[R] Correct interpretation of a regression coefficient

[J C Nash]

Scale can be quite important to success in applying algorithms.
In various of the nlsr, optim and optimx routines, there is provision
for scaling, and though I'm the maintainer / part creator of some
of these, my preference is to build the scale into my (nonlinear)
models. While not all algorithms are affected in the same way,
my experience is that getting the model set up so the parameters
fall in the range .1 to 10 does make things a bit easier to read
and to gauge "strange" results.

Sorry this isn't more prescriptively helpful.

JN


On 2026-03-08 14:15, Brian Smith wrote:
> Hi Michael,
> 
> You made an interesting point that, scale of the underlying variable
> may be vastly different as compared with other variables in the
> equation.
> 
> Could I use logarithm of that variable instead of raw? Another
> possibility is that we could standardise that variable. But IMO, for
> out of sample prediction, the interpretation of standardisation is not
> straightforward.
> 
> On Sun, 8 Mar 2026 at 23:05, Michael Dewey <lists using dewey.myzen.co.uk> wrote:
>>
>> Dear Brian
>>
>> You have not given us much to go on here but the problem is often
>> related to the scale of the variables. So if the coefficient is per year
>> tryin to re-express time in months or weeks or days.
>>
>> Michael
>>
>> On 08/03/2026 11:50, Brian Smith wrote:
>>> Hi,
>>>
>>> My question is not directly related to R, but rather a basic question
>>> about statistics. I am hoping to receive valuable insights from the
>>> expert statisticians in this group.
>>>
>>> In some cases, when fitting a simple OLS regression, I obtain an
>>> estimated beta coefficient that is very small—for example, 0.00034—yet
>>> it still appears statistically significant based on the p-value.
>>>
>>> I am trying to understand how to interpret such a result in practical
>>> terms. From a magnitude perspective, such a small coefficient would
>>> not be expected to meaningfully affect the predicted response value,
>>> but statistically it is still considered significant.
>>>
>>> I would greatly appreciate any insights or explanations regarding this
>>> phenomenon.
>>>
>>> Thanks for your time.
>>>
>>> ______________________________________________
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>>
>> --
>> Michael Dewey
>>
> 
> ______________________________________________
> R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
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> PLEASE do read the posting guide https://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.