# Interpretation of regression output for different models

I am quite new to econometrics, hence, not very familiar with interpreting regression outputs. To me, the resources I've found online are quite confusing and cannot give me some practical guidance in interpreting the following regression output similar to one that I have found in a paper:

Background: The analysis should analyse the impact of experiencing a certain common incident on the opinion of people for pro-unification. Survey took place in different regions (10 regions). The incidents can occur in solely 3 different types: A, B and C. We assume that there is no other type of incident. So the general form of the regression is: $$opinion=\alpha + \beta*incident + \epsilon$$. Please note that I left out the subscripts for simplicity reasons. As you can see from the regression output table, the equation given is for the basic model(1).

Let's try to interpret the regression outputs: (1) People who experiencing any kind of event are compared with people who experience no event at all. The coefficient for taking part in any of the 3 incidents is 0.01. The effect is not significant (0.05). (2) Model(1) + individual control variables. Still not significant. (3) Model (2) + seasonal control variables. Still not significant. (8) The opinions of the people who experience type A events are compared towards people who take part in any other type of event or none. The effect is not significant (0.18).

Questions: (4)(5)(6)How to interpret the two coefficients of each of the models? What do we compare here? (7) How to interpret the 3 coefficients of this model? What is the main comparison?

Further:

1. R-squared is very low. Does is mean, that our model does not fit at all? I have read that for observational data, a low R-squared is very common and can be accepted?
2. The survey were taken from 10 different regions. Hence we adjust for country fixed effects by clustering by country. For this regression output, robust standard errors were used. Do you think that for robust SE 10 regions are too less? I have read somewhere that for robust SE, one should have as many clusters as possible?
3. Do these successive models make sense in the order they are right now? Is there a model that would make more sense?

Your help and ideas are very appreciated. Thanks. Also if you have good sources where I can find some practical guidance for such interpretations of regression outputs, please share.

• I rolled back the edits. Vandalism of old questions goes against our rules on this site. See our help center for more details.
– 1muflon1
Jul 13, 2022 at 15:26

## 1 Answer

Questions: (4)(5)(6)How to interpret the two coefficients of each of the models? What do we compare here? (7) How to interpret the 3 coefficients of this model? What is the main comparison?

Assuming that incident $$i, i=[A,B,C]$$ is always a dummy variable, then in (4) the coefficient on incident A tells you what is the additional effect of incident A on opinion of unification controlling for incident. In this case the additional effect would be 0.15 but the effect is not significant so we can't reject the null. Then (5) and (6) tells you the same thing for incident B and C respectively.

Regarding 7, the incident A is presumably dummy that is set to 1 if incident 1 occurs and zero otherwise, so it would tell you the effect of incident A occurring compared to situation when incident A doesn't occur. The same goes for B and C.

R-squared is very low. Does is mean, that our model does not fit at all? I have read that for observational data, a low R-squared is very common and can be accepted?

It is common to have low $$R^2$$ in panels but 0.005 is really low. Typically, depending on field 1% (0.01) - 5% (0.05) would still be acceptable but 0.5% is quite low. However, this is not very surprising none of the main coefficients of interest is significant.

The survey were taken from 10 different regions. Hence we adjust for country fixed effects by clustering by country. For this regression output, robust standard errors were used. Do you think that for robust SE 10 regions are too less? I have read somewhere that for robust SE, one should have as many clusters as possible?

Yes you want to have ideally approximately 40 clusters see Angrist and Pischke Mostly Harmless Econometrics 319. Actually authors recommend 42 clusters but that's just a nod to Douglas Adams The Hitchhiker's Guide to the Galaxy.

You should consider bootstrapped errors, but frankly I don't think it will change much. That's not to say you should still do it but don't expect it to make things significant.

Do these successive models make sense in the order they are right now? Is there a model that would make more sense?

It makes sense to present models as you did in a table to show reader how sensitive the results are. Whether it would make sense to do more is hard to say without knowing more about the research.

• Hi! Thank you so much for the thorough answer. It helped a lot. Jun 14, 2022 at 1:08
• I will look into bootstrapped errors. I have two follow up questions: 1) To me it's quite confusing with using the incident and then another incident_type dummy simultaneously since they are correlated? Why can one use it like this? And in (7) the dummy incident is left out?; 2) For my identification strategy I have also checked for balance of covariates by comparing the means of the covariates of control and treatment (via OLS; covariate on treatment). The R-squared is 0. Any better options for balance check? Jun 14, 2022 at 1:16
• @randomname 1.) yes but as long correlation is not too high (e.g. usually correlation of above 0.9-0.95) you won't have multicollinearity issue (but this is something you might want to check by calculating VIFs - but since R^2 is so low I dont think there is multicollinearity (multicollinearity affects t-stat but not R^2), in any case you can do that as an extra check. 2. As I see it there simply isn't a relationship between the variables of interest and opinion on unification, I don't think doing anything else will yield different results
– 1muflon1
Jun 14, 2022 at 8:02
• @randomname A) clustering doesnt help with endogeneity, it helps with heteroskedasticity or autocorrelation. Also adding controls only helps with endogeneity in a sense that omitted variable bias can be considered form of endogeneity, but if you believe there is some reverse causality you need to use IV. B) I dont think there is any (class of) model that will magically produce high R^2. The problem is that in your case the incidents (and controls as well) have no explanatory power. My suggestion is to find better model in a sense that you will find better controls, and different variable
– 1muflon1
Jun 14, 2022 at 22:48
• of interest since here clearly the incidents have no effect on your dependent variable (unless there is actually some reverse causality so these results are biased). Check what sort of controls people use in literature. C) one last thing that could be a problem is small sample, since you are using parametric model you should have at least 30 observations per independent regressor. D) also goal of science is not to find positive results or high fit (high R^2), if data say there is no relationship between variables then thats a plausible outcome to consider
– 1muflon1
Jun 14, 2022 at 22:49