How to interpret the coefficient of a limited independent Variable (Index)?

I assume this is a very simple question, however I am not sure about it.

I have a regression table in front of me that contains the coefficients of a linear regression. The dependent variable is scaled metrically, the independent variable of interest is an index limited from 0 to 1. If I want to interpret the influence the index has on the dependent variable (lets suppose 4.803), what is correct:

1. If the indepvar increases about 1 unit, the depvar increase about 4.803.
2. If the indepvar increases about 1 percent, the depvar increase about 4.803.
3. If the indepvar increases about 1/100, the depvar increase about 4.803.

I am relatively sure that it has to be 2 or 3, because 1 would imply an increase of the indepvar from 0 to 1.

I would appreciate a short comment on that. Thanks in advance!

Kind regards Sam

Well, it is actualy 1). A regression coefficient is just the change in $$y$$ for a unit change in $$x$$. It is up to us humans to make sure that the unit of $$x$$ is meaningfull. For example, we could multiply $$x$$ by a 100 before including it in our regression model to get interpretation number 3.
• Linear regression is not about percentages, it is just an absolute change. It is just additive. For one unit change in $x$ you get $\beta$ units more/less of $y$. Sep 17, 2022 at 10:53