Potholes in New York City and Regression Analysis Source: OR/MS Today (July, 201
ID: 387435 • Letter: P
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Potholes in New York City and Regression Analysis
Source: OR/MS Today (July, 2014), https://www.informs.org/ORMS-Today/Private-Articles/June-Volume-41-Number-3/POTHOLE-ANALYTICS
New York is famous for many things, but one thing it does not like to be known for is its large and numerous potholes. David Letterman used to joke: "There is a pothole so big on 8th Avenue it has its own Starbucks in it." When it comes to potholes, some years seem to be worse than others. This winter was an exceptionally bad year. City workers filled a record 300,000 potholes during the first 4 months of 2014. That's an astounding accomplishment.
But potholes are to some extent a measure of municipal competence and are costly in many ways. NYC's poor streets cost the average motorist an estimated $800 per year in repair work and new tires. There has been a steady and dramatic increase in potholes from around 70,000- 80,000 in the 1990s to the devastatinglyhigh 200,000- 300,000 range in the most recent years. One theory is that bad weather causes the potholes. Using inches of snowfall as a measure of the severity of the winter, the graph below shows a plot of the number of potholes vs. the inches of snow each winter. (R-squared = 0.32).
Research showed that the city would need to resurface at least 1,000 miles of roads per year just to stay even with road deterioration. Any amount below that would contribute to a "gap" or backlog of streets needing repair. The graph below shows the plot of potholes vs. the gap. With an R-squared of 0.81, there is a very strong relationship between the increase in the "gap" and the number of potholes. It is obvious that the real reason for the steady and substantial increase in the number of potholes is due to the increasing gap in road resurfacing.
A third model performs a regression analysis using the resurfacing gap and inches of snow as 2 independent variables and number of potholes as the dependent variable. That regression model's R squared is 0.91.
Potholes = 7801.5 + 80.6 x Resurfacing Gap + 930.1 x Inches of Snow
Critical Thinking Questions
1. Potholes are
A.
a result of global warming.
B.
a problem that can be solved with safer driving.
C.
costly to the city and its residents.
D.
a declining problem in NYC.
2. The first graph (snowfall in inches vs. the number of potholes)
A.
indicates that snow explains about 32% of pothole creation.
B.
is an example of time-series analysis.
C.
has an extremely high R-squared.
D.
shows that the observation points are all very close to the regression line.
3. An R-squared of 0.81
A.
indicates a strong relationship between the two variables.
B.
is 3 times better than an R-squared of 0.32.
C.
means the correlation coefficient is 0.81.
D.
indicates that 19% of pothole creation is explained by the road repair "gap."
4. Multiple regression here
A.
means that 91% of variation in potholes is explained by the "gap" and by snow.
B.
indicates that two variables do a better job of explaining the number of potholes than one variable does.
C.
is a better predictor of potholes than snow alone.
D.
All of the above.
350000.0 300000.0 250000.0 200000.0 50000.0 100000.0 50000.0 y-2246.1x+115860 Series Linear (Series) 0.0 .0 10.0 20.0 300 40.0 S0.O 600 70.0Explanation / Answer
Answer.
1) potholes are
A) result of global warming
2) The first graph (snowfall in inches vs. the number of potholes)
A) aindicates that snow explains about 32% of pothole creation.
3) An R-squared of 0.81
A)indicates a strong relationship between the two variables.
4)Multiple regression here
D) all of the above
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