I am working with a large dataset for regression purposes and am attempting to predict test scores using various societal / demographic factors. There are two scores, math and reading, that I am trying to combine into one. However, I am not sure how to go about this.
Ideally, I would like to create a sort of "composite score" for each county in the dataset based on a combination of its average reading and math scores in standard deviation units from the mean.
For instance, Jefferson County has a reading score of -0.31122487 std. dev. units from the mean and a math score of -0.43663327 std. dev. units from the mean. What would be the most reasonable way to attain a composite score (also in std. dev. units from the mean) so to speak from which to run my regression? I would be applying this formula throughout the dataset. These scores in std. dev. units are the only datapoints provided relating to test scores.
Any help is much appreciated!
I think you are asking how to recover $C = M + V$ (or the z-score of $C$), given the z-score for $M$ and the z-score for $V$. Here, $C$, $M$, and $V$ stand for "combined", "math", and "verbal", respectively. This is not possible without knowing the means and standard deviations of the $M$ and $V$ variables.
The only reasonable thing you could do in the absence of the mean/standard-deviation information is to make the certainly-incorrect assumption that $M$ and $V$ have equal standard deviations, in which case adding their z-scores gives you a z-score for $C$.