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      <text>43.1.1.2 Regression</text>
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      <text><![CDATA[<h3>Regression</h3>

<p>As we have already noted, relationship(s) between variables are of interest to engineers who may
wish to determine the degree of association existing between independent and dependent variables.
Knowing this often helps engineers to make predictions and, on this basis, to forecast and plan.
Essentially, regression analysis provides a sound knowledge base from which accurate estimates of
the values of a dependent variable may be made once the values of related independent variables are known.</p>

It is worth noting that in practice the choice of independent variable(s) may be made by the engineer
on the basis of experience and/or prior knowledge since this may indicate to the engineer which
independent variables are likely to have a substantial influence on the dependent variable. In summary, we may state that the principle objectives of regression analysis are:&nbsp;<p><br></p><div class="editor-indent" style="margin-left: 30px;"><p>&nbsp;(a) to enable accurate estimates of the values of a dependent variable to be made from known values of a set of independent variables;</p></div><div class="editor-indent" style="margin-left: 30px;"><p>&nbsp;(b) to enable estimates of errors resulting from the use of a regression line as a basis of prediction.</p><p><br></p></div>


Note that if a regression line is represented as \(y = f(x)\) where \(x\) is the independent variable, then
the actual function used (linear, quadratic, higher degree polynomial etc.) may be obtained via the use of a theoretical analysis or perhaps a scatter diagram (see below) of some real data. Note that a regression line represented as \(y = f(x)\) is called a <b>regression line of \(y\) on \(x\).</b>]]></text>
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