Possible regression biases with GDP [x] vs Health expenditure [y] (both per capita) I am regressing per capita health expenditure on per capita GDP. I have 3 data columns (health expenditure, gdp, population) 

So my regression function is healthexpenditure/population = b0 + b1.(gdp/population)

1) My question will be what are the possible problems of this model? Is dividing dependent and independent variable with population number problematic? This is a theoritical question, I want to explore possible biases in my simple model.

2) Suppose that I have plotted my data and it looks like this. Do you see a problem that are related?
There could be a question of whether your model and graph should be based on a linear relationship or a log-log relationship

The slightly widening residuals apparent in your linear graph seems to understate the real issue illustrated in a linear-axis graph from Gapminder. The green outlier at the top is the USA while the small red outliers on the right are rich but small Gulf and SEAsian countries, and the presence of both of these could exert excessive leverage on your regression coefficients



This left-right disparity in residuals does not look so bad with the same Gapminder data plotted with log-log scales.  It also spreads out the big cluster of developing countries in the bottom-left corner between those which are extremely poor and those which are not so poor and so allows their relative difference to influence your model estimates