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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

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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.

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  • $\begingroup$ Maarten, thanks for the clarification. I see, it definitely made sense to ask here. Just to make sure I got it right. If y is a percentage value, an increase of 1 units of x would yield to an increase of 4803 % of y? And if x would get multiplied by 100, the coefficient is about 0.048, that would mean if x increases 1 unit, y would increase by 4,8%? $\endgroup$
    – Sam
    Sep 17, 2022 at 10:21
  • $\begingroup$ 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 $y$. $\endgroup$ Sep 17, 2022 at 10:53

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