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<p>
Previous: <a href="Linear-regression-with-a-constant-term.html#Linear-regression-with-a-constant-term" accesskey="p" rel="previous">Linear regression with a constant term</a>, Up: <a href="Linear-regression.html#Linear-regression" accesskey="u" rel="up">Linear regression</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Linear-regression-without-a-constant-term-1"></a>
<h4 class="subsection">38.2.2 Linear regression without a constant term</h4>

<p>The functions described in this section can be used to perform
least-squares fits to a straight line model without a constant term,
<em>Y = c_1 X</em>.
</p>
<dl>
<dt><a name="index-gsl_005ffit_005fmul"></a>Function: <em>int</em> <strong>gsl_fit_mul</strong> <em>(const double * <var>x</var>, const size_t <var>xstride</var>, const double * <var>y</var>, const size_t <var>ystride</var>, size_t <var>n</var>, double * <var>c1</var>, double * <var>cov11</var>, double * <var>sumsq</var>)</em></dt>
<dd><p>This function computes the best-fit linear regression coefficient
<var>c1</var> of the model <em>Y = c_1 X</em> for the datasets (<var>x</var>,
<var>y</var>), two vectors of length <var>n</var> with strides <var>xstride</var> and
<var>ystride</var>.  The errors on <var>y</var> are assumed unknown so the 
variance of the parameter <var>c1</var> is estimated from
the scatter of the points around the best-fit line and returned via the
parameter <var>cov11</var>.  The sum of squares of the residuals from the
best-fit line is returned in <var>sumsq</var>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005ffit_005fwmul"></a>Function: <em>int</em> <strong>gsl_fit_wmul</strong> <em>(const double * <var>x</var>, const size_t <var>xstride</var>, const double * <var>w</var>, const size_t <var>wstride</var>, const double * <var>y</var>, const size_t <var>ystride</var>, size_t <var>n</var>, double * <var>c1</var>, double * <var>cov11</var>, double * <var>sumsq</var>)</em></dt>
<dd><p>This function computes the best-fit linear regression coefficient
<var>c1</var> of the model <em>Y = c_1 X</em> for the weighted datasets
(<var>x</var>, <var>y</var>), two vectors of length <var>n</var> with strides
<var>xstride</var> and <var>ystride</var>.  The vector <var>w</var>, of length <var>n</var>
and stride <var>wstride</var>, specifies the weight of each datapoint. The
weight is the reciprocal of the variance for each datapoint in <var>y</var>.
</p>
<p>The variance of the parameter <var>c1</var> is computed using the weights
and returned via the parameter <var>cov11</var>.  The weighted sum of
squares of the residuals from the best-fit line, <em>\chi^2</em>, is
returned in <var>chisq</var>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005ffit_005fmul_005fest"></a>Function: <em>int</em> <strong>gsl_fit_mul_est</strong> <em>(double <var>x</var>, double <var>c1</var>, double <var>cov11</var>, double * <var>y</var>, double * <var>y_err</var>)</em></dt>
<dd><p>This function uses the best-fit linear regression coefficient <var>c1</var>
and its covariance <var>cov11</var> to compute the fitted function
<var>y</var> and its standard deviation <var>y_err</var> for the model <em>Y =
c_1 X</em> at the point <var>x</var>.
</p></dd></dl>

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<div class="header">
<p>
Previous: <a href="Linear-regression-with-a-constant-term.html#Linear-regression-with-a-constant-term" accesskey="p" rel="previous">Linear regression with a constant term</a>, Up: <a href="Linear-regression.html#Linear-regression" accesskey="u" rel="up">Linear regression</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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