回归分析

什么是回归分析

回归分析：根据数据，确定两个或两个以上变量之间的相互依赖的定量关系
函数表达式：

线性回归

线性回归：回归分析中，变量和应变量存在线性关系
函数表达式：y=ax+b
eg : 距离S=速度

回归问题求解

如何找到最合适的? 假设 为变量， 为对应的结果， 为模型输出的结果 要使 尽可能接近

梯度下降法 寻找极小值的一种方法。通过向函数上当前点对应梯度（或者是近似梯度）的反方向的规定步长距离点经行迭代搜索，直到在极小点收敛。

最后会逐渐接近极小值点

调用Scikit-learn求解线性回归问题

import pandas as pd  
import matplotlib  
matplotlib.use('TkAgg')  
from matplotlib import pyplot as plt  
import sklearn  
from sklearn.linear_model import LinearRegression  
import numpy as np  
from sklearn.metrics import mean_squared_error,r2_score  
data = pd.read_csv('1.csv')  
#print(type(data),data.shape)  
#data 赋值  
x = data.loc[:,'x']  
y = data.loc[:,'y']  
# 展示图形  
#plt.figure()  
#plt.scatter(x,y)  
#plt.show()  
lr_model = LinearRegression()  
x = np.array(x)  
x = x.reshape(-1,1)  
y = np.array(y)  
y = y.reshape(-1,1)  
lr_model.fit(x,y)  
y_pred = lr_model.predict(x)  
print(y_pred)  
y_3 = lr_model.predict([[3.5]])     #预测x = 3.5时y的值  
print(y_3)  
  
#a/b print  
a = lr_model.coef_  
b = lr_model.intercept_  
print(a,b)  
  
print("-------------------------------------------")  
MSE = mean_squared_error(y,y_pred)  
R2 = r2_score(y,y_pred)  
print(MSE,R2)  
plt.plot(y,y_pred)  
plt.show()

"""  
  
数据说明：  
Avg.AreaIncome:区域平均收入  
Avg.Area House Age:平均房屋年龄  
Avg.Area Number of Rooms:平均房间数量  
Area Population:区域人口  
size:尺寸  
Price:价格  
  
"""  
  
#load the data  
import pandas as pd  
import numpy as np  
import matplotlib  
import matplotlib.pyplot as plt  
matplotlib.use('TkAgg')  
from sklearn.linear_model import LinearRegression  
from sklearn.metrics import mean_squared_error,r2_score  
  
data = pd.read_csv('usa_house_price.csv')  
data.head()     #数据快速预览  
fig = plt.figure(figsize = (10,10))  
fig1 = plt.subplot(231)  
plt.scatter(data['AreaIncome'], data['Price'])  
# 与上者等价 plt.scatter(data.loc[:,'Avg.AreaIncome'], data.loc[:,'Price'])plt.title('Price VS AreaIncome')  
plt.show()  
  
#define x and y  
x = data.loc[:,'size']  
y = data.loc[:,'Price']  
x = np.array(x).reshape(-1,1)  
  
#set up the linear regression model  
LR1 = LinearRegression()  
#train the model  
LR1.fit(x,y)  
  
#calculate the price vs size  
#均方误差 (MSE) 和 决定系数 (R² Score)y_pred_1 = LR1.predict(x)  
print(y_pred_1)  
mean_squared_error_1 = mean_squared_error(y,y_pred_1)  
r2_score_1 = r2_score(y,y_pred_1)  
print(mean_squared_error_1,r2_score_1)  
fig2 = plt.figure(figsize=(8,5))  
plt.scatter(x,y)  
plt.plot(x,y_pred_1,'r')  
plt.show()  
  
#define x_multi  
x_multi = data.drop(['Price'],axis=1)  
  
#set up 2nd linear model  
LR_multi = LinearRegression()  
  
#train the model  
LR_multi.fit(x_multi,y)  
  
#make prediction  
y_pred_multi = LR_multi.predict(x_multi)  
print(y_pred_multi)  
mean_squared_error_multi = mean_squared_error(y,y_pred_multi)  
r2_score_multi = r2_score(y,y_pred_multi)  
print(mean_squared_error_multi,r2_score_multi)  
fig3 = plt.figure(figsize=(8,5))  
plt.scatter(y,y_pred_multi)  
plt.show()  
  
x_text = [65000,5,5,30000,200]  
x_text = np.array(x_text).reshape(-1,1)  
print(x_text)  
y_text_pred = LR_multi.predict(x_text)  
print(y_text_pred)