# Confidence interval of slope in linear regression

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

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Is this what you're looking for? weibull.com/DOEWeb/… –  Christopher Aden Dec 21 '10 at 19:51

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

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ok thanks, stating the statistic was a mistake. I meant z or t table. –  Justin Meltzer Dec 21 '10 at 19:46

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.

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(+1) It seems to me this advice is complementary rather than countervailing. After all, using Student's t matters when the degrees of freedom are small and that's usually where you can't detect heteroscedasticity anyway. So with lots of data you can check assumptions and protect yourself somewhat with robust SEs and, furthermore, you won't really care whether you're using t tables or z tables. –  whuber Dec 21 '10 at 21:54

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.

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It seems like a contradiction... –  mbq Dec 21 '10 at 20:58
@Firefeather Don't you mean to say "do use" rather than "don't use"?? –  whuber Dec 21 '10 at 21:07
It definitely seems like the poster made a mistake here. –  Dason Dec 21 '10 at 21:07
@whuber: Oops! Thanks for the catch. (Darn it, my reputation is headed the wrong direction now!) –  Firefeather Dec 21 '10 at 21:19
@Firefeather I just sent it back in the correct direction ;-). –  whuber Dec 21 '10 at 21:23