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# An example of calculating least-squares linear regression fit in Ruby | |
# | |
# This is free and unencumbered software released into the public domain. | |
# | |
# Anyone is free to copy, modify, publish, use, compile, sell, or | |
# distribute this software, either in source code form or as a compiled | |
# binary, for any purpose, commercial or non-commercial, and by any | |
# means. | |
# | |
# In jurisdictions that recognize copyright laws, the author or authors | |
# of this software dedicate any and all copyright interest in the | |
# software to the public domain. We make this dedication for the benefit | |
# of the public at large and to the detriment of our heirs and | |
# successors. We intend this dedication to be an overt act of | |
# relinquishment in perpetuity of all present and future rights to this | |
# software under copyright law. | |
# | |
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, | |
# EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF | |
# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. | |
# IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR | |
# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, | |
# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR | |
# OTHER DEALINGS IN THE SOFTWARE. | |
# | |
# For more information, please refer to <https://unlicense.org> | |
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 |
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