Regression T Statistic
Overview
Under the assumption of
residual normality
the variable defined as
{% Z = \frac{\hat{\beta}_i - \beta_i}{se(\hat{\beta}_i)} %}
where {% se(\hat{\beta}_i) %} is the estimated standard error of {% \beta_i %},
is shown to be distributed under a
t distribution
P-Value
The p value converts the t statistic to a probability. That is, it is
value of p that returns the t-statistic when (1-p) is plugged into the
cumulative distribution function
of the t-statistic.
It is generally interpreted to mean that the probability that the given coefficient is zero is less than the value of
the p value.
(see
Hypothesis Testing)
As an example, if the p value is less than 0.05, it is interpreted to mean that the probability that the coefficient is zero
is less than 5%.
