## Congestion, Freeways, and Size, Redux

As a followup to my previous post about the TTI’s new congestion report, I finally did a multivariate regression analysis, with the dependent variable being cost and the independent variables being size and freeway lane-miles per capita. Such an analysis reduces the regression coefficient between freeways and congestion even more, to -42.5 from the uncontrolled -233. More interestingly, if we log all numbers (population, congestion cost, and freeways), the regression coefficient becomes a positive 0.02 – that is, adding freeways is correlated with making congestion a little worse.

Of course, it’s not literally true that adding freeways makes congestion worse. There’s a correlation if we look at the variables in some way, but it’s not going to have any statistical significance. Therefore tweaking variables slightly can make a correlation go from weakly positive to weakly negative.

In univariate regression, we can think about the square of the correlation as the percentage of the variance that is explained by the regression line. Freeway lane-miles per capita explain 3.8% of the variance in congestion (and logging either variable makes this number smaller); with 101 urban areas surveyed, it’s statistically significant, but barely so. But after controlling for population, this proportion drops to 0.7%. Thus, any sentence of the form “adding one freeway lane-mile per thousand people only cuts \$42.5 from the annual congestion cost per capita” is inherently misleading: the correlation is so weak that some cities can reduce congestion without building the requisite amount of roads, or building any roads at all (for example, nearly all American cities in the last five years, congestion having crashed in the oil price boom and the recession), while others can keep building but see congestion increase (for example, Houston since the 1980s, and even today).

It goes without saying that such analysis is not going to appear in the TTI report itself. The TTI gets funding from APTA and the American Road and Transportation Builders Association. It pays lip service to congestion pricing as a solution to congestion, and instead talks a lot about building public transportation and even more about building freeways to keep up with demand. American cities may be building freeways faster than their population growth, but cities that enact no traffic restraint and just pour concrete can expect demand to grow faster than population as people become more hypermobile.