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<title>Linear fitting without a constant term - GNU Scientific Library -- Reference Manual</title>
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<h3 class="section">36.3 Linear fitting without a constant term</h3>
<p>The functions described in this section can be used to perform
least-squares fits to a straight line model without a constant term,
Y = c_1 X.
<div class="defun">
— Function: int <b>gsl_fit_mul</b> (<var>const double * x, const size_t xstride, const double * y, const size_t ystride, size_t n, double * c1, double * cov11, double * sumsq</var>)<var><a name="index-gsl_005ffit_005fmul-2378"></a></var><br>
<blockquote><p>This function computes the best-fit linear regression coefficient
<var>c1</var> of the model Y = c_1 X 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></blockquote></div>
<div class="defun">
— Function: int <b>gsl_fit_wmul</b> (<var>const double * x, const size_t xstride, const double * w, const size_t wstride, const double * y, const size_t ystride, size_t n, double * c1, double * cov11, double * sumsq</var>)<var><a name="index-gsl_005ffit_005fwmul-2379"></a></var><br>
<blockquote><p>This function computes the best-fit linear regression coefficient
<var>c1</var> of the model Y = c_1 X 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>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, \chi^2, is
returned in <var>chisq</var>.
</p></blockquote></div>
<div class="defun">
— Function: int <b>gsl_fit_mul_est</b> (<var>double x, double c1, double cov11, double * y, double * y_err</var>)<var><a name="index-gsl_005ffit_005fmul_005fest-2380"></a></var><br>
<blockquote><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 Y =
c_1 X at the point <var>x</var>.
</p></blockquote></div>
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