I am having a little difficulty understanding my results - could someone help me understand how to interpret, and if my process is sensible? Here is an example of what I am doing
I am trying to determine if drug_a, which is a synthetic hormone_a has an affect on hormone_b. First, I have log-transformed the data for hormone_a and hormone_b as they were both positively skewed. Normalization was successful.
When I compare the two groups (on/not on drug_a), the group on drug_a has a lower mean and median log10(hormone_b); this difference was significant (p<0.00) on an independent t-test assuming unequal variance (Levine p<0.05), and mann-whitney u.
At this point - I am thinking "ok, so maybe taking drug_a reduces hormone_b - cool." But, I want to take it a step further. I look to see if there are any other factors that are different between groups. As it turns out, the group on drug_a is older, and (not surprisingly) has a greater level of hormone_a.
So, to determine which factor is driving the difference in hormone_b - I performed a linear regression using hormone_b as the dependent variable. On multivariable linear regression all factors that were included (drug_a, hormone_a, and age) were predictive of hormone_b level. Great, - here is my question though:
The beta-value for hormone_a was positive which suggests that as hormone_a increases, so does hormone_b. This goes against what I expected - what am I missing here?