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## Re: [Help-gsl] Where oh where did the correlation cofficient go?

 From: Jack Denman Subject: Re: [Help-gsl] Where oh where did the correlation cofficient go? Date: Fri, 25 May 2007 06:31:49 -0700

```At 02:25 AM 5/23/2007, you wrote:
>At Mon, 21 May 2007 23:11:15 -0700,
>Jack Denman wrote:
>> I discovered this great library, but in the linear regression code I
>> cannot find a way to get the correlation coefficient "rho" or r that
>> indicates the degree if fit. Am I missing something?
>
>Hello,
>
>We return the covariance matrix which gives more
>information, you can calculate the correlation
>coefficient from it as rho = c11/sqrt(c00*c11).
>
>--
>Brian Gough

I must have done something wrong. I created the results of an ideal linear
function of y = mx +b and did the regression on the values and calculated the
value of rho. I did this to check the accuracy of my code. The answer was off
by a factor of roughly fifty ( rho = 0.02 ). I used both unweighted and
neutrally weighted function calls. Below is listed the results and the code.

Where did I go wrong?

BTW: Thanks for the book advertisement.

Jack Denman
Fullerton California

*********************RESULTS************************************************************

# best fit: Y = 8.2 + 0.45 X
# covariance matrix:
# [ 0.0490741, -0.000925926  -0.000925926, 2.34412e-05]
# chisq = 1.54727e-28
r = 0.0218556
# best fit: Y = 8.2 + 0.45 X
# covariance matrix:
# [ 9.35661e-32, -1.7654e-33  -1.7654e-33, 4.46936e-35]
# sumsq = 1.48717e-28
r = 0.0218556
fit: -23.7 -2.465
hi : -23.7 -2.465
lo : -23.7 -2.465
fit: -22.91 -2.1095
hi : -22.91 -2.1095
lo : -22.91 -2.1095
fit: -22.12 -1.754
hi : -22.12 -1.754
lo : -22.12 -1.754
fit: -21.33 -1.3985
hi : -21.33 -1.3985
lo : -21.33 -1.3985
fit: -20.54 -1.043
hi : -20.54 -1.043
lo : -20.54 -1.043

*****************************CODE
*********************************************************
#include <stdio.h>
#include <math.h>
#include <gsl/gsl_fit.h>
/*
int gsl_fit_linear (
const double *x,
const size_t xstride,
const double *y,
const size_t ystride,
const size_t n,
double *c0,
double *c1,
double *cov_00,
double *cov_01,
double *cov_11,
*/
int main ( void )
{
int     i, n = 80;
double  x[80] = {\
0.000000,  1.000000,   2.000000, 3.000000,   4.000000,  5.000000,
6.000000,  7.000000,  8.000000,  9.000000, \
10.000000, 11.000000, 12.000000, 13.000000, 14.000000, 15.000000,
16.000000, 17.000000, 18.000000, 19.000000, 20.000000,\
21.000000, 22.000000, 23.000000, 24.000000, 25.000000, 26.000000,
27.000000, 28.000000, 29.000000, 30.000000, 31.000000,\
32.000000, 33.000000, 34.000000, 35.000000, 36.000000, 37.000000,
38.000000, 39.000000, 40.000000, 41.000000, 42.000000,\
43.000000, 44.000000, 45.000000, 46.000000, 47.000000, 48.000000,
49.000000, 50.000000, 51.000000, 52.000000, 53.000000,\
54.000000, 55.000000, 56.000000, 57.000000, 58.000000, 59.000000,
60.000000, 61.000000, 62.000000, 63.000000, 64.000000,\
65.000000, 66.000000, 67.000000, 68.000000, 69.000000, 70.000000,
71.000000, 72.000000, 73.000000, 74.000000, 75.000000,\
76.000000, 77.000000, 78.000000, 79.000000};
double y [80]= {\
8.200000,  8.650000,  9.100000,  9.550000, 10.000000, 10.450000,
10.900000, 11.350000, 11.800000, 12.250000, 12.700000, 13.150000,\
13.600000, 14.050000, 14.500000, 14.950000, 15.400000, 15.850000,
16.300000, 16.750000, 17.200000, 17.650000, 18.100000, 18.550000,\
19.000000, 19.450000, 19.900000, 20.350000, 20.800000, 21.250000,
21.700000, 22.150000, 22.600000, 23.050000, 23.500000, 23.950000,\
24.400000, 24.850000, 25.300000, 25.750000, 26.200000, 26.650000,
27.100000, 27.550000, 28.000000, 28.450000, 28.900000, 29.350000,\
29.800000, 30.250000, 30.700000, 31.150000, 31.600000, 32.050000,
32.500000, 32.950000, 33.400000, 33.850000, 34.300000, 34.750000,\
35.200000, 35.650000, 36.100000, 36.550000, 37.000000, 37.450000,
37.900000, 38.350000, 38.800000, 39.250000, 39.700000, 40.150000,\
40.600000, 41.050000, 41.500000, 41.950000, 42.400000, 42.850000,
43.300000, 43.750000};

double  w[80];
for  ( i = 0; i < 80; i++ )
w[i] = 1.0;

#if 0
int     i, n = 4;
double  x[4] = { 1970, 1980, 1990, 2000 };
double  y[4] = { 12, 11, 14, 13 };
#endif
double  c0, c1, cov00, cov01, cov11, chisq;
double  cov_00, cov_01, cov_11, sumsq;
size_t  xstride, ystride;
int rc;
gsl_fit_wlinear ( x, 1, w, 1, y, 1, n, &c0, &c1, &cov00, &cov01, &cov11,
&chisq );
printf ( "# best fit: Y = %g + %g X\n", c0, c1 );
printf ( "# covariance matrix:\n" );
printf ( "# [ %g, %g  %g, %g]\n", cov00, cov01, cov01, cov11 );
printf ( "# chisq = %g\n", chisq );
printf ("r = %g\n", cov11 / sqrt (cov00 * cov11 ) );
//for ( i = 0; i < n; i++ )
//      printf ( "data: %g %g %g\n", x[i], y[i], 1/sqrt(w[i]) );
gsl_fit_linear  ( x, 1, y, 1, n, &c0, &c1, &cov_00, &cov_01, &cov_11,
&sumsq );
printf ( "# best fit: Y = %g + %g X\n", c0, c1 );
printf ( "# covariance matrix:\n" );
printf ( "# [ %g, %g  %g, %g]\n", cov_00, cov_01, cov_01, cov_11 );
printf ( "# sumsq = %g\n", sumsq );
printf ("r = %g\n", cov_11 / sqrt (cov_00 * cov_11 ) );

//    for ( i = 0; i < n; i++ )
//      printf ( "data: %g %g\n", x[i], y[i] );
printf ( "\n" );
for ( i = -30; i < 130; i++ )
{
double  xf = x[0] + ( i / 100.0 ) * ( x[n - 1] - x[0] );
double  yf, yf_err;
/*      gsl_fit_linear_est ( xf, c0, c1, cov00, cov01, cov11, &yf, &yf_err ); */
gsl_fit_linear_est ( xf, c0, c1, cov_00, cov_01, cov_11, &yf, &yf_err );
printf ( "fit: %g %g\n", xf, yf );
printf ( "hi : %g %g\n", xf, yf + yf_err );
printf ( "lo : %g %g\n", xf, yf - yf_err );
}
return 0;
}

```

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