Consider the linear regression equation:
y_i = w_0 + \mathbf{w}^T\mathbf{x}_i + \epsilon_i = w_0 + \sum_{j=1}^d w_jx_{ij}+\epsilon_i$$ where the value of $\epsilon$ can be modelled using normal distribution:\epsilon_i \sim N(0, \sigma^2), \\ i = 1, \ldots, N
\frac{\hat{w}j - w_j}{s{\hat{w}j}} \sim t{N-d-1}, \\ j = 0,\ldots, d