[quote]From: Robert Chung

Date: Wed, 7 May 2008 11:09:10 -0700 (PDT)

Local: Thurs, May 8 2008 4:09 am

Subject: Re: Aero Testing Sheets - Update (Chung & Regression Methods)

> On May 7, 12:04 pm, Robert Chung

> > Andy (Coggan): with the regression method, using the proper model specification

> > always dominates.

> But (somewhat rhetorically) what is the "proper model specification"?

> The two alternatives are mathematically equivalent, the physics don't

> really help you decide, and the argument could be made that a power

> meter is just as much a force (torque) meter. To me, then, it comes

> down to how errors in the underlying measurements impact the precision

> of the CdA estimate, and that's what I can't decide (since the noise

> isn't necessarily "white", I don't think that a simple uncertainty

> analysis will suffice).

Since this is rhetorical, you almost surely already know the answer

but for those who don't, Andy's right, the physics models don't help,

and the mathematics are equivalent. What's not equivalent is the

statistical model. The underlying linear regression model is unbiased

and efficient (i.e., lowest variance) when the Gauss-Markov

assumptions are met. The "usual" regression model (where one regresses

W/v on v^2) will produce inefficient (though consistent aka

asymptotically unbiased) estimates because of heteroscedasticity.

However, over the range of v we usually see for these kinds of field

tests, I expect the efficiency loss will be relatively small. The

bottom line is that it's slightly better to use whatever the PM

reports rather than to transform the variables, though only very

slightly.

BTW, you're right that the errors aren't "white." Note, for example,

systematic holes in the SRM's speed reporting. [/quote]

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