What do you do with a non significant parameter in a regression?

Question

This is probably a silly question but when you do a multivariate regression and carry out significance tests and find one of the parameters is not significant, how do you deal with it? Do you just ignore that variable when you estimate the dependent variable?

Answer 1

This is actually a good question. There are a couple different ways to handle this, but you don't want to simply ignore it and estimate the dependent variable with just a portion of the variables in your model. The model will provide better estimates when you use all the parameters, even if some of them are quite small. One thing to keep in mind is that even when coefficients are statistically insignificant, there's no guarantee that they're actually equal to zero; you just can't be sure that they're NOT equal to zero.

Another option is to re-run the regression without the insignificant variable or variables. I realize this might be what you meant, but I'm not sure. All other things being equal, it is better to have fewer variables than many. The choice of whether to leave the poorly-performing variable in the model should be an essentially theoretical one. If you're pretty sure that the variable has some actual relationship, leave it in. If the model makes sense without that variable in, go ahead and run a new one.