My model consists of both log independent and dependent variables, and percentage share, as well as number of people and etc. My dependent variable is log(GPD per capita in USD), my statistic package output said "7.9" I would like to ask in this case, how can I interpret the constant term? because it is significant at 1 percent, although I remember asking one of my instructor about necessity of interpreting intercept for linear model. I was told that it is not necessary to do so, however, since I saw that it is highly significant and only a few of my independent variables give significant results. I thought interpreting constant is helpful to know if all independent being set to zero, how much the base GPD per capita in USD will be. Could anyone who is acknowledged about converting this number into absolute USD ? Thank you!
Solved – How to interpret intercept when the dependent variable is in log form
fixed-effects-modelinterpretationlog-linearlogarithmregression
Best Answer
An intercept can be interpreted as the average value of your outcome (dependent variable, in your terms) for the subgroup of observations defined such that your covariates (independent variables, in your terms) are equal to 0. In your case, the outcome is the average of the log GDP per capita, and the estimate of the intercept is 7.9. The corresponding value in levels is exp(7.9), which is roughly equal to 2700 USD per capita. Note that, because the average of the log is not the log of the average, you cannot say that the average GDP per capita on this subgroup is equal to 2700 USD per capita.
Interpreting this intercept is only desirable when you choose your covariates in a way that setting them to zero makes sense. For instance, it makes sense to set to zero a covariate that is a dummy for the country being landlocked. It would make less sense to set to zero a covariate like life expectancy. If you want to interpret the value of your intercept, I would advise to choose your covariates with care, or to transform them (by subtracting the mean, for instance) in a way that setting them to zero results in a sensible situation.
Significance tests the equality of the coefficient to 0. A very significant estimate means that you can reject the null hypothesis that this coefficient is equal to 0. In your case, this is not very interesting, because you would expect that some average of log GDP per capita should always be greater than 0.