3.9.5.5 OriginC: Regression Analysis

1 Version Info
2 Linear Regression
3 Multiple Linear Regression
4 Nonlinear Regression

Version Info

Minimum Origin Version Required: Origin 8 SR0

Linear Regression

#include <oc_nag.h>
//#include  <nag\OC_nag_ex.h> //not need, only oc_nag.h required.
void nag_linear_regression_ex1()
{
   // data input directly by vector
   vector vx = {1,0,4,7.5,2.5,0,10,5}; 
   vector vy = {20,15.5,28.3,45,24.5,10,99,31.2};
   vector vw = {1,1,1,1,1,1,1,1};

					
   Nag_SumSquare mean = Nag_AboutMean;
   int  n;
   n = vx.GetSize();
			
   double a, b, err_a, err_b, rsq, rss, df;
		
   g02cac(mean, n, vx, vy, vw, &a, &b, &err_a, &err_b, &rsq, &rss,
             &df, NAGERR_DEFAULT);


        
   // output intepretation: a+b*x  b is the slope, a is the intercept   
   if (mean == Nag_AboutMean)
     {
       printf("\nRegression constant a = %6.4f\n\n", a);
       printf("Standard error of the regression constant a = %6.4f\n\n",err_a); 
     }
	
   printf("Regression coefficient b = %6.4f\n\n", b);
   printf("Standard error of the regression coefficient b = %6.4f\n\n",err_b);

   printf("The regression coefficient of determination = %6.4f\n\n", rsq);
   printf("The sum of squares of the residuals about the " "regression = %6.4f\n\n", rss);
   printf("Number of degrees of freedom about the " "regression = %6.4f\n\n",df);  

    //Expected Result:      
    //Regression constant a = 7.5982
 
    //Standard error of the regression constant a = 6.6858
    //
    //Regression coefficient b = 7.0905
    //
    //Standard error of the regression coefficient b = 1.3224
    //
    //The regression coefficient of determination = 0.8273
    //
    //The sum of squares of the residuals about the regression = 965.2454
    //
    //Number of degrees of freedom about the regression = 6.0000
 
}

#include <oc_nag.h>
//#include  <nag\OC_nag_ex.h>  //not need, only oc_nag.h required.
void nag_linear_regression_ex2()
{
// obtain regression data from an Origin Worksheet
    Worksheet wks=Project.ActiveLayer();
    if(!wks)
        printf("no active worksheet found\n");    
    Dataset dsSrcX(wks,0); // assume that the x, y data and weight data are in the first three columns
    Dataset dsSrcY(wks,1);
    Dataset dsSrcW(wks,2);
    int nSize;
    vector vx(nSize);
    vector vy(nSize);
    vector vw(nSize);
    vx=dsSrcX;
    vy=dsSrcY;
    vw=dsSrcW;

    int  n;
    n = vx.GetSize();
    Nag_SumSquare mean = Nag_AboutMean;

    double a, b, err_a, err_b, rsq, rss, df;
		
   g02cac(mean, n, vx, vy, vw, &a, &b, &err_a, &err_b, &rsq, &rss,
             &df, NAGERR_DEFAULT);
 
       
   // output intepretation: a+b*x  b is the slope, a is the intercept 
   if (mean == Nag_AboutMean)
     {
       printf("\nRegression constant a = %6.4f\n\n", a);
       printf("Standard error of the regression constant a = %6.4f\n\n",err_a); 
     }
	
   printf("Regression coefficient b = %6.4f\n\n", b);
   printf("Standard error of the regression coefficient b = %6.4f\n\n",err_b);

   printf("The regression coefficient of determination = %6.4f\n\n", rsq);
   printf("The sum of squares of the residuals about the " "regression = %6.4f\n\n", rss);
   printf("Number of degrees of freedom about the " "regression = %6.4f\n\n",df);  

  

