Data dictionary

The data was obtained from the UCI Machine Learning repository.

Variable	Description	Data type
instant	record index	Numeric
dtday	Date	Datetime
season	season (1:winter, 2:spring, 3:summer, 4:fall)	Categorical
yr	year (0: 2011, 1:2012)	Categorical
mnth	month ( 1 to 12)	Categorical
holiday	weather day is holiday or not	Categorical, binomial
weekday	day of the week	Categorical
workingday	if day is neither weekend nor holiday is 1, otherwise is 0.	Categorical, binomial
weathersit	1: Clear, Few clouds, Partly cloudy, Partly cloudy; 2: Mist + Cloudy, Mist + Broken clouds, Mist + Few clouds, Mist; 3: Light Snow, Light Rain + Thunderstorm + Scattered clouds, Light Rain + Scattered clouds; 4: Heavy Rain + Ice Pallets + Thunderstorm + Mist, Snow + Fog	Categorical
temp	Normalized temperature in Celsius	Numerical
atemp	Normalized feeling temperature in Celsius	Numerical
hum	Normalized humidity	Numerical
windspeed	Normalized wind speed	Numerical
casual	Count of casual users	Numerical
registered	Count of registered users	Numerical
cnt	Count of total rental bikes including casual and registered (target)	Numerical

Load the data

import pandas as pd
import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt
import plotly.express as px

bike_df = pd.read_csv("bike_rental_raw.csv")
bike_df

	instant	dteday	season	yr	mnth	holiday	weekday	workingday	weathersit	temp	atemp	hum	windspeed	casual	registered	cnt
0	1	2011-01-01	1	0	1	0	6	0	2	0.344167	0.363625	0.805833	0.160446	331	654	985
1	2	2011-01-02	1	0	1	0	0	0	2	0.363478	0.353739	0.696087	0.248539	131	670	801
2	3	2011-01-03	1	0	1	0	1	1	1	0.196364	0.189405	0.437273	0.248309	120	1229	1349
3	4	2011-01-04	1	0	1	0	2	1	1	0.200000	0.212122	0.590435	0.160296	108	1454	1562
4	5	2011-01-05	1	0	1	0	3	1	1	0.226957	0.229270	0.436957	0.186900	82	1518	1600
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
726	727	2012-12-27	1	1	12	0	4	1	2	0.254167	0.226642	0.652917	0.350133	247	1867	2114
727	728	2012-12-28	1	1	12	0	5	1	2	0.253333	0.255046	0.590000	0.155471	644	2451	3095
728	729	2012-12-29	1	1	12	0	6	0	2	0.253333	0.242400	0.752917	0.124383	159	1182	1341
729	730	2012-12-30	1	1	12	0	0	0	1	0.255833	0.231700	0.483333	0.350754	364	1432	1796
730	731	2012-12-31	1	1	12	0	1	1	2	0.215833	0.223487	0.577500	0.154846	439	2290	2729

731 rows × 16 columns

bike_df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 731 entries, 0 to 730
Data columns (total 16 columns):
 #   Column      Non-Null Count  Dtype  
---  ------      --------------  -----  
 0   instant     731 non-null    int64  
 1   dteday      731 non-null    object 
 2   season      731 non-null    int64  
 3   yr          731 non-null    int64  
 4   mnth        731 non-null    int64  
 5   holiday     731 non-null    int64  
 6   weekday     731 non-null    int64  
 7   workingday  731 non-null    int64  
 8   weathersit  731 non-null    int64  
 9   temp        731 non-null    float64
 10  atemp       731 non-null    float64
 11  hum         731 non-null    float64
 12  windspeed   731 non-null    float64
 13  casual      731 non-null    int64  
 14  registered  731 non-null    int64  
 15  cnt         731 non-null    int64  
dtypes: float64(4), int64(11), object(1)
memory usage: 91.5+ KB

bike_df.shape

(731, 16)

