Do we only use T distribution for confidence interval of Beta for linear regression or we can also normal distribution? Is it that when sample size is less than 30 then we use T distribution else Normal distribution.
2026-04-01 12:18:17.1775045897
Do we only use T distribution for confidence interval of Beta for linear regression or we can also normal distribution?
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Off hand I wouldn't use the normal approximation to the t-distribution unless the number of degrees of freedom is perhaps $100$ or more, but I may change my mind about that after some further thought.
This notion of using $\ge30$ probably comes from confusion of this with a quite different rough rule of thumb: the sum of i.i.d. random variables is approximately normally distributed if there are at least $30$ of them. But that is a quite different rule applied to a quite different circumstance, and in some ways isn't all that good. With a highly skewed distribution, $30$ is not enough, and with a fairly symmetric distribution without outliers, $10$ might be enough for many purposes.
If errors are normally distributed and independent, and all have the same variance, then the t-distribution gives an exact confidence interval for the slope in simple linear regression.