T statistic for intercept and coefficient

Question

So, assuming that W0 is the intercept and W1 is the coefficient in a simple linear regression model, the way to calculate a t statistic for W1 is

(W1-0) /std error of w1

Now, my question is how do I calculate the t statistic for W0?

Do I just substitute W1 by W0 in the above equation or is it some other method?

Thank you, in advance.

Answer 1

Test statistic for any individual regression coefficient (this determined whether a specific regressor makes a contribution to the model).

• Null Hypothesis: $H_{0}: \beta_{j} = 0$ where $j$ is the j-th term in the model (intercept or another term).
• Alternative Hypothesis: $H_{A}: \beta_{j} \neq 0$ (significance)

Test Statistic: $t_{obs} = \frac{\hat{\beta}_{j}}{se(\hat{\beta}_{j})}, df = n-k-1$

All of these t-statistics appear in the Analysis of Variance table.

Please note that the test is marginal (i.e. model dependent); therefore, this test does NOT determine whether the specific regressor is important in isolation from the effects of other regressors.