bike_df.describe().T

	count	mean	std	min	25%	50%	75%	max
instant	731.0	366.000000	211.165812	1.000000	183.500000	366.000000	548.500000	731.000000
season	731.0	2.496580	1.110807	1.000000	2.000000	3.000000	3.000000	4.000000
yr	731.0	0.500684	0.500342	0.000000	0.000000	1.000000	1.000000	1.000000
mnth	731.0	6.519836	3.451913	1.000000	4.000000	7.000000	10.000000	12.000000
holiday	731.0	0.028728	0.167155	0.000000	0.000000	0.000000	0.000000	1.000000
weekday	731.0	2.997264	2.004787	0.000000	1.000000	3.000000	5.000000	6.000000
workingday	731.0	0.683995	0.465233	0.000000	0.000000	1.000000	1.000000	1.000000
weathersit	731.0	1.395349	0.544894	1.000000	1.000000	1.000000	2.000000	3.000000
temp	731.0	0.495385	0.183051	0.059130	0.337083	0.498333	0.655417	0.861667
atemp	731.0	0.474354	0.162961	0.079070	0.337842	0.486733	0.608602	0.840896
hum	731.0	0.627894	0.142429	0.000000	0.520000	0.626667	0.730209	0.972500
windspeed	731.0	0.190486	0.077498	0.022392	0.134950	0.180975	0.233214	0.507463
casual	731.0	848.176471	686.622488	2.000000	315.500000	713.000000	1096.000000	3410.000000
registered	731.0	3656.172367	1560.256377	20.000000	2497.000000	3662.000000	4776.500000	6946.000000
cnt	731.0	4504.348837	1937.211452	22.000000	3152.000000	4548.000000	5956.000000	8714.000000

Data Prepatation and Visualisation

## Convert dteday to datetime

bike_df['dteday'] = pd.to_datetime(bike_df['dteday'])

bike_df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 731 entries, 0 to 730
Data columns (total 16 columns):
 #   Column      Non-Null Count  Dtype         
---  ------      --------------  -----         
 0   instant     731 non-null    int64         
 1   dteday      731 non-null    datetime64[ns]
 2   season      731 non-null    int64         
 3   yr          731 non-null    int64         
 4   mnth        731 non-null    int64         
 5   holiday     731 non-null    int64         
 6   weekday     731 non-null    int64         
 7   workingday  731 non-null    int64         
 8   weathersit  731 non-null    int64         
 9   temp        731 non-null    float64       
 10  atemp       731 non-null    float64       
 11  hum         731 non-null    float64       
 12  windspeed   731 non-null    float64       
 13  casual      731 non-null    int64         
 14  registered  731 non-null    int64         
 15  cnt         731 non-null    int64         
dtypes: datetime64[ns](1), float64(4), int64(11)
memory usage: 91.5 KB

# Convert mnth, yr, holiday, weekday, workingday and weathersit to categorical variables

bike_df['season'] = bike_df['season'].astype('category')
bike_df['mnth'] = bike_df['mnth'].astype('category')
bike_df['yr'] = bike_df['yr'].astype('category')
bike_df['holiday'] = bike_df['holiday'].astype('category')
bike_df['weekday'] = bike_df['weekday'].astype('category')
bike_df['workingday'] = bike_df['workingday'].astype('category')
bike_df['weathersit'] = bike_df['weathersit'].astype('category')

bike_df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 731 entries, 0 to 730
Data columns (total 16 columns):
 #   Column      Non-Null Count  Dtype         
---  ------      --------------  -----         
 0   instant     731 non-null    int64         
 1   dteday      731 non-null    datetime64[ns]
 2   season      731 non-null    category      
 3   yr          731 non-null    category      
 4   mnth        731 non-null    category      
 5   holiday     731 non-null    category      
 6   weekday     731 non-null    category      
 7   workingday  731 non-null    category      
 8   weathersit  731 non-null    category      
 9   temp        731 non-null    float64       
 10  atemp       731 non-null    float64       
 11  hum         731 non-null    float64       
 12  windspeed   731 non-null    float64       
 13  casual      731 non-null    int64         
 14  registered  731 non-null    int64         
 15  cnt         731 non-null    int64         
dtypes: category(7), datetime64[ns](1), float64(4), int64(4)
memory usage: 57.9 KB

bike_df.head(10)

	instant	dteday	season	yr	mnth	holiday	weekday	workingday	weathersit	temp	atemp	hum	windspeed	casual	registered	cnt
0	1	2011-01-01	1	0	1	0	6	0	2	0.344167	0.363625	0.805833	0.160446	331	654	985
1	2	2011-01-02	1	0	1	0	0	0	2	0.363478	0.353739	0.696087	0.248539	131	670	801
2	3	2011-01-03	1	0	1	0	1	1	1	0.196364	0.189405	0.437273	0.248309	120	1229	1349
3	4	2011-01-04	1	0	1	0	2	1	1	0.200000	0.212122	0.590435	0.160296	108	1454	1562
4	5	2011-01-05	1	0	1	0	3	1	1	0.226957	0.229270	0.436957	0.186900	82	1518	1600
5	6	2011-01-06	1	0	1	0	4	1	1	0.204348	0.233209	0.518261	0.089565	88	1518	1606
6	7	2011-01-07	1	0	1	0	5	1	2	0.196522	0.208839	0.498696	0.168726	148	1362	1510
7	8	2011-01-08	1	0	1	0	6	0	2	0.165000	0.162254	0.535833	0.266804	68	891	959
8	9	2011-01-09	1	0	1	0	0	0	1	0.138333	0.116175	0.434167	0.361950	54	768	822
9	10	2011-01-10	1	0	1	0	1	1	1	0.150833	0.150888	0.482917	0.223267	41	1280	1321

