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<h3 class="section">2.12 Function LinearRegression</h3>
<p><a name="index-LinearRegression-60"></a>
<!-- LinearRegression ../inst/LinearRegression.m -->
-*- texinfo -*-
<div class="defun">
— Function File: [<var>p</var>,<var>e_var</var>,<var>r</var>,<var>p_var</var>,<var>y_var</var>] = <b>LinearRegression</b> (<var>F,y</var>)<var><a name="index-LinearRegression-61"></a></var><br>
— Function File: [<var>p</var>,<var>e_var</var>,<var>r</var>,<var>p_var</var>,<var>y_var</var>] = <b>LinearRegression</b> (<var>F,y,w</var>)<var><a name="index-LinearRegression-62"></a></var><br>
<blockquote><p>
general linear regression
determine the parameters p_j (j=1,2,...,m) such that the function
f(x) = sum_(i=1,...,m) p_j*f_j(x) is the best fit to the given values y_i = f(x_i)
parameters:
<ul>
<li><var>F</var> is an n*m matrix with the values of the basis functions at
the support points. In column j give the values of f_j at the points
x_i (i=1,2,...,n)
<li><var>y</var> is a column vector of length n with the given values
<li><var>w</var> is n column vector of of length n vector with the weights of data points
</ul>
return values:
<ul>
<li><var>p</var> is the vector of length m with the estimated values of the parameters
<li><var>e_var</var> is the estimated variance of the difference between fitted and measured values
<li><var>r</var> is the weighted norm of the residual
<li><var>p_var</var> is the estimated variance of the parameters p_j
<li><var>y_var</var> is the estimated variance of the dependend variables
</ul>
Caution:
do NOT request <var>y_var</var> for large data sets, as a n by n matrix is
generated
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</p></blockquote></div>
<p>See also <a href="../octave/XREFregress.html#XREFregress">regress</a>, <a href="XREFleasqr.html#XREFleasqr">leasqr</a>,
<a href="XREFnonlin_005fcurvefit.html#XREFnonlin_005fcurvefit">nonlin_curvefit</a>,
<a href="../octave/XREFpolyfit.html#XREFpolyfit">polyfit</a>, <a href="XREFwpolyfit.html#XREFwpolyfit">wpolyfit</a>,
<a href="XREFexpfit.html#XREFexpfit">expfit</a>.
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