NAG Library Manual, Mark 29.3
Interfaces:  FL   CL   CPP   AD
```/* nag_correg_linregm_fit_stepwise (g02efc) Example Program.
*
* Copyright 2023 Numerical Algorithms Group.
*
* Mark 29.3, 2023.
*/

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

int main(void) {
/* Scalars */
double fin, fout, rms, rsq, sw, tau;
Integer df, exit_status, i, j, m, n, pdx;

/* Arrays */
double *b = 0, *c = 0, *se = 0, *wmean = 0, *x = 0;
Integer *isx = 0;

/* Nag types */
Nag_OrderType order;
Nag_SumSquare mean;
Nag_Comm comm;
NagError fail;

#ifdef NAG_COLUMN_ORDER
#define X(I, J) x[(J - 1) * pdx + I - 1]
order = Nag_ColMajor;
#else
#define X(I, J) x[(I - 1) * pdx + J - 1]
order = Nag_RowMajor;
#endif

INIT_FAIL(fail);

exit_status = 0;

printf(
"nag_correg_linregm_fit_stepwise (g02efc) Example Program Results\n\n");

/* Skip heading in data file */
scanf("%*[^\n]");
scanf("%" NAG_IFMT " %" NAG_IFMT " %lf %lf %lf", &n, &m, &fin, &fout, &tau);
scanf("%*[^\n]");

if (n > 1 && m > 1) {
/* Allocate memory */
if (!(b = NAG_ALLOC(m + 1, double)) ||
!(c = NAG_ALLOC((m + 1) * (m + 2) / 2, double)) ||
!(se = NAG_ALLOC(m + 1, double)) ||
!(wmean = NAG_ALLOC(m + 1, double)) ||
!(x = NAG_ALLOC(n * (m + 1), double)) ||
!(isx = NAG_ALLOC(m, Integer))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
} else {
printf("Invalid n or m.\n");
exit_status = 1;
return exit_status;
}

#ifdef NAG_COLUMN_ORDER
pdx = n;
#else
pdx = m + 1;
#endif

for (i = 1; i <= n; ++i) {
for (j = 1; j <= m + 1; ++j) {
scanf("%lf", &X(i, j));
}
}
scanf("%*[^\n]");

for (j = 1; j <= m; ++j) {
scanf("%" NAG_IFMT "", &isx[j - 1]);
}
scanf("%*[^\n]");

/* nag_correg_ssqmat (g02buc).
* Computes sums of squares and cross-products of deviations
* from the mean for the augmented matrix
*/
nag_correg_ssqmat(order, mean, n, m + 1, x, pdx, 0, &sw, wmean, c, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_correg_ssqmat (g02buc).\n%s\n.", fail.message);
exit_status = 1;
goto END;
}

fflush(stdout);

/* Perform stepwise selection of variables using
* nag_correg_linregm_fit_stepwise (g02efc):
*   Stepwise linear regression.
*/
nag_correg_linregm_fit_stepwise(
m, n, wmean, c, sw, isx, fin, fout, tau, b, se, &rsq, &rms, &df,
nag_correg_linregm_fit_stepwise_sample_monfun, &comm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_correg_linregm_fit_stepwise (g02efc).\n%s\n.",
fail.message);
exit_status = 1;
goto END;
}

/* Display summary information for fitted model */
printf("\n");
printf("Fitted Model Summary\n");
printf("%-10s   %-10s%19s\n", "Term", " Estimate", "Standard Error");
printf("%-10s   %11.3e%17.3e\n", "Intercept:", b[0], se[0]);
for (i = 1; i <= m; ++i) {
j = isx[i - 1];
if (j == 1 || j == 2) {
printf("%-10s%3" NAG_IFMT "%11.3e%17.3e\n", "Variable:", i, b[i], se[i]);
}
}
printf("\n");
printf("RMS: %-12.3e\n\n", rms);

END:
NAG_FREE(b);
NAG_FREE(c);
NAG_FREE(se);
NAG_FREE(wmean);
NAG_FREE(x);
NAG_FREE(isx);

return exit_status;
}
```