NAG Library Manual, Mark 28.6
```/* nag_correg_linregm_fit (g02dac) Example Program.
*
* Copyright 2022 Numerical Algorithms Group.
*
* Mark 28.6, 2022.
*/

#include <math.h>
#include <nag.h>
#include <stdio.h>

static int ex1(void);
static int ex2(void);

int main(void) {
Integer exit_status_ex1 = 0;
Integer exit_status_ex2 = 0;

printf("nag_correg_linregm_fit (g02dac) Example Program Results\n\n");

/* Skip heading in data file */
scanf("%*[^\n] ");

exit_status_ex1 = ex1();
exit_status_ex2 = ex2();

return (exit_status_ex1 == 0 && exit_status_ex2 == 0) ? 0 : 1;
}

#define X(I, J) x[(I)*tdx + J]

static int ex1(void) {
Integer exit_status = 0, i, ip, j, m, n, rank, *sx = 0, tdq, tdx;
char nag_enum_arg[40];
double *b = 0, *com_ar = 0, *cov = 0, df, *h = 0, *p = 0, *q = 0;
double *res = 0, rss, *se = 0, tol, *wt = 0, *wtptr, *x = 0, *y = 0;
Nag_Boolean svd, weight;
Nag_IncludeMean mean;
NagError fail;

INIT_FAIL(fail);

printf("Example 1\n");
/* Skip heading in data file */
scanf("%*[^\n]");
scanf("%" NAG_IFMT " %" NAG_IFMT "", &n, &m);
scanf(" %39s", nag_enum_arg);
/* nag_enum_name_to_value (x04nac).
* Converts NAG enum member name to value
*/
weight = (Nag_Boolean)nag_enum_name_to_value(nag_enum_arg);
scanf(" %39s", nag_enum_arg);
mean = (Nag_IncludeMean)nag_enum_name_to_value(nag_enum_arg);
if (n >= 2 && m >= 1) {
if (!(h = NAG_ALLOC(n, double)) || !(res = NAG_ALLOC(n, double)) ||
!(wt = NAG_ALLOC(n, double)) || !(x = NAG_ALLOC(n * m, double)) ||
!(y = NAG_ALLOC(n, double)) || !(sx = NAG_ALLOC(m, Integer))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
tdx = m;
} else {
printf("Invalid n or m.\n");
exit_status = 1;
return exit_status;
}
if (weight) {
wtptr = wt;
for (i = 0; i < n; i++) {
for (j = 0; j < m; j++)
scanf("%lf", &X(i, j));
scanf("%lf%lf", &y[i], &wt[i]);
}
} else {
wtptr = (double *)0;
for (i = 0; i < n; i++) {
for (j = 0; j < m; j++)
scanf("%lf", &X(i, j));
scanf("%lf", &y[i]);
}
}
for (j = 0; j < m; j++)
scanf("%" NAG_IFMT "", &sx[j]);
/* Calculate ip */
ip = 0;
if (mean == Nag_MeanInclude)
ip += 1;
for (i = 0; i < m; i++)
if (sx[i] > 0)
ip += 1;

if (!(b = NAG_ALLOC(ip, double)) ||
!(cov = NAG_ALLOC((ip * ip + ip) / 2, double)) ||
!(p = NAG_ALLOC(ip * (ip + 2), double)) ||
!(q = NAG_ALLOC(n * (ip + 1), double)) ||
!(com_ar = NAG_ALLOC(ip * ip + ip, double)) ||
!(se = NAG_ALLOC(ip, double))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
tdq = ip + 1;

/* Set tolerance */
tol = 0.00001e0;
/* nag_correg_linregm_fit (g02dac).
