多维线性拟合回归问题 python

新冠肺炎–球重大公共卫生事件，美国是当前疫情最严重的国家，其感染人数与死亡人数居世界首位。目前以获取从2020.1.28-2020.9.9之间的数据，请利用所学知识，采用2020.1.28-2020.8.31的数据建立模型，并用9.1-9.9数据进行模型测试。
完成时间：约2020年10月25日

数据格式如下：
2020.1.28 0 5 0 0
2020.1.29 0 5 0 0
2020.1.30 1 6 0 0
2020.1.31 0 6 0 0

本图为预测2020年365天的回归曲线的预测值图形，今天写报告时，为10月25日，美国实际总确诊人数接近850万，print(linear_reg2.predict(poly_reg.fit_transform(predictarr0))[298],predictdaysdata[298]) 输出为[10264119.70637152] 2020.10.25，也即预测为1002万，相比较有着一定的差距。

使用较高阶数进行拟合，则短期内数据精准度较高，长期预测发生极大的数据波动：如下图

使用较低阶数进行拟合，则长期内数据精准度较高：如下图

源代码

#（1）
# -*- coding: utf-8 -*-
import numpy as np
import pandas as pd
from datetime import datetime
from datetime import timedelta
import matplotlib.pyplot as plt
from sklearn.preprocessing import PolynomialFeatures
from sklearn.linear_model import LinearRegression
#import sys



if __name__ == "__main__":
        
    io = r'C:\Users\x\Desktop\大数据\2\02.美国新冠肺炎疫情历史总数据9.9.xlsx'
    
    data = pd.read_excel(io, sheet_name = 0)
    lenofdata = len(data)
    
    arr0 = []
    arr1 = []
    arr2 = []
    arr3 = []
    arr4 = []
    daysdata = []
    predictdaysdata = []
    
    startdate = datetime.strptime("2020.1.01","%Y.%m.%d")
    for num in range(0,lenofdata-1):
        nowline = data.loc[num].values
        
        dateintext = datetime.strptime(nowline[0], '%Y.%m.%d')
        days = (dateintext-startdate).days#得出数据集中的日期距离2020.1.1的天数作为预测的因变量
        
        daysdata.append(nowline[0])
        arr0.append([days])
        arr1.append([nowline[1]])
        arr2.append([nowline[2]])
        arr3.append([nowline[3]])
        arr4.append([nowline[4]])
        
    predictarr0 = []
    for i in range(0,365):
        predictdaysdata.append((startdate+timedelta(days=i)).strftime("%Y.%m.%d"))
        predictarr0.append([i])
    
    
    poly_reg = PolynomialFeatures(degree=3)
    xarr = poly_reg.fit_transform(arr0)
    predictxarr = poly_reg.fit_transform(predictarr0)

    linear_reg1 = LinearRegression()
    linear_reg1.fit(xarr, arr1)
    
    linear_reg2 = LinearRegression()
    linear_reg2.fit(xarr, arr2)
    
    linear_reg3 = LinearRegression()
    linear_reg3.fit(xarr, arr3)
    
    linear_reg4 = LinearRegression()
    linear_reg4.fit(xarr, arr4)
    
    plt.rcParams['font.sans-serif']=['FangSong']
    plt.rcParams['axes.unicode_minus']=False
    plt.figure(figsize=(100,100))
    fig = plt.figure()  
    
    ax0 = fig.add_subplot(1,1,1)
    ax0.plot(daysdata, arr1, "o", label="新增",markersize =0.3 )
    ax0.plot(daysdata, linear_reg1.predict(poly_reg.fit_transform(arr0)), label="新增预测",alpha=0.5)
    plt.xticks("")
    plt.legend()
    
    #ax1 = fig.add_subplot(4,1,2)
    ax0.plot(daysdata, arr2,"o", label="总确诊",markersize =0.3 )
    ax0.plot(daysdata, linear_reg2.predict(poly_reg.fit_transform(arr0)), label="总确诊预测",alpha=0.5)
    plt.xticks("")
    plt.legend()

    #ax2 = fig.add_subplot(4,1,3)
    ax0.plot(daysdata, arr3,"o", label="治愈",markersize =0.3 )
    ax0.plot(daysdata, linear_reg3.predict(poly_reg.fit_transform(arr0)), label="治愈预测",alpha=0.5)
    plt.xticks("")
    plt.legend()
    
