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authorJohannes Ranke <jranke@uni-bremen.de>2022-03-23 10:32:36 +0100
committerJohannes Ranke <jranke@uni-bremen.de>2022-03-31 18:35:09 +0200
commitf4fcef8228ebd5a1a73bc6edc47b5efa259c2e20 (patch)
treef9e0489c8941257b5055783a443f4859212ad4f1 /docs/reference/inverse.predict.html
parent4c2b22d75cc5102ddc595ea479c46bfdb46c1016 (diff)
Use 'investr' conditionally in tests, updates
Most prominently, a README was added, giving a nice overview for the people visiting the github page, the package page on CRAN, or the online docs at pkgdown.jrwb.de. The maintainer e-mail address was also updated.
Diffstat (limited to 'docs/reference/inverse.predict.html')
-rw-r--r--docs/reference/inverse.predict.html350
1 files changed, 138 insertions, 212 deletions
diff --git a/docs/reference/inverse.predict.html b/docs/reference/inverse.predict.html
index aece430..cb9fe98 100644
--- a/docs/reference/inverse.predict.html
+++ b/docs/reference/inverse.predict.html
@@ -1,46 +1,5 @@
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-<meta property="og:title" content="Predict x from y for a linear calibration — inverse.predict" />
-<meta property="og:description" content="This function predicts x values using a univariate linear model that has been
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Predict x from y for a linear calibration — inverse.predict • chemCal</title><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Predict x from y for a linear calibration — inverse.predict"><meta property="og:description" content="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,
@@ -49,28 +8,14 @@
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." />
-
-
-
-
-<!-- mathjax -->
-<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script>
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-
-<!--[if lt IE 9]>
+ This is elaborated in the package vignette."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
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<script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
-<![endif]-->
-
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+<![endif]--></head><body data-spy="scroll" data-target="#toc">
+
- <body data-spy="scroll" data-target="#toc">
<div class="container template-reference-topic">
- <header>
- <div class="navbar navbar-default navbar-fixed-top" role="navigation">
+ <header><div class="navbar navbar-default navbar-fixed-top" role="navigation">
<div class="container">
<div class="navbar-header">
<button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#navbar" aria-expanded="false">
@@ -81,19 +26,12 @@
</button>
<span class="navbar-brand">
<a class="navbar-link" href="../index.html">chemCal</a>
- <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.2.2</span>
+ <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.3</span>
</span>
</div>
<div id="navbar" class="navbar-collapse collapse">
- <ul class="nav navbar-nav">
- <li>
- <a href="../index.html">
- <span class="fas fa-home fa-lg"></span>
-
- </a>
-</li>
-<li>
+ <ul class="nav navbar-nav"><li>
<a href="../articles/chemCal.html">Get started</a>
</li>
<li>
@@ -102,25 +40,19 @@
<li>
<a href="../news/index.html">Changelog</a>
</li>
- </ul>
- <ul class="nav navbar-nav navbar-right">
- <li>
- <a href="https://github.com/jranke/chemCal/">
+ </ul><ul class="nav navbar-nav navbar-right"><li>
+ <a href="https://github.com/jranke/chemCal/" class="external-link">
<span class="fab fa-github fa-lg"></span>
</a>
</li>
- </ul>
-
- </div><!--/.nav-collapse -->
+ </ul></div><!--/.nav-collapse -->
</div><!--/.container -->
</div><!--/.navbar -->
- </header>
-
-<div class="row">
+ </header><div class="row">
<div class="col-md-9 contents">
<div class="page-header">
<h1>Predict x from y for a linear calibration</h1>
@@ -141,166 +73,160 @@
This is elaborated in the package vignette.</p>
</div>
- <pre class="usage"><span class='fu'>inverse.predict</span><span class='op'>(</span><span class='va'>object</span>, <span class='va'>newdata</span>, <span class='va'>...</span>,
- <span class='va'>ws</span>, alpha<span class='op'>=</span><span class='fl'>0.05</span>, var.s <span class='op'>=</span> <span class='st'>"auto"</span><span class='op'>)</span></pre>
+ <div id="ref-usage">
+ <div class="sourceCode"><pre class="sourceCode r"><code><span class="fu">inverse.predict</span><span class="op">(</span><span class="va">object</span>, <span class="va">newdata</span>, <span class="va">...</span>,
+ <span class="va">ws</span>, alpha<span class="op">=</span><span class="fl">0.05</span>, var.s <span class="op">=</span> <span class="st">"auto"</span><span class="op">)</span></code></pre></div>
+ </div>
- <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
- <table class="ref-arguments">
- <colgroup><col class="name" /><col class="desc" /></colgroup>
- <tr>
- <th>object</th>
- <td><p>A univariate model object of class <code><a href='https://rdrr.io/r/stats/lm.html'>lm</a></code> or
