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+<title>inverse.predict. chemCal 0.1-35.900</title>
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+ <header>
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+
+ <h1>Predict x from y for a linear calibration</h1>
+
+<div class="row">
+ <div class="span8">
+ <h2>Usage</h2>
+ <pre><div>inverse.predict(object, newdata, ..., ws, alpha=0.05, var.s&nbsp;=&nbsp;"auto")</div></pre>
+
+ <h2>Arguments</h2>
+ <dl>
+ <dt>object</dt>
+ <dd>
+ A univariate model object of class <code><a href='http://www.inside-r.org/r-doc/stats/lm'>lm</a></code> or
+ <code><a href='http://www.inside-r.org/r-doc/MASS/rlm'>rlm</a></code>
+ with model formula <code>y ~ x</code> or <code>y ~ x - 1</code>.
+ </dd>
+ <dt>newdata</dt>
+ <dd>
+ A vector of observed y values for one sample.
+ </dd>
+ <dt>...</dt>
+ <dd>
+ Placeholder for further arguments that might be needed by
+ future implementations.
+ </dd>
+ <dt>ws</dt>
+ <dd>
+ The weight attributed to the sample. This argument is obligatory
+ if <code>object</code> has weights.
+ </dd>
+ <dt>alpha</dt>
+ <dd>
+ The error tolerance level for the confidence interval to be reported.
+ </dd>
+ <dt>var.s</dt>
+ <dd>
+ The estimated variance of the sample measurements. The default is to take
+ the residual standard error from the calibration and to adjust it
+ using <code>ws</code>, if applicable. This means that <code>var.s</code>
+ overrides <code>ws</code>.
+ </dd>
+ </dl>
+
+ <div class="Value">
+ <h2>Value</h2>
+
+ <p><dl>
+ A list containing the predicted x value, its standard error and a
+ confidence interval.
+</dl></p>
+
+ </div>
+
+ <div class="Description">
+ <h2>Description</h2>
+
+ <p>This function predicts x values using a univariate linear model that has been
+ generated for the purpose of calibrating a measurement method. Prediction
+ intervals are given at the specified confidence level.
+ The calculation method was taken from Massart et al. (1997). In particular,
+ Equations 8.26 and 8.28 were combined in order to yield a general treatment
+ of inverse prediction for univariate linear models, taking into account
+ weights that have been used to create the linear model, and at the same
+ time providing the possibility to specify a precision in sample measurements
+ differing from the precision in standard samples used for the calibration.
+ This is elaborated in the package vignette.</p>
+
+ </div>
+
+ <div class="Note">
+ <h2>Note</h2>
+
+ <p>The function was validated with examples 7 and 8 from Massart et al. (1997).</p>
+
+ </div>
+
+ <div class="References">
+ <h2>References</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,
+ p. 200</p>
+
+ </div>
+
+ <h2 id="examples">Examples</h2>
+ <pre class="examples"><div class='input'># This is example 7 from Chapter 8 in Massart et al. (1997)
+data(massart97ex1)
+m &lt;- lm(y ~ x, data = massart97ex1)
+inverse.predict(m, 15) # 6.1 +- 4.9
+</div>
+<div class='output'>$Prediction
+[1] 6.09381
+
+$`Standard Error`
+[1] 1.767278
+
+$Confidence
+[1] 4.906751
+
+$`Confidence Limits`
+[1] 1.187059 11.000561
+
+</div>
+<div class='input'>inverse.predict(m, 90) # 43.9 +- 4.9
+</div>
+<div class='output'>$Prediction
+[1] 43.93983
+
+$`Standard Error`
+[1] 1.767747
+
+$Confidence
+[1] 4.908053
+
+$`Confidence Limits`
+[1] 39.03178 48.84788
+
+</div>
+<div class='input'>inverse.predict(m, rep(90,5)) # 43.9 +- 3.2
+</div>
+<div class='output'>$Prediction
+[1] 43.93983
+
+$`Standard Error`
+[1] 1.141204
+
+$Confidence
+[1] 3.168489
+
+$`Confidence Limits`
+[1] 40.77134 47.10832
+
+</div></pre>
+ </div>
+ <div class="span4">
+ <!-- <ul>
+ <li>inverse.predict</li><li>inverse.predict.lm</li><li>inverse.predict.rlm</li><li>inverse.predict.default</li>
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