Strong spurious correlations enhanced in appearance with mismatched dual axes

I stumbled across a potentially fascinating website titled Spurious Correlations that looks at relationships between odd variables. Here are two examples:

According to the site, both of these pairs have correlations higher than 0.94. In other words, very strong.

One issue: using dual axes can throw things off. The bottom chart above shows a negative relationship – but this is only because the axes are different. The top chart makes it look like the lines really go together – but the axes are way off from each other with the left side ranging from 29-34 and the right side ranging from 300-900. Overall, the charts reinforce the strong correlations between the two variables but using dual axes can be misleading.

How related are home sales and car sales?

Americans like big houses as well as cars. But, are sales of homes related to sales of cars?

Driving to work the other day I heard a radio analyst assert that the recent increase in home sales is responsible for the increase in automobile sales (McMansions come with at least two car garages you know!) The short piece didn’t offer much in terms of quantitative information and this made me wonder what data was used to support such a claim. The analyst could have looked at SEC (Securities and Exchange Commission) filings, the equities and derivatives market, or perhaps research from industry associations such as the National Association of Realtors; the latter would prompt me to consider confirmation bias.

If only considering home sales, Federal Reserve Board economist Andrew Paciorek recently published an engaging paper describing the effects of household formation on housing demand. Paciorek asserts that in the past 30 years the aging population has moved into smaller homes, which is intuitive from the practicality it offers seniors. Paciorek also postulates that the poor labor market has depressed the headship rate, which is defined as the percent of people who are heads of household via U.S. Census population projections.

According to the S&P/Case Shiller Home Price Index report, the average U.S. home is now worth approximately 10 percent more than it was a year ago, marking the largest annual improvement since the market turned south in 2006. What of the automobile market though? American popular culture paints home and car ownership as inseparable in the “American Dream”. The most recent J.D. Power report projects August sales to increase 12 percent compared to last year, the highest monthly sales volume since 2006.

It would be easy to paint a picture of recovery for these industries based on sales revenues, although there is no indication of a casual relationship between the two. These reports are meant for the average consumer only in a sense to stir up positive sentiment, which in turn spurs more discretionary spending. It is more plausible that these reports are meant for the real stakeholders: shareholders and potential investors. We can surmise that in a world of algorithmic high frequency trading and complex derivatives based on yet other derivatives, that the common equities market does not always correlate to the real-world P&L performance. I recall a former boss’s retort of traditional value investing: ‘The market can stay irrational longer than you can stay solvent’.

The conclusion here is that this is a “common sense explanation” without much merit in data. And, I wonder if this is a classic case of the casual observer making a spurious association: both car sales and home sales go back in a better economy.

This is also interesting because of the number of times in the last decade or so when journalists and commentators have linked the building of McMansions to consuming other large objects, particularly SUVs. The idea behind these comparisons is that Americans in general have learned to consumer more bigger items. However, I’ve never seen any data that the same people who purchase McMansions are necessarily the same people purchasing SUVs, super-sized fast food, bulk items at big box stores, and other large items that fit into a category of excessive consumption.