#Create correlation matrix for numerical variables
correlation_matrix = bike_df.corr() 
plt.figure(figsize=(12,10))
sns.heatmap(data=correlation_matrix, annot = True, fmt='.2f', linewidths=.5)

<AxesSubplot:>

# Look for outliers

fig = px.histogram(bike_df, x="cnt",
                   marginal="box", 
                   hover_data=bike_df.columns)
fig.show()

# Bike hire by season
fig = px.violin(bike_df, y = "cnt", x = "season", color = "season", box = True, points = "all",
               hover_data = bike_df.columns)
fig.update_layout(title_text = "Bike hire by season")
fig.update_yaxes(title = "Total number of hired bikes")
fig.update_xaxes(title = "Season")
fig.show()

# Bike hire by year
fig = px.violin(bike_df, y = "cnt", x = "yr", color = "yr", box = True, points = "all",
               hover_data = bike_df.columns)
fig.update_layout(title_text = "Bike hire by year")
fig.update_yaxes(title = "Total number of hired bikes")
fig.update_xaxes(title = "Year")
fig.show()

# Bike hire by month
fig = px.violin(bike_df, y = "cnt", x = "mnth", color = "mnth", box = True, points = "all",
               hover_data = bike_df.columns)
fig.update_layout(title_text = "Bike hire by month")
fig.update_yaxes(title = "Total number of hired bikes")
fig.update_xaxes(title = "Month")
fig.show()

# Bike hire by holiday
fig = px.violin(bike_df, y = "cnt", x = "holiday", color = "holiday", box = True, points = "all",
               hover_data = bike_df.columns)
fig.update_layout(title_text = "Bike hire by holiday")
fig.update_yaxes(title = "Total number of hired bikes")
fig.update_xaxes(title = "Holiday")
fig.show()

# Bike hire by week day
fig = px.violin(bike_df, y = "cnt", x = "weekday", color = "weekday", box = True, points = "all",
               hover_data = bike_df.columns)
fig.update_layout(title_text = "Bike hire by week day")
fig.update_yaxes(title = "Total number of hired bikes")
fig.update_xaxes(title = "Week day")
fig.show()

# Bike hire by work day
fig = px.violin(bike_df, y = "cnt", x = "workingday", color = "workingday", box = True, points = "all",
               hover_data = bike_df.columns)
fig.update_layout(title_text = "Bike hire by work day")
fig.update_yaxes(title = "Total number of hired bikes")
fig.update_xaxes(title = "Work day")
fig.show()

# Bike hire by weather type
fig = px.violin(bike_df, y = "cnt", x = "weathersit", color = "weathersit", box = True, points = "all",
               hover_data = bike_df.columns)
fig.update_layout(title_text = "Bike hire by weather")
fig.update_yaxes(title = "Total number of hired bikes")
fig.update_xaxes(title = "Weather")
fig.show()

# Bike hire by date
fig = px.line(bike_df, x="dteday", y="cnt", title='Bike hired by day', hover_data = bike_df.columns)
fig.update_yaxes(title = "Total number of hired bikes")
fig.update_xaxes(title = "Date")
fig.show()

# Linear relationship?
fig = px.scatter(bike_df, x="temp", y="cnt", title='Bike hired by temperature', hover_data = bike_df.columns)
fig.update_yaxes(title = "Total number of hired bikes")
fig.update_xaxes(title = "Temperature")
fig.show()

# Linear relationship?
fig = px.scatter(bike_df, x="hum", y="cnt", title='Bike hired by humidity', hover_data = bike_df.columns)
fig.update_yaxes(title = "Total number of hired bikes")
fig.update_xaxes(title = "Humidity")
fig.show()

