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不靠谱的预测：今年双十一的销量是 6213 亿元

Y.an • • 产品运营, 投稿

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。

import pandas as pd


# 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
double11_sales = {'2009年': [0.50],
                  '2010年':[9.36],
                  '2011年':[34],
                  '2012年':[191],
                  '2013年':[350],
                  '2014年':[571],
                  '2015年':[912],
                  '2016年':[1207],
                  '2017年':[1682],
                  '2018年':[2135],
                  '2019年':[2684],
                  '2020年':[4982],
                 }


df = pd.DataFrame(double11_sales).T.reset_index()
df.rename(columns={'index':'年份',0:'销量'},inplace=True)
df['年份int'] = [[i] for i in list(range(1,len(df['年份'])+1))]
df
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不靠谱的预测：今年双十一的销量是 6213 亿元

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
import plotly as py
import plotly.graph_objs as go
import numpy as np


year = df[:]['年份']
sales = df['销量']


trace = go.Scatter(
    x=year,
    y=sales,
    mode='markers'
)
data = [trace]


layout = go.Layout(title='2009年-2020年天猫淘宝双十一历年销量')


fig = go.Figure(data=data, layout=layout)


fig.show()
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不靠谱的预测：今年双十一的销量是 6213 亿元

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]
df_2009_2019
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不靠谱的预测：今年双十一的销量是 6213 亿元

通过以下代码生成二次项数据：

from sklearn.preprocessing import PolynomialFeatures
poly_reg = PolynomialFeatures(degree=2)
X_ = 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.],
[  1.,   2.,   4.],
[  1.,   3.,   9.],
[  1.,   4.,  16.],
[  1.,   5.,  25.],
[  1.,   6.,  36.],
[  1.,   7.,  49.],
[  1.,   8.,  64.],
[  1.,   9.,  81.],
[  1.,  10., 100.],
[  1.,  11., 121.]])
from sklearn.linear_model import LinearRegression
regr = LinearRegression()
regr.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_)
y
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
import plotly as py
import plotly.graph_objs as go
import numpy as np
year = list(df['年份'])
sales = df['销量']
trace1 = go.Scatter(
x=year,
y=sales,
mode='markers',
name="实际销量"       # 第一个图例名称
)
XX_ = poly_reg.fit_transform(list(df['年份int'])+[[13]])
regr = LinearRegression()
regr.fit(X_,list(df_2009_2019['销量']))
trace2 = go.Scatter(
x=list(df['年份']),
y=regr.predict(XX_),
mode='lines',
name="拟合数据",  # 第2个图例名称
)
data = [trace1,trace2]
layout = go.Layout(title='天猫淘宝双十一历年销量',
xaxis_title='年份',
yaxis_title='销量')
fig = go.Figure(data=data, layout=layout)
fig.show()
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不靠谱的预测：今年双十一的销量是 6213 亿元

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：

from sklearn.preprocessing import PolynomialFeatures
poly_reg = PolynomialFeatures(degree=5)
X_ = poly_reg.fit_transform(list(df['年份int']))
## 预测2020年
regr = LinearRegression()
regr.fit(X_,list(df['销量']))
LinearRegression()
XXX_ = poly_reg.fit_transform(list(df['年份int'])+[[13]])
# 散点图
import plotly as py
import plotly.graph_objs as go
import numpy as np
year = list(df['年份'])
sales = df['销量']
trace1 = go.Scatter(
x=year+['2021年','2022年','2023年'],
y=sales,
mode='markers',
name="实际销量"       # 第一个图例名称
)
trace2 = go.Scatter(
x=year+['2021年','2022年','2023年'],
y=regr.predict(XXX_),
mode='lines',
name="预测销量"       # 第一个图例名称
)
trace3 = go.Scatter(
x=['2021年'],
y=[regr.predict(XXX_)[-1]],
mode='markers',
name="2021年预测销量"       # 第一个图例名称
)
data = [trace1,trace2,trace3]
layout = go.Layout(title='天猫淘宝双十一历年销量',
xaxis_title='年份',
yaxis_title='销量')
fig = go.Figure(data=data, layout=layout)
fig.show()
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不靠谱的预测：今年双十一的销量是 6213 亿元

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()
df_new['年份int'] = df['年份int'].apply(lambda x: x[0])
df_new
.dataframe tbody tr th {
    vertical-align: top;
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不靠谱的预测：今年双十一的销量是 6213 亿元
#  多项式回归预测次数选择
# 计算 m 次多项式回归预测结果的 MSE 评价指标并绘图
from sklearn.pipeline import make_pipeline
from sklearn.metrics import mean_squared_error
train_df = df_new[:int(len(df)*0.95)]
test_df = df_new[int(len(df)*0.5):]
# 定义训练和测试使用的自变量和因变量
train_x = train_df['年份int'].values
train_y = train_df['销量'].values
# print(train_x)
test_x = test_df['年份int'].values
test_y = test_df['销量'].values
train_x = train_x.reshape(len(train_x),1)
test_x = test_x.reshape(len(test_x),1)
train_y = train_y.reshape(len(train_y),1)
mse = [] # 用于存储各最高次多项式 MSE 值
m = 1 # 初始 m 值
m_max = 10 # 设定最高次数
while m <= m_max:
model = make_pipeline(PolynomialFeatures(m, include_bias=False), LinearRegression())
model.fit(train_x, train_y) # 训练模型
pre_y = model.predict(test_x) # 测试模型
mse.append(mean_squared_error(test_y, pre_y.flatten())) # 计算 MSE
m = m + 1
print("MSE 计算结果: ", mse)
# 绘图
plt.plot([i for i in range(1, m_max + 1)], mse, 'r')
plt.scatter([i for i in range(1, m_max + 1)], mse)
# 绘制图名称等
plt.title("MSE of m degree of polynomial regression")
plt.xlabel("m")
plt.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')
不靠谱的预测：今年双十一的销量是 6213 亿元

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

希望这篇文章带着对 Python 的多项式回归和 Plotly可视化绘图还不熟悉的同学一起练习一下。

本文出品：CDA数据分析师

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