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Summary

Description
English: Illustration of least squares fitting. The data (red dots) are at co-ordinates (1,6), (2,5), (3,7) and (4,10). A linear approximation is obtained using least-squares estimation (blue line). Created using python.
Date
Source Own work
Author Krishnavedala
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File:Linear_least_squares_example2.png

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Source Code
from matplotlib.pyplot import *
from numpy import *
from mpl_toolkits.axisartist import *

x,y = [1.,2.,3.,4.], [6., 5., 7., 10.]
A = vstack([x, ones(len(x))]).T
b2,b1 = linalg.lstsq(A,y)[0]
x2 = arange(0,5,0.1)
y2 = lambda xx: b1+b2*xx

fig = figure(figsize=(3,3))
ax = Subplot(fig,"111",axisbg='none')
fig.add_subplot(ax)
ax.axis["right"].set_visible(False)
ax.axis["top"].set_visible(False)
ax.plot(x,y,'ro',label="Data")
ax.plot(x2,y2(x2),label="curve fit",lw=2)
ymin, ymax = [], []
for i in range(len(x)):
	yy = y2(x[i])
	if yy >= y[i]:
		ymin, ymax = append(ymin,y[i]), append(ymax,yy)
	else:
		ymin, ymax = append(ymax,yy), append(ymin,y[i])
ax.vlines(x,ymin, ymax,color='g',linestyles='solid',lw=1.5)
ax.set_ylabel("y",fontsize=12)
ax.set_xlabel("x",fontsize=12)
ax.grid(True)
ax.minorticks_on()
ax.set_xlim(0,5)
ax.set_ylim(4,10.5)
ax.legend(frameon=True, handletextpad=0,loc='upper left',\
	labelspacing=.05)
setp(ax.get_legend().get_texts(),fontsize=12)

fig.savefig("Linear_least_squares_example2.svg",bbox_inches="tight",\
	pad_inches=.15)

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GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.
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inception

9 June 2011

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Date/TimeThumbnailDimensionsUserComment
current03:35, 10 June 2011Thumbnail for version as of 03:35, 10 June 2011279 × 274 (50 KB)Krishnavedala{{Information |Description ={{en|1=Illustration of w:Linear_least_squares_(mathematicsleast squares fitting. The data (red dots) are at co-ordinates (1,6), (2,5), (3,7) and (4,10). A linear approximation is obtained using least-squares estimation

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