# Linear relationship?
fig = px.scatter(bike_df, x="windspeed", y="cnt", title='Bike hired by wind speed', hover_data = bike_df.columns)
fig.update_yaxes(title = "Total number of hired bikes")
fig.update_xaxes(title = "Wind speed")
fig.show()

bike_df.set_index("dteday", inplace = True)
bike_df.head(10)

	instant	season	yr	mnth	holiday	weekday	workingday	weathersit	temp	atemp	hum	windspeed	casual	registered	cnt
dteday
2011-01-01	1	1	0	1	0	6	0	2	0.344167	0.363625	0.805833	0.160446	331	654	985
2011-01-02	2	1	0	1	0	0	0	2	0.363478	0.353739	0.696087	0.248539	131	670	801
2011-01-03	3	1	0	1	0	1	1	1	0.196364	0.189405	0.437273	0.248309	120	1229	1349
2011-01-04	4	1	0	1	0	2	1	1	0.200000	0.212122	0.590435	0.160296	108	1454	1562
2011-01-05	5	1	0	1	0	3	1	1	0.226957	0.229270	0.436957	0.186900	82	1518	1600
2011-01-06	6	1	0	1	0	4	1	1	0.204348	0.233209	0.518261	0.089565	88	1518	1606
2011-01-07	7	1	0	1	0	5	1	2	0.196522	0.208839	0.498696	0.168726	148	1362	1510
2011-01-08	8	1	0	1	0	6	0	2	0.165000	0.162254	0.535833	0.266804	68	891	959
2011-01-09	9	1	0	1	0	0	0	1	0.138333	0.116175	0.434167	0.361950	54	768	822
2011-01-10	10	1	0	1	0	1	1	1	0.150833	0.150888	0.482917	0.223267	41	1280	1321

Observations

• The total number of bikes hired was moderately correlated to the temperature, feeling temperature and count of casual users. Additionally, the bikes hired was highly correlated to the count of registered users. Since the total rental bikes is a sum of the casual and registered users, these variables were dropped from the dataset. Furthermore, the temp and atemp variables were correlated, thus, atemp was dropped from the dataset.

• The bike rental is influenced by the season, year, month, holiday and weather type. In contrast, the week day and working day do not influence the amount of bikes hired. For this reason, weekday and instant were deleted from the dataset.

• The variable date has an effect on the number of bike rentals which is represented on the different months. This is also captured with the month variable.

• The variable instant represents an index in the dataset, which was removed to avoid overfitting of the model.

bike_df = bike_df.drop(columns = ["weekday", "workingday", "instant", "casual", "registered", "atemp"])
bike_df.columns

Index(['season', 'yr', 'mnth', 'holiday', 'weathersit', 'temp', 'hum',
       'windspeed', 'cnt'],
      dtype='object')

#Check for missing values
bike_df.isnull().sum()

season        0
yr            0
mnth          0
holiday       0
weathersit    0
temp          0
hum           0
windspeed     0
cnt           0
dtype: int64

# Save clean dataframe
bike_df.to_csv("bike_rental_clean.csv", index=False)

Data Segregation

# Separate target

features_name = bike_df.columns[:8]
X = bike_df[features_name]
y = bike_df["cnt"]
print("The features are", X.columns)
print("The target variable is", y.name)

The features are Index(['season', 'yr', 'mnth', 'holiday', 'weathersit', 'temp', 'hum',
       'windspeed'],
      dtype='object')
The target variable is cnt

from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X,y, random_state=123)
print('Training dataset: X_train=', X_train.shape, ', y_train', y_train.shape)
print('Testing dataset: X_test=', X_test.shape, ', y_test', y_test.shape)

Training dataset: X_train= (548, 8) , y_train (548,)
Testing dataset: X_test= (183, 8) , y_test (183,)

Naive Baseline

baseline = np.mean(y_train)
y_baseline = np.repeat(baseline, len(y_test))


from sklearn.metrics import mean_squared_error
 
naive_MSE = mean_squared_error(y_test, y_baseline)
naive_RMSE=np.sqrt(naive_MSE)
print("Naive baseline RMSE: ", round(naive_RMSE, 2))
print("Naive baseline MSE: ", round(naive_MSE, 2))

Naive baseline RMSE:  1806.52
Naive baseline MSE:  3263499.33

Dummy baseline

from sklearn.dummy import DummyRegressor

dummy_baseline = DummyRegressor(strategy="median")
dummy_baseline.fit(X_train, y_train)

prediction = dummy_baseline.predict(y_test)

dummy_MSE = mean_squared_error(y_test, prediction)
dummy_RMSE = np.sqrt(dummy_MSE)
print("Dummy regression baseline RMSE: ", round(dummy_RMSE, 2))
print("Dummy regression baseline MSE: ", round(dummy_MSE, 2))

Dummy regression baseline RMSE:  1800.18
Dummy regression baseline MSE:  3240664.92