多元最小二乘法c语言实现

多元最小二乘法（Multiple Linear Regression）可以用于数据拟合和预测，可以使用C语言实现。以下是一个简单的C语言实现多元最小二乘法的示例代码：

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

#define MAX 100

void multipleLinearRegression(double x[][MAX], double y[], int n, int m, double beta[]);
void transpose(double x[][MAX], double xt[][MAX], int n, int m);
void matrixMultiplication(double a[][MAX], double b[][MAX], double c[][MAX], int n1, int m1, int n2, int m2);

int main()
{
    int n, m, i, j;
    double x[MAX][MAX], y[MAX], beta[MAX];

    printf("Enter the number of observations: ");
    scanf("%d", &n);

    printf("Enter the number of independent variables: ");
    scanf("%d", &m);

    printf("Enter the independent variables: \n");
    for(i = 0; i < n; i++)
    {
        printf("Observation %d: ", i + 1);
        for(j = 0; j < m; j++)
        {
            scanf("%lf", &x[i][j]);
        }
    }

    printf("Enter the dependent variable: \n");
    for(i = 0; i < n; i++)
    {
        printf("Observation %d: ", i + 1);
        scanf("%lf", &y[i]);
    }

    multipleLinearRegression(x, y, n, m, beta);

    printf("The regression equation is: y = ");
    for(i = 0; i < m; i++)
    {
        printf("%lf x%d + ", beta[i], i + 1);
    }
    printf("%lf\n", beta[m]);

    return 0;
}

void multipleLinearRegression(double x[][MAX], double y[], int n, int m, double beta[])
{
    double xt[MAX][MAX], xtx[MAX][MAX], xty[MAX], inv[MAX][MAX], det = 0;
    int i, j, k;

    transpose(x, xt, n, m);
    matrixMultiplication(xt, x, xtx, m, n, n, m);
    matrixMultiplication(xt, y, xty, m, n, n, 1);

    for(i = 0; i < m; i++)
    {
        for(j = 0; j < m; j++)
        {
            inv[i][j] = 0;
        }
    }

    for(i = 0; i < m; i++)
    {
        for(j = 0; j < m; j++)
        {
            double a[MAX][MAX], b[MAX][MAX];
            int r, c;

            for(k = 0; k < m; k++)
            {
                for(r = 0; r < m; r++)
                {
                    a[k][r] = xtx[k][r];
                }
            }

            for(k = 0; k < m; k++)
            {
                if(k == i) b[k][0] = 1;
                else b[k][0] = 0;
            }

            for(k = 0; k < m; k++)
            {
                if(k == j) b[k][1] = 1;
                else b[k][1] = 0;
            }

            for(k = m; k < 2 * m; k++)
            {
                for(r = 0; r < m; r++)
                {
                    a[r][k] = b[r][k - m];
                }
            }

            for(c = 0; c < 2 * m; c++)
            {
                for(k = c + 1; k < 2 * m; k++)
                {
                    double f = a[k][c] / a[c][c];
                    for(r = c; r < 2 * m; r++)
                    {
                        a[k][r] -= f * a[c][r];
                    }
                }
            }

            double p = 1;
            for(k = 0; k < m; k++)
            {
                p *= a[k][k];
            }

            det += p * pow(-1, i + j);
            inv[j][i] = p * pow(-1, i + j);
        }
    }

    for(i = 0; i < m; i++)
    {
        for(j = 0; j < m; j++)
        {
            inv[i][j] /= det;
        }
    }

    matrixMultiplication(inv, xty, beta, m, m, m, 1);
}

void transpose(double x[][MAX], double xt[][MAX], int n, int m)
{
    int i, j;

    for(i = 0; i < m; i++)
    {
        for(j = 0; j < n; j++)
        {
            xt[i][j] = x[j][i];
        }
    }
}

void matrixMultiplication(double a[][MAX], double b[][MAX], double c[][MAX], int n1, int m1, int n2, int m2)
{
    int i, j, k;

    for(i = 0; i < n1; i++)
    {
        for(j = 0; j < m2; j++)
        {
            c[i][j] = 0;
            for(k = 0; k < n2; k++)
            {
                c[i][j] += a[i][k] * b[k][j];
            }
        }
    }
}

这个程序接受用户输入自变量和因变量的数据，然后计算多元最小二乘法的系数，并输出回归方程。