}

Multiple Linear Regression

#include <oc_nag.h>
//#include  <nag\OC_nag_ex.h>  //not need, only oc_nag.h required.
void nag_regsn_mult_linear_ex()
{
	
		
	double rss, tol;
	int i, ip, rank, j, m, n;
	double df;
	Boolean svd;
	char weight, meanc;
	Nag_IncludeMean mean;
	double b[20];
	double cov[210], h[20], p[440];
	double res[20], se[20];
	double com_ar[495];
  	double wt[20];
	matrix q;
	q.SetSize(20, 21);
	double *wtptr;
	n = 12;
	m = 4;
	mean = Nag_MeanInclude;
	wtptr =NULL;
	
	// input data is only the first four columns, the design matrix
	matrix x = 	{{1.0, 0.0, 0.0, 0.0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
			 {0.0, 0.0, 0.0, 1.0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
			 {0.0, 1.0, 0.0, 0.0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
			 {0.0, 0.0, 1.0, 0.0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
			 {0.0, 0.0, 0.0, 1.0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
			 {0.0, 1.0, 0.0, 0.0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
			 {0.0, 0.0, 0.0, 1.0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},	
			 {1.0, 0.0, 0.0, 0.0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},		  
			 {0.0, 0.0, 1.0, 0.0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
			 {1.0, 0.0, 0.0, 0.0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},		  
			 {0.0, 0.0, 1.0, 0.0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},     
			 {0.0, 1.0, 0.0, 0.0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},		  
			 {0.0, 0.0, 0.0, 0.0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},	
			 {0.0, 0.0, 0.0, 0.0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
			 {0.0, 0.0, 0.0, 0.0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
			 {0.0, 0.0, 0.0, 0.0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
			 {0.0, 0.0, 0.0, 0.0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
			 {0.0, 0.0, 0.0, 0.0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
			 {0.0, 0.0, 0.0, 0.0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
			 {0.0, 0.0, 0.0, 0.0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}
			};

	double y[20] = {33.63, 39.62, 38.18, 41.46, 38.02, 35.83, 
			35.99, 36.58, 42.92, 37.80, 40.43, 37.89}; // the y data
		
	int sx[20] = {1, 1, 1, 1};
	
	printf("The  input data are as follows\n");
	printf("n = 12, m = 4, tol = 0.000001e0\n");
	printf("x\n");
	for(i = 0; i < n; i++) 
	{
		for(j = 0; j < m; j++)
			printf("%2.1f, ",x[i][j]);
			printf("\n");
	}
	printf("\ny\n");
	for(i = 0; i < n; i ++)
	{
		printf("%5.3f, ", y[i]);
		if((i + 1) % 7 == 0)
			printf("\n");
	}
		
	ip = 0;
	if (mean==Nag_MeanInclude)
		ip += 1;
	for (i=0; i<m; i++)
		if (sx[i]>0) ip += 1;
	tol = 0.00001e0;
		
	nag_regsn_mult_linear(mean, n, x, 20, m, sx, ip, y,
		wtptr, &rss, &df, b, se, cov, res, h, q, 21, &svd, &rank, p, tol, com_ar, NAGERR_DEFAULT);

	if (svd)
	{	printf("\nModel not of full rank, rank = %4ld\n", rank);
		ASSERT( rank == 4 );
	}
	
	printf("Residual sum of squares = %12.4e\n", rss);	
	printf("Degrees of freedom = %3.1f\n\n", df);
	

	printf("Variable       Parameter           Estimate Standard error\n\n");  // the standard error
	for (j=0; j<ip; j++)
		printf("%6ld%20.4e%20.4e\n", j+1, b[j], se[j]);
	
	
	printf("\n");
	printf("Obs            Residuals           h\n\n");  // the residuals
	for (i=0; i<n; i++)
		printf("%6ld%20.4e%20.4e\n", i+1, res[i], h[i]);
		
