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Can I use log-log/linear regression models by taking the natural logarithm of some variables?

Imagine I have a dependent variable $y$ and independent variables $x_1$, $x_2$, and $x_3$. Can I run the following regression:

$$\log(y) = \log(x_1)+\log(x_2) + x_3$$

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  • $\begingroup$ What is name of that model?log(y)=log(x1)+log(x2)+x3 $\endgroup$
    – hifza kanwal
    Jul 5 at 5:09

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You can absolutely mix logged and unlogged variables on the right hand side. For example, one never logs dummy or negative variables for obvious reasons.

However, I do think it is good to have principled reasons for doing this in your analysis.

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