linearRegressionFit function

List<double> linearRegressionFit(List<List<double>> X, List<double> y)

Implementation

List<double> linearRegressionFit(List<List<double>> X, List<double> y) {
  final n = X.length;
  if (n == 0) return [0.0];
  final m = X[0].length;
  if (y.length != n) throw ArgumentError('X and y length mismatch');

  // Build design matrix with intercept column and compute normal equation
  // using X^T * X and X^T * y. For small m this is acceptable.
  final xtx = List.generate(m + 1, (_) => List<double>.filled(m + 1, 0.0));
  final xty = List<double>.filled(m + 1, 0.0);

  for (var i = 0; i < n; i++) {
    final row = [1.0, ...X[i]];
    final yi = y[i];
    for (var a = 0; a <= m; a++) {
      for (var b = 0; b <= m; b++) {
        xtx[a][b] += row[a] * row[b];
      }
      xty[a] += row[a] * yi;
    }
  }

  // Solve linear system xtx * beta = xty using Gaussian elimination
  final A = List.generate(m + 1, (i) => List<double>.from(xtx[i]));
  final B = List<double>.from(xty);
  final dim = m + 1;

  for (var i = 0; i < dim; i++) {
    // pivot
    var pivot = i;
    for (var r = i + 1; r < dim; r++) {
      if (A[r][i].abs() > A[pivot][i].abs()) pivot = r;
    }
    if (A[pivot][i].abs() < 1e-12) continue; // singular-ish
    if (pivot != i) {
      final tmp = A[i];
      A[i] = A[pivot];
      A[pivot] = tmp;
      final bt = B[i];
      B[i] = B[pivot];
      B[pivot] = bt;
    }
    final div = A[i][i];
    for (var j = i; j < dim; j++) {
      A[i][j] /= div;
    }
    B[i] /= div;
    for (var r = 0; r < dim; r++) {
      if (r == i) continue;
      final factor = A[r][i];
      for (var c = i; c < dim; c++) {
        A[r][c] -= factor * A[i][c];
      }
      B[r] -= factor * B[i];
    }
  }
  return B;
}