作者：曹鑫
双十一到今年已经是13个年头，每年大家都在满心期待看着屏幕上的数字跳动，年年打破记录。而2019年的天猫双11的销售额却被一位微博网友提前7个月用数据拟合的方法预测出来了。他的预测值是2675.37或者2689.00亿元，而实际成交额是2684亿元。只差了5亿元，误差率只有千分之一。
但如果你用同样的方法去做预测2020年的时候，发现，预测是3282亿，实际却到了4982亿。原来2020改了规则，实际上统计的是11月1到11日的销量，理论上已经不能和历史数据合并预测，但咱们就为了图个乐，主要是为了练习一下Python的多项式回归和可视化绘图。
把预测先发出来：今年双十一的销量是9029.688亿元！坐等双十一，各位看官回来打我的脸。
NO.01、统计历年双十一销量数据
从网上搜集来历年淘宝天猫双十一销售额数据，单位为亿元，利用Pandas整理成Dataframe，又添加了一列'年份int'，留作后续的计算使用。
importpandasaspd\n\n\n#数据为网络收集，历年淘宝天猫双十一销售额数据，单位为亿元，仅做示范\ndouble11_sales={'2009年':[0.50],\n'2010年':[9.36],\n'2011年':[34],\n'2012年':[191],\n'2013年':[350],\n'2014年':[571],\n'2015年':[912],\n'2016年':[1207],\n'2017年':[1682],\n'2018年':[2135],\n'2019年':[2684],\n'2020年':[4982],\n}\n\n\ndf=pd.DataFrame(double11_sales).T.reset_index()\ndf.rename(columns={'index':'年份',0:'销量'},inplace=True)\ndf['年份int']=[[i]foriinlist(range(1,len(df['年份'])+1))]\ndf
.dataframetbodytrth{\nvertical-align:top;\n}\n\n\n.dataframetheadth{\ntext-align:right;\n}
NO.02、绘制散点图
利用plotly工具包，将年份对应销售量的散点图绘制出来，可以明显看到2020年的数据立马飙升。
#散点图\nimportplotlyaspy\nimportplotly.graph_objsasgo\nimportnumpyasnp\n\n\nyear=df[:]['年份']\nsales=df['销量']\n\n\ntrace=go.Scatter(\nx=year,\ny=sales,\nmode='markers'\n)\ndata=[trace]\n\n\nlayout=go.Layout(title='2009年-2020年天猫淘宝双十一历年销量')\n\n\nfig=go.Figure(data=data,layout=layout)\n\n\nfig.show()
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NO.03、引入Scikit-Learn库搭建模型
一元多次线性回归
我们先来回顾一下2009-2019年的数据多么美妙。先只选取2009-2019年的数据：
df_2009_2019=df[:-1]\ndf_2009_2019
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通过以下代码生成二次项数据：
fromsklearn.preprocessingimportPolynomialFeatures\npoly_reg=PolynomialFeatures(degree=2)\nX_=poly_reg.fit_transform(list(df_2009_2019['年份int']))
1.第一行代码引入用于增加一个多次项内容的模块PolynomialFeatures
2.第二行代码设置最高次项为二次项，为生成二次项数据（x平方）做准备
3.第三行代码将原有的X转换为一个新的二维数组X_，该二维数据包含新生成的二次项数据（x平方）和原有的一次项数据（x）
X_的内容为下方代码所示的一个二维数组，其中第一列数据为常数项（其实就是X的0次方），没有特殊含义，对分析结果不会产生影响；第二列数据为原有的一次项数据（x）；第三列数据为新生成的二次项数据（x的平方）。
X_
array([[1.,1.,1.],\n[1.,2.,4.],\n[1.,3.,9.],\n[1.,4.,16.],\n[1.,5.,25.],\n[1.,6.,36.],\n[1.,7.,49.],\n[1.,8.,64.],\n[1.,9.,81.],\n[1.,10.,100.],\n[1.,11.,121.]])
fromsklearn.linear_modelimportLinearRegression\nregr=LinearRegression()\nregr.fit(X_,list(df_2009_2019['销量']))
LinearRegression()
1.第一行代码从Scikit-Learn库引入线性回归的相关模块LinearRegression；
2.第二行代码构造一个初始的线性回归模型并命名为regr；
3.第三行代码用fit()函数完成模型搭建，此时的regr就是一个搭建好的线性回归模型。
NO.04、模型预测
接下来就可以利用搭建好的模型regr来预测数据。加上自变量是12，那么使用predict()函数就能预测对应的因变量有，代码如下：
XX_=poly_reg.fit_transform([[12]])
XX_
array([[1.,12.,144.]])
