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I'm running a non-linear regression model where my outcome variable is $Y$ and my dependent variables are $GDP$ and $Population$. Sometimes, I want to include $GDP/Population$ (i.e. GDP per capita).

So that my model converges faster, I standardize my variables (i.e. subtract the mean and divide by standard deviation) before I run the regressions.

When I want to include $GDP/Population$ in my regression, should I calculate this variable (using un-standardized values) before rescaling? Or should I use the standardized values of GDP and Population to calculate GDP and population?

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I would rescale after finding $GDP/Population$ because the ratio of standardised GDP to standardised population doesn't represent an interpretable statistic.

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