How to interpret a regression table with logged DVs?

Question

I'm writing a research paper and am using R for my quantitative analysis. I'm using OLS regression and have needed to perform a log transformation on my dependent variables for linearity however I don't understand my regression table anymore and was hoping someone could help me to interpret it.

In order for the log regression to run I needed to filter the zeros using this code, which could explain also why my results looks different as well as the effect of the log: Code to get rid of zeros

Without the log, it used to look like this:

After the regression, it looks like this:

Answer 1

very nice analysis, thanks for sharing them.

Several suggestions:

• To make reports comparable consider to apply 'filtering zeros' in both reports. Currently you applied the filter only for the log models.
• Or as an option instead of using transformation log(tax) do the log(tax+1). In this case tax=0 will be mapped to log(1+0) = 0. This will allow to use even zero datapoints. Of course this will change the models accuracy.

Back to your reports. The reports are very brief (compared to standard OLS regression report). Thus based on the numbers you provided you can judge: 1)quality of the models and 2) the significance of variables.

Model quality

• First of all look on Adjusted R2. The higher the R2 the better the model. R2 shows % of the dependent variable explained by factors. For example 44.5% of log-tax model is explained by factors. To sum up log models show higher predicting power. But of course this might be because you have filtered part of the dataset for building log-models.

Effects direction and effects significance

• Then you can check which coefficients turned to zero. For example Num Employees was an important factor (non zero with three stars) in predicting tax and is zero in log tax model. Here you should use an expert opinion to decide which model shows true relationship, i.e. does num employees have any effect on tax or not and etc.
• Pay attention to sign of the factors. For example in tax model Num Employees coefficient is -14.347. This means that Num Employees have negative effect on taxes, i.e. the more employees you have the lower are taxes.
• Finally you should pay attention to stars near each coefficient. Three stars near a factor coefficient means that the factor is important for the model and the model will be much weaker if you'll exclude the factor. Coefficients without start are called insignificant. Such coefficients may be excluded from the model without significant drops in R2 (predicting accuracy). Or more simply speaking we are not sure that they are not zeros. Yes, in the table you might see non-zero values, but there is a high probability that actually the effect is zero. Usually you need more data to become more sure about such factors. For example, let's check EM 2022 in log-tax model, the coefficient is -13.998, while this is a big value it doesn't have the stars, thus insignificant. So there is still high probability that might be zero what means that factor EM 2022 doesn't affect the log-tax. In such cases you can't say that the EM 2022 have negative effect on the log-tax, you say that effect is negative, but insignificant, thus we can't rely on this negative relationship.