Re: [Help-gsl] how to use gsl_stats_tss after gsl_multifit_linear to get R^2

[Timothée Flutre]

Hello,

I would do the following:

double r2 = 1 - chisq / gsl_stats_tss(y->data, y->stride, y->size);

The function is described in the manual, section 21 (Statistics) subsection
1 (Mean, Standard Deviation and Variance):

https://www.gnu.org/software/gsl/manual/html_node/Mean-and-standard-deviation-and-variance.html#Mean-and-standard-deviation-and-variance

Best,
Tim

2016-01-21 18:00 GMT+01:00 <address@hidden>:

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>    1. how to use gsl_stats_tss after gsl_multifit_linear to get R^2
>       (jean-michel richer)
>
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Thu, 21 Jan 2016 17:13:16 +0100
> From: jean-michel richer <address@hidden>
> To: <address@hidden>
> Subject: [Help-gsl] how to use gsl_stats_tss after gsl_multifit_linear
>         to get R^2
> Message-ID: <address@hidden>
> Content-Type: text/plain; charset=UTF-8; format=flowed
>
>
> Hi,
> I am using "gsl_multifit_linear" to perform multiple linear
> regression and it works fine, but I would like to get the
> R^2 value. In the documentation it is said that it can be
> obtained from :
>
> "R^2 = 1 - \chi^2 / TSS, where the total sum of squares
> (TSS) of the observations may be computed from gsl_stats_tss"
>
> However I don't know how to use "gsl_stats_tss", I didn't find
> some example on internet !
> This function has the following prototype :
>
>   double gsl_stats_tss (const double data[], size_t stride, size_t n)
>
> but what is data, stride and n ?
>
> The source code I am using is as follows:
> ===================================================
>
>         int N = v.size();
>         int P = 10;
>
>         gsl_vector *y; // observed data
>         gsl_matrix *X; // data used to predict : cste + ...
>         gsl_vector *c; // the coefficients c0, c1, ...
>         gsl_matrix *cov;
>
>         // allocate space for the matrices and vectors
>         X = gsl_matrix_alloc(N, P); // this is an input
>         y = gsl_vector_alloc(N); //this is an input
>
>         c = gsl_vector_alloc(P); //this is an output
>         cov = gsl_matrix_alloc(P, P); //this is an output
>
>         // fill the matrices X and y
>         u32 i = 0;
>         for (auto z : v) {
>                 gsl_matrix_set(X, i, 0, static_cast<f64>(1)); // because
> cste
>                 gsl_matrix_set(X, i, 1,
> static_cast<f64>(z->get(Instance::K)));
>                 gsl_matrix_set(X, i, 2,
> static_cast<f64>(z->get(Instance::L)));
>                 gsl_matrix_set(X, i, 3,
> static_cast<f64>(z->get(Instance::R)));
>                 gsl_matrix_set(X, i, 4,
> static_cast<f64>(z->get(Instance::N)));
>                 gsl_matrix_set(X, i, 5,
> static_cast<f64>(z->get(Instance::G)));
>                 gsl_matrix_set(X, i, 6,
> static_cast<f64>(z->get(Instance::S)));
>                 gsl_matrix_set(X, i, 7,
> static_cast<f64>(z->get(Instance::RN)));
>                 gsl_matrix_set(X, i, 8,
> static_cast<f64>(z->get(Instance::RG)));
>                 gsl_matrix_set(X, i, 9,
> static_cast<f64>(z->get(Instance::RB)));
>                 // expected value
>                 gsl_vector_set(y, i,
> static_cast<f64>(z->get(Instance::B)));
>                 ++i;
>         }
>
>         // allocate temporary work space for gsl
>         gsl_multifit_linear_workspace *work;
>         work = gsl_multifit_linear_alloc(N, P);
>
>         // now do the fit
>         gsl_multifit_linear(X, y, c, cov, &chisq, work);
>
> ===================================================
> So after this how can I compute R^2 ?
> Thanks for your help in advance.
> JM
>
>
>
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