- <code><a href='https://rdrr.io/pkg/MASS/man/rlm.html'>rlm</a></code>
- with model formula <code>y ~ x</code> or <code>y ~ x - 1</code>.</p></td>
- </tr>
- <tr>
- <th>newdata</th>
- <td><p>A vector of observed y values for one sample.</p></td>
- </tr>
- <tr>
- <th>...</th>
- <td><p>Placeholder for further arguments that might be needed by
- future implementations.</p></td>
- </tr>
- <tr>
- <th>ws</th>
- <td><p>The weight attributed to the sample. This argument is obligatory
- if <code>object</code> has weights.</p></td>
- </tr>
- <tr>
- <th>alpha</th>
- <td><p>The error tolerance level for the confidence interval to be reported.</p></td>
- </tr>
- <tr>
- <th>var.s</th>
- <td><p>The estimated variance of the sample measurements. The default is to take
+ <div id="arguments">
+ <h2>Arguments</h2>
+ <dl><dt>object</dt>
+<dd><p>A univariate model object of class <code><a href="https://rdrr.io/r/stats/lm.html" class="external-link">lm</a></code> or
+ <code><a href="https://rdrr.io/pkg/MASS/man/rlm.html" class="external-link">rlm</a></code>
+ with model formula <code>y ~ x</code> or <code>y ~ x - 1</code>.</p></dd>
+<dt>newdata</dt>
+<dd><p>A vector of observed y values for one sample.</p></dd>
+<dt>...</dt>
+<dd><p>Placeholder for further arguments that might be needed by
+ future implementations.</p></dd>
+<dt>ws</dt>
+<dd><p>The weight attributed to the sample. This argument is obligatory
+ if <code>object</code> has weights.</p></dd>
+<dt>alpha</dt>
+<dd><p>The error tolerance level for the confidence interval to be reported.</p></dd>
+<dt>var.s</dt>
+<dd><p>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>.</p></td>
- </tr>
- </table>
-
- <h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>
-
+ overrides <code>ws</code>.</p></dd>
+</dl></div>
+ <div id="value">
+ <h2>Value</h2>
<p>A list containing the predicted x value, its standard error and a
confidence interval.</p>
- <h2 class="hasAnchor" id="note"><a class="anchor" href="#note"></a>Note</h2>
-
+ </div>
+ <div id="note">
+ <h2>Note</h2>
<p>The function was validated with examples 7 and 8 from Massart et al. (1997).
Note that the behaviour of inverse.predict changed with chemCal version
0.2.1. Confidence intervals for x values obtained from calibrations with
replicate measurements did not take the variation about the means into account.
Please refer to the vignette for details.</p>
- <h2 class="hasAnchor" id="references"><a class="anchor" href="#references"></a>References</h2>
-
+ </div>
+ <div id="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 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
- <pre class="examples"><div class='input'><span class='co'># This is example 7 from Chapter 8 in Massart et al. (1997)</span>
-<span class='va'>m</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/lm.html'>lm</a></span><span class='op'>(</span><span class='va'>y</span> <span class='op'>~</span> <span class='va'>x</span>, data <span class='op'>=</span> <span class='va'>massart97ex1</span><span class='op'>)</span>
-<span class='fu'>inverse.predict</span><span class='op'>(</span><span class='va'>m</span>, <span class='fl'>15</span><span class='op'>)</span> <span class='co'># 6.1 +- 4.9</span>
-</div><div class='output co'>#&gt; $Prediction
-#&gt; [1] 6.09381
-#&gt;
-#&gt; $`Standard Error`
-#&gt; [1] 1.767278
-#&gt;
-#&gt; $Confidence
-#&gt; [1] 4.906751
-#&gt;
-#&gt; $`Confidence Limits`
-#&gt; [1] 1.187059 11.000561
-#&gt; </div><div class='input'><span class='fu'>inverse.predict</span><span class='op'>(</span><span class='va'>m</span>, <span class='fl'>90</span><span class='op'>)</span> <span class='co'># 43.9 +- 4.9</span>
-</div><div class='output co'>#&gt; $Prediction
-#&gt; [1] 43.93983
-#&gt;
-#&gt; $`Standard Error`
-#&gt; [1] 1.767747
-#&gt;
-#&gt; $Confidence
-#&gt; [1] 4.908053
-#&gt;
-#&gt; $`Confidence Limits`
-#&gt; [1] 39.03178 48.84788
-#&gt; </div><div class='input'><span class='fu'>inverse.predict</span><span class='op'>(</span><span class='va'>m</span>, <span class='fu'><a href='https://rdrr.io/r/base/rep.html'>rep</a></span><span class='op'>(</span><span class='fl'>90</span>,<span class='fl'>5</span><span class='op'>)</span><span class='op'>)</span> <span class='co'># 43.9 +- 3.2</span>
-</div><div class='output co'>#&gt; $Prediction
-#&gt; [1] 43.93983
-#&gt;
-#&gt; $`Standard Error`
-#&gt; [1] 1.141204
-#&gt;
-#&gt; $Confidence
-#&gt; [1] 3.168489
-#&gt;
-#&gt; $`Confidence Limits`
-#&gt; [1] 40.77134 47.10832
-#&gt; </div><div class='input'>
-<span class='co'># For reproducing the results for replicate standard measurements in example 8,</span>
-<span class='co'># we need to do the calibration on the means when using chemCal &gt; 0.2</span>
-<span class='va'>weights</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/with.html'>with</a></span><span class='op'>(</span><span class='va'>massart97ex3</span>, <span class='op'>{</span>
