DC Bike Sharing

Background:

Bike sharing systems are new generation of traditional bike rentals where whole process from membership, rental and return has become automatic. Through these systems, users can easily rent a bike from a particular position and return back at another position. Currently, there are about over 500 bike-sharing programs around the world which is composed of over 500 thousand bicycles. Today, there exists great interest in these systems due to their important role in traffic, environmental and health issues.

Apart from interesting real-world applications of bike sharing systems, the characteristics of data being generated by these systems make them attractive for the research. Opposed to other transport services such as bus or subway, the duration of travel, departure and arrival position is explicitly recorded in these systems. This feature turns bike sharing system into a virtual sensor network that can be used for sensing mobility in the city. Hence, it is expected that most of important events in the city could be detected via monitoring these data.

Use the R code below to load the bike sharing dataset and recode a few variables of interest.

# this data comes from: http://archive.ics.uci.edu/ml/datasets/Bike+Sharing+Dataset

library(car) # for recode & vif functions

bike <- read.csv(file.choose(), header=T) # load day.csv

# un-normalize select variables

bike$atemp.u <- bike$atemp *50

bike$temp.u <- bike$temp *41

bike$hum.u <- bike$hum *100

bike$wind.u <- bike$wind *67

# create seasonal subsets

bike.spring <- subset(bike, bike$season==1)

bike.summer <- subset(bike, bike$season==2)

bike.fall <- subset(bike, bike$season==3)

bike.winter <- subset(bike, bike$season==4)

Variable descriptions (for those used in the homework):

season: 1 =spring, 2=summer, 3=fall, 4=winter

mnth: month (1 to 12)

holiday: weather day is holiday is 1 or not is 0(extracted from http://dchr.dc.gov/page/holiday-schedule)

workingday: if day is neither weekend nor holiday is 1, otherwise is 0.

temp: Normalized temperature in Celsius. The values are divided to 41 (max)

temp.u: recode of temp back to Celsius un-normalized

atemp: Normalized feeling temperature in Celsius. The values are divided to 50 (max)

atemp.u: recode of feeling temperature back to Celsius un-normalized

hum: Normalized humidity. The values are divided to 100 (max)

hum.u: recode of humidity un-normalized, units: grams of water vapor per kilogram of dry air

windspeed: Normalized wind speed. The values are divided to 67 (max)

wind.u: recode of windspeed un-normalized. Unit of measurement: miles per hour.

cnt: count of total rental bikes including both casual and registered

1A) Using the full bike data, perform a multiple regression on the total number of bikes rented per day by season, month, holiday, working day, and the un-normalizedversions of temperature, humidity, and windspeed. Be sure to know which variables in the model are quantitative and which are categoricaluse them appropriate in the regression model. Use spring as the reference category for season.

1B) Rewrite the default regression equation given here. Replace the Xs and Y with your variable names. Replace the betas with the corresponding regression coefficients. Indicate if the entire model was statistically significant or not.

1C) Assess each of the following regression assumptions. If it is okmark ok next to the assumption. If it is not ok, identify what you believe to be the problem.

Unbiased data

Variables are interval-ratio (recall if/how exceptions are made here)

DV is normally distributed

Linearity

Normality (Errors are normally distributed)

Homoskedasticity (Errors are constant & independent)

No (influential) outliers

What are code I should use?