Good Friday and Easter Monday are public holidays in Australia and UK (the former day is holiday in US in 12 states). For many down here, including those who don’t pay much nevermind to symbols, Good Friday is traditionally the day to eat Hot Cross Buns. For the last few years, the Melbourne Age newspaper has rated a dozen such buns for quality, as well as listing their price.
http://www.goodfood.com.au/good-food/search.html?ss=Good+Food&text=bunfight&type=
We would expect that, quality would increase, to some extent with price, although it would eventually flatten out (e.g. thrice as expensive doesn’t always mean thrice as good). Graphing programs such as Graphpad, Kaleidagraph and SigmaPlot, as well as R and most Stats packages, can readily fit a plethora of polynomial and other nonlinearities, but I used Stata to perform a preliminary scatterplot of the relationship between tasters’ score (out of 10) and price per bun (A$), smoothed using Bill Cleveland’s locally weighted least squares Lowess/Loess algorithm. http://en.wikipedia.org/wiki/Lowess
The relationship shown above is vaguely linear or, rather, ‘monotonic’, at least until I can have a better go with some nonlinear routines.
A simple linear regression model accounts for around 42% of the variation in taste, in this small and hardly random sample, returning the equation y=1.71*unitprice+1.98, suggesting (at best) that subjective taste, not necessarily representing anyone in particular, increases by 1.7 with every dollar increase in unit price.
But the fun really begins when looking at the residuals, the difference between the actual taste score, and that predicted using the above model. Some buns had negative residuals, indicating (surprise surprise!) that their taste was (much) lower than expected, given their price. I won’t mention the negatives.
As to the positives, two bakeries, Woodfrog Bakery in St. Kilda (Melbourne, Australia) and Candied Bakery in Spotswood (ditto), both cost $2.70 each and so were predicted to have a taste score out of 10 of 6.6, yet Woodfrog hopped in with an actual score 8.5 and Candied with an actual score of 8.
The results can’t be generalised, prove nothing at all, and mean extremely little, except to suggest that regression residuals can perhaps be put to interesting uses, but please take care in trying this at home! Tread softly and carry a big (regression) book e.g Tabachnick and Fidell’s Using Multivariate Statistics
(or the Manga Guide to Regression, when published! http://www.nostarch.com/mg_regressionanalysis.htm)
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