曾国藩的"顺势而为"在PostgreSQL中的价值体现

后人对曾国藩的一些评论：“曾国藩顺势而为成就一番事业，并一定程度上做了一些推动历史前进的事情”。

“顺势而为”这个词实在是用得太好了，我们身在数字时代，更加应该懂得顺势而为的道理，比如在金融行业中，不断变化的股价；在物联网的传感器中，不断上报的数字；由数据监测不断画出的曲线等等，这些无不体现着一个字：“势”。

我们来看看使用PostgreSQL数据库如何抓住这个“势”呢？

首先贴一个最小二乘法least-squares-fit的小故事(取自百度) :

1801年，意大利天文学家朱赛普·皮亚齐发现了第一颗小行星谷神星。经过40天的跟踪观测后，由于谷神星运行至太阳背后，使得皮亚齐失去了谷神星的位置。随后全世界的科学家利用皮亚齐的观测数据开始寻找谷神星，但是根据大多数人计算的结果来寻找谷神星都没有结果。时年24岁的高斯也计算了谷神星的轨道。奥地利天文学家海因里希·奥尔伯斯根据高斯计算出来的轨道重新发现了谷神星。

高斯使用的最小二乘法的方法发表于1809年他的著作《天体运动论》中。
法国科学家勒让德于1806年独立发现“最小二乘法”，但因不为世人所知而默默无闻。
勒让德曾与高斯为谁最早创立最小二乘法原理发生争执。
1829年，高斯提供了最小二乘法的优化效果强于其他方法的证明，因此被称为高斯-马尔可夫定理.

上面的故事说明通过已有数据可以对未来的数据进行预测. 但是预测结果是否准确有不确定因素, 所以需要不断的调整和校验.

如何做回归分析呢? (取自百度)

研究一个或多个随机变量Y1 ，Y2 ，…，Yi与另一些变量X1、X2，…，Xk之间的关系的统计方法，又称多重回归分析。通常称Y1，Y2，…，Yi为因变量，X1、X2，…，Xk为自变量。回归分析是一类数学模型，特别当因变量和自变量为线性关系时，它是一种特殊的线性模型。最简单的情形是一个自变量和一个因变量，且它们大体上有线性关系，这叫一元线性回归，即模型为Y=a+bX+ε，这里X是自变量，Y是因变量，ε是随机误差，通常假定随机误差的均值为0，方差为σ^2（σ^2大于0）σ^2与X的值无关。若进一步假定随机误差遵从正态分布，就叫做正态线性模型。一般的情形，它有k个自变量和一个因变量，因变量的值可以分解为两部分：一部分是由于自变量的影响，即表示为自变量的函数，其中函数形式已知，但含一些未知参数；另一部分是由于其他未被考虑的因素和随机性的影响，即随机误差。当函数形式为未知参数的线性函数时，称线性回归分析模型；当函数形式为未知参数的非线性函数时，称为非线性回归分析模型。当自变量的个数大于1时称为多元回归，当因变量个数大于1时称为多重回归。

回归分析的主要内容为：

①从一组数据出发，确定某些变量之间的定量关系式，即建立数学模型并估计其中的未知参数。估计参数的常用方法是最小二乘法。

②对这些关系式的可信程度进行检验。

③在许多自变量共同影响着一个因变量的关系中，判断哪个（或哪些）自变量的影响是显著的，哪些自变量的影响是不显著的，将影响显著的自变量入模型中，而剔除影响不显著的变量，通常用逐步回归、向前回归和向后回归等方法。

④利用所求的关系式对某一生产过程进行预测或控制。回归分析的应用是非常广泛的，统计软件包使各种回归方法计算十分方便。

在回归分析中，把变量分为两类。一类是因变量，它们通常是实际问题中所关心的一类指标，通常用Y表示；而影响因变量取值的的另一类变量称为自变量，用X来表示。

回归分析研究的主要问题是：

（1）确定Y与X间的定量关系表达式，这种表达式称为回归方程；

（2）对求得的回归方程的可信度进行检验；

（3）判断自变量X对因变量Y有无影响；

（4）利用所求得的回归方程进行预测和控制。

一个例子 :

例如，如果要研究质量和用户满意度之间的因果关系，从实践意义上讲，产品质量会影响用户的满意情况，因此设用户满意度为因变量，记为Y；质量为自变量，记为X。根据图8－3的散点图，可以建立下面的线性关系： Y=A+BX+§

