mhjensen
163 lines
5.4 KiB
HTML
163 lines
5.4 KiB
HTML
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'sections': [('Regression analysis, overarching aims', 2, None, '___sec0'),
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('General linear models', 2, None, '___sec1')]}
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<!-- ------------------- main content ---------------------- -->
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<center><h1>Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</h1></center> <!-- document title -->
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<p>
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<!-- author(s): Morten Hjorth-Jensen -->
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<center>
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<b>Morten Hjorth-Jensen</b> [1, 2]
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<!-- institution(s) -->
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<center>[1] <b>Department of Physics, University of Oslo</b></center>
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<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
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<br>
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<center><h4>Oct 11, 2017</h4></center> <!-- date -->
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<br>
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<p>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="___sec0">Regression analysis, overarching aims </h2>
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<b></b>
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<p>
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<p>
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Regression modeling deals with the description of the sampling distribution of a given random variable \( y \) varies as function of another variable or a set of such variables \( \hat{x} =[x_0, x_1,\dots, x_p] \).
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The first variable is called the <b>dependent</b>, the <b>outcome</b> or the <b>response</b> variable while the set of variables \( \hat{x} \) is called the independent variable, or the predictor variable or the explanatory variable.
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<p>
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A regression model aims at finding a likelihood function \( p(y\vert \hat{x}) \), that is the conditional distribution for \( y \) with a given \( \hat{x} \). The estimation of \( p(y\vert \hat{x}) \) is made using a data set with
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<ul>
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<li> \( n \) cases \( i = 0, 1, 2, \dots, n-1 \)</li>
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<li> Response (dependent or outcome) variable \( y_i \) with \( i = 0, 1, 2, \dots, n-1 \)</li>
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<li> \( p \) Explanatory (independent or predictor) variables \( \hat{x}_i=[x_{i0}, x_{i1}, \dots, x_{ip}] \) with \( i = 0, 1, 2, \dots, n-1 \)</li>
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</ul>
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The goal of the regression analysis is to extract/exploit relationship between \( y_i \) and \( \hat{x}_i \) in or to infer causal dependencies, approximations to the likelihood functions, functional relationships and to make predictions .
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<p>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="___sec1">General linear models </h2>
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<b></b>
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<p>
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more text to come
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</div>
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<!-- ------------------- end of main content --------------- -->
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<center style="font-size:80%">
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<!-- copyright --> © 1999-2017, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
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</center>
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