Analysing the ANOVA table

Let’s go back to lecture 6 where we met the ANOVA.

The F statistic value: MS\(_\mathrm{model}\)/MS\(_\mathrm{residuals}\) provides a test statistic that allows us to test whether there is any evidence that at least one of the model parameters is not zero.

\(\newline\) The null hypothesis is

\(\newline\) H\(_0: \beta_1, \ldots, \beta_k = 0\).

\(\newline\) which will be tested against the alternative that at least one of the parameters is not zero. If the null hypothesis is true, the statistic has an F(Df\(_\mathrm{model}\), Df\(_\mathrm{residuals}\)) distribution. This implies that

\[F = { MS_\mathrm{model} \over MS_\mathrm{residuals}} \sim F(Df_\mathrm{model}, Df_\mathrm{residuals}). \]

If H\(_0\) is false, we would expect MS\(_\mathrm{residuals}\) to be smaller than MS\(_\mathrm{model}\) and so large values of F should lead us to reject H\(_0\). i.e. for large values of F the p-value will be small.