9 5766.517
## 10    10 5199.226
## 11    11 4247.183
## 12    12 3403.806

plot(bike$mnth,bike$cnt, main = "renting of bikes per month")

Renting of bikes per weekday

aggregate(bike$cnt, by=list(Day_of_the_week=bike$weekday), mean)

##   Day_of_the_week        x
## 1               0 4228.829
## 2               1 4338.124
## 3               2 4510.663
## 4               3 4548.538
## 5               4 4667.260
## 6               5 4690.288
## 7               6 4550.543

plot(bike$weekday,bike$cnt, main = "renting of bikes per weekday")

Renting of bikes on holidays

aggregate(bike$cnt, by=list(Holiday=bike$holiday), mean)

##   Holiday        x
## 1       0 4527.104
## 2       1 3735.000

plot(bike$holiday,bike$cnt, main = "renting of bikes on holidays vs regular days")

Renting of bikes according to weather

aggregate(bike$cnt, by=list(Type_of_weather=bike$weathersit), mean)

##   Type_of_weather        x
## 1               1 4876.786
## 2               2 4035.862
## 3               3 1803.286

plot(bike$weathersit,bike$cnt, main = "renting of bikes according to weather")

plot(bike$temp,bike$cnt, main = "renting of bikes according to weather")

9. R code for Statistical tests

T-test for Count and Weekday

t.test(bike$cnt~bike$holiday)

## 
##  Welch Two Sample t-test
## 
## data:  bike$cnt by bike$holiday
## t = 1.7047, df = 21.007, p-value = 0.103
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -174.1953 1758.4038
## sample estimates:
## mean in group 0 mean in group 1 
##        4527.104        3735.000

T-test for Count and Seasons

t.test(bike$cnt,bike$season)

## 
##  Welch Two Sample t-test
## 
## data:  bike$cnt and bike$season
## t = 62.831, df = 730, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  4361.187 4642.518
## sample estimates:
##  mean of x  mean of y 
## 4504.34884    2.49658

Linear model including all the variables related to calender related data

model1 <- lm(bike$cnt~bike$season+bike$yr+bike$mnth+bike$holiday+bike$weekday+bike$workingday+bike$weathersit)
summary(model1)

## 
## Call:
## lm(formula = bike$cnt ~ bike$season + bike$yr + bike$mnth + bike$holiday + 
##     bike$weekday + bike$workingday + bike$weathersit)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5009.1  -906.5    74.0   927.1  3893.4 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      2680.48     195.71  13.697  < 2e-16 ***
## bike$season       944.59      75.25  12.552  < 2e-16 ***
## bike$yr          2147.47      92.74  23.157  < 2e-16 ***
## bike$mnth         -87.83      24.24  -3.623 0.000311 ***
## bike$holiday     -602.40     288.29  -2.090 0.037006 *  
## bike$weekday       72.55      23.26   3.120 0.001883 ** 
## bike$workingday   233.08     103.15   2.260 0.024133 *  
## bike$weathersit -1000.85      85.49 -11.708  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1252 on 723 degrees of freedom
## Multiple R-squared:  0.5862, Adjusted R-squared:  0.5822 
## F-statistic: 146.3 on 7 and 723 DF,  p-value: < 2.2e-16

From the above analysis, we can conclude that holiday and workingday are less related to count than other variables.

Linear model including all the variables related to temperature data

model2 <- lm(bike$cnt~bike$windspeed+bike$hum+bike$atemp+bike$temp+bike$weathersit)
summary(model2)

## 
## Call:
## lm(formula = bike$cnt ~ bike$windspeed + bike$hum + bike$atemp + 
##     bike$temp + bike$weathersit)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4235.2 -1069.0  -102.9  1076.9  3725.3 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       3815.1      352.5  10.824  < 2e-16 ***
## bike$windspeed   -3986.2      729.3  -5.466 6.34e-08 ***
## bike$hum         -1962.2      495.6  -3.959 8.26e-05 ***
## bike$atemp        4488.8     2560.2   1.753 0.079974 .  
## bike$temp         2436.4     2263.7   1.076 0.282163    
## bike$weathersit   -469.8      125.6  -3.739 0.000199 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1410 on 725 degrees of freedom
## Multiple R-squared:  0.474,  Adjusted R-squared:  0.4703 
## F-statistic: 130.7 on 5 and 725 DF,  p-value: < 2.2e-16

From the above analysis, we can conclude that temperature variables are less related to count than other variables.

