Linear regression interpretation

[Arina Pershina]

Hello!

I want to build an OLS model where the independent variable is the number of technologies used in the company, the dependent one is a financial indicator (e.g., cost savings). The initial IV distribution is not normal, because the number of 0 is large, for this purpose it is supposed to take log(x+1) to make a distribution normal.

Assuming that the model is constructed, the results need to be interpreted. Since the logarithm of IV is taken, "if X changes by 1%, DV ...". Returning to the fact that the independent variable is the number of technologies, the wording about a 1% change sounds very wrong.

Can you give me a hint on how to deal with this situation?

[Nick Cox]

There is no rule that any marginal distribution of any variable in regression must or even ideally should be normal, and in any case no guarantee whatsoever that log (x + 1) is normally distributed tor any variable x. A good way to see that is to appreciate that indicator variables with values (0, 1) are standard as predictors in regression, but there is no scope to transform their distributions to anything but another pair of spikes.

As you appear to have just two variables, a starting point for any advice is just a scatter plot. It could well be that zero is special for either variable, but that has to be thought through on e.g. economic grounds.

Note that something like

lpoly y x, bw(0.2)  biweight

has a helpful effect of plotting conditional means of y for integer x. It may even suggest that the model you want could be

regress y i.x

(or ANOVA!)