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    <h1>Calibration data from Massart et al. (1997), example 3</h1>
    
    <div class="hidden name"><code>massart97ex3.Rd</code></div>
    </div>

    <div class="ref-description">
    
    <p>Sample dataset from p. 188 to test the package.</p>
    
    </div>

    <pre class="usage"><span class='fu'>data</span>(<span class='no'>massart97ex3</span>)</pre>
        
    <h2 class="hasAnchor" id="format"><a class="anchor" href="#format"></a>Format</h2>

    <p>A dataframe containing 6 levels of x values with 5
  observations of y for each level.</p>
    
    <h2 class="hasAnchor" id="source"><a class="anchor" href="#source"></a>Source</h2>

    <p>Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong, S., Lewi, P.J.,
  Smeyers-Verbeke, J. (1997) Handbook of Chemometrics and Qualimetrics: Part A,
  Chapter 8.</p>
    

    <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
    <pre class="examples"><div class='input'><span class='fu'>data</span>(<span class='no'>massart97ex3</span>)
<span class='fu'>attach</span>(<span class='no'>massart97ex3</span>)</div><div class='output co'>#&gt; <span class='message'>The following objects are masked from massart97ex3 (pos = 3):</span>
#&gt; <span class='message'></span>
#&gt; <span class='message'>    x, y</span></div><div class='input'><span class='no'>yx</span> <span class='kw'>&lt;-</span> <span class='fu'>split</span>(<span class='no'>y</span>, <span class='no'>x</span>)
<span class='no'>ybar</span> <span class='kw'>&lt;-</span> <span class='fu'>sapply</span>(<span class='no'>yx</span>, <span class='no'>mean</span>)
<span class='no'>s</span> <span class='kw'>&lt;-</span> <span class='fu'>round</span>(<span class='fu'>sapply</span>(<span class='no'>yx</span>, <span class='no'>sd</span>), <span class='kw'>digits</span> <span class='kw'>=</span> <span class='fl'>2</span>)
<span class='no'>w</span> <span class='kw'>&lt;-</span> <span class='fu'>round</span>(<span class='fl'>1</span> / (<span class='no'>s</span>^<span class='fl'>2</span>), <span class='kw'>digits</span> <span class='kw'>=</span> <span class='fl'>3</span>)
<span class='no'>weights</span> <span class='kw'>&lt;-</span> <span class='no'>w</span>[<span class='fu'>factor</span>(<span class='no'>x</span>)]
<span class='no'>m</span> <span class='kw'>&lt;-</span> <span class='fu'>lm</span>(<span class='no'>y</span> ~ <span class='no'>x</span>, <span class='kw'>w</span> <span class='kw'>=</span> <span class='no'>weights</span>)
<span class='fu'>calplot</span>(<span class='no'>m</span>)</div><div class='output co'>#&gt; <span class='warning'>Warning: Assuming constant prediction variance even though model fit is weighted</span></div><div class='img'><img src='massart97ex3-1.png' alt='' width='700' height='433' /></div><div class='input'>
<span class='co'># The following concords with the book p. 200</span>
<span class='fu'>inverse.predict</span>(<span class='no'>m</span>, <span class='fl'>15</span>, <span class='kw'>ws</span> <span class='kw'>=</span> <span class='fl'>1.67</span>)  <span class='co'># 5.9 +- 2.5</span></div><div class='output co'>#&gt; $Prediction
#&gt; [1] 5.865367
#&gt; 
#&gt; $`Standard Error`
#&gt; [1] 0.8926109
#&gt; 
#&gt; $Confidence
#&gt; [1] 2.478285
#&gt; 
#&gt; $`Confidence Limits`
#&gt; [1] 3.387082 8.343652
#&gt; </div><div class='input'><span class='fu'>inverse.predict</span>(<span class='no'>m</span>, <span class='fl'>90</span>, <span class='kw'>ws</span> <span class='kw'>=</span> <span class='fl'>0.145</span>) <span class='co'># 44.1 +- 7.9</span></div><div class='output co'>#&gt; $Prediction
#&gt; [1] 44.06025
#&gt; 
#&gt; $`Standard Error`
#&gt; [1] 2.829162
#&gt; 
#&gt; $Confidence
#&gt; [1] 7.855012
#&gt; 
#&gt; $`Confidence Limits`
#&gt; [1] 36.20523 51.91526
#&gt; </div><div class='input'>
<span class='co'># The LOD is only calculated for models from unweighted regression</span>
<span class='co'># with this version of chemCal</span>
<span class='no'>m0</span> <span class='kw'>&lt;-</span> <span class='fu'>lm</span>(<span class='no'>y</span> ~ <span class='no'>x</span>)
<span class='fu'>lod</span>(<span class='no'>m0</span>)</div><div class='output co'>#&gt; $x
#&gt; [1] 5.407085
#&gt; 
#&gt; $y
#&gt;        1 
#&gt; 13.63911 
#&gt; </div><div class='input'>
<span class='co'># Limit of quantification from unweighted regression</span>
<span class='fu'>loq</span>(<span class='no'>m0</span>)</div><div class='output co'>#&gt; $x
#&gt; [1] 13.97764
#&gt; 
#&gt; $y
#&gt;       1 
#&gt; 30.6235 
#&gt; </div><div class='input'>
<span class='co'># For calculating the limit of quantification from a model from weighted</span>
<span class='co'># regression, we need to supply weights, internally used for inverse.predict</span>
<span class='co'># If we are not using a variance function, we can use the weight from</span>
<span class='co'># the above example as a first approximation (x = 15 is close to our</span>
<span class='co'># loq approx 14 from above).</span>
<span class='fu'>loq</span>(<span class='no'>m</span>, <span class='kw'>w.loq</span> <span class='kw'>=</span> <span class='fl'>1.67</span>)</div><div class='output co'>#&gt; $x
#&gt; [1] 7.346195
#&gt; 
#&gt; $y
#&gt;        1 
#&gt; 17.90777 
#&gt; </div><div class='input'># The weight for the loq should therefore be derived at x = 7.3 instead
# of 15, but the graphical procedure of Massart (p. 201) to derive the 
# variances on which the weights are based is quite inaccurate anyway. 
</div></pre>
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