[Question] How to tell if coefficient standard error is high or low when compared to estimated coefficient?

Generally, you'll ask yourself if your estimate is statistically significant, that is, if the data provides evidence this parameter you've estimated isn't actually zero. The simplest way to assess this possibility is with a t-test.

The procedure is quite simple:

  • Calculate t-statistic by dividing the point estimate by the standard error
  • It has a Student-t distribution with n-1 degrees of freedom, where n is your sample size.
  • Calculate the probability of the t-statistic you have, let's call it p.
  • (1-p) is the estimate's p-value. The smaller it is, the better.

The t-statistic of this estimate is 7.257, which is quite good. In general, with modest sample sizes, anything above 2.5 will yield a p-value smaller than 5% - which is the threshold most of us use in practical applications.

Note that small p-values aren't all there is to properly estimating a model.

/r/statistics Thread