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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 <- split(y, x)
ybar <- sapply(yx, mean)
s <- round(sapply(yx, sd), digits = 2)
w <- round(1 / (s^2), digits = 3)
weights <- w[factor(x)]
m <- 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
$`Confidence Limits`
[1] 36.20523 51.91526
</div>
<div class='input'>
# The LOD is only calculated for models from unweighted regression
# with this version of chemCal
m0 <- lm(y ~ x)
lod(m0)
</div>
<div class='output'>$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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