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

[Patrick Alken]

This is a good answer. Just want to add you can look at the wiki page:

https://en.wikipedia.org/wiki/Coefficient_of_determination

to see the formula for R^2 (which should help to better understand the 
comment in the manual).

Perhaps I should add this formula to the documentation of that chapter.

Patrick

On 01/21/2016 10:50 AM, Timothée Flutre wrote:
> 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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