}

Nonlinear Regression

#include <OC_nag.h>

//Callback to calculate objective subfunction values, and (optionally) its Jacobian
void NAG_CALL objfun_callback(int m, int n, double p[], double f[], 
			      double fjac[], int tdfjac,Nag_Comm *comm)
{
#define FJAC(I,J) fjac[(I)*tdfjac +(J)]
	
	static vector x = {
		8.0, 8.0, 10.0, 10.0, 10.0, 10.0, 12.0, 12.0, 12.0, 12.0, 14.0, 14.0,
		14.0, 16.0, 16.0, 16.0, 18.0, 18.0, 20.0, 20.0, 20.0, 22.0, 22.0, 22.0,
		24.0, 24.0, 24.0, 26.0, 26.0, 26.0, 28.0, 28.0, 30.0, 30.0, 30.0, 32.0,
		32.0, 34.0, 36.0, 36.0, 38.0, 38.0, 40.0, 42.0};
	
	double temp;	
	for(int i = 0; i < m; ++i)
	{
		//evaluate objective subfunction f(i+1) only if required
		if(comm->needf == i+1 || comm->needf == 0)
		{
			temp = exp(-p[1] * (x[i] - 8.0));
			f[i] = p[0] + (.49 - p[0]) * temp;			
		}
		//evaluate the Jacobian if required
		if(comm->flag == 2)
		{
			FJAC(i, 0) = 1.0 - temp;
			FJAC(i, 1) = -(0.49 - p[0]) * (x[i] - 8.0) * temp;
		}		
	}	
}

//Callback to calculate nonlinear constraints and (optinally) its Jacobian
static void NAG_CALL confun_callback(int n, int ncnlin, int needc[], double p[], 
			            double conf[], double cjac[], Nag_Comm *comm)
{
#define CJAC(I, J) cjac[(I)*n + (J)]
	
	//First call to confun. Set all Jacobian elements to zero.
	//Note that this will only work when options.obj_deriv = TRUE(default)
	if(comm->first == true)		
		CJAC(0, 0) = CJAC(0, 1) = 0.0;
	
	if(needc[0] > 0)
	{
		conf[0] = -.09 - p[0]*p[1] + 0.49*p[1];
		if(comm->flag == 2)
		{
			CJAC(0, 0) = -p[1];
			CJAC(0, 1) = -p[0] + .49;
		}
	}
}

void nag_opt_nlin_lsq_ex()
{
	vector y = {0.49, 0.49, 0.48, 0.47, 0.48, 0.47, 0.46, 0.46, 0.45, 0.43, 0.45,
				0.43, 0.43, 0.44, 0.43, 0.43, 0.46, 0.45, 0.42, 0.42, 0.43, 0.41,
				0.41, 0.40, 0.42, 0.40, 0.40, 0.41, 0.40, 0.41, 0.41, 0.40, 0.40,
				0.40, 0.38, 0.41, 0.40, 0.40, 0.41, 0.38, 0.40, 0.40, 0.39, 0.39};
	
	int m = y.GetSize(), n = 2;
	int tda = n, tdfjac = n;
	int nclin = 1, ncnlin = 1;
	
	vector p = {0.4, 0.0};//initial parameters
	vector a = {1.0, 1.0};//linear constraints
	vector bl = {0.4, -4.0, 1.0, 0.0}; //lower bounds
	vector bu = {1.0e+25, 1.0e+25, 1.0e+25, 1.0e+25}; //upper bounds
	vector f(m), fjac(m*n);
	double objf;
	
	Nag_E04_Opt options;
	nag_opt_init(&options);
	strcpy(options.outfile, "c:\\nag_opt_nlin_lsq_ex.txt");
	
	NagError fail;
	
	e04unc(m, n, nclin, ncnlin, a, tda, bl, bu, y, objfun_callback, confun_callback,
		p, &objf, f, fjac, tdfjac, &options, NAGCOMM_NULL, &fail);
			
	if(fail.code == NE_NOERROR)
	{
		printf("fitting paramters: %lf %lf \n", p[0], p[1]);
		printf("value of objective function: %lf \n", objf);	
	}
	else
	{
		printf("fitting failed, error code = %d", fail.code);
	}
	
	//Expected Result:  
	//fitting paramters: 0.419953 1.284845 
	//value of objective function: 0.014230
}

3.9.5.5 OriginC: Regression Analysis

Contents

Version Info

Linear Regression

Multiple Linear Regression

Nonlinear Regression