# 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.

• Please make this question more specific. In its current form it does not conform to the guidelines of this site. It cannot have one definite answer. – mpiktas Apr 24 '15 at 13:26
• There might be some useful discussion here – Glen_b Apr 25 '15 at 19:53

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.
• in my application I try to evaluate the price of a real-estate depending on their characteristics. I'm using the Hedonic-Method. In some papers is written that the semi-log form would be the best, but for different real estates, I got different forms which give the best result. – Paul Apr 27 '15 at 7:25
• but most of the estimations are better when using the semi-log form – Paul Apr 27 '15 at 13:50

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.

• There is a lucid introductory survey within Edward R. Tufte. 1974. Data analysis for politics and policy. Englewood Cliffs, NJ: Prentice-Hall. At the time of writing it's available for USD 2 from www.edwardtufte.com (This kind of stuff doesn't date.) – Nick Cox Apr 24 '15 at 13:50