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0.0.2 Question 1b For this assignment, we’ll be using this data to study bike usage in Washington, DC. Based on the granularity and the variables present in the data, what might some limitations of using this data be? What are two additional data categories/variables that one could collect to address some of these limitations? We could lack information regarding the duration of the user’s bike ride due to the absence of a variable monitoring the time spent riding. One way to address this is by introducing two variables to capture the average durations of bike rides for both casual and registered users. 3

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0.0.5 Question 3c The density plots do not show us how the counts for registered and casual riders vary together. Use sns.lmplot (documentation) to make a scatter plot to investigate the relationship between casual and registered counts. This time, let’s use the bike DataFrame to plot hourly counts instead of daily counts. The lmplot function will also try and draw a linear regression line (just as you saw in Data 8). Color the points in the scatterplot according to whether or not the day is a working day (your colors do not have to match ours exactly, but they should be different based on whether the day is a working day). Hints: * Check out this helpful tutorial on lmplot . * There are many points in the scatter plot, so make them small to help reduce overplotting. Check out the scatter_kws parameter of lmplot . * Generate and plot the linear regression line by setting a parameter of lmplot to True . Can you find this in the documentation? We will discuss the concept of linear regression later in the course. * You can set the height parameter if you want to adjust the size of the lmplot . * Add a descriptive title and axis labels for your plot. * You should be using the bike DataFrame to create your plot. * It is okay if the scales of your x and y axis (i.e., the numbers labeled on the two axes) are different from those used in the provided example. In [58]: sns . set(font_scale =1 ) # This line automatically makes the font size a bit bigger on the plot. Y sns . lmplot(data = bike, x = 'casual' , y = 'registered' , hue = 'workingday' , height =6 , scatter_kws = { 's' : 2 , 'alpha' : 1 }) plt . title( 'Comparison of Casual vs Registered Riders on Working and Non-working Days' ) Out[58]: Text(0.5, 1.0, 'Comparison of Casual vs Registered Riders on Working and Non-working Days') 9

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0.0.8 Question 4b With some modification to your 4a code (this modification is not in scope), we can generate the plot above. In your own words, describe what the lines and the color shades of the lines signify about the data. What does each line and color represent? Hint : You may find it helpful to compare it to a contour or topographical map as shown here . Every line or contour on the graph delineates a segment of a probability density function, and the varying shades indicate distinct density levels between these segments. Darker shades correspond to regions with higher density values. 15

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0.2 6: Understanding Daily Patterns 0.2.1 Question 6a Let’s examine the behavior of riders by plotting the average number of riders for each hour of the day over the entire dataset (that is, bike DataFrame ), stratified by rider type. Your plot should look like the plot below. While we don’t expect your plot’s colors to match ours exactly, your plot should have a legend in the plot and different colored lines for different kinds of riders, in addition to the title and axis labels. In [62]: average_counts = bike . groupby( 'hr' )[[ 'casual' , 'registered' ]] . agg(np . mean) sns . lineplot(data = average_counts, x = 'hr' , y = 'casual' , label = 'casual' ) sns . lineplot(data = average_counts, x = 'hr' , y = 'registered' , label = 'registered' ) plt . xlabel( 'Hour of the Day' ) plt . ylabel( 'Average Count' ) plt . title( 'Average Count of Casual vs. Registered by Hour' ) plt . legend() Out[62]: <matplotlib.legend.Legend at 0x7f3dd04fe450> 21

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0.2.2 Question 6b What can you observe from the plot? Discuss your observations and hypothesize about the meaning of the peaks in the registered riders’ distribution. Registered riders show peak bike riding activity during early mornings around 8 AM and in the evenings, particularly between 4-5 PM. Similarly, casual riders also exhibit a peak in bike riding during the evening at approximately 5 PM. Broadly speaking, early mornings and late afternoons/evenings emerge as the prime periods for bike riding, aligning with common work commute hours—either departing for work or returning from work. Notably, the distribution line for casual riders appears more flattened compared to registered riders, indicating their less frequent bike riding habits. 23

