Over the past few weeks, I've been working on one of my most ambitious projects to date: buillding a model that predicts how many people might fly on any given nonstop route and then visualizing it in an interesting way. I took a course on data science this past semester where I learned quite a bit about statistics, machine learning, and data visualization, so I figured this would be a great opportunity to apply my skills to a topic I find very interesting.
Below is an interactive visualization showing the model results (it works on mobile devices too, although you may need to scroll.) It's presented as a map with the 280 largest U.S. airports -- you can click on any two airports and the info box at right will present the actual number of nonstop passengers per day each way (PDEW) in Q3 2019, the total number of passengers (with any number of stops), and the predicted number of nonstop PDEW based on the model. The model, of course, is intended to be used with nonstop routes that don't currently exist, but you can still look at existing nonstop routes too for purposes of comparison!
After presenting the visualization, I'm going to briefly discuss my methodology after the break but go play with the model first! You can choose as many city pairs as you want -- once you're done looking at one route, just click on another two cities. And as a forewarning, it's definitely not perfect!
Now that you've had a chance to play around for a bit, on to the methodology! You can look at the Jupyter notebook in which I built the model here. My basic plan was to use the same Department of Transportation DB1B data I've used in a few posts now to build a model for how many passengers might be expected to fly on any nonstop route (airline excluded) based on a factors such as the distance of a route, total passengers at the origin and destination airports, etc.
Using DB1B data from Q3 2019, my first step was to calculate five main metrics for the top ~280 U.S. commercial airports: average market coupons (number of stops), average flight distance in miles, average flight price in dollars, total passengers in the quarter, and the population of the surrounding metropolitan area. Then, for each existing nonstop flight, I found the total number of passengers in that quarter and combined this data with the airport information for both origin and destination airports in a single dataframe that contained all the information about each route and its airports.
With the data gathered, the next step was to perform a regression to predict the number of passengers on a new nonstop route given information about the route and origin/destination airports. I excluded any flights with greater than 350,000 passengers in the quarter (of which there are only a few) as they are huge outliers and could skew the model. I first attempted a linear regression, but the issue was that flights that would likely have extremely low passenger counts would predict a negative number of passengers. This is just an inherent issue with linear regression, so I explored a few other types of regression including logistic and exponential before landing on a Poisson distribution that considers event probability (which fits the idea of number of passengers flying) and critically excludes negative values. The regression table is shown below:
Generalized Linear Model Regression Results
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Dep. Variable: PASSENGERS_route No. Observations: 3058
Model: GLM Df Residuals: 3048
Model Family: Poisson Df Model: 9
Link Function: log Scale: 1.0000
Method: IRLS Log-Likelihood: -1.4802e+06
Date: Tue, 20 Apr 2021 Deviance: 2.9321e+06
Time: 21:29:21 Pearson chi2: 3.25e+06
No. Iterations: 5
Covariance Type: nonrobust
==========================================================================================
coef std err z P>|z| [0.025 0.975]
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const 11.7094 0.006 1930.331 0.000 11.697 11.721
market_distance_route -0.0004 5.52e-07 -787.274 0.000 -0.000 -0.000
market_fare_origin -0.0007 1.4e-05 -52.244 0.000 -0.001 -0.001
market_coupons_origin -2.3898 0.003 -689.831 0.000 -2.397 -2.383
market_distance_origin 0.0008 1.73e-06 461.121 0.000 0.001 0.001
PASSENGERS_origin 2.342e-06 2.63e-09 889.163 0.000 2.34e-06 2.35e-06
market_fare_dest -0.0008 1.4e-05 -54.667 0.000 -0.001 -0.001
market_coupons_dest -2.3892 0.003 -688.984 0.000 -2.396 -2.382
market_distance_dest 0.0007 1.72e-06 434.013 0.000 0.001 0.001
PASSENGERS_dest 2.406e-06 2.66e-09 902.920 0.000 2.4e-06 2.41e-06
==========================================================================================
The 9 variables considered in the regression -- 1 about the route, and 4 each about the destination and origin airport -- all have p-values of zero, indicating statistical signifigance. Similarly, splitting the dataset up into train/test sets and calculating the mean-square error shows that the model performs quite similarly on both datasets, indicating that this regression is at least relatively consistent.
The last step of the data analysis was just calculating the predicted number of passengers using this regression for any given route, and then I got started on the visualization. I used D3.js, an incredibly customizable visualizations package that let me make this really cool map, complete with clicking and choosing the airports of interests and drawing paths, which was definitely one of my favorite parts of this project!
While you've probably seen that the model makes pretty decent predictions in many cases, it's not hard to find routes where the model makes no sense! PVD-BOS, for example, predicts 318 PDEW which is obviously nuts, but because there are few routes so short and generally longer routes have fewer passengers, this is an unfortunate byproduct of regression. Similarly, the model is unable to account for qualitative observations about why people might travel between two cities. Many flights to Florida, for example, are likely underestimated because it's hard to tell a model that Florida has lots of beaches. And high-volume routes like JFK-LAX or BOS-SFO (more than 1000 PDEW or so) are usually underestimated by the model since there are so few very high-volume flights like these incorporated into the regression. And while some estimates look pretty reasonable, some random routes just aren't even close! Predicting air travel demand isn't easy, and capturing it in a simple regression isn't likely to be easy either. I definitely don't think this is the most possible accurate model, but it's a good start that generally provides decent estimates and was certainly fun to build.
While the model obviously isn't perfect, I'm pretty proud of its relative accuracy given the pretty small account of information taken into account using entirely public data. Overall, this has been a pretty fun project over the past few weeks exploring airline data, working with statistics and ML techniques, and making fun visualizations! As always, shoot me an email if you have any thoughts on my work -- I always love to hear it!