Definition

Assume that $y \sim N_{n} (X β, I_{n} σ^{2})$ The null hypothesis $H_{0} : β_{j} = β_{j, 0}$ can be tested with the test statistic $t_{j} = \frac{β ^ _{j} - β _{j, 0}}{SE ( β ^ _{j} )} \sim t (n - p)$ where $SE (\hat{β}_{j})$ is the Standard Error for Regression Coefficient $β_{j}$ .