[R] Correct interpretation of a regression coefficient

[Richard O'Keefe]

You have run into the fact that "is it there" (statistical significance)
and "does it matter" (practical significance) are two different things.  As
to whether the coefficient is of practical significance, looking at its
bigness is not the way to go.  A small coefficient multiplying a large
variable can have a large result, just as a large coefficient multiplying a
small variable can have a small result.

One thing you can do is to fit your model and then use the ?drop1 function
to see the effect of dropping each coefficient from the model.  You might
even use ?step with direction="backward" for this if there are other
coefficients you think might be unnecessary.

Perhaps the

On Mon, 9 Mar 2026 at 00:51, Brian Smith <briansmith199312 using gmail.com> 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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