fair interpretation of regression result

[Akira Ito]

Hi all,

I am trying to find a proper way to interpret regression results.
To discuss economic significance of the coefficient, some papers interpret their results like the following:
One unit increase in X increases Y by [coefficient of X], which is 20 percent of the mean value of Y variable.

It sounds okay, but I don't think it is always a fair method.

My outcome variable varies between -50 and 50. The mean value is about 3.
The regression results say one unit increase in X variable increases Y by 2.6, which is 87 percent of the mean value of Y.
I don't think this is a fair interpretation because the range of Y is -50 to 50.
If the range is somehow adjusted to from 0 to 100 and the mean value of Y is, therefore, 53,
the interpretation becomes like "one unit increase in X variable increases Y by 2.6, which is 5 percent of the mean value of Y. "

Is there a better way to explain the result?

[Clyde Schechter]

You are right, if your variable does not have an absolute location for its range, then referring to percentage of the mean is meaningless. The reasonable way to report it is that a unit increase in X is associated with a 2.6 unit increase in Y. There's nothing more to say, and that's very, very understandable. Leave it there. Percentages are just not applicable to this kind of Y variable.

By the way, since you want to represent your results fairly, you should definitely avoid saying that an increase in X increases Y... because that implies causality. Unless you are dealing with experimental data, or have some other compelling reason to think of the relationship as causal, you should only say that an increase in X is associated with some change in Y.