One counter argument is that they probably applied a basic linear least squares fit to the data. Simple linear regression, using the L2 loss i.e. (y-f(x))^2, is extremely sensitive to large outliers (like Birmingham and Manchester). Without more medium-size cities in the 1-2M range it's hard to say for sure.
If you didn't have those data points, the story would be that the UK has much more productive cities (per size) than France. The trend line with those two cities removed is far steeper; practically vertical! And in fact if their analysis of Birmingham is correct - that it's effectively a much smaller city and should be placed further left on the graph - then it would also support a much steeper line.
What does that tell you? Probably that the population size of British cities is not a good feature to use to estimate productivity. Or that Birmingham and Manchester are outliers - they are huge cities compared to most of the rest of the UK, for a start.
That's not to say that the article is wrong. Public transport in large cities is pretty poor outside London. I don't doubt that if Birmingham had a decent mass transit system, it would be more profitable.
They also avoided the issue of Manchester, which does have a dense public transport system (similar to Liverpool), but is also punching below its weight.
Never mind that they're assuming that France is the benchmark (despite drawing a trend line on the UK), they included Edinburgh which is a capital ...
If you didn't have those data points, the story would be that the UK has much more productive cities (per size) than France. The trend line with those two cities removed is far steeper; practically vertical! And in fact if their analysis of Birmingham is correct - that it's effectively a much smaller city and should be placed further left on the graph - then it would also support a much steeper line.
This is what the plot looks like without Birmingham and Manchester: https://imgur.com/a/yhT5VoD
I suspect you'd get a similar result if you used a more robust estimator like the Huber loss: https://en.wikipedia.org/wiki/Huber_loss
What does that tell you? Probably that the population size of British cities is not a good feature to use to estimate productivity. Or that Birmingham and Manchester are outliers - they are huge cities compared to most of the rest of the UK, for a start.
That's not to say that the article is wrong. Public transport in large cities is pretty poor outside London. I don't doubt that if Birmingham had a decent mass transit system, it would be more profitable.
They also avoided the issue of Manchester, which does have a dense public transport system (similar to Liverpool), but is also punching below its weight.
Never mind that they're assuming that France is the benchmark (despite drawing a trend line on the UK), they included Edinburgh which is a capital ...