F-Test
Overview
The F-Test tests the overall significance of a regression. That is, it tests the hypothesis
{% \beta_1 = \beta_2 = ... \beta_n = 0 %}
The test is dependent on the assumption of
normality.
Analysis of Variance (ANOVA)
Using the techniques of
Analysis of Variance (ANOVA),
it can be shown that
{% F = \frac{ESS/df}{RSS/df} %}
is distributed as the
F distribution
, where
{% TSS = \sum y_i ^2 %}
and
{% ESS = \beta_1 \sum y_i x_{1,i} + \beta_2 \sum y_i x_{2,i} ?+ ... + \beta_n \sum y_i x_{n,i} %}
