Linear Regression modeling with effect on/off and when on, effect is measured Consider a student dataset with parameters grades (GPA), do they have a computer (COMP), and if yes, how old (AGE), and other parameters (ETC).
I want to measure the effect of having a computer on the GPA, but also, the age of the computer that you use. If my linear regression model is:
GPA = COMP + AGE + ETC 

Then, when {COMP = 0; AGE = 0} (someone with no computer), but AGE being 0 means that their computer is new. I can't make AGE starts at 1 and keep AGE=0 for COMP=0 because the distance between AGE=0 and AGE=1 means nothing.
I think I should have an interaction variable:
GPA = COMP*AGE + ETC

where AGE starts at 1, so that it doesn't nullify COMP when the computer is new.
Is this the correct approach to capture effects that are on/off, and when the effect is on, we measure something about it?
 A: This is a bit too long for a comment. If one separates the data into two populations, with and without a computer, one can first check (curiosity) if the the GPAs are different in those categories (using a Mann–Whitney U test if not normal, and independent t-test if normal). 
Next, one can perform two regressions, both with the other factors, and the one including computer age and one without computers. These will produce n and m estimates of the GPA and as well one can check their separate correlations to the GPA subsets (and an independent r-value test). 
One can then test if the GPA estimates are significantly different between groups and in what direction. Then, one can combine both estimates of GPA to see how the combination plots (two color) and correlates to measured GPA. Next, one can test for difference of variance (With Levene's test if normal and Conover squared-ranks test if not) of 1) GPA(predicted with computers' age)-GPA(measured with computers) compared to 2) GPA(predicted without computers)-GPA(measured without computers). This would again give some indication of how well the GPA is predicted comparatively in both groups. 
A bit of warning, I would not just try multiple linear regression of the linear combinations of variables, but would, as usual determine if data transforms (logarithms, exponentiation, reciprocals, roots and powers, offsets, and mixtures of these) produce more accurate results, I would try also poly fitting, poly fittings of logarithms, etc. Finding the proper method of regression is an art form, but can improve the predictive ability of the result multiple fold. Using weights, regularization, multiple linear median regression, bivariate regression, maximum likelihood and other robust techniques may be useful.