- <span class='va'>yx</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/split.html'>split</a></span><span class='op'>(</span><span class='va'>y</span>, <span class='va'>x</span><span class='op'>)</span>
- <span class='va'>ybar</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/lapply.html'>sapply</a></span><span class='op'>(</span><span class='va'>yx</span>, <span class='va'>mean</span><span class='op'>)</span>
- <span class='va'>s</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/Round.html'>round</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/lapply.html'>sapply</a></span><span class='op'>(</span><span class='va'>yx</span>, <span class='va'>sd</span><span class='op'>)</span>, digits <span class='op'>=</span> <span class='fl'>2</span><span class='op'>)</span>
- <span class='va'>w</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/Round.html'>round</a></span><span class='op'>(</span><span class='fl'>1</span> <span class='op'>/</span> <span class='op'>(</span><span class='va'>s</span><span class='op'>^</span><span class='fl'>2</span><span class='op'>)</span>, digits <span class='op'>=</span> <span class='fl'>3</span><span class='op'>)</span>
-<span class='op'>}</span><span class='op'>)</span>
-
-<span class='va'>massart97ex3.means</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/aggregate.html'>aggregate</a></span><span class='op'>(</span><span class='va'>y</span> <span class='op'>~</span> <span class='va'>x</span>, <span class='va'>massart97ex3</span>, <span class='va'>mean</span><span class='op'>)</span>
-
-<span class='va'>m3.means</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/lm.html'>lm</a></span><span class='op'>(</span><span class='va'>y</span> <span class='op'>~</span> <span class='va'>x</span>, w <span class='op'>=</span> <span class='va'>weights</span>, data <span class='op'>=</span> <span class='va'>massart97ex3.means</span><span class='op'>)</span>
-
-<span class='fu'>inverse.predict</span><span class='op'>(</span><span class='va'>m3.means</span>, <span class='fl'>15</span>, ws <span class='op'>=</span> <span class='fl'>1.67</span><span class='op'>)</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='op'>(</span><span class='va'>m3.means</span>, <span class='fl'>90</span>, ws <span class='op'>=</span> <span class='fl'>0.145</span><span class='op'>)</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'>
-</div></pre>
+ <div id="ref-examples">
+ <h2>Examples</h2>
+ <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span class="co"># This is example 7 from Chapter 8 in Massart et al. (1997)</span></span>
+<span class="r-in"><span class="va">m</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/stats/lm.html" class="external-link">lm</a></span><span class="op">(</span><span class="va">y</span> <span class="op">~</span> <span class="va">x</span>, data <span class="op">=</span> <span class="va">massart97ex1</span><span class="op">)</span></span>
+<span class="r-in"><span class="fu">inverse.predict</span><span class="op">(</span><span class="va">m</span>, <span class="fl">15</span><span class="op">)</span> <span class="co"># 6.1 +- 4.9</span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> $Prediction</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 6.09381</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> $`Standard Error`</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 1.767278</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> $Confidence</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 4.906751</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> $`Confidence Limits`</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 1.187059 11.000561</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-in"><span class="fu">inverse.predict</span><span class="op">(</span><span class="va">m</span>, <span class="fl">90</span><span class="op">)</span> <span class="co"># 43.9 +- 4.9</span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> $Prediction</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 43.93983</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> $`Standard Error`</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 1.767747</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> $Confidence</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 4.908053</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> $`Confidence Limits`</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 39.03178 48.84788</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-in"><span class="fu">inverse.predict</span><span class="op">(</span><span class="va">m</span>, <span class="fu"><a href="https://rdrr.io/r/base/rep.html" class="external-link">rep</a></span><span class="op">(</span><span class="fl">90</span>,<span class="fl">5</span><span class="op">)</span><span class="op">)</span> <span class="co"># 43.9 +- 3.2</span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> $Prediction</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 43.93983</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> $`Standard Error`</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 1.141204</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> $Confidence</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 3.168489</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> $`Confidence Limits`</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 40.77134 47.10832</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-in"></span>
