from sklearn import linear_model
from sklearn.linear_model import LinearRegression
import matplotlib.pyplot as plt#用于作圖
from pylab import *
mpl.rcParams['font.sans-serif'] = ['SimHei']
mpl.rcParams['axes.unicode_minus'] = False
import numpy as np#用于創(chuàng)建向量
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reg=linear_model.LinearRegression(fit_intercept=True,normalize=False)
x=[[32.50235],[53.4268],[61.53036],[47.47564],[59.81321],[55.14219],[52.14219],[39.29957],
?[48.10504],[52.55001],[45.41873],[54.35163],[44.16405],[58.16847],[56.72721]]
y=[31.70701,68.7776,62.56238,71.54663,87.23093,78.21152,79.64197,59.17149,75.33124,71.30088,55.16568,82.47885,62.00892
,75.39287,81.43619]
reg.fit(x,y)
k=reg.coef_#獲取斜率w1,w2,w3,...,wn
b=reg.intercept_#獲取截距w0
x0=np.arange(30,60,0.2)
y0=k*x0+b
print("k={0},b={1}".format(k,b))
plt.scatter(x,y)
plt.plot(x0,y0,label='LinearRegression')
plt.xlabel('X')
plt.ylabel('Y')
plt.legend()
plt.show()

k=[1.36695374],b=0.13079331831460195

#方法1
import numpy as np
import matplotlib.pyplot as plt
from pylab import *
mpl.rcParams['font.sans-serif'] = ['SimHei']
mpl.rcParams['axes.unicode_minus'] = False
#數(shù)據(jù)生成
data = []
for i in range(100):
? ? x = np.random.uniform(3., 12.)
? ? # mean=0, std=1
? ? eps = np.random.normal(0., 1)
? ? y = 1.677 * x + 0.039 + eps
? ? data.append([x, y])
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data = np.array(data)
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#統(tǒng)計(jì)誤差
# y = wx + b
def compute_error_for_line_given_points(b, w, points):
? ? totalError = 0
? ? for i in range(0, len(points)):
? ? ? ? x = points[i, 0]
? ? ? ? y = points[i, 1]
? ? ? ? # computer mean-squared-error
? ? ? ? totalError += (y - (w * x + b)) ** 2
? ? # average loss for each point
? ? return totalError / float(len(points))
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#計(jì)算梯度
def step_gradient(b_current, w_current, points, learningRate):
? ? b_gradient = 0
? ? w_gradient = 0
? ? N = float(len(points))
? ? for i in range(0, len(points)):
? ? ? ? x = points[i, 0]
? ? ? ? y = points[i, 1]
? ? ? ? # grad_b = 2(wx+b-y)
? ? ? ? b_gradient += (2/N) * ((w_current * x + b_current) - y)
? ? ? ? # grad_w = 2(wx+b-y)*x
? ? ? ? w_gradient += (2/N) * x * ((w_current * x + b_current) - y)
? ? # update w'
? ? new_b = b_current - (learningRate * b_gradient)
? ? new_w = w_current - (learningRate * w_gradient)
? ? return [new_b, new_w]
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#迭代更新
def gradient_descent_runner(points, starting_b, starting_w, learning_rate, num_iterations):
? ? b = starting_b
? ? w = starting_w
? ? # update for several times
? ? for i in range(num_iterations):
? ? ? ? b, w = step_gradient(b, w, np.array(points), learning_rate)
? ? return [b, w]
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def main():
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? ? learning_rate = 0.0001
? ? initial_b = 0 ?# initial y-intercept guess
? ? initial_w = 0 ?# initial slope guess
? ? num_iterations = 1000
? ? print("迭代前 b = {0}, w = {1}, error = {2}"
? ? ? ? ? .format(initial_b, initial_w,
? ? ? ? ? ? ? ? ? compute_error_for_line_given_points(initial_b, initial_w, data))
? ? ? ? ? )
? ? print("Running...")
? ? [b, w] = gradient_descent_runner(data, initial_b, initial_w, learning_rate, num_iterations)
? ? print("第 {0} 次迭代結(jié)果 b = {1}, w = {2}, error = {3}".
? ? ? ? ? format(num_iterations, b, w,
? ? ? ? ? ? ? ? ?compute_error_for_line_given_points(b, w, data))
? ? ? ? ? )
? ? plt.plot(data[:,0],data[:,1], color='b', marker='+', linestyle='--',label='true')
? ? plt.plot(data[:,0],w*data[:,0]+b,color='r',label='predict')
? ? plt.xlabel('X')
? ? plt.ylabel('Y')
? ? plt.legend()
? ? plt.show()
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?
if __name__ == '__main__':
? ? main()
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?

