Ruby script to calculate a multiple regression function.

regression_multi.rb

#! /usr/local/bin/ruby
#*********************************************
# Ruby script to calculate a multiple regression function.
#*********************************************
#
class Array
  def reg_multi(y)
    # 元の数、変量内のサンプル数
    e_size, s_size = self.size, y.size
    # 以下の場合は例外スロー
    # - 引数の配列が Array クラスでない
    # - 自身配列が空
    # - 配列サイズが異なれば例外
    raise "Argument is not a Array class!"    unless y.class == Array
    raise "Self array is nil!"                if     e_size == 0
    raise "Argument array size is invalid!"   unless self[0].size == s_size
    1.upto(e_size - 1) do |i|
      raise "Argument array size is invalid!" unless self[0].size == self[i].size
    end
    x1, x2 = self
    sum_x1   = x1.sum
    sum_x2   = x2.sum
    sum_y    = y.sum
    sum_x1x1 = x1.map { |a| a * a }.sum
    sum_x1x2 = x1.zip(x2).map { |a, b| a * b }.sum
    sum_x1y  = x1.zip(y).map { |a, b| a * b }.sum
    sum_x2x1 = sum_x1x2
    sum_x2x2 = x2.map { |a| a * a }.sum
    sum_x2y  = x2.zip(y).map { |a, b| a * b }.sum
    mtx = [
      [s_size, sum_x1  , sum_x2  , sum_y  ],
      [sum_x1, sum_x1x1, sum_x1x2, sum_x1y],
      [sum_x2, sum_x2x1, sum_x2x2, sum_x2y]
    ]
    # 連立方程式を解く (ガウスの消去法)
    return gauss_e(mtx)
  end

private
  # ガウスの消去法
  def gauss_e(ary)
    # 行数
    n = ary.size
    # 前進消去
    0.upto(n - 2) do |k|
      (k + 1).upto(n - 1) do |i|
        if ary[k][k] == 0
          puts "解けない！"
          exit 1
        end
        d = ary[i][k] / ary[k][k].to_f
        (k + 1).upto(n) do |j|
          ary[i][j] -= ary[k][j] * d
        end
      end
    end
    # 後退代入
    (n - 1).downto(0) do |i|
      if ary[i][i] == 0
        puts "解けない！"
        exit 1
      end
      d = ary[i][n]
      (i + 1).upto(n - 1) do |j|
        d -= ary[i][j] * ary[j][n]
      end
      ary[i][n] = d / ary[i][i].to_f
    end
    return ary.map { |a| a[-1] }
  end
end

# 説明(独立)変数と目的(従属)変数
ary_x = [
  [17.5, 17.0, 18.5, 16.0, 19.0, 19.5, 16.0, 18.0, 19.0, 19.5],
  [30, 25, 20, 30, 45, 35, 25, 35, 35, 40]
]
ary_y = [45, 38, 41, 34, 59, 47, 35, 43, 54, 52]
# 重回帰式算出(b0, b1, b2, ...)
reg_multi = ary_x.reg_multi(ary_y)
# 結果出力
ary_x.each_with_index do |x, i|
  puts "説明変数 X#{i + 1} = {#{ary_x[i].join(', ')}}"
end
puts "目的変数 Y  = {#{ary_y.join(', ')}}"
puts "---"
p reg_multi