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leastsquares.py
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leastsquares.py
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#
# The MIT License (MIT)
#
# Copyright (c) 2016 Scott J. Johnson
#
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in all
# copies or substantial portions of the Software.
#
# 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 OR COPYRIGHT HOLDERS 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.
#
def leastsquares(x, y):
'''
Example implementation of the Least Squares method for calculating a best-fit line through a set of points.
Linear least squares
Args:
x: array of floats representing x values for each point
y: array of floats representing y values for each point
Returns:
(float, float): representing the y-intercept and slope of the best-fit line
Raises:
ValueError: if the two arrays are not the same length
'''
if len(x) != len(y):
raise ValueError('Point arrays must be equal length')
numberOfPoints = len(x)
sumX = sum(x)
sumY = sum(y)
sumXYProduct = sum(x[i] * y[i] for i in range(numberOfPoints))
sumXSquared = sum(map(lambda a: a ** 2, x))
xBar = sumX / numberOfPoints
yBar = sumY / numberOfPoints
a1 = (numberOfPoints * sumXYProduct - sumX * sumY) / (numberOfPoints * sumXSquared - sumX ** 2)
a0 = yBar - a1 * xBar
return a0, a1
# example data
x = (1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0)
y = (0.5, 2.5, 2.0, 4.0, 3.5, 6.0, 5.5)
print ("least squares fit ==> y = %.10f + %.10fx" % leastsquares(x, y))