I am undertaking a study looking at patients with AF (a heart rhythm disorder).

I'm looking at how continuous baseline variable (X) predicts a improvement (a continuous measure of function) (Y) after a discrete treatment.

I plan on using regressional analysis after collecting the before and after data in my cohort.

My question is-

I want to look at lots of other independent variables in the same cohort (e.g. hair colour, height, age, blood tests) for association with Y.

1. Can I do this by simply replacing the new variable with X and plotting a new regression chart? (Assuming independence).

2. Do I need to increase my sample size if I am doing this additional variable analysis.

Thanks very much for your help with this,

Nick