[R] Correct interpretation of a regression coefficient

[David Stevens]

Hi Brian,

This phenomenon is sometimes known as 'distinction without a 
difference', with 'distinction' referring to whether a parameter (in 
this case the regression coefficient) is identifiable, based on the 
experimental design. With enough observations of high precision, even 
scientifically insignificant quantities can be distinguished 
statistically. 'Difference' refers to the science - is this difference 
important to the scientific process? R can't make that judgment. That's 
the job of the domain scientist.

David K Stevens, PhD, PE, Professor Emeritus
Civil and Environmental Engineering
Utah Water Research Laboratory
Utah State University
8200 Old Main Hill
Logan, UT 84322-8200
david.stevens using usu.edu
(435) 797-3229 (office)

On 3/8/2026 4:50 AM, 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.
>
> ______________________________________________
> R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide https://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.