多元线性回归实战（二元）

一：算法具体实现

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
data=np.genfromtxt("data1.csv",delimiter=",")
x_data=data[:,:-1]
y_data=data[:,-1]
lr=0.0001
k1=k2=b=0
epoches=1000
def compute_error(k1,k2,b,x_data,y_data):
    totalError=0
    for i in range(0,len(x_data)):
        totalError+=(y_data[i]-(k1*x_data[i,0]+k2*x_data[i,1]+b))**2
    return totalError/float(len(x_data))
def function(x_data,y_data,k1,k2,b,lr,epoches):
    m = float(len(x_data))
    for i in range(epoches):
        k1_grad=k2_grad=b_grad=0
        for j in range(0,len(x_data)):
            b_grad+=(1/m)*((k1*x_data[j,0]+k2*x_data[j,1]+b)-y_data[j])
            k1_grad+=(1/m)*x_data[j,0]*((k1*x_data[j,0]+k2*x_data[j,1]+b)-y_data[j])
            k2_grad+=(1/m)*x_data[j,1]*((k1*x_data[j,0]+k2*x_data[j,1]+b)-y_data[j])
        k1-=(lr*k1_grad)
        k2-=(lr*k2_grad)
        b-=(lr*b_grad)
    return k1,k2,b
compute_error(k1,k2,b,x_data,y_data)
k1,k2,b=function(x_data,y_data,k1,k2,b,lr,epoches)
ax=plt.figure().add_subplot(111,projection="3d")
ax.scatter(x_data[:,0],x_data[:,1],y_data,c="r",marker="o",s=100)
x0=x_data[:,0]
x1=x_data[:,1]
x0,x1=np.meshgrid(x0,x1)
z=k1*x0+k2*x1+b
ax.plot_surface(x0,x1,z)
ax.set_xlabel("x")
ax.set_ylabel("y")
ax.set_zlabel("z")
plt.show()

 

二：sklearn调用实现

import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import LinearRegression
from mpl_toolkits.mplot3d import Axes3D
data=np.genfromtxt("data1.csv",delimiter=",")
x_data=data[:,:-1]
y_data=data[:,-1]
model=LinearRegression()
model.fit(x_data,y_data)
LinearRegression(copy_X=True,fit_intercept=True,n_jobs=1,normalize=False)
ax=plt.figure().add_subplot(111,projection="3d")
ax.scatter(x_data[:,0],x_data[:,1],y_data,c="r",marker="o",s=100)
x0=x_data[:,0]
x1=x_data[:,1]
x0,x1=np.meshgrid(x0,x1)
z=model.coef_[0]*x0+model.coef_[1]*x1+model.intercept_
ax.plot_surface(x0,x1,z)
ax.set_xlabel("x")
ax.set_ylabel("y")
ax.set_zlabel("z")
plt.show()