Sampling Distribution Of The Slope

The normal distribution is applicable when the residuals are heavily skewed.

The sample slope always follows a normal distribution independent of sample size.

When the sample size is small (e.g., $n = 15$), the statistic $\frac{b - \beta}{s_b}$ follows a t-distribution with $df = 15 - 2 = 13$.

A t-distribution with $df = n - 1$ is used to test the slope.