Linear model including all the variables

model3 <-lm(bike$cnt~bike$season+bike$yr+bike$mnth+bike$holiday+bike$weekday+bike$workingday+bike$weathersit+bike$windspeed+bike$hum)
summary(model3)

## 
## Call:
## lm(formula = bike$cnt ~ bike$season + bike$yr + bike$mnth + bike$holiday + 
##     bike$weekday + bike$workingday + bike$weathersit + bike$windspeed + 
##     bike$hum)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4916.0  -917.1   112.6   921.6  3501.7 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      3147.19     313.02  10.054  < 2e-16 ***
## bike$season       899.44      74.19  12.123  < 2e-16 ***
## bike$yr          2155.91      91.48  23.566  < 2e-16 ***
## bike$mnth         -94.77      23.84  -3.975 7.74e-05 ***
## bike$holiday     -593.91     282.54  -2.102   0.0359 *  
## bike$weekday       77.07      22.89   3.367   0.0008 ***
## bike$workingday   225.15     101.12   2.226   0.0263 *  
## bike$weathersit -1066.68     107.44  -9.928  < 2e-16 ***
## bike$windspeed  -3062.71     632.35  -4.843 1.56e-06 ***
## bike$hum          563.64     432.63   1.303   0.1930    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1227 on 721 degrees of freedom
## Multiple R-squared:  0.6037, Adjusted R-squared:  0.5988 
## F-statistic:   122 on 9 and 721 DF,  p-value: < 2.2e-16

Linear model including well associated variables

model4 <-lm(bike$cnt~bike$season+bike$yr+bike$mnth+bike$holiday+bike$weekday+bike$workingday+bike$weathersit+bike$windspeed)
summary(model4)

## 
## Call:
## lm(formula = bike$cnt ~ bike$season + bike$yr + bike$mnth + bike$holiday + 
##     bike$weekday + bike$workingday + bike$weathersit + bike$windspeed)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4861.3  -903.0    95.9   933.5  3528.5 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      3417.80     234.29  14.588  < 2e-16 ***
## bike$season       903.34      74.17  12.180  < 2e-16 ***
## bike$yr          2142.34      90.93  23.560  < 2e-16 ***
## bike$mnth         -92.38      23.78  -3.885 0.000112 ***
## bike$holiday     -596.58     282.67  -2.111 0.035153 *  
## bike$weekday       74.33      22.80   3.259 0.001169 ** 
## bike$workingday   222.44     101.15   2.199 0.028185 *  
## bike$weathersit  -979.20      83.91 -11.669  < 2e-16 ***
## bike$windspeed  -3309.88     603.52  -5.484 5.74e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1228 on 722 degrees of freedom
## Multiple R-squared:  0.6028, Adjusted R-squared:  0.5984 
## F-statistic:   137 on 8 and 722 DF,  p-value: < 2.2e-16

This model, includes all the variables significantly related to count.

Linear model including highly associated variables

model5 <-lm(bike$cnt~bike$season+bike$yr+bike$mnth+bike$weekday+bike$weathersit+bike$windspeed)
summary(model5)

## 
## Call:
## lm(formula = bike$cnt ~ bike$season + bike$yr + bike$mnth + bike$weekday + 
##     bike$weathersit + bike$windspeed)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5014.4  -915.3   134.9   923.4  3362.8 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      3511.98     225.75  15.557  < 2e-16 ***
## bike$season       916.71      74.59  12.290  < 2e-16 ***
## bike$yr          2141.37      91.58  23.383  < 2e-16 ***
## bike$mnth         -97.04      23.91  -4.059 5.47e-05 ***
## bike$weekday       81.21      22.84   3.555 0.000403 ***
## bike$weathersit  -961.08      84.33 -11.397  < 2e-16 ***
## bike$windspeed  -3349.88     607.68  -5.513 4.92e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1236 on 724 degrees of freedom
## Multiple R-squared:  0.596,  Adjusted R-squared:  0.5926 
## F-statistic:   178 on 6 and 724 DF,  p-value: < 2.2e-16

This model includes all the variables highly related to count. This model contains 4% less variation associated with Count, but is simpler as it contains lesser variables.