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Ruby script to calculate a simple regression curve.
#! /usr/local/bin/ruby
#*********************************************
# Ruby script to calculate a simple regression curve.
#*********************************************
#
class Array
def reg_line(y)
# 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 self.size == 0
raise "Argument array size is invalid!" unless self.size == y.size
n = self.size # number of items
m_x = self.sum / n.to_f # avg(X)
m_y = y.sum / n.to_f # avg(Y)
m_x2 = self.map { |x| x ** 2 }.sum / n.to_f # avg(X^2)
m_x3 = self.map { |x| x ** 3 }.sum / n.to_f # avg(X^3)
m_x4 = self.map { |x| x ** 4 }.sum / n.to_f # avg(X^4)
m_xy = self.zip(y).map { |a, b| a * b }.sum / n.to_f # avg(X * Y)
m_x2y = self.zip(y).map { |a, b| a * a * b }.sum / n.to_f # avg(X^2 * Y)
s_xx = m_x2 - m_x * m_x # Sxx
s_xy = m_xy - m_x * m_y # Sxy
s_xx2 = m_x3 - m_x * m_x2 # Sxx2
s_x2x2 = m_x4 - m_x2 * m_x2 # Sx2x2
s_x2y = m_x2y - m_x2 * m_y # Sx2y
b = s_xy * s_x2x2 - s_x2y * s_xx2
b /= s_xx * s_x2x2 - s_xx2 * s_xx2
c = s_x2y * s_xx - s_xy * s_xx2
c /= s_xx * s_x2x2 - s_xx2 * s_xx2
a = m_y - b * m_x - c * m_x2
{a: a, b: b, c: c}
end
end
# 説明変数と目的変数
#ary_x = [107, 336, 233, 82, 61, 378, 129, 313, 142, 428]
#ary_y = [286, 851, 589, 389, 158, 1037, 463, 563, 372, 1020]
ary_x = [83, 71, 64, 69, 69, 64, 68, 59, 81, 91, 57, 65, 58, 62]
ary_y = [183, 168, 171, 178, 176, 172, 165, 158, 183, 182, 163, 175, 164, 175]
puts "説明変数 X = {#{ary_x.join(', ')}}"
puts "目的変数 Y = {#{ary_y.join(', ')}}"
puts "---"
# 単回帰曲線算出
reg_line = ary_x.reg_line(ary_y)
puts "a = #{reg_line[:a]}"
puts "b = #{reg_line[:b]}"
puts "c = #{reg_line[:c]}"
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