Question

Refer to OM in Action on "NYC's Potholes and Regression Analysis" and find the expected number of potholes based on the regression function defined in this paragraph.

Assume resurfacing gap is = 2000, and Inches of snow is = 45

OM in Action NYC's Potholes and Regression Analysis New York is famous for many things, but one it does not like to be known for is its large and numerous potholes. David Letterman used to joke: "There is a Any amount below that would contribute to a "gap" or backlog of streets need- ing repair. The graph below shows the plot of potholes versus the gap. With an r of .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. 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. The winter of 2014 was an exceptionally bad year. City workers filled a record 300,000 potholes during the first 4 months of the year. That's an astounding accomplishment But potholes are to some extent a measure of municipal competence-and they are costly. 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 350,000 300,000 devastatingly high 200,000-300,000 range in 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 y=15,495+ 91.1x 2 = 81 250,000 200,000 versus the inches of snow each winter 150,000 350,000 100,000 300,000 50,000 y=115,860 2,246.1x r2=32 250,000 0 500 1,000 1,500 2,000 2,500 3,000 200,000 Backlog of streets needing repair 150,000 third model performs a regression analysis using the resurfacing gap and inches of snow as two independent variables and number of potholes as the dependent variable. That regression model's r2 is .91. 100,000 50,000 Potholes =7,801.5 80.6 X Resurfacing gap L. 70 930.1 X Inches of snow 10 30 60 20 40 50 Inches of snow Sources: OR/MS Today (June, 2014) and New York Daily News (March 5, 2014) 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. No. of p otholes f potholes ON

Answer 1

Note that the third model has r² = 0.91. So, in this case, as high as 91% of the variability of the dependent variable can be explained using the model compared to the other two for which the r² value is 0.32 and 0.81. So, we chose this particular model.

Using this model:

Potholes = 7801.5 + 80.6 * Resurfacing gap + 930.1 * Inches of snow

Given, Resurfacing gap = 2000 and Inches of snow = 45

No. of potholes = 7801.5 + 80.6 * 2000 + 930.1 * 45

= 210856.

So,

the expected number of potholes based on the regression function = 210,856