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      <text>43.1.4.1 Significance testing for regression</text>
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      <text><![CDATA[<h3>Significance testing for regression</h3>

Note that the results in this Section apply to the simple linear model only. Some additions are necessary before the results can be generalized.

The discussions so far pre-suppose that a linear model adequately describes the relationship between
the variables. We can use a significance test involving the distribution to decide whether or not \(y\) is
linearly dependent on \(x\). We set up the following hypotheses:
\[ H_0 : \beta = 0 \hspace{1cm} \text{and} \hspace{1cm} H_1: \beta \neq 0 \]

<div class="HELM_keypoint">
<h4>Key Point</h4>
<p><b>Significance Test for Regression</b>&nbsp;</p><p>The test statistic is
\[ F_{test} = \dfrac{SS_R}{SS_E/(n-2)} \]
where \(SS_R = SS_T - SS_E\) and rejection at the \(5\%\) level of significance occurs if
\[F_{test} &gt; f_{0.05, 1, n-2} \]
</p>
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Note that we have one degree of freedom since we are testing only one parameter \( (m)\) and that \(n\)
denotes the number of pairs of \( (x, y) \) values. A set of tables giving the \(5\%\) values of the \(F\)-distribution is given at the end of this Workbook (Table 1).]]></text>
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