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+--- Thread: Rationale for 15C L.R. result order? (/thread-196830.html)
Rationale for 15C L.R. result order? - Mike Fikes - 09-20-2011
I suspect that, in most scenarios, the slope of a given line is more "meaningful" than the value of its y-intercept, yet the L.R. operation on the 15C returns the slope in the Y register.
(A criticism of this choice is made in "HP-15C: FIRST IMPRESSIONS OF AN HP-41 USER" attached by Gene Wright to Some 15c files from HHC 2010 recently.)
Is there a logical argument that can be used to defend the choice that HP made for the 15C? Perhaps it facilitates certain use cases?
Edited: 20 Sept 2011, 4:09 p.m. after one or more responses were posted
Re: Rationale for 15C L.R. result order? - Walter B - 09-20-2011
Can't tell you a logical argument but only an historical. L.R. returns the regression parameters in this order since the HP-32E at least. So we did keep it this way for the WP 34S, too.
Addendum:
Quote:Hmmh, the author of that article only claims the reverse order would be "more natural" without giving any rationale for this claim :-/ Looks like there are simply just two ways and HP chose one :-)
A criticism of this choice is made in "HP-15C: FIRST IMPRESSIONS OF AN HP-41 USER"
Edited: 20 Sept 2011, 4:09 p.m.
Re: Rationale for 15C L.R. result order? - Mike Fikes - 09-20-2011
Right. With respect to being more "natural" I would argue that (to me at least) it would have been more natural, in the following sense:
In algebra class, you learn the formula for a line is y = mx + b. Because of this, I expect m to be "first" (in the X register), followed by b in the Y register.
Re: Rationale for 15C L.R. result order? - Walter B - 09-20-2011
Well, what's pushed on the stack first ends higher up :-) So what you see may be the consequence of m ENTER b . BTW, what's the rationale behind the abbreviations "m" and "b"?
Re: Rationale for 15C L.R. result order? - Mike Fikes - 09-20-2011
Good question :) Evidently even John Conway put forth a conjecture on this one. (Presumably the John Conway.)
Edited: 20 Sept 2011, 5:28 p.m.
Re: Rationale for 15C L.R. result order? - Crawl - 09-20-2011
My guess: For estimating x.
There already is an estimating y function, but not for x.
To estimate x, you'd do
1. LR
2. CHS
3. y
4. +
5. Swap
6. divide
If the m, b order was different, it seems you'd want to do the same steps, but add an extra swap to get it to what it currently is. So why not have the swap built in?
Re: Rationale for 15C L.R. result order? - Martin Pinckney - 09-20-2011
Quote:It has always been thus...
BTW, what's the rationale behind the abbreviations "m" and "b"?
Re: Rationale for 15C L.R. result order? - Gerson W. Barbosa - 09-20-2011
Re: Rationale for 15C L.R. result order? - Walter B - 09-21-2011
Olá Gerson, obrigado! Interesting article :-)
Re: Rationale for 15C L.R. result order? - Dieter - 09-21-2011
Well, of course real statisticians (tm) know that simple linear regression is just a warm-up for the real thing (multiple linear and nonlinear regression). They usually think further and use models with a larger number of variables. And so we finally get
y = a0 + a1x1 + a2x2 + a3x3 + ...So it's fine that a0 is returned in X and a1 in Y. :-)
Dieter