    #ax3 = fig.add_subplot(4,1,4)
    ax0.plot(daysdata, arr4,"o", label="死亡",markersize =0.3 )
    ax0.plot(daysdata, linear_reg4.predict(poly_reg.fit_transform(arr0)), label="死亡预测",alpha=0.5)
    plt.xticks(arr0[::50])
    plt.legend()
    
    #ax.plot(arr0,arr3,label="治愈")
    #ax.plot(arr0,arr4,label="死亡")
    plt.xticks(arr0[::50])
    plt.legend()
    plt.savefig('2.png',dpi=1500)


#（2）

# -*- coding: utf-8 -*-
import numpy as np
import pandas as pd
from datetime import datetime
from datetime import timedelta
import matplotlib.pyplot as plt
from sklearn.preprocessing import PolynomialFeatures
from sklearn.linear_model import LinearRegression
#import sys



if __name__ == "__main__":
        
    io = r'C:\Users\x\Desktop\大数据\2\02.美国新冠肺炎疫情历史总数据9.9.xlsx'
    
    data = pd.read_excel(io, sheet_name = 0)
    lenofdata = len(data)
    
    arr0 = []
    arr1 = []
    arr2 = []
    arr3 = []
    arr4 = []
    daysdata = []
    predictdaysdata = []
    
    startdate = datetime.strptime("2020.1.01","%Y.%m.%d")
    for num in range(0,lenofdata-1):
        nowline = data.loc[num].values
        
        dateintext = datetime.strptime(nowline[0], '%Y.%m.%d')
        days = (dateintext-startdate).days#得出数据集中的日期距离2020.1.1的天数作为预测的因变量
        
        daysdata.append(nowline[0])
        arr0.append([days])
        arr1.append([nowline[1]])
        arr2.append([nowline[2]])
        arr3.append([nowline[3]])
        arr4.append([nowline[4]])
        
    predictarr0 = []
    for i in range(0,365):
        predictdaysdata.append((startdate+timedelta(days=i)).strftime("%Y.%m.%d"))
        predictarr0.append([i])
    
    
    poly_reg = PolynomialFeatures(degree=3)
    xarr = poly_reg.fit_transform(arr0)
    predictxarr = poly_reg.fit_transform(predictarr0)

    linear_reg1 = LinearRegression()
    linear_reg1.fit(xarr, arr1)
    
    linear_reg2 = LinearRegression()
    linear_reg2.fit(xarr, arr2)
    
    linear_reg3 = LinearRegression()
    linear_reg3.fit(xarr, arr3)
    
    linear_reg4 = LinearRegression()
    linear_reg4.fit(xarr, arr4)
    
    plt.rcParams['font.sans-serif']=['FangSong']
    plt.rcParams['axes.unicode_minus']=False
    plt.figure(figsize=(100,100))
    fig = plt.figure()  
    
    ax0 = fig.add_subplot(4,1,1)
    ax0.plot(daysdata, arr1, "o", label="新增",markersize =0.3 )
    ax0.plot(daysdata, linear_reg1.predict(poly_reg.fit_transform(arr0)), label="新增预测",alpha=0.5)
    plt.xticks("")
    plt.legend()
    
    ax1 = fig.add_subplot(4,1,2)
    ax1.plot(daysdata, arr2,"o", label="总确诊",markersize =0.3 )
    ax1.plot(daysdata, linear_reg2.predict(poly_reg.fit_transform(arr0)), label="总确诊预测",alpha=0.5)
    plt.xticks("")
    plt.legend()

    ax2 = fig.add_subplot(4,1,3)
    ax2.plot(daysdata, arr3,"o", label="治愈",markersize =0.3 )
    ax2.plot(daysdata, linear_reg3.predict(poly_reg.fit_transform(arr0)), label="治愈预测",alpha=0.5)
    plt.xticks("")
    plt.legend()
    
    ax3 = fig.add_subplot(4,1,4)
    ax3.plot(daysdata, arr4,"o", label="死亡",markersize =0.3 )
    ax3.plot(daysdata, linear_reg4.predict(poly_reg.fit_transform(arr0)), label="死亡预测",alpha=0.5)
    plt.xticks(arr0[::50])
    plt.legend()
    
