Can I keep a model, where R-square is very low, (0.1361) but the independent variables seem to be very significant?

[Thomas Lehnsherr]

I used 3 indep var.

[Clyde Schechter]

The answer depends on how you want to use the model's results. If your goal is to use the model to predict future outcomes based on the predictors, than a low R² model would not be fit for purpose. But if your goal is to quantify the effects of the independent variables on the outcome, then the relevant things to look at are the coefficients themselves and their confidence intervals: do these suggest that you have with sufficient precision to be useful estimated those effects and can confidently classify them as being important or unimportant in the real world.

Statistical significance itself is not useful, and the American Statistical Association suggests its use be abandoned. See https://www.tandfonline.com/doi/full...5.2019.1583913 for the "executive summary" and https://www.tandfonline.com/toc/utas20/73/sup1 for all 43 supporting articles. Or https://www.nature.com/articles/d41586-019-00857-9 for the tl;dr.

Also, I would point out that R² = 0.1361 is not all that low, depending on the context.

[Mike Lacy]

I recall a joking conversation with a chemist/statistician friend of mine, and he said that if had an R² of 0.6, he would presume that something was wrong because it was way too low, while I as a sociologist would also presume something was wrong but because it was way too high.

[Joro Kolev]

"If you like your regression model, you can keep it !", Barack Obama famously said.

Otherwise the answers to your question would be very tribal, and different tribes would give you different answers.

Econometricians tend to think that the R-squared is not very interesting (if interesting at all), and all that matters is whether you can precisely estimate a causal effect. In other words the interesting thing in a regression is whether you have specified the regression well, and you do not have omitted variables, reverse causality and measurement error, and then whether your causal effect of the variable is precisely estimated (judged by a p-value or confidence interval say).

[Carlo Lazzaro]

Thomas:
as an aside to previous excellent advice, it might well be that 3 predictors only are not enough to give a fair and true view of the data generating process you're investigating.
In addition, please read and act on the FAQ as far as sharing what you typed and what Stata gave you back is concerned. Thanks.
As you can see the previous replies cannot be more than educated guesses (even if based on an outstanding quantitative knowlegde).

[Thomas Lehnsherr]

Thank you.
Btw, my field is management. (I guess that counts a lot in assessing whether the R-squared is reasonable or not.)

[Carlo Lazzaro]

Thomas:
the research field is obviously relevant.
The usual recommendations is to skim through the literature you're familiar with and see what other researchers did when presented with your very same research topic.