# Interpretation of coefficients and their confidence intervals in a regression analysis

Note: apologies in advance if this is a duplicate, I didn't find a similar q in my search

Can you compare two independent variables and their confidence intervals in a regression model?

I am running a regression model exploring the effect ethnicity and immigration status has on British identity. I have used White British people as my control group.

The table shows, for example that their is enough evidence Second Generation Indians have a stronger British Identity than White British people.

But given the confidence intervals. Could I also state that Second Generation Indians (with a coefficient between 0.544 and 1.819) have a stronger British identity than First Generation Indians (with a coefficient between -0.357 and 0.417). Or does this go beyond what a regression model should be used for? Should I even interpret coefficients that are not statistically significant?

• Using a separate contrast you can compare First Generation Indians with Second Generation Indians. Alternatively, you could refit your model using First Generation Indians as the reference group. This will produce a coefficient representing the desired comparison. Commented Dec 5, 2021 at 14:41
• Just a little note: Infinite loglikelihood sounds bad (bottom of your table), you should check if something went wrong during model fitting. Or maybe I am missing something? Commented Dec 5, 2021 at 16:17

It's appropriate to briefly discuss/mention any coefficient's value, but if it's not significant, you have to briefly end any statement with "but it's not significant." It also depends: some readers/audience may wonder why you are discussing a predictor that wasn't significant. Whereas molecular biology lab directors need to know if a predictor has a p-value that's less than 0.1, so they can determine its biological importance and then consider increasing the sample size if it's biologically meaningful/interesting. Other audiences will expect you to apply an e.g. Bonferroni correction to all the p-values in a table, by adjusting $$\alpha=0.05$$ to be $$\alpha^* =0.05/\#\mathrm{tests}$$. So while you may see significant predictors in the table, someone in an audience will have already applied the Bonferroni adjustment to your p-values in their head and may see nothing! This latter case is usually what happens for conservative reasons.