MATH 4044 Statistics for Data Sciences Assignment 1 Data Description cb capital bikeshare capital bikeshare ONLINE SHOP SHOP HOW > Bike Sharing Systems Bike sharing systems are a new generation of bike rentals where the whole process from membership, rental and return has become automatic. Through these systems, a user is able to easily rent a bike from a particular position and return the bike at another posi- tion. Currently, there are over 500 bike-sharing programs around the world, with some of the best and largest found in Hangzhou (China), Paris (France), London (England), New York City (US) and Montreal (Canada). Great interest in these systems exists due to their role in addressing traffic congestion, environmental impact and population health issues in big cities. The data for this assignment comes from one such program, called Capital Bikeshare, operating in Washington in the US. It has over 3000 bicycles that can be rented from over 350 stations across Washington, D.C., Arlington and Alexandria, VA and Montgomery County, MD. Their website encourages users to check out bikes for a trip to work, to run errands, go shopping, or visit friends and family. Users can join Capital Bikeshare for one to three days (casual membership), or for a month or a year (registered membership). Access to the Capital Bikeshare fleet of bikes is available 24 hours a day, 365 days a year. The first 30 minutes of each trip are free. You will use data derived from Capital Bikeshare trip records to build a statistical model for the purposes of predicting the total number of rentals per day. References and Data Sources: . Bache, K. & Lichman, M. (2013). UCI Machine Learning Repository http:MATH 4044 Statistics for Data Sciences Assignment 1 / /archive. ics . uci . edu/ml Irvine, CA: University of California, School of In- formation and Computer Science. . Fanace-T, Hadi, and Gama, Joao, 'Event labeling combining ensemble detectors and background knowledge', Progress in Artificial Intelligence (2013): pp. 1-15, Springer Berlin Heidelberg. . http://capitalbikeshare . com/system-data Data file for this assignment The data file for this assignment is called daily . sas7bdat and contains daily counts of bike rentals for 2011 and 2012, derived from Capital Bikeshare trip history data, with additional weather and seasonal information. The data was downloaded from the UCI Machine Learning Repository. Variables in that file are: Variable Description instant Record index dteday Date season winter, spring summer, autumn (northern hemisphere) yr 0-2011, 1=2012 month Month (January to December) weekday Day of the week (Monday to Sunday) workingday Working day=1, weekend and public holiday = 0 temp Normalised temperature in degrees Celsius; observed temperature di- vided by 41 (max) atemp Normalised 'feels like' temperature in degrees Celsius; values divided by 50 (max) hum Normalised humidity; observed values divided by 100 (max) windspeed Normalised wind speed; observed values divided by 67 (max) casual Count of casual users registered Count of registered users count Total count of bike rentals (casual and registered).MATH 4044 Statistics for Data Sciences Assignment 1 Assignment Tasks Question 1 (20 marks) (a) (10 marks) Use SAS to study the distribution of the number of registered users per day (registered) by season. Obtain measures of location, disper- sion, skewness and kurtosis. Obtain a boxplot, histogram and a quantile- quantile plot. Also carry out Normal Goodness-of-fit tests. What are the key features of these distributions? (b) (10 marks) Now use SAS to obtain boxplots of registered by season, and by yr, respectively. Similarly, obtain boxplots of casual by season and yr. What do the boxplots suggests about the pattern and trend, if any, of bike rentals? Question 2 (60 marks) (a) (8 marks) Obtain a Pearson correlation matrix relating variables registered, atemp, temp, hum and windspeed. Also obtain a scatterplot matrix of the same variables. Discuss the relationships. (b) (12 marks) In this question, we investigate observations where workingday=1. Fit a simple regression model relating registered on working days to atemp, with registered as the dependent variable. Discuss the fitted relationship and the goodness of fit. Examine residual plots and influence diagnostics and comment on the residual patterns. (c) (20 marks) In this question, we investigate observations where workingday=1. Extend your multiple regression model for registered on working day by in- cluding the numerical and categorical predictors. In building your model consider as many potential explanatory variables as possible (you may need to define additional dummy variables). You can use stepwise selection to help you find the most parsimonious (simplest) model with the highest R-square. Be sure to check for collinearity and keep in mind that neither casual nor count should be used as explanatory variables for the total number of users. Summarise how your final model was obtained, including rationale for any modelling decisions you have made, and indicate why that final was considered the 'best'. Report and interpret your final model in detail, including a discussion of model diagnostics. Are there any observations that may require further in- spection due to their influence on the model? (d) (20 marks) In this question, we investigate observations where workingday=0. Build a multiple regression model for registered on non-working day, similar to question ()MATH 4044 Statistics for Data Sciences Assignment 1 Summarise how your final model was obtained, including rationale for any modelling decisions you have made. Report and interpret the final model. Compare and contrast the model with that obtained in question (c), and compare the effects of the predictors on registered for working and non- working day. Question 3 (20 marks) Write a summary of your findings from Questions 1 and 2. Keep the technical details of the analyses that led you to these conclusions to the absolute minimum. Rather, focus on practical significance and present your findings in non-specialist terms. One to two paragraphs (up to a page) will be sufficient. Hints: In order to study the regression for a specific group of observations, we can use the where statement. In particular, to build a regression model for working days, we can use proc reg data=. . . model . . . where workingday=1; run