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0.2.3 Question 7b In our case, with the bike ridership data, we want 7 curves, one for each day of the week. The x-axis will be the temperature (as given in the 'temp' column), and the y-axis will be a smoothed version of the proportion of casual riders. You should use statsmodels.nonparametric.smoothers_lowess.lowess just like the example above. Un- like the example above, plot ONLY the lowess curve. Do not plot the actual data, which would result in overplotting. For this problem, the simplest way is to use a loop. You do not need to match the colors on our sample plot as long as the colors in your plot make it easy to distinguish which day they represent. Hints: * Start by plotting only one day of the week to make sure you can do that first. Then, consider using a for loop to repeat this plotting operation for all days of the week. • The lowess function expects the y coordinate first, then the x coordinate. You should also set the return_sorted field to False . • You will need to rescale the normalized temperatures stored in this dataset to Fahrenheit values. Look at the section of this notebook titled ‘Loading Bike Sharing Data’ for a description of the (normalized) temperature field to know how to convert back to Celsius first. After doing so, convert it to Fahrenheit. By default, the temperature field ranges from 0.0 to 1.0. In case you need it, Fahrenheit = Celsius × 9 5 + 32 . Note: If you prefer plotting temperatures in Celsius, that’s fine as well! Just remember to convert accordingly so the graph is still interpretable. In [69]: from statsmodels.nonparametric.smoothers_lowess import lowess plt . figure(figsize = ( 10 , 8 )) # BEGIN SOLUTION for day in bike[ 'weekday' ] . unique(): this_day = bike[bike[ 'weekday' ] == day] . copy() this_day[ 'temp' ] = this_day[ 'temp' ] * 41 * 9 / 5 + 32 ysmooth = lowess(this_day[ 'prop_casual' ], this_day[ 'temp' ], return_sorted = False ) sns . lineplot(x = this_day[ 'temp' ], y = ysmooth, label = day) plt . title( "Temperature vs Casual Rider Proportion by Weekday" ) plt . xlabel( "Temperature (Fahrenheit)" ) plt . ylabel( "Casual Rider Proportion" ) plt . legend(); # plt.savefig("images/curveplot_temp_prop_casual", bbox_inches='tight', dpi=300); # END SOLUTION 25

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0.2.4 Question 7c What do you observe in the above plot? How is prop_casual changing as a function of temperature? Do you notice anything else interesting? With rising temperatures, there’s a notable uptick in the proportion of casual riders. This effect is particu- larly pronounced on weekends, where the trendline sharply ascends with increasing temperature. It’s likely attributed to the fact that weekends provide an ideal opportunity for casual riders to go biking, especially during warmer weather, possibly due to their time off from work or having more leisure hours. 27

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0.2.5 Question 8a Imagine you are working for a bike-sharing company that collaborates with city planners, transportation agencies, and policymakers in order to implement bike-sharing in a city. These stakeholders would like to reduce congestion and lower transportation costs. They also want to ensure the bike-sharing program is implemented equitably. In this sense, equity is a social value that informs the deployment and assessment of your bike-sharing technology. Equity in transportation includes: Improving the ability of people of different socio-economic classes, gen- ders, races, and neighborhoods to access and afford transportation services and assessing how inclusive transportation systems are over time. Do you think the bike data as it is can help you assess equity? If so, please explain. If not, how would you change the dataset? You may discuss how you would change the granularity, what other kinds of variables you’d introduce to it, or anything else that might help you answer this question. Note : There is no single “right” answer to this question – we are looking for thoughtful reflection and commentary on whether or not this dataset, in its current form, encodes information about equity. The current bike dataset lacks suffcient context for assessing equity. To enhance its capacity in this regard, we should consider augmenting the dataset with additional personal information about the users, such as gender, race, and place of origin. Incorporating these variables can serve as an initial step towards conducting comprehensive analyses on equity within the bike-sharing system 29

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0.2.6 Question 8b Bike sharing is growing in popularity , and new cities and regions are making efforts to implement bike- sharing systems that complement their other transportation offerings. The goals of these efforts are to have bike sharing serve as an alternate form of transportation in order to alleviate congestion, provide geographic connectivity, reduce carbon emissions, and promote inclusion among communities. Bike-sharing systems have spread to many cities across the country. The company you work for asks you to determine the feasibility of expanding bike sharing to additional cities in the US. Based on your plots in this assignment, would you recommend expanding bike sharing to additional cities in the US? If so, what cities (or types of cities) would you suggest? Please list at least two reasons why, and mention which plot(s) you drew your analysis from. Note : There isn’t a set right or wrong answer for this question. Feel free to come up with your own conclusions based on evidence from your plots! Examining the plot in 5a illustrating the hourly average count of both registered and casual bike riders, a notable pattern emerges. The peak in average rider count for registered riders aligns with typical commute hours at 8 AM and 5 PM. This pattern underscores how biking can present a practical and cost-effcient alternative for mitigating traffc congestion during these busy commute periods. 31

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