    #ax.plot(arr0,arr3,label="治愈")
    #ax.plot(arr0,arr4,label="死亡")
    plt.xticks(arr0[::50])
    plt.legend()
    plt.savefig('1.png',dpi=1500)

#（3）

# -*- coding: utf-8 -*-
import numpy as np
import pandas as pd
from datetime import datetime
from datetime import timedelta
import matplotlib.pyplot as plt
from sklearn.preprocessing import PolynomialFeatures
from sklearn.linear_model import LinearRegression
#import sys



if __name__ == "__main__":
        
    io = r'C:\Users\x\Desktop\大数据\2\02.美国新冠肺炎疫情历史总数据9.9.xlsx'
    
    data = pd.read_excel(io, sheet_name = 0)
    lenofdata = len(data)
    
    arr0 = []
    arr1 = []
    arr2 = []
    arr3 = []
    arr4 = []
    daysdata = []
    predictdaysdata = []
    
    startdate = datetime.strptime("2020.1.01","%Y.%m.%d")
    for num in range(0,lenofdata-1):
        nowline = data.loc[num].values
        
        dateintext = datetime.strptime(nowline[0], '%Y.%m.%d')
        days = (dateintext-startdate).days#得出数据集中的日期距离2020.1.1的天数作为预测的因变量
        
        daysdata.append(nowline[0])
        arr0.append([days])
        arr1.append([nowline[1]])
        arr2.append([nowline[2]])
        arr3.append([nowline[3]])
        arr4.append([nowline[4]])
        
    predictarr0 = []
    for i in range(0,365):
        predictdaysdata.append((startdate+timedelta(days=i)).strftime("%Y.%m.%d"))
        predictarr0.append([i])
    
    
    poly_reg = PolynomialFeatures(degree=3)
    xarr = poly_reg.fit_transform(arr0)
    predictxarr = poly_reg.fit_transform(predictarr0)

    linear_reg1 = LinearRegression()
    linear_reg1.fit(xarr, arr1)
    
    linear_reg2 = LinearRegression()
    linear_reg2.fit(xarr, arr2)
    
    linear_reg3 = LinearRegression()
    linear_reg3.fit(xarr, arr3)
    
    linear_reg4 = LinearRegression()
    linear_reg4.fit(xarr, arr4)
    
    plt.rcParams['font.sans-serif']=['FangSong']
    plt.rcParams['axes.unicode_minus']=False
    plt.figure(figsize=(100,100))
    fig = plt.figure()  
    
    ax0 = fig.add_subplot(1,1,1)
    #ax0.plot(daysdata, arr1, "o", label="新增",markersize =0.3 )
    ax0.plot(predictdaysdata, linear_reg1.predict(poly_reg.fit_transform(predictarr0)), label="新增预测",alpha=0.5)
    plt.xticks("")
    plt.legend()
    
    #ax1 = fig.add_subplot(4,1,2)
    #ax0.plot(daysdata, arr2,"o", label="总确诊",markersize =0.3 )
    ax0.plot(predictdaysdata, linear_reg2.predict(poly_reg.fit_transform(predictarr0)), label="总确诊预测",alpha=0.5)
    plt.xticks("")
    plt.legend()

    #ax2 = fig.add_subplot(4,1,3)
    #ax0.plot(daysdata, arr3,"o", label="治愈",markersize =0.3 )
    ax0.plot(predictdaysdata, linear_reg3.predict(poly_reg.fit_transform(predictarr0)), label="治愈预测",alpha=0.5)
    plt.xticks("")
    plt.legend()
    
    #ax3 = fig.add_subplot(4,1,4)
    #ax0.plot(daysdata, arr4,"o", label="死亡",markersize =0.3 )
    ax0.plot(predictdaysdata, linear_reg4.predict(poly_reg.fit_transform(predictarr0)), label="死亡预测",alpha=0.5)
    plt.xticks(predictarr0[::50])
    plt.legend()
    
    #ax.plot(arr0,arr3,label="治愈")
    #ax.plot(arr0,arr4,label="死亡")
    plt.xticks(predictarr0[::80])
    plt.legend()
    plt.savefig('3.png',dpi=1500)


#5.

