Confidence Interval for Regression Coefficient

Definition

Assume that $\mathbf{y}\sim N_n(\mathbf{X}\mathbf{\beta },{\mathbf{I}}_n{\sigma }^2)$ The $100(1-\alpha )\%$ confidence interval for ${\beta }_j$ is defined as ${\hat{\beta }}_j\pm t_{\alpha /2}(n-p)SE({\hat{\beta }}_j)$ where $SE({\hat{\beta }}_j)$ is the Standard Error for Regression Coefficient ${\beta }_j$, and $p-1$ is the number of explanatory variables.