linear_fit.rb

# An example of calculating least-squares linear regression fit in Ruby
#
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class LinearFit < Struct.new :m, :b, :r
  def inspect
    "y = #{m.round(2)} x + #{b.round(2)}\n" +
      "r = #{r.round(2)}"
  end

  ###
  # Given a list of points, perform a linear regression.  +points+ is a list of
  # XY coordinate tuples.  For example:
  #
  #     fit = LinearFit.from_points([[1, 2], [2, 4]])
  #
  # This function returns an instance of a `LinearFit`
  # object that contains the values `m` and `b` from the equation `y = mx + b`
  # as well as the correlation `r` value
  def self.from_points points
    # Calculate Mean
    x_tmp = 0
    y_tmp = 0

    points.each { |x, y| x_tmp += x; y_tmp += y }

    x_mean = x_tmp / points.length.to_f
    y_mean = y_tmp / points.length.to_f

    # Calculate Sample Standard Deviation
    x_tmp = 0
    y_tmp = 0

    points.each { |x, y|
      x_tmp += (x - x_mean) ** 2
      y_tmp += (y - y_mean) ** 2
    }

    s_x = Math.sqrt(x_tmp / (points.length - 1))
    s_y = Math.sqrt(y_tmp / (points.length - 1))

    # Calculate Correlation
    r = points.inject(0) { |memo, (x, y)|
      memo + (((x - x_mean) / s_x) * ((y - y_mean) / s_y))
    } / (points.length - 1)

    # Calculate m and b
    m = r * (s_y / s_x)
    b = y_mean - (x_mean * m)

    new m, b, r
  end
end

if __FILE__ == $0
  ## Demo

  # Make some points with a little noise
  points = 100.times.map { |x| [x + 1, x + rand] }
  p LinearFit.from_points points
end