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In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values?

I'm currently conducting a spatial regression analysis. I'm trying to decide whether my response variable needs to be log transformed. I understand that regression analyses assume normality of the residuals. I also understand that the best way to calculate how close to normality the data is is by inspecting the skewness/kurtosis figures (closer to 0 the better).

The stats package I'm using (S.A.M.) gives two different figures for both skewness and kurtosis. One is for the response variable data and the other is the skewness/kurtosis of the residuals. I'm a bit confused as to which of these figures is the one I should be concentrating on, the response variable skewness or the residuals skewness?

I hope this all makes sense.

Many thanks for any help

Ben

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Ben Coleman
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    Several questions appear to already answer this question, What if residuals are normally distributed, but y is not? and Left skewed vs. symmetric distribution observed. The only thing I would note is though you should look at the distribution (via a QQ-plot or a histogram) and not solely rely on estimates of skewness. – Andy W Feb 03 '12 at 13:06
  • ok thanks, I have a histogram of the residuals from both a log-transformed and a non-transformed analysis however it is hard to see which is the closer to normal distribution by eye. This is why I'm using the skewness figures to help me. In the log transformed analysis the response variable skewness is lower, however in the residuals skewness the non-logtransformed is lower. I understand that for a regression analysis it's the residuals being normally distributed that's important, so therefore is it the residuals skewness that's the more important figure? many thanks – Ben Coleman Feb 03 '12 at 14:14
  • Histograms are poor tools for evaluating normality, Ben. Use a q-q plot. This will show you specifically how the residuals deviate from normality. That enables you to make better decisions about their possible effects on the regression. (This is one of many reasons why only inspecting summary statistics like skewness, kurtosis, or the K-S statistic is not a good default way to evaluate residuals.) – whuber Feb 03 '12 at 15:01

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