y=regr.predict(XX_)\ny
array([3282.23478788])
这里我们就得到了如果按照这个趋势2009-2019的趋势预测2020的结果，就是3282，但实际却是4982亿，原因就是上文提到的合并计算了，金额一下子变大了，绘制成图，就是下面这样：
#散点图\nimportplotlyaspy\nimportplotly.graph_objsasgo\nimportnumpyasnp\n\n\nyear=list(df['年份'])\nsales=df['销量']\n\n\ntrace1=go.Scatter(\nx=year,\ny=sales,\nmode='markers',\nname="实际销量"#第一个图例名称\n)\n\n\nXX_=poly_reg.fit_transform(list(df['年份int'])+[[13]])\nregr=LinearRegression()\nregr.fit(X_,list(df_2009_2019['销量']))\ntrace2=go.Scatter(\nx=list(df['年份']),\ny=regr.predict(XX_),\nmode='lines',\nname="拟合数据",#第2个图例名称\n)\n\n\n\n\ndata=[trace1,trace2]\n\n\nlayout=go.Layout(title='天猫淘宝双十一历年销量',\nxaxis_title='年份',\nyaxis_title='销量')\n\n\nfig=go.Figure(data=data,layout=layout)\n\n\nfig.show()
-
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NO.05、预测2021年的销量
既然数据发生了巨大的偏离，咱们也别深究了，就大力出奇迹。同样的方法，把2020年的真实数据纳入进来，二话不说拟合一样，看看会得到什么结果：
fromsklearn.preprocessingimportPolynomialFeatures\npoly_reg=PolynomialFeatures(degree=5)\nX_=poly_reg.fit_transform(list(df['年份int']))
##预测2020年\nregr=LinearRegression()\nregr.fit(X_,list(df['销量']))
LinearRegression()
XXX_=poly_reg.fit_transform(list(df['年份int'])+[[13]])
#散点图\nimportplotlyaspy\nimportplotly.graph_objsasgo\nimportnumpyasnp\n\n\nyear=list(df['年份'])\nsales=df['销量']\n\n\ntrace1=go.Scatter(\nx=year+['2021年','2022年','2023年'],\ny=sales,\nmode='markers',\nname="实际销量"#第一个图例名称\n)\n\n\n\n\ntrace2=go.Scatter(\nx=year+['2021年','2022年','2023年'],\ny=regr.predict(XXX_),\nmode='lines',\nname="预测销量"#第一个图例名称\n)\n\n\ntrace3=go.Scatter(\nx=['2021年'],\ny=[regr.predict(XXX_)[-1]],\nmode='markers',\nname="2021年预测销量"#第一个图例名称\n)\n\n\ndata=[trace1,trace2,trace3]\n\n\nlayout=go.Layout(title='天猫淘宝双十一历年销量',\nxaxis_title='年份',\nyaxis_title='销量')\n\n\nfig=go.Figure(data=data,layout=layout)\n\n\nfig.show()
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NO.06、多项式预测的次数到底如何选择
在选择模型中的次数方面，可以通过设置程序，循环计算各个次数下预测误差，然后再根据结果反选参数。
df_new=df.copy()\ndf_new['年份int']=df['年份int'].apply(lambdax:x[0])\ndf_new
.dataframetbodytrth{\nvertical-align:top;\n}\n\n\n.dataframetheadth{\ntext-align:right;\n}
#多项式回归预测次数选择\n#计算m次多项式回归预测结果的MSE评价指标并绘图\nfromsklearn.pipelineimportmake_pipeline\nfromsklearn.metricsimportmean_squared_error\n\n\ntrain_df=df_new[:int(len(df)*0.95)]\ntest_df=df_new[int(len(df)*0.5):]\n\n\n#定义训练和测试使用的自变量和因变量\ntrain_x=train_df['年份int'].values\ntrain_y=train_df['销量'].values\n#print(train_x)\n\n\ntest_x=test_df['年份int'].values\ntest_y=test_df['销量'].values\n\n\ntrain_x=train_x.reshape(len(train_x),1)\ntest_x=test_x.reshape(len(test_x),1)\ntrain_y=train_y.reshape(len(train_y),1)\n\n\nmse=[]#用于存储各最高次多项式MSE值\nm=1#初始m值\nm_max=10#设定最高次数\nwhilem<=m_max:\nmodel=make_pipeline(PolynomialFeatures(m,include_bias=False),LinearRegression())\nmodel.fit(train_x,train_y)#训练模型\npre_y=model.predict(test_x)#测试模型\nmse.append(mean_squared_error(test_y,pre_y.flatten()))#计算MSE\nm=m+1\n\n\nprint("MSE计算结果:",mse)\n#绘图\nplt.plot([iforiinrange(1,m_max+1)],mse,'r')\nplt.scatter([iforiinrange(1,m_max+1)],mse)\n\n\n#绘制图名称等\nplt.title("MSEofmdegreeofpolynomialregression")\nplt.xlabel("m")\nplt.ylabel("MSE")
MSE计算结果:[1088092.9621201046,481951.27857828484,478840.8575107471,477235.9140442428,484657.87153138855,509758.1526412842,344204.1969956556,429874.9229308078,8281846.231771571,146298201.8473966]
Text(0,0.5,'MSE')
从误差结果可以看到，次数取2到8误差基本稳定，没有明显的减少了，但其实你试试就知道，次数选择3的时候，预测的销量是6213亿元，次数选择5的时候，预测的销量是9029亿元，对于销售量来说，这个范围已经够大的了。我也就斗胆猜到9029亿元，我的胆量也就预测到这里了，破万亿就太夸张了，欢迎胆子大的同学留下你们的预测结果，让我们11月11日，拭目以待吧。
NO.07、总结最后
