Dear all!
i am not sure how to interpret a log transformed dependent variable Y and a non-transformed independet variable X when beta is high.
In my example the regression coefficient (beta) of the independet variable is 13.061.
To interpret this, i would calculate the following: 100 * (exp(β)−1) = 100 * (exp(13.061)-1) = 47.023.971,4 %
So a one unit increase in X would lead to a 47.023.971,4% increase in Y? I think this interpretating does not make sense, when the coefficient is high.
Is there any alternative way to interpret the "high" beta coefficient?
Thank you for your answer ind advance!!
Hello Lena,
If "beta" is the unstandardized regression coefficient, then "one unit increase in X" means an increase of one score point on whatever the X scale happens to be; if "beta" is the standardized regression coefficient, then "one unit increase in X" means an increase of one standard deviation on the X scale, not one score point.
If the DV is routinely reported/interpreted as (natural) log units, then don't bother with the exponentiation. Variables which have huge ranges, positively skewed distributions, and/or non-linear (e.g., exponential, geometric) relationships with other common variables are often candidates for being reported using log scales.
For (unstandardized) B = 13.061, each one score point increase in X is estimated by the model to yield a 13.061-point increase in Y (in log units). That's a pretty potent independent variable. On the untransformed Y scale, that would imply an increase of ~ 470,204 units (which, for me, argues for the use of transformed scores). With such a value, I don't see the utility of trying to express this as a percent increase.
For (standardized) regression coefficient = 13.061, each one SD increase in X is estimated by the model to yield a 13.061 SD increase in Y (in log units).
Good luck with your work.
Having such a large β when the dependent variable (Y) is log-transformed is often an indication that the nominator is very close to zero. You should check this and evaluate if these small (close-to-zero) values make sense and if they are determined with sufficient precision, and if the log-transformation is valid for such small values (is the relationship still log-linear in this range?).
When β refers to the contrast of "group B vs. group A", and Y is almost zero in group A, then log(Y) is almost minus infinity in group A and β is almost plus infinitity.
First of all: why would you do this log-transformation?
Method Non-linear regression -Why you shouldn't take the logarithms...
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