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It is common to taking logs of variables when perform a regression analysis. But the observations will become negative after logs transformation when it is less than 1. Is this the possible concerns? (e.g. log(0.5) = -0.6931, but log(5)= 1.6094)

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    $\begingroup$ Can you use negative temperatures in a weather forecast or does it break the regression? $\endgroup$ – Giskard Sep 6 '16 at 13:42
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    $\begingroup$ If your variables of concern are always positive, and your regression extrapolates to give a negative prediction, you could have problems. But if you have taken logarithms and then get a negative prediction then take anti-logarithms (exponentiation if working in base $e$) of that to give you a positive result $\endgroup$ – Henry Sep 6 '16 at 13:50
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    $\begingroup$ @Henry I do not understand. Why would it be a concern that the predicted value of log of a variable is negative? This does not make the variable itself negative. $\endgroup$ – Giskard Sep 6 '16 at 14:22
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    $\begingroup$ @denesp: exactly the opposite. If you are modelling, for example, hours worked, and your extrapolation gives a negative result for certain circumstances, that may be an issue. But if you are modelling logarithms of hours worked and your extrapolation gives a negative result for certain circumstances, that is less of a problem as it translates into a small positive number of hours ($\lt 1$) $\endgroup$ – Henry Sep 6 '16 at 14:26
  • $\begingroup$ What is the underlying problem you are tring to solve? The question as it stands is barely meaningful. $\endgroup$ – EnergyNumbers Nov 13 '16 at 16:37
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As stated already there is no problem if log(x) is negative. However, you would want to be careful if x=0 or if x<0 because then the logs are undefined. So as long as x>0 then there are no problems at all.

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No, $\log(x)$ being negative is not a problem what so ever.

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