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*

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:

A criticism of this choice is made in "HP-15C: FIRST IMPRESSIONS OF AN HP-41 USER"

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 :-)

*Edited: 20 Sept 2011, 4:09 p.m. *

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.

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"?

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. *

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?

Quote:

BTW, what's the rationale behind the abbreviations "m" and "b"?

It has always been thus...

OlĂˇ Gerson, obrigado! Interesting article :-)

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 = a_{0} + a_{1}x_{1} + a_{2}x_{2} + a_{3}x_{3 }+ ...

So it's fine that a

_{0} is returned in X and a

_{1} in Y. :-)

Dieter