# -*- coding: utf-8 -*-
import numpy as np
import pandas as pd
from datetime import datetime
from datetime import timedelta
import matplotlib.pyplot as plt
from sklearn.preprocessing import PolynomialFeatures
from sklearn.linear_model import LinearRegression
#import sys



if __name__ == "__main__":
        
    io = r'C:\Users\x\Desktop\大数据\2\02.美国新冠肺炎疫情历史总数据9.9.xlsx'
    
    data = pd.read_excel(io, sheet_name = 0)
    lenofdata = len(data)
    
    arr0 = []
    arr1 = []
    arr2 = []
    arr3 = []
    arr4 = []
    daysdata = []
    predictdaysdata = []
    
    startdate = datetime.strptime("2020.1.01","%Y.%m.%d")
    for num in range(0,lenofdata-10):
        nowline = data.loc[num].values
        
        dateintext = datetime.strptime(nowline[0], '%Y.%m.%d')
        days = (dateintext-startdate).days#得出数据集中的日期距离2020.1.1的天数作为预测的因变量
        
        daysdata.append(nowline[0])
        arr0.append([days])
        arr1.append([nowline[1]])
        arr2.append([nowline[2]])
        arr3.append([nowline[3]])
        arr4.append([nowline[4]])
        
    predictarr0 = []
    for i in range(0,365):
        predictdaysdata.append((startdate+timedelta(days=i)).strftime("%Y.%m.%d"))
        predictarr0.append([i])
    
    
    poly_reg = PolynomialFeatures(degree=3)
    xarr = poly_reg.fit_transform(arr0)
    predictxarr = poly_reg.fit_transform(predictarr0)

    linear_reg1 = LinearRegression()
    linear_reg1.fit(xarr, arr1)
    
    linear_reg2 = LinearRegression()
    linear_reg2.fit(xarr, arr2)
    
    linear_reg3 = LinearRegression()
    linear_reg3.fit(xarr, arr3)
    
    linear_reg4 = LinearRegression()
    linear_reg4.fit(xarr, arr4)
    
    for i in range(0,10):
        print(linear_reg1.predict(poly_reg.fit_transform(predictarr0))[244+i] ,
              linear_reg2.predict(poly_reg.fit_transform(predictarr0))[244+i],   
               linear_reg3.predict(poly_reg.fit_transform(predictarr0))[244+i], 
                linear_reg4.predict(poly_reg.fit_transform(predictarr0))[244+i], 
                 predictdaysdata[244+i])

    
    plt.rcParams['font.sans-serif']=['FangSong']
    plt.rcParams['axes.unicode_minus']=False
    plt.figure(figsize=(100,100))
    fig = plt.figure()  
    
    ax0 = fig.add_subplot(1,1,1)
    #ax0.plot(daysdata, arr1, "o", label="新增",markersize =0.3 )
    ax0.plot(predictdaysdata, linear_reg1.predict(poly_reg.fit_transform(predictarr0)), label="新增预测",alpha=0.5)
    plt.xticks("")
    plt.legend()
    
    #ax1 = fig.add_subplot(4,1,2)
    #ax0.plot(daysdata, arr2,"o", label="总确诊",markersize =0.3 )
    ax0.plot(predictdaysdata, linear_reg2.predict(poly_reg.fit_transform(predictarr0)), label="总确诊预测",alpha=0.5)
    plt.xticks("")
    plt.legend()

    #ax2 = fig.add_subplot(4,1,3)
    #ax0.plot(daysdata, arr3,"o", label="治愈",markersize =0.3 )
    ax0.plot(predictdaysdata, linear_reg3.predict(poly_reg.fit_transform(predictarr0)), label="治愈预测",alpha=0.5)
    plt.xticks("")
    plt.legend()
    
    #ax3 = fig.add_subplot(4,1,4)
    #ax0.plot(daysdata, arr4,"o", label="死亡",markersize =0.3 )
    ax0.plot(predictdaysdata, linear_reg4.predict(poly_reg.fit_transform(predictarr0)), label="死亡预测",alpha=0.5)
    plt.xticks(predictarr0[::50])
    plt.legend()
    
    #ax.plot(arr0,arr3,label="治愈")
    #ax.plot(arr0,arr4,label="死亡")
    plt.xticks(predictarr0[::80])
    plt.legend()
    plt.savefig('3.png',dpi=1500)