I am trying to fit piecewise linear fit as shown in fig.1 for a data set

![enter image description here][1]

This figure was obtained by setting on the lines. I attempted to apply a piecewise linear fit using the code:

    from scipy import optimize
	import matplotlib.pyplot as plt
	import numpy as np


	x = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ,11, 12, 13, 14, 15])
	y = np.array([5, 7, 9, 11, 13, 15, 28.92, 42.81, 56.7, 70.59, 84.47, 98.36, 112.25, 126.14, 140.03])


	def linear_fit(x, a, b):
	    return a * x + b
	fit_a, fit_b = optimize.curve_fit(linear_fit, x[0:5], y[0:5])[0]
	y_fit = fit_a * x[0:7] + fit_b
	fit_a, fit_b = optimize.curve_fit(linear_fit, x[6:14], y[6:14])[0]
	y_fit = np.append(y_fit, fit_a * x[6:14] + fit_b)


	figure = plt.figure(figsize=(5.15, 5.15))
	figure.clf()
	plot = plt.subplot(111)
	ax1 = plt.gca()
	plot.plot(x, y, linestyle = &#39;&#39;, linewidth = 0.25, markeredgecolor=&#39;none&#39;, marker = &#39;o&#39;, label = r&#39;\textit{y_a}&#39;)
	plot.plot(x, y_fit, linestyle = &#39;:&#39;, linewidth = 0.25, markeredgecolor=&#39;none&#39;, marker = &#39;&#39;, label = r&#39;\textit{y_b}&#39;)
	plot.set_ylabel(&#39;Y&#39;, labelpad = 6)
	plot.set_xlabel(&#39;X&#39;, labelpad = 6)
	figure.savefig(&#39;test.pdf&#39;, box_inches=&#39;tight&#39;)
	plt.close()    

But this gave me fitting of the form in fig. 2, I tried playing with the values but no change I can&#39;t get the fit of the upper line proper. The most important requirement for me is how can I get Python to get the gradient change point. In essence ***I want Python to recognize and fit two linear fits in the appropriate range. How can this be done in Python?***

![enter image description here][2]


  [1]: http://i.stack.imgur.com/Thrit.png
  [2]: http://i.stack.imgur.com/UjrF6.png

All Piecewise Solutions on Gang of Coders

Total of 1 Piecewise Solutions

How to apply piecewise linear fit in Python?