#方法2
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import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import matplotlib as mpl
mpl.rcParams["font.sans-serif"]=["SimHei"]
mpl.rcParams["axes.unicode_minus"]=False
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# y = wx + b
#Import data
file=pd.read_csv("data.csv")
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def compute_error_for_line_given(b, w):
? ? totalError = np.sum((file['y']-(w*file['x']+b))**2)
? ? return np.mean(totalError)
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def step_gradient(b_current, w_current, ?learningRate):
? ? b_gradient = 0
? ? w_gradient = 0
? ? N = float(len(file['x']))
? ? for i in range (0,len(file['x'])):
? ? ? ? # grad_b = 2(wx+b-y)
? ? ? ? b_gradient += (2 / N) * ((w_current * file['x'] + b_current) - file['y'])
? ? ? ? # grad_w = 2(wx+b-y)*x
? ? ? ? w_gradient += (2 / N) * file['x'] * ((w_current * file['x'] + b_current) - file['x'])
? ? # update w'
? ? new_b = b_current - (learningRate * b_gradient)
? ? new_w = w_current - (learningRate * w_gradient)
? ? return [new_b, new_w]
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def gradient_descent_runner( starting_b, starting_w, learning_rate, num_iterations):
? ? b = starting_b
? ? w = starting_w
? ? # update for several times
? ? for i in range(num_iterations):
? ? ? ? b, w = step_gradient(b, w, ?learning_rate)
? ? return [b, w]
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def main():
? ? learning_rate = 0.0001
? ? initial_b = 0 ?# initial y-intercept guess
? ? initial_w = 0 ?# initial slope guess
? ? num_iterations = 100
? ? print("Starting gradient descent at b = {0}, w = {1}, error = {2}"
? ? ? ? ? .format(initial_b, initial_w,
? ? ? ? ? ? ? ? ? compute_error_for_line_given(initial_b, initial_w))
? ? ? ? ? )
? ? print("Running...")
? ? [b, w] = gradient_descent_runner(initial_b, initial_w, learning_rate, num_iterations)
? ? print("After {0} iterations b = {1}, w = {2}, error = {3}".
? ? ? ? ? format(num_iterations, b, w,
? ? ? ? ? ? ? ? ?compute_error_for_line_given(b, w))
? ? ? ? ? )
? ? plt.plot(file['x'],file['y'],'ro',label='線性回歸')
? ? plt.xlabel('X')
? ? plt.ylabel('Y')
? ? plt.legend()
? ? plt.show()
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?
?
?
if __name__ == '__main__':
? ? main()

Starting gradient descent at b = 0, w = 0, error = 75104.71822821398
Running...
After 100 iterations b = 0 ? ? 0.014845
1 ? ? 0.325621
2 ? ? 0.036883
3 ? ? 0.502265
4 ? ? 0.564917
5 ? ? 0.479366
6 ? ? 0.568968
7 ? ? 0.422619
8 ? ? 0.565073
9 ? ? 0.393907
10 ? ?0.216854
11 ? ?0.580750
12 ? ?0.379350
13 ? ?0.361574
14 ? ?0.511651
dtype: float64, w = 0 ? ? 0.999520
1 ? ? 0.994006
2 ? ? 0.999405
3 ? ? 0.989645
4 ? ? 0.990683
5 ? ? 0.991444
6 ? ? 0.989282
7 ? ? 0.989573
8 ? ? 0.988498
9 ? ? 0.992633
10 ? ?0.995329
11 ? ?0.989490
12 ? ?0.991617
13 ? ?0.993872
14 ? ?0.991116
dtype: float64, error = 6451.5510231710905

