linear probability model interpretation I have a question regarding the interpretation of a log independent variable in a linear-probability model.
For example: I have $\log(GDP)$ as my independent variable and the coefficient is 0.35. Can I then interpret the result as follows: A one UNIT increase in the log of GDP is associated with a 3.5% increase in the probability that $Y = 1$?
I know that this question was answered elsewhere, however, people talked about a PERCENT instead of unit increase and this confused me.
 A: If your $y$ variable is binary, i.e. 0 or 1, then one interpretation of your coefficient can be is as follows: a one unit increase in log GDP would increase $y$ by .35. 
But let's clarify your other area of concern. Let's express this model as follows
$$y_{i} = \beta_{0} + \beta_{1}log(GDP_{i}) + u_{i}.$$
If $y_{i} \in [0,1]$, then we can think about the dependent variable as measured in terms of percentage. Right? Recall $\Delta{log(x)} \approx \%\Delta x$. What happens when we add a little extra to GDP? Let's call the new dependent variable $\tilde{y}_{i}$. Hence, we can write the following
$$\tilde{y}_{i} - y_{i} = \beta_{1}\left\{log(GDP_{i} + \delta) - log(GDP_{i})\right\}.$$
Hence, 
$$\beta_{1} = \frac{\tilde{y}_{i} - y_{i}}{log(GDP_{i} + \delta) - log(GDP_{i})}$$.
Therefore, if the change in $y$ is very small, we can think of numerator as a percentage point change in $y$. Thus, it has the interpretation of elasticity, i.e. $\beta_{1}$ is the percent point by which the dependent variable responds to a given percentage change in the independent variable. Hopefully that clarifies both areas of confusion for you!
