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  1. #include <stdio.h>
  2. #include <math.h>
  3.  
  4. int main() {
  5.     // 与えられたデータセット (8組)
  6.     double x[8] = {0.15708, 0.23982, 0.37400, 0.57120, 0.82674, 1.04720, 1.23200, 1.43452};
  7.     double y[8] = {0.98769, 0.97138, 0.93087, 0.84125, 0.67728, 0.50000, 0.33236, 0.13586};
  8.  
  9.     double Sx2 = 0, Sx4 = 0, Sy = 0, Sx2y = 0;
  10.  
  11.     // 正規方程式に必要な各合計値の計算
  12.     for (int i = 0; i < 8; i++) {
  13.         double x2 = x[i] * x[i];
  14.         Sx2 += x2;
  15.         Sx4 += x2 * x2;
  16.         Sy += y[i];
  17.         Sx2y += x2 * y[i];
  18.     }
  19.  
  20.     // 正規方程式の行列要素設定
  21.     double A11 = 8,     A12 = Sx2;
  22.     double A21 = Sx2,   A22 = Sx4;
  23.  
  24.     double B1 = Sy,     B2 = Sx2y;
  25.  
  26.     // 2元連立方程式を解く (クラメルの公式 / 行列式デタミナント)
  27.     double det = A11 * A22 - A12 * A21;
  28.     double a1 = (B1 * A22 - A12 * B2) / det;
  29.     double a2 = (A11 * B2 - B1 * A21) / det;
  30.  
  31.     // 結果の出力
  32.     printf("=========================================\n");
  33.     printf("モデル (1): y = a1 + a2*x^2 計算結果\n");
  34.     printf("=========================================\n");
  35.     printf("求められた係数:\n");
  36.     printf("  a1 = %.6f\n", a1);
  37.     printf("  a2 = %.6f\n", a2);
  38.  
  39.     // 残差平方和 (誤差の2乗和 E) の計算
  40.     double E = 0;
  41.     for (int i = 0; i < 8; i++) {
  42.         double yhat = a1 + a2 * x[i] * x[i];
  43.         double diff = y[i] - yhat;
  44.         E += diff * diff;
  45.     }
  46.  
  47.     printf("\n近似式による偏差の2乗和 (誤差 E):\n");
  48.     printf("  E = %.10f\n", E);
  49.  
  50.     // Excelプロット用の予測値出力 (yhatのみ)
  51.     printf("\n近似式による y の予測値 (Excelグラフ作成用):\n");
  52.     for (int i = 0; i < 8; i++) {
  53.         double yhat = a1 + a2 * x[i] * x[i];
  54.         printf("%f\n", yhat);
  55.     }
  56.     printf("=========================================\n");
  57.  
  58.     return 0;
  59. }
Success #stdin #stdout 0s 5320KB
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stdout
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=========================================
モデル (1): y = a1 + a2*x^2 計算結果
=========================================
求められた係数:
  a1 = 0.985005
  a2 = -0.423999

近似式による偏差の2乗和 (誤差 E):
  E = 0.0016966201

近似式による y の予測値 (Excelグラフ作成用):
0.974543
0.960619
0.925697
0.846667
0.695202
0.520035
0.341448
0.112479
=========================================
https://ideone.com/hvPHMd
language:
C (gcc 8.3)
created:
16 hours ago
visibility:
public

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