# How to compute goodness of fit after applying logarithmic transformation?

I want to estimate the parameters of a function of general form $y = a \cdot x^b$. I applied a log-log transformation to obtain a linear function of the form $\log y = \log a + b \times \log x$. I have fitted the linear model in MATLAB.

MATLAB computes the goodness of a fit in terms of sum of squares error (SSE) and (adjusted) R bar. I want to report these numbers but they are probably meaningless given that in fact $\log a$ and not $a$ has been estimated. How do I fix this?

• what kind of fix do you want? If your true model is $y=a\cdot x^b\cdot\varepsilon$, where $\varepsilon$ is the log normal, then all the statistics from the linear model are meaningful. Jun 20, 2011 at 10:52
• @mpiktas I need to transform the fitted value for log a back by doing this: a = exp(log a) Jun 20, 2011 at 13:42
• @mpiktas I can also transform the 95% confidence bounds back in the same way. So, how do I compute the statistics from the linear model given one of the two parameters has been exp-ed? Jun 20, 2011 at 13:51
• you can use delta method, look at the corresponding wikipedia page and the link given at the end of that page. Jun 20, 2011 at 20:36