Dear Sir,
As per your advice, I am attaching below the markdown format of html codes:
<!DOCTYPE html>
<html lang="en">
<head>
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<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta name="generator" content="Asciidoctor 2.0.18">
<title>Introduction</title>
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<div class="sect1">
<h2 id="_introduction">Introduction</h2>
<div class="sectionbody">
<div class="paragraph">
<p>In a oneway classification, the typical analysis of variance model for the value <strong><em>Y<sub>ij</sub></em></strong> of the <em>j<sup>th</sup></em> observation in the <em>i<sup>th</sup></em> class is given by,</p>
</div>
<div id="eq:lin-model" class="stemblock">
<div class="title">Basic linear model</div>
<div class="content">
\[Y_{ij} = \mu_i + e_{ij}\]
</div>
</div>
<div class="paragraph">
<p>where the \(\mu_i\) in the basic linear model at <a href="#eq:lin-model">Equation (1)</a>, represent the population means of the <strong><em>classes</em></strong> and the \(e_{ij}\) are
the \(j^{th}\) residuals for the \(i^{th}\) class. But suppose that on each unit we have also measured another variable latexmah:[X_{ij}] that is linearly related to \(Y_{ij}\). It is natural to set up the model,</p>
</div>
<div id="lin-model-X" class="stemblock">
<div class="title">Basic covariance model with linear regression of <strong>Y</strong> on covariate <strong>X</strong></div>
<div class="content">
\[Y_{ij} = \mu_i + \beta (X_{ij}-\bar X)+ \epsilon_{ij}\]
</div>
</div>
<div id="lin-model-X-alpha" class="stemblock">
<div class="title">Basic covariance model in CRD with linear regression of <strong>Y</strong> on covariate <strong>X</strong></div>
<div class="content">
\[Y_{ij} = \mu + \alpha_i + \beta (X_{ij}-\bar X)+ \epsilon_{ij}\]
</div>
</div>
<div class="paragraph">
<p>where, \(\alpha_i = \mu_i - \mu\) and \(\beta\) is the regression coefficient of <strong><em>Y</em></strong> on <strong><em>X</em></strong>. The <a href="#lin-model-X">Equation (2)</a> is a typical <strong><em>model for the analysis of covariance after removing the general means \(\mu\) from group means \(\mu_i\)</em></strong> and the <a href="#lin-model-X-alpha">Equation (3)</a> is a typical <strong><em>model for the analysis of covariance in CRD</em></strong>.</p>
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Last updated 2023-08-07 14:32:39 +0530
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