Another is stationarity–the system may or may not have stationary behavior in terms of the specific parameters here. Maybe the equation holds up over time, or maybe it doesn’t (as it didn’t with, for example, mortgage foreclosure rates up to last year, or on bond spreads up to the LCTM debacle, etc). Even decades of stable data don’t ‘prove’ stationarity, as we all found out.

And finally, we don’t know which input data are necessarily significant, and which are noisy (and will actually make the model *worse* as a result of their inclusion, given spurious correlations in finite samples). The three input variables for the wine equation above may be the most meaningful, or they might not be (there may be other, more significant variables at play)–but the equation alone won’t warn you against that. See factor analysis or PCA.

Given all that, the equation’s significance really has to be qualified in a few specific ways–it’s not the best quantitative model of wine quality—it’s merely the best _linear_, _historical_sample_based_, _limited_input_ model of wine quality. You can do polynomial (or fourier, or wavelet, etc) regression instead of linear; you can try to model the internal generators of wine quality rather than only using the historical top-line numbers; and you can try to look at a broader set of candidate inputs.

Oh, and another good book in the ‘Fooled By Randomness’ tradition (and with a foreward by Nassim Taleb)–Pablo Triana’s recent “Lecturing Birds on Flying”.

As a “team sport played by individuals”, baseball is an easier sport to isolate the impact of individual performance on team performance, but football and basketball are catching up by developing stats that meaningfully capture the impact of individuals on team performance. The inability of past stats to capture the impact of “personality” or “team character” is a signal that analysts are using the wrong stats, not that stats can’t be used to understand what’s going on.