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

int main() {
double x[8] = {0.15708, 0.23982, 0.37400, 0.57120, 0.82674, 1.04720, 1.23200, 1.43452};
double y[8] = {0.98769, 0.97138, 0.93087, 0.84125, 0.67728, 0.50000, 0.33236, 0.13586};

double Sx2 = 0, Sx4 = 0, Sy = 0, Sx2y = 0;

for (int i = 0; i < 8; i++) {
double x2 = x[i] * x[i];
Sx2 += x2;
Sx4 += x2 * x2;
Sy += y[i];
Sx2y += x2 * y[i];
}

// Normal equation matrix
double A11 = 8, A12 = Sx2;
double A21 = Sx2, A22 = Sx4;

double B1 = Sy, B2 = Sx2y;

// Solve 2x2 system
double det = A11 * A22 - A12 * A21;
double a1 = ( B1 * A22 - A12 * B2 ) / det;
double a2 = ( A11 * B2 - B1 * A21 ) / det;

printf("Model 1 coefficients:\n");
printf("a1 = %.6f\n", a1);
printf("a2 = %.6f\n", a2);

// Compute squared error
double E = 0;
for (int i = 0; i < 8; i++) {
double yhat = a1 + a2 * x[i] * x[i];
double diff = y[i] - yhat;
E += diff * diff;
}

printf("Squared error E = %.10f\n", E);

printf("\nModel 1 predicted values:\n");
for (int i = 0; i < 8; i++) {
double yhat = a1 + a2 * x[i] * x[i];
printf("%f\n", yhat);
}

return 0;
}