Differences between log-log, semi-log and linear regression Can somebody please explain the differences between using the in the linear/semi-log/log form and also pros and cons of each other.
 A: Terminology differs greatly among (sub-(sub-))disciplines, but I suspect you mean just a linear regression where both the y and the x are log transformed (log-log), where either the y or the x is log transformed (semi-log) or both the y and x are not transformed (linear).
The pros and cons just boil down to what fits the data and/or theory best.
A: Pick the transformations that make logical sense for you application. Before you see the data, how do you think changes in $x$ affect changes in $y$? 


*

*For $y = a + bx$, $\Delta y = b\Delta x$. Meaning, a 1 unit increase in $x$ results in a $b$ unit increase in $y$. 

*For $\log(y) = a + bx$, $\%\Delta y = b\Delta x$. Meaning, a 1 unit increase in $x$ results in $y$ being multiplied by $(1+b)$. 

*For $y = a + b \log(x)$, $\Delta y = b\%\Delta x$. Meaning, a doubling in $x$ results in a $b$ unit increase in $y$.

*For $\log(y) = a + b \log(x)$, $\%\Delta y = b\%\Delta x$. Meaning, a doubling in $x$ results in $y$ being multiplied by $(1+b)$. 

*If none of these interpretations make sense for your application, you might need a different transformation. 

