Does including both raw  and per capita measures as predictors reduce significance of either predictor? I'm running a regression on independent variables, some of which are measured in different units, for example:


*

*The amount of broadband connections in a country

*The amount of broadband connections in a country per 100 people


Since the second is not perfectly correlated with the first (it is divided by the population divided by 100), I assume there is no issue including both measurements in an OLS regression. The question is, will it diminish the significance of either coefficient?
 A: Whether there's a problem or not is dependent upon the degree of correlation, not whether it's perfect (and dividing by 100 doesn't affect the correlation one bit).  
Yes, what each coefficient will be reduced to, (depending on the regression method) is the unique variance contributed by each of these factors over and above what is contributed by the other factors.  Therefore, they will change.  Let's say I wanted to use height and weight as predictors of self esteem.  These are two correlated variables but let's assume they're not correlated too much and they're allowed in my regression together.  Perhaps I checked the tolerance and it's OK.  When they're both part of the regression then the coefficient I find for height is not a simple effect of height but instead the effect of height that's extra over and above the effect of weight that is correlated with it.  If I had left weight out then the effect of height would include part of the effect of weight (the part correlated with height).
So, not only will the coefficients change in value but the interpretation of them will change as well.  Consider how you would interpret the unique contribution of the amount of broadband connections over and above the amount of broadband connections/country.  Think about that, because that's what your regression would be about with both included.
You might want to consider how you would interpret an alternate regression using the same information.  What if you made raw population and number of connections the two predictors?  They too will be correlated, but far less so.  Now think about what it would mean to have an effect of the number of connections that's over and above the effect of the population.  To me, that's a more sensible idea.  But, it's your study and I have no idea your research questions.