* Fits a general (multiple) linear regression model
*/
nag_correg_linregm_fit(mean, n, x, tdx, m, sx, ip, y, wtptr, &rss, &df, b, se,
cov, res, h, q, tdq, &svd, &rank, p, tol, com_ar,
&fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_correg_linregm_fit (g02dac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

if (svd)
printf("Model not of full rank, rank = %4" NAG_IFMT "\n\n", rank);
printf("Residual sum of squares = %13.4e\n", rss);
printf("Degrees of freedom = %3.1f\n\n", df);
printf("Variable    Parameter estimate   Standard error\n\n");
for (j = 0; j < ip; j++)
printf("%6" NAG_IFMT "%20.4e%20.4e\n", j + 1, b[j], se[j]);
printf("\n");
printf("    Obs         Residuals              h\n\n");
for (i = 0; i < n; i++)
printf("%6" NAG_IFMT "%20.4e%20.4e\n", i + 1, res[i], h[i]);

END:
NAG_FREE(h);
NAG_FREE(res);
NAG_FREE(wt);
NAG_FREE(x);
NAG_FREE(y);
NAG_FREE(sx);
NAG_FREE(b);
NAG_FREE(cov);
NAG_FREE(p);
NAG_FREE(q);
NAG_FREE(com_ar);
NAG_FREE(se);

return exit_status;
}

#undef x

#define X(I, J) x[(I)*tdx + J]
static int ex2(void) {
Integer exit_status = 0;
Integer i, ip, rank, j, m, mmax, n, degree, digits, tdx, tdq;
double df;
Nag_Boolean svd;
Nag_IncludeMean mean;
double *h = 0, *res = 0, *wt = 0, *x = 0, *y = 0;
double *b = 0, *cov = 0, *p = 0, *q = 0, *com_ar = 0, *se = 0;
double *wtptr = (double *)0; /* don't use weights */
Integer *sx = 0;
NagError fail;

INIT_FAIL(fail);

printf("\n\n\nExample 2\n");
/* Skip heading in data file */
scanf(" %*[^\n]");

/* Use mean = Nag_MeanInclude */

mean = Nag_MeanInclude;
scanf("%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "", &degree, &n, &digits);
mmax = degree + 1;
if (n >= 1) {
if (!(h = NAG_ALLOC(n, double)) || !(res = NAG_ALLOC(n, double)) ||
!(wt = NAG_ALLOC(n, double)) || !(x = NAG_ALLOC(n * mmax, double)) ||
!(y = NAG_ALLOC(n, double)) || !(sx = NAG_ALLOC(mmax, Integer))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
tdx = mmax;
} else {
printf("Invalid n.\n");
exit_status = 1;
return exit_status;
}

/* Set tolerance */
tol = pow(10.0, -(double)digits);
m = degree;
ip = degree + 1;
if (!(b = NAG_ALLOC(ip, double)) ||
!(cov = NAG_ALLOC((ip * ip + ip) / 2, double)) ||
!(p = NAG_ALLOC(ip * (ip + 2), double)) ||
!(q = NAG_ALLOC(n * (ip + 1), double)) ||
!(com_ar = NAG_ALLOC(ip * ip + ip, double)) ||
!(se = NAG_ALLOC(ip, double))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
tdq = ip + 1;

for (i = 0; i < ip - 1; ++i)
sx[i] = 1;

for (i = 0; i < n; i++) {
scanf("%lf%lf", &X(i, degree - 1), &y[i]);
for (j = 0; j < degree; ++j)
X(i, j) = pow(X(i, degree - 1), (double)(degree - j));
}

/* nag_correg_linregm_fit (g02dac), see above. */
nag_correg_linregm_fit(mean, n, x, tdx, m, sx, ip, y, wtptr, &rss, &df, b, se,
cov, res, h, q, tdq, &svd, &rank, p, tol, com_ar,
&fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_correg_linregm_fit (g02dac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

printf("Regression estimates  (mean = Nag_MeanInclude) \n\n");
printf("Coefficient    Estimate         Standard error\n\n");
for (j = 1; j < ip; j++)
printf("a(%" NAG_IFMT ")%20.4e%20.4e\n", degree + 1 - j, b[j], se[j]);
printf("a(0)%20.4e%20.4e\n", b[0], se[0]);
printf("\n\n");

/* Use mean = Nag_MeanZero */

mean = Nag_MeanZero;

m = degree + 1;
for (i = 0; i < ip; ++i)
sx[i] = 1;

for (i = 0; i < n; i++)
X(i, m - 1) = 1.0;

/* nag_correg_linregm_fit (g02dac), see above. */
nag_correg_linregm_fit(mean, n, x, tdx, m, sx, ip, y, wtptr, &rss, &df, b, se,
cov, res, h, q, tdq, &svd, &rank, p, tol, com_ar,
&fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_correg_linregm_fit (g02dac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

printf("Regression estimates  (mean = Nag_MeanZero) \n\n");
printf("Coefficient    Estimate         Standard error\n\n");
for (j = 0; j < ip; j++)
printf("a(%" NAG_IFMT ")%20.4e%20.4e\n", degree - j, b[j], se[j]);
printf("\n\n");

END:
NAG_FREE(h);
NAG_FREE(res);
NAG_FREE(wt);
NAG_FREE(x);
NAG_FREE(y);
NAG_FREE(sx);
NAG_FREE(b);
NAG_FREE(cov);
NAG_FREE(p);
NAG_FREE(q);
NAG_FREE(com_ar);
NAG_FREE(se);

return exit_status;
}
```