T-Test of a Regression Coefficient

Where [math]\displaystyle{ \hat{\beta} }[/math] is a coefficient, [math]\displaystyle{ n }[/math] is the effective number of observations (note that this is different to the effective sample size where repeated observations exist for each respondent) and [math]\displaystyle{ se_{\beta} }[/math] is the standard error of the coefficient, the test statistic is:

[math]\displaystyle{ t=\frac{\hat{\beta}}{se_{\beta}} }[/math],

where:

[math]\displaystyle{ p = 2\Pr(t_{n-k} \ge |t|) }[/math],

[math]\displaystyle{ k }[/math] is the number of parameters, including the intercept (where applicable).