Python怎么实现线性回归

Python怎么实现线性回归，很多新手对此不是很清楚，为了帮助大家解决这个难题，下面小编将为大家详细讲解，有这方面需求的人可以来学习下，希望你能有所收获。

1、概述

（1）人工智能学习

（2）机器学习

（3）有监督学习

（4）线性回归

2、线性回归

（1）实现步骤

• 根据随机初始化的 w x b 和 y 来计算 loss

• 根据当前的 w x b 和 y 的值来计算梯度

• 更新梯度，循环将新的 w′ 和 b′ 复赋给 w 和 b ，最终得到一个最优的 w′ 和 b′ 作为方程最终的

（2）数学表达式

3、代码实现（Python）

（1）机器学习库（sklearn.linear_model）

代码：

from sklearn import linear_modelfrom sklearn.linear_model import LinearRegressionimport matplotlib.pyplot as plt#用于作图from pylab import *mpl.rcParams['font.sans-serif'] = ['SimHei']mpl.rcParams['axes.unicode_minus'] = Falseimport numpy as np#用于创建向量  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_#获取斜率w1,w2,w3,...,wnb=reg.intercept_#获取截距w0x0=np.arange(30,60,0.2)y0=k*x0+bprint("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()

结果：

k=[1.36695374],b=0.13079331831460195

（2）Python详细实现（方法1）

代码：

#方法1import numpy as npimport matplotlib.pyplot as pltfrom pylab import *mpl.rcParams['font.sans-serif'] = ['SimHei']mpl.rcParams['axes.unicode_minus'] = False#数据生成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]) data = np.array(data) #统计误差# y = wx + bdef 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))  #计算梯度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] #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]  def main():     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} 次迭代结果 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()  if __name__ == '__main__':    main()

结果：

迭代前 ：b = 0, w = 0, error = 186.61000821356697
Running...
第 1000 次迭代结果：b = 0.20558501549252192, w = 1.6589067569038516, error = 0.9963685680112963

（3）Python详细实现（方法2）

代码：

#方法2 import numpy as npimport pandas as pdimport matplotlib.pyplot as pltimport matplotlib as mplmpl.rcParams["font.sans-serif"]=["SimHei"]mpl.rcParams["axes.unicode_minus"]=False  # y = wx + b#Import datafile=pd.read_csv("data.csv") def compute_error_for_line_given(b, w):    totalError = np.sum((file['y']-(w*file['x']+b))**2)    return np.mean(totalError) 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]  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]  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='线性回归')    plt.xlabel('X')    plt.ylabel('Y')    plt.legend()    plt.show()    if __name__ == '__main__':    main()

结果：

Starting gradient descent at b = 0, w = 0, error = 75104.71822821398Running...After 100 iterations b = 0     0.0148451     0.3256212     0.0368833     0.5022654     0.5649175     0.4793666     0.5689687     0.4226198     0.5650739     0.39390710    0.21685411    0.58075012    0.37935013    0.36157414    0.511651dtype: float64, w = 0     0.9995201     0.9940062     0.9994053     0.9896454     0.9906835     0.9914446     0.9892827     0.9895738     0.9884989     0.99263310    0.99532911    0.98949012    0.99161713    0.99387214    0.991116dtype: float64, error = 6451.5510231710905

数据：

（4）Python详细实现（方法3）

#方法3 import numpy as np points = np.genfromtxt("data.csv", delimiter=",")#从数据读入到返回需要两个迭代循环，第一个迭代将文件中每一行转化为一个字符串序列，#第二个循环迭代对每个字符串序列指定合适的数据类型:# y = wx + bdef 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))  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]  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()

4、案例——房屋与价格、尺寸

（1）代码

#1.导入包import matplotlib.pyplot as pltimport numpy as npimport pandas as pdfrom sklearn import linear_model #2.加载训练数据，建立回归方程# 取数据集(1)datasets_X = []     #存放房屋面积datasets_Y = []     #存放交易价格fr = open('房价与房屋尺寸.csv','r')    #读取文件，r: 以只读方式打开文件，w: 打开一个文件只用于写入。lines = fr.readlines()              #一次读取整个文件。for line in lines:                  #逐行进行操作，循环遍历所有数据    items = line.strip().split(',')    #去除数据文件中的逗号,strip()用于移除字符串头尾指定的字符（默认为空格或换行符）或字符序列。                                       #split（' '）: 通过指定分隔符对字符串进行切片，如果参数 num 有指定值，则分隔 num+1 个子字符串。    datasets_X.append(int(items[0]))   #将读取的数据转换为int型，并分别写入    datasets_Y.append(int(items[1])) length = len(datasets_X)              #求得datasets_X的长度，即为数据的总数datasets_X = np.array(datasets_X).reshape([length,1])   #将datasets_X转化为数组，并变为1维，以符合线性回归拟合函数输入参数要求datasets_Y = np.array(datasets_Y)                    #将datasets_Y转化为数组 #取数据集(2)'''fr = pd.read_csv('房价与房屋尺寸.csv',encoding='utf-8')datasets_X=fr['房屋面积']datasets_Y=fr['交易价格']''' minX = min(datasets_X)maxX = max(datasets_X)X = np.arange(minX,maxX).reshape([-1,1])        #以数据datasets_X的最大值和最小值为范围，建立等差数列，方便后续画图。                                                #reshape([-1,1]），转换成１列，reshape([２,－1]）：转换成两行linear = linear_model.LinearRegression()      #调用线性回归模块，建立回归方程，拟合数据linear.fit(datasets_X, datasets_Y) #3.斜率及截距print('Coefficients:', linear.coef_)      #查看回归方程系数(k)print('intercept:', linear.intercept_)    ##查看回归方程截距(b)print('y={0}x+{1}'.format(linear.coef_,linear.intercept_)) #拟合线 # 4.图像中显示plt.scatter(datasets_X, datasets_Y, color = 'red')plt.plot(X, linear.predict(X), color = 'blue')plt.xlabel('Area')plt.ylabel('Price')plt.show()

（2）结果

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

（3）数据

第一列是房屋面积，第二列是交易价格：

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