# Logarithmic regression of form $y=a+b \log(x_1)+c\log(x_2)$ using R [closed]

How can I fit a logarithmic regression equation of form $y=a+b (\log (x_1)) + c(\log(x_2))$ on a data set using R?

Here the main concern is that data contain zeros multiple times, so R will give infinity in the output.

I have tried adding some constant to the $x$ variables, such as log(x1+0.00001) to avoid Inf but

Is there any specific way to calculate this constant so that results are not affected?

https://dl.dropbox.com/u/53624395/11.csv : LINK FOR DATA FILE ON WHICH I WANT TO PERFORM THE OPERATION.This is time series data and i have to perform logarithmic regression of form y=a+b(logx1)+c(logx2). and find a,b,c and then check is there any such type of relation exists or not.

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## closed as off topic by whuber♦Jan 11 '13 at 15:45

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Why are you transforming the predictors? – Macro Jan 10 '13 at 4:43
Of course results are affected by any change to the transformation. 'Not affected' compared to what? What are you seeking to achieve? Why are you taking logs of something that can be zero? – Glen_b Jan 10 '13 at 6:38
Any statistical package should give infinity. Try remove zeros from your data before modelling. – mpiktas Jan 10 '13 at 8:08
Very closely related: stats.stackexchange.com/questions/30728/…. – whuber Jan 10 '13 at 13:55
@whuber: Okies I have flagged this question for transferring it to stackoverflow. :) thank you. :) – Komal Jan 11 '13 at 15:43

1. You can shift your data ( $x_i\mapsto x_i+\mathrm{constant}_i$)

2. You can try and do $y= a + b \log\left(\frac{x_1}{x_2}\right)$ or similar, you can use a sort of Laplace smoothing in this case $y= a + b * \log\left(\frac{x_1+1}{x_2+1}\right)$

3. You can weight your data such that you kind of kill the very high ones, you can use $t\mapsto e^{-\frac{1}{t}}$ as weight for example.

4. ...etc

It would be easier if you have a data example I guess .. But then it is ups to you to have a play around and see what suits you the best!

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Presumably the subscript $i$ on the constant is a typo. – Scortchi Jan 10 '13 at 12:14
I meant $x1 \mapsto x1+ c_1$ where $c_1$ is a shift for every single component of $x_1$ and same for $x_2$ – dfhgfh Jan 10 '13 at 12:35
Of course, I didn't read carefully enough – Scortchi Jan 10 '13 at 12:59
DATA ON WHICH IT IS TO PERFORMED This is time series data and i have to perform logarithmic regression of form y=a+b(logx1)+c(logx2). and find a,b,c and then check is there any such type of relation exists or not. – Komal Jan 11 '13 at 5:25