+<span class="r-in"><span class="co"># For reproducing the results for replicate standard measurements in example 8,</span></span>
+<span class="r-in"><span class="co"># we need to do the calibration on the means when using chemCal &gt; 0.2</span></span>
+<span class="r-in"><span class="va">weights</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/with.html" class="external-link">with</a></span><span class="op">(</span><span class="va">massart97ex3</span>, <span class="op">{</span></span>
+<span class="r-in"> <span class="va">yx</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/split.html" class="external-link">split</a></span><span class="op">(</span><span class="va">y</span>, <span class="va">x</span><span class="op">)</span></span>
+<span class="r-in"> <span class="va">ybar</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</span><span class="va">yx</span>, <span class="va">mean</span><span class="op">)</span></span>
+<span class="r-in"> <span class="va">s</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/Round.html" class="external-link">round</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</span><span class="va">yx</span>, <span class="va">sd</span><span class="op">)</span>, digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span>
+<span class="r-in"> <span class="va">w</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/Round.html" class="external-link">round</a></span><span class="op">(</span><span class="fl">1</span> <span class="op">/</span> <span class="op">(</span><span class="va">s</span><span class="op">^</span><span class="fl">2</span><span class="op">)</span>, digits <span class="op">=</span> <span class="fl">3</span><span class="op">)</span></span>
+<span class="r-in"><span class="op">}</span><span class="op">)</span></span>
+<span class="r-in"></span>
+<span class="r-in"><span class="va">massart97ex3.means</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/stats/aggregate.html" class="external-link">aggregate</a></span><span class="op">(</span><span class="va">y</span> <span class="op">~</span> <span class="va">x</span>, <span class="va">massart97ex3</span>, <span class="va">mean</span><span class="op">)</span></span>
+<span class="r-in"></span>
+<span class="r-in"><span class="va">m3.means</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/stats/lm.html" class="external-link">lm</a></span><span class="op">(</span><span class="va">y</span> <span class="op">~</span> <span class="va">x</span>, w <span class="op">=</span> <span class="va">weights</span>, data <span class="op">=</span> <span class="va">massart97ex3.means</span><span class="op">)</span></span>
+<span class="r-in"></span>
+<span class="r-in"><span class="fu">inverse.predict</span><span class="op">(</span><span class="va">m3.means</span>, <span class="fl">15</span>, ws <span class="op">=</span> <span class="fl">1.67</span><span class="op">)</span> <span class="co"># 5.9 +- 2.5</span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> $Prediction</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 5.865367</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> $`Standard Error`</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 0.8926109</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> $Confidence</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 2.478285</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> $`Confidence Limits`</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 3.387082 8.343652</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-in"><span class="fu">inverse.predict</span><span class="op">(</span><span class="va">m3.means</span>, <span class="fl">90</span>, ws <span class="op">=</span> <span class="fl">0.145</span><span class="op">)</span> <span class="co"># 44.1 +- 7.9</span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> $Prediction</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 44.06025</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> $`Standard Error`</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 2.829162</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> $Confidence</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 7.855012</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> $`Confidence Limits`</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 36.20523 51.91526</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-in"></span>
+</code></pre></div>
+ </div>
</div>
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