Can I include two predictors (A & B) in one regression model if predictor A is dependent on B? I want to include two predictors (total brain volume and corrected gray matter volume) into one regression model in order to predict the level of cognition (dependent variable). However, this corrected gray matter volume is calculated as:
gray matter volume / total brain volume = corrected gray matter volume
making the regression model look like this:
Total brain volume + (gray matter volume / total brain volume) = cognition
Is this statistically sounds or are there issues with total brain volume essentially featuring twice in one model?
 A: Your suggested model for cognition score implies that the influence of gray-matter volume on cognition depends on total brain volume. Another way to investigate this is to do a simple linear regression of cognition on total brain volume and gray-matter volume but include an interaction term between those two predictors. In R this could be coded as:

cognition ~ totalBrainVolume + grayMatterVolume + totalBrainVolume:grayMatterVolume 

or 

cognition ~ totalBrainVolume * grayMatterVolume

don't know the SPSS syntax. This approach has the advantage of documenting how much the correction of gray matter volume for total brain volume, implicit in your model, matters.
A: I think you may have collinearity problem if the gray matter volum and total brain volum are proportional. If two volumes are not very proportional, then I think it might be OK. The followings are some simulations. 
set.seed(123)
y<-rnorm(100,20,2) #cognition
x1<-rnorm(100,10,1) #total brain volume
x2<-rnorm(100,2,1)  #gray matter volume
x3<-x1/x2 #gray mattervolume/total brain volume
x4<-x1/2 #gray matter volume and total volum are proporitonal
fit1 <- lm(y ~ x1 + x3)
fit2 <- lm(y ~ x1 + x4)
summary(fit1)
summary(fit2)


