File:Polyreg scheffe uk.svg
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Size of this PNG preview of this SVG file: 540 × 360 pixels. Other resolutions: 320 × 213 pixels | 640 × 427 pixels | 1,024 × 683 pixels | 1,280 × 853 pixels | 2,560 × 1,707 pixels.
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[edit]DescriptionPolyreg scheffe uk.svg |
English: Plot of a cubic polynomial fit using multiple least squares to a simulated data set. Along with the point estimate, a 95% simultaneous confidence band constructed using Scheffe's method is shown. Labelled in Ukrainian.
Українська: Графік допасування до імітованих даних кубічного многочлену із застосуванням декількох найменших квадратів. Разом із точковою оцінкою показано одночасно 95 %-ву довірчу смугу, побудовану із застосуванням методу Шефе. |
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SVG development InfoField | This plot was created with Matplotlib. |
Source code InfoField | Python codeimport numpy as np
import matplotlib.pyplot as plt
import scipy.special as sp
## Розмір вибірки.
n = 100
## Значення предиктора.
XV = np.random.uniform(low=-4, high=4, size=n)
XV.sort()
## Матриця плану.
X = np.ones((n,4))
X[:,1] = XV
X[:,2] = XV**2
X[:,3] = XV**3
## Істинні коефіцієнти.
beta = np.array([0, 0.1, -0.25, -0.25], dtype=np.float64)
## Істинні значення відгуку.
EY = np.dot(X, beta)
## Спостережувані значення відгуку.
Y = EY + np.random.normal(size=n)*np.sqrt(20)
## Отримати оцінки коефіцієнтів.
u,s,vt = np.linalg.svd(X,0)
v = np.transpose(vt)
bhat = np.dot(v, np.dot(np.transpose(u), Y)/s)
## Допасовані значення.
Yhat = np.dot(X, bhat)
## СКП та КСКП.
MSE = ((Y-EY)**2).sum()/(n-X.shape[1])
s = np.sqrt(MSE)
## Ці множники використовуються в побудові інтервалу Шефе.
XtX = np.dot(np.transpose(X), X)
V = [np.dot(X[i,:], np.linalg.solve(XtX, X[i,:])) for i in range(n)]
V = np.array(V)
## F-квантиль, що використовується в побудові інтервалу Шефе.
QF = sp.fdtri(X.shape[1], n-X.shape[1], 0.95)
## Нижня та верхня межі довірчої смуги.
D = s*np.sqrt(X.shape[1]*QF*V)
LB,UB = Yhat-D,Yhat+D
## Створити графік.
plt.clf()
plt.plot(XV, Y, 'o', ms=3, color='grey')
plt.plot(XV, EY, '-', color='blue', label = "Істина")
plt.plot(XV, Yhat, '-', color='green', label = "Оцінка")
plt.plot(XV, LB, '-', color='red', label = "ДС")
plt.plot(XV, UB, '-', color='red')
plt.legend(frameon=False)
plt.ylim([-25,20])
plt.gca().set_yticks([-20,-10,0,10,20])
plt.xlim([-4,4])
plt.gca().set_xticks([-4,-2,0,2,4])
plt.xlabel("X")
plt.ylabel("Y")
plt.savefig("polyreg_scheffe_uk.pdf")
plt.savefig("polyreg_scheffe_uk.svg")
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Licensing
[edit]This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
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- Under the following conditions:
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 15:41, 8 March 2021 | 540 × 360 (38 KB) | Olexa Riznyk (talk | contribs) | Uploaded a work by * File:Polyreg scheffe.svg: {{ut|Skbkekas}} * derivative work: {{Ut|Olexa Riznyk}} from * File:Polyreg scheffe.svg with UploadWizard |
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The following other wikis use this file:
- Usage on uk.wikipedia.org
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Width | 432pt |
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Height | 288pt |