Confidence interval of slope in linear regression

Question

When computing a confidence interval of slope in linear regression, should you use the z- or t-statistic?

Answer 1

If you're doing linear regression using least squares, you should use base confidence intervals on Student's t-distribution.

Answer 2

Depends on assumptions on your disturbances. If they are normal and homoscedastic, then yes use t-statistic. In economic applications though these assumptions rarely hold, so in that case I would suggest using z-statistic with robust standard errors.

Answer 3

Rule of thumb: Use Student's t distribution if you must estimate the variance.

Since the distribution's variance is estimated (not known), you should use Student's t distribution rather than the standard normal distribution (z), which requires a known variance.

Although the t distribution becomes almost exactly the same as the z distribution when the degrees of freedom (think size of the sample) are large, it is (in my experience) quite rare that the z distribution is used instead of the t distribution in cases like this.