What is the implication of having small in-sample mean and standard deviation of the dependent variable?

[Wessel Ster]

Dear all,

I have been trying to search an answer to this question for several hours now. I figured I would try and draw from the expertise of others (as my question might be easy to answer for advanced statisticians).

I am running a panel data regression, with socio-economic development as an independent variable, and a proxy for individualism as my dependent variable. I gathered data from the World Value Survey (aggregated to the country-level) to compute the measure for a scale (0-1) for the individualism-collectivism construct. scores lower to 0 indicate higher individualism, and scores closer to 1 higher collectivism. Now, the in-sample mean and st. dev of this proxy are really small at .7513 and .04690, respectively. I was wondering how this affects the magnitude of my coefficients (for interpretation purposes)?

All help would be greatly appreciated!

Thanks very much.

[Clyde Schechter]

The in-sample mean affects only the constant term (if your regression has one). The standard deviation scales the coefficients. So, for example, if you were to rescale the measure to 0-100, the sd would go to 0.4690, and all of the regression coefficients would increase by a factor of 10 as well. Your standard errors and confidence intervals will also scale by the same factor of 10. Test statistics and p-values will be unchanged.