#方法3
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import numpy as np
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points = np.genfromtxt("data.csv", delimiter=",")
#從數(shù)據(jù)讀入到返回需要兩個迭代循環(huán)，第一個迭代將文件中每一行轉(zhuǎn)化為一個字符串序列，
#第二個循環(huán)迭代對每個字符串序列指定合適的數(shù)據(jù)類型:
# y = wx + b
def compute_error_for_line_given_points(b, w, points):
? ? totalError = 0
? ? for i in range(0, len(points)):
? ? ? ? x = points[i, 0]
? ? ? ? y = points[i, 1]
? ? ? ? # computer mean-squared-error
? ? ? ? totalError += (y - (w * x + b)) ** 2
? ? # average loss for each point
? ? return totalError / float(len(points))
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def step_gradient(b_current, w_current, points, learningRate):
? ? b_gradient = 0
? ? w_gradient = 0
? ? N = float(len(points))
? ? for i in range(0, len(points)):
? ? ? ? x = points[i, 0]
? ? ? ? y = points[i, 1]
? ? ? ? # grad_b = 2(wx+b-y)
? ? ? ? b_gradient += (2 / N) * ((w_current * x + b_current) - y)
? ? ? ? # grad_w = 2(wx+b-y)*x
? ? ? ? w_gradient += (2 / N) * x * ((w_current * x + b_current) - y)
? ? # update w'
? ? new_b = b_current - (learningRate * b_gradient)
? ? new_w = w_current - (learningRate * w_gradient)
? ? return [new_b, new_w]
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def gradient_descent_runner(points, starting_b, starting_w, learning_rate, num_iterations):
? ? b = starting_b
? ? w = starting_w
? ? # update for several times
? ? for i in range(num_iterations):
? ? ? ? b, w = step_gradient(b, w, np.array(points), learning_rate)
? ? return [b, w]
?
?
def main():
? ? learning_rate = 0.0001
? ? initial_b = 0 ?# initial y-intercept guess
? ? initial_w = 0 ?# initial slope guess
? ? num_iterations = 1000
? ? print("Starting gradient descent at b = {0}, w = {1}, error = {2}"
? ? ? ? ? .format(initial_b, initial_w,
? ? ? ? ? ? ? ? ? compute_error_for_line_given_points(initial_b, initial_w, points))
? ? ? ? ? )
? ? print("Running...")
? ? [b, w] = gradient_descent_runner(points, initial_b, initial_w, learning_rate, num_iterations)
? ? print("After {0} iterations b = {1}, w = {2}, error = {3}".
? ? ? ? ? format(num_iterations, b, w,
? ? ? ? ? ? ? ? ?compute_error_for_line_given_points(b, w, points))
? ? ? ? ? )
?
?
if __name__ == '__main__':
? ? main()

#1.導(dǎo)入包
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from sklearn import linear_model
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#2.加載訓(xùn)練數(shù)據(jù)，建立回歸方程
# 取數(shù)據(jù)集(1)
datasets_X = [] ? ? #存放房屋面積
datasets_Y = [] ? ? #存放交易價格
fr = open('房價與房屋尺寸.csv','r') ? ?#讀取文件，r: 以只讀方式打開文件，w: 打開一個文件只用于寫入。
lines = fr.readlines() ? ? ? ? ? ? ?#一次讀取整個文件。
for line in lines: ? ? ? ? ? ? ? ? ?#逐行進(jìn)行操作，循環(huán)遍歷所有數(shù)據(jù)
? ? items = line.strip().split(',') ? ?#去除數(shù)據(jù)文件中的逗號,strip()用于移除字符串頭尾指定的字符（默認(rèn)為空格或換行符）或字符序列。
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?#split（‘ '）: 通過指定分隔符對字符串進(jìn)行切片，如果參數(shù) num 有指定值，則分隔 num+1 個子字符串。
? ? datasets_X.append(int(items[0])) ? #將讀取的數(shù)據(jù)轉(zhuǎn)換為int型，并分別寫入
? ? datasets_Y.append(int(items[1]))
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length = len(datasets_X) ? ? ? ? ? ? ?#求得datasets_X的長度，即為數(shù)據(jù)的總數(shù)
datasets_X = np.array(datasets_X).reshape([length,1]) ? #將datasets_X轉(zhuǎn)化為數(shù)組，并變?yōu)?維，以符合線性回歸擬合函數(shù)輸入?yún)?shù)要求
datasets_Y = np.array(datasets_Y) ? ? ? ? ? ? ? ? ? ?#將datasets_Y轉(zhuǎn)化為數(shù)組
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#取數(shù)據(jù)集(2)
'''fr = pd.read_csv('房價與房屋尺寸.csv',encoding='utf-8')
datasets_X=fr['房屋面積']
datasets_Y=fr['交易價格']'''
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minX = min(datasets_X)
maxX = max(datasets_X)
X = np.arange(minX,maxX).reshape([-1,1]) ? ? ? ?#以數(shù)據(jù)datasets_X的最大值和最小值為范圍，建立等差數(shù)列，方便后續(xù)畫圖。
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? #reshape([-1,1]），轉(zhuǎn)換成１列，reshape([２,－1]）：轉(zhuǎn)換成兩行
linear = linear_model.LinearRegression() ? ? ?#調(diào)用線性回歸模塊，建立回歸方程，擬合數(shù)據(jù)
linear.fit(datasets_X, datasets_Y)
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#3.斜率及截距
print('Coefficients:', linear.coef_) ? ? ?#查看回歸方程系數(shù)(k)
print('intercept:', linear.intercept_) ? ?##查看回歸方程截距(b)
print('y={0}x+{1}'.format(linear.coef_,linear.intercept_)) #擬合線
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# 4.圖像中顯示
plt.scatter(datasets_X, datasets_Y, color = 'red')
plt.plot(X, linear.predict(X), color = 'blue')
plt.xlabel('Area')
plt.ylabel('Price')
plt.show()

Coefficients: [0.14198749]
intercept: 53.43633899175563
y=[0.14198749]x+53.43633899175563