I would like to know how to interpret the coefficient if the DV is in log while IV is in not in log but the value is in percentage (interest rate). As far as I know, if DV in log, the coefficient of B should be times with 100. However, I am not sure in the case of IV in percentage. Do we still need to multiply by 100?
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Presumably regression is implied. – Nick Cox Nov 15 '15 at 14:33
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This issue is discussed in detail in this CV thread on the log transformation.
Graham Cookson's response is explicit in providing the following interpretations for the four combinations of logged vs not logged response and predictor variables:
Y and X -- a one unit increase in X would lead to a β increase/decrease in Y
Log Y and Log X -- a 1% increase in X would lead to a β% increase/decrease in Y
Log Y and X -- a one unit increase in X would lead to a β∗100 % increase/decrease in Y
Y and Log X -- a 1% increase in X would lead to a β/100 increase/decrease in Y
The nuance in the case of your question is how this is handled wrt percentages. The same question would hold for all four combinations of logged vs not logged variables. The answer would have to be software specific in terms of how a percentage is stored, formatted and, subsequently, analyzed, e.g., Excel would do this one way, whereas SAS, R or Matlab might handle it another.
In this way and depending on how, e.g., 79.74% is stored (i.e., is it 0.7974 or 79.74?) would alter the interpretation and inference.
Given that, I would test a few possible values to see how percentages are handled by your software.
Mike Hunter
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On the reference to Graham Cookson's answer: Answers in a thread can change position for various reasons, so it is simplest not to refer to position at all. I've edited accordingly. – Nick Cox Nov 18 '15 at 01:05