Just what exactly does the Lesotho Loti have to do with Palo Alto median prices?

December 5, 2006

Pat Kitano notes with his usual insight that spontaneity is both the joy and bane of blogging. In a rush of post-Martian Flu exuberance, I showed what looked to be a pretty neat correlation between the NASDAQ and Palo Alto median home prices. Alas, the spontaneity of that moment led me to not dig quite deep enough…

Enter reader Greg, whose facility with numbers and patterns has led to previous interesting discussions. He suggested running some regression analysis (for those who missed Stats 101, “regression analysis” is simply finding relationships between different groups of numbers.) I did that and came up — surprisingly — empty-handed: it turned out there was actually very little correlation, mathematically speaking, between the NASDAQ and Palo Alto median home prices. Puzzling, puzzling indeed, because the graph showed at least a rough correlation.

Greg ran a regression of his own comparing Palo Alto median home prices vs. the number of months since January 1997…and found a reasonably strong correlation, an R-squared value of 75% for those who care about such things.

Here’s a graph:

regression1-custom.png
The wavy blue line indicates Palo Alto median home prices; the straight pink line is the prediction, based simply on the number of months since January 1997.

Fortunately, all was not lost, as it turns out that while the NASDAQ alone was not a very good predictor, adding it to the mix turned out to increase the accuracy of the predictions, resulting in an R-squared value of 85%. The chart:

regression002-custom.png
Again, the blue line represents Palo Alto median home prices, while the pink line represents the predicted median home price, based on both the number of months since January 1997 and the NASDAQ.

What does this all mean? In a nutshell, this entire analysis proved what we all already know to be true: Palo Alto real estate prices in the last 10 years have tended to go up. The key predictor of prices is simply time; adding in other variables like the NASDAQ improves the predictive power, but the main indicator — by far — is simply that of time.

Which brings us back to the Lesotho Loti. Just for the fun of it, I ran one more regression, this time between Palo Alto median home prices and two variables: the number of months since January 1997, and the exchange rate between the US Dollar and the Lesotho Loti. (Yep, I’m the kind of person who “just for the fun of it” runs regressions. For other like-minded people, the R-squared for this regression was 75%.)

The graph:

regression003-custom.png
So does this mean that the exchange rate of the US dollar vs. the Lesotho Loti is an accurate predictor of Palo Alto median home prices? Not at all…it simply means that adding in that variable doesn’t really detract from the predictive power of the time factor.

Geek out.

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Written by Kevin · Filed Under Analysis, For buyers, For sellers, Palo Alto, Real estate | 5 Comments