Tuesday, July 21, 2009

Correlation in everything

PARKING rates are holding firm despite the economic downturn, according to Colliers International, a property company. European cities have some of the highest daily parking rates, with Amsterdam and London coming out on top. Tokyo is the most expensive place to leave your car outside Europe. Honolulu is second behind New York among America's cities. Drivers in London fork out the most for a monthly unreserved space. The cheapest parking in the survey is in India, where a spot in Chennai costs 96 cents a day. ~The Economist

Felix Salmon pointed this out in his blog links the other day and with a quick rebuke marked that the series relationship between daily parking rates and monthly parking rates was highly uncorrelated. Normally I would take his word at gospel but perhaps I should be more skeptical. (In general as opposed to explicitly when reading Felix's work.) So I quickly entered the data into a spreadsheet and looked at an x-y scatter plot. While it was true that the regression line did come out with a less than desirable r-squared figure of 59.97%, which in lay terms means that the line can explain almost 60% of the variance of the points from the "best-fit" linear regression line produced. So Felix is correct not much of a natural correlation, so much for those who love to extrapolate out series.

So let's extrapolate out the series to see what happens. Taking the daily rate and multiplying it by 30 days to see what happens. Obviously if you pay up front you should be expected to earn a discount. Also by purchasing in bulk and thus giving the merchant sticky expected cash flows, which the merchant can extrapolate to his peril, you should also receive a discount.

Now the series looks much more promising. Below is a graph of the monthly discount from paying up front versus paying the daily rate 30 times. You can see the discount's median is almost 64% and the average is about 57%. The series is also drawn from the above table so you can see that as the daily rate drops so does the discount, which is also expected because price levels matter. I am quite certain Felix wrote this in passing as he boarded his plane for Beijing but I think he may have written too quickly without a full analysis.

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