Getting the p-value for linear regression in the C function gsl_fit_linear () from the GSL library

Question

I am trying to reproduce some code from R to C, so I am trying to set linear regression using the gsl_fit_linear() function.

In R, I would use the lm () function, which returns the value p to match using this code:

 lmAvgs<- lm( c(1.23, 11.432, 14.653, 21.6534) ~ c(1970, 1980, 1990, 2000) ) summary(lmAvgs) 

I have no idea how to go from C output to p-value, my code looks something like this:

 int main(void) { int i, n = 4; double x[4] = { 1970, 1980, 1990, 2000 }; double y[4] = {1.23, 11.432, 14.653, 21.6534}; double c0, c1, cov00, cov01, cov11, sumsq; gsl_fit_linear (x, 1, y, 1, n, &c0, &c1, &cov00, &cov01, &cov11, &sumsq); } 

It seems to calculate the slope and intercept correctly, but I don't know how to get the p value. I am new to statistics and C!

Answer 1

All Inclusive: http://en.wikipedia.org/wiki/Ordinary_least_squares . but here is a piece of code that displays a result similar to the final (lmAvgs) in R. To run it, you need the GSL Library :

 int n = 4; double x[4] = { 1970, 1980, 1990, 2000}; double y[4] = {1.23, 11.432, 14.653, 21.6534}; double c0, c1, cov00, cov01, cov11, sumsq; gsl_fit_linear (x, 1, y, 1, n, &c0, &c1, &cov00, &cov01, &cov11, &sumsq); cout<<"Coefficients\tEstimate\tStd. Error\tt value\tPr(>|t|)"<<endl; double stdev0=sqrt(cov00); double t0=c0/stdev0; double pv0=t0<0?2*(1-gsl_cdf_tdist_P(-t0,n-2)):2*(1-gsl_cdf_tdist_P(t0,n-2));//This is the p-value of the constant term cout<<"Intercept\t"<<c0<<"\t"<<stdev0<<"\t"<<t0<<"\t"<<pv0<<endl; double stdev1=sqrt(cov11); double t1=c1/stdev1; double pv1=t1<0?2*(1-gsl_cdf_tdist_P(-t1,n-2)):2*(1-gsl_cdf_tdist_P(t1,n-2));//This is the p-value of the linear term cout<<"x\t"<<c1<<"\t"<<stdev1<<"\t"<<t1<<"\t"<<pv1<<endl; double dl=n-2;//degrees of liberty double ym=0.25*(y[0]+y[1]+y[2]+y[3]); //Average of vector y double sct=pow(y[0]-ym,2)+pow(y[1]-ym,2)+pow(y[2]-ym,2)+pow(y[3]-ym,2); // sct = sum of total squares double R2=1-sumsq/sct; cout<<"Multiple R-squared: "<<R2<<", Adjusted R-squared: "<<1-double(n-1)/dl*(1-R2)<<endl; double F=R2*dl/(1-R2); double p_value=1-gsl_cdf_fdist_P(F,1,dl); cout<<"F-statistic: "<<F<<" on 1 and "<<n-2<<" DF, p-value: "<<p_value<<endl; 

What gives:

 Coefficients Estimate Std. Error t value Pr(>|t|) Intercept -1267.91 181.409 -6.98922 0.0198633 x 0.644912 0.0913886 7.05681 0.0194956 Multiple R-squared: 0.961389, Adjusted R-squared: 0.942083 F-statistic: 49.7986 on 1 and 2 DF, p-value: 0.0194956 

R gives:

 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -1.268e+03 1.814e+02 -6.989 0.0199 * c(1970, 1980, 1990, 2000) 6.449e-01 9.139e-02 7.057 0.0195 * --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 2.044 on 2 degrees of freedom Multiple R-squared: 0.9614, Adjusted R-squared: 0.9421 F-statistic: 49.8 on 1 and 2 DF, p-value: 0.01950