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      <h1>Calibration data from Massart et al. (1997), example 3</h1>

<div class="row">
  <div class="span8">
    <h2>Usage</h2>
    <pre><div>data(massart97ex3)</div></pre>
        
    <div class="Description">
      <h2>Description</h2>

      <p>Sample dataset from p. 188 to test the package.</p>
  
    </div>

    <div class="Format">
      <h2>Format</h2>

      <p>A dataframe containing 6 levels of x values with 5
  observations of y for each level.</p>
  
    </div>

    <div class="Source">
      <h2>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>
  
    </div>
    
    <h2 id="examples">Examples</h2>
    <pre class="examples"><div class='input'>data(massart97ex3)
attach(massart97ex3)
</div>
<strong class='message'>Die folgenden Objekte sind maskiert von massart97ex3 (pos = 3):

    x, y
</strong>
<div class='input'>yx &lt;- split(y, x)
ybar &lt;- sapply(yx, mean)
s &lt;- round(sapply(yx, sd), digits = 2)
w &lt;- round(1 / (s^2), digits = 3)
weights &lt;- w[factor(x)]
m &lt;- lm(y ~ x, w = weights)
calplot(m)
</div>
<strong class='warning'>Warning message:
Assuming constant prediction variance even though model fit is weighted
</strong>
<p><img src='massart97ex3-5.png' alt='' width='540' height='400' /></p>
<div class='input'>
# The following concords with the book p. 200
inverse.predict(m, 15, ws = 1.67)  # 5.9 +- 2.5
</div>
<div class='output'>$Prediction
[1] 5.865367

$`Standard Error`
[1] 0.8926109

$Confidence
[1] 2.478285

$`Confidence Limits`
[1] 3.387082 8.343652

</div>
<div class='input'>inverse.predict(m, 90, ws = 0.145) # 44.1 +- 7.9
</div>
<div class='output'>$Prediction
[1] 44.06025

$`Standard Error`
[1] 2.829162

$Confidence
[1] 7.855012

$`Confidence Limits`
[1] 36.20523 51.91526

</div>
<div class='input'>
# The LOD is only calculated for models from unweighted regression
# with this version of chemCal
m0 &lt;- lm(y ~ x) 
lod(m0)
</div>
<div class='output'>$x
[1] 5.407085

$y
       1 
13.63911 

</div>
<div class='input'>
# Limit of quantification from unweighted regression
loq(m0)
</div>
<div class='output'>$x
[1] 13.97764

$y
      1 
30.6235 

</div>
<div class='input'>
# For calculating the limit of quantification from a model from weighted
# regression, we need to supply weights, internally used for inverse.predict
# If we are not using a variance function, we can use the weight from
# the above example as a first approximation (x = 15 is close to our
# loq approx 14 from above).
loq(m, w.loq = 1.67)
</div>
<div class='output'>$x
[1] 7.346195

$y
       1 
17.90777 

</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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