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<document xmlns="http://cnx.rice.edu/cnxml" xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:bib="http://bibtexml.sf.net/" id="id30355191">
<name>What is Regression Analysis?</name>
<metadata>
  <md:version>1.1</md:version>
  <md:created>2006/02/21 09:23:57.622 US/Central</md:created>
  <md:revised>2006/02/22 07:57:13.936 US/Central</md:revised>
  <md:authorlist>
      <md:author id="kolobl">
      <md:firstname>Lekulana</md:firstname>
      <md:othername>Emmanuel</md:othername>
      <md:surname>Kolobe</md:surname>
      <md:email>klekulana@hotmail.com</md:email>
    </md:author>
  </md:authorlist>

  <md:maintainerlist>
    <md:maintainer id="kolobl">
      <md:firstname>Lekulana</md:firstname>
      <md:othername>Emmanuel</md:othername>
      <md:surname>Kolobe</md:surname>
      <md:email>klekulana@hotmail.com</md:email>
    </md:maintainer>
  </md:maintainerlist>
  
  <md:keywordlist>
    <md:keyword>linear regression</md:keyword>
    <md:keyword>Non-linear regression</md:keyword>
    <md:keyword>Regression Analysis</md:keyword>
    <md:keyword>Regression line</md:keyword>
  </md:keywordlist>

  <md:abstract>This module introduces regression analysis and gives examples of regression analysis.</md:abstract>
</metadata>
<content>
<para id="id29034460"><term>Regression analysis</term> is any statistical method
where the mean of one or more random variables is predicted based on
other measured random variables [<link src="http://en.wikipedia.org/wiki/Regression_analysis">Wikipedia2006R</link>]. There are two types of <term>regression
analysis</term>, chosen according to whether the data approximate a
straight line, when 
<link src="http://cnx.rice.edu/content/m13449/latest">linear
regression</link> is used, or not, when 
<link src="http://cnx.rice.edu/content/m13450/latest">
non-linear regression</link> is used.</para>
<para id="id30416175">A regression line is a line drawn through a
scatterplot of two variables. The line is chosen so that it comes
as close to the points as possible. <term>Regression analysis</term>, on the
other hand, is more than curve fitting. It involves fitting a model
with both deterministic and stochastic components. The
deterministic component is called the predictor and the stochastic
component is called the error term.</para>
<para id="id30495887">The simplest form of a regression model
contains a 
<link src="http://cnx.rice.edu/content/m13446/latest">dependent
variable</link>, also called the "Y-variable" and a single 
<link src="http://cnx.rice.edu/content/m13448/latest">
independent variable</link>, also called the "X-variable".</para>
<figure id="element-309"><name>Regression Analysis Graph</name>
  <media type="image/gif" src="picture_regression_analysis.gif"/>
  <caption>This graph taken from [<link src="http://www.12manage.com/methods_regression_analysis.html">12manage</link>], shows the simple use of regression analysis. It has both the observed and the predicted values, with the slope of 1.</caption></figure><example id="element-78"><para id="element-458">Examples of the regression of Y on X: 
         
	</para><para id="element-970">1. The dependence of the blood pressure Y on the age X of a person. </para><para id="element-368">2. The dependence of the weight Y of certain animals on their daily ration of food X.</para>
</example><para id="id30197208"/>
<para id="id30340798"><emphasis><term>References:</term></emphasis></para>
<para id="id26622358">Wikipedia2006R. "<emphasis>Regression Analysis</emphasis>," 
<link src="http://en.wikipedia.org/wiki/Regression_analysis">
http://en.wikipedia.org/wiki/Regression_analysis</link>, Last
Accessed on 20 February 2006</para><para id="element-499">12manage. <emphasis>Regression Analysis</emphasis>. Accessed on February 20, 2006. At <link src="http://www.12manage.com/methods_regression_analysis.html">http://www.12manage.com/methods_regression_analysis.html</link></para><para id="element-710">Author of Assignment 3: Lekulana Kolobe
</para><para id="element-415">Author of Assignment 1: Arnold Mwesigye</para>
</content>
</document>