式中：A和B为待定参数，A为回归直线的截距；B为回归直线的斜率，表示X变化一个单位时，Y的平均变化情况；§为依赖于用户满意度的随机误差项。

对于经验回归方程： y=0.857+0.836x

回归直线在y轴上的截距为0.857、斜率0.836，即质量每提高一分，用户满意度平均上升0.836分；或者说质量每提高1分对用户满意度的贡献是0.836分。

在PostgreSQL中提供了回归分析的一些聚合函数,

`regr_avgx(Y, X)`	double precision	double precision	average of the independent variable (sum(X)/N)
`regr_avgy(Y, X)`	double precision	double precision	average of the dependent variable (sum(Y)/N)
`regr_count(Y, X)`	double precision	bigint	number of input rows in which both expressions are nonnull
`regr_intercept(Y, X)`	double precision	double precision	y-intercept of the least-squares-fit linear equation determined by the (X, Y) pairs
`regr_r2(Y, X)`	double precision	double precision	square of the correlation coefficient
`regr_slope(Y, X)`	double precision	double precision	slope of the least-squares-fit linear equation determined by the (X, Y) pairs
`regr_sxx(Y, X)`	double precision	double precision	sum(X^2) - sum(X)^2/N ("sum of squares" of the independent variable)
`regr_sxy(Y, X)`	double precision	double precision	sum(XY) - sum(X) sum(Y)/N ("sum of products" of independent times dependent variable)
`regr_syy(Y, X)`	double precision	double precision	sum(Y^2) - sum(Y)^2/N ("sum of squares" of the dependent variable)

本文会用到如下几个 :

regr_intercept, 计算截距.

regr_slope, 计算斜率.

regr_r2, 计算相关性, 相关性越高, 说明这组数据用于预估的准确度越高.

下面来举个例子 :

将最近一年的某个业务的日访问量数据统计放到一张测试表.

利用这一年的数据进行一元回归分析, 要预测的是因变量, 用作预测的是自变量. 因为要预测的数据未发生, 所以我们可以把时间交错一下, 就可以作为自变量来使用.

例如下面这组数据, 自变量就是数据下移一行产生的. :

因变量 | 自变量
 48000 | 54624
 47454 | 48000
 56766 | 47454
 60488 | 56766
 58191 | 60488
 57443 | 58191
 54277 | 57443
 55508 | 54277
 52716 | 55508
 63748 | 52716
 43462 | 63748
 44248 | 43462
 40145 | 44248

如果影响的因素较多, 需要做多元回归, 你可以选择PostgreSQL R语言插件来分析.

本文做的是一元回归的例子, 接下来进入测试 :

创建一张过去365天的某业务的日下载量数据表.

digoal=> create table test as select row_number() over(order by dt) as rn,cnt from
         (select date(createtime) as dt, count(*) as cnt from tbl_app_download where createtime>=( date(now())-366 ) and createtime<( date(now())-1 ) group by date(createtime)) as t;
SELECT 365

数据大概是这样的

digoal=> select * from test;
....
 329 |   36293
 330 |   40886
 331 |   34465
 332 |   30785
 333 |   33318
 334 |   34480
....

接下来我们要来测试在不同数据范围内的回归的线性相关性,

例如最近362天的数据交错后的回归线性相关性.

digoal=> select count(*),regr_r2(t.cnt,test.cnt) from
(select rn-1 as rn,cnt from test) as t,test where t.rn=test.rn and test.rn>2;
 count |      regr_r2
-------+-------------------
   362 | 0.835282212765017
(1 row)

但是如果时间放大到最近363天, 相关性就降低到0.32915622582628了

digoal=> select count(*),regr_r2(t.cnt,test.cnt) from
(select rn-1 as rn,cnt from test) as t,test where t.rn=test.rn and test.rn>1;
 count |     regr_r2
-------+------------------
   363 | 0.32915622582628
(1 row)

我们要不断的尝试来得到更好的相关性, 当获得最高的相关性(接近1)时, 预测数据最准确.

接下来我们看看以上两个时间段产生的截距和斜率的预测准确度.

截距

digoal=> select count(*),regr_intercept(t.cnt,test.cnt) from
(select rn-1 as rn,cnt from test) as t,test where t.rn=test.rn and test.rn>2;
 count |  regr_intercept
-------+------------------
   362 | 6274.25023499543
(1 row)

斜率

digoal=> select count(*),regr_slope(t.cnt,test.cnt) from
(select rn-1 as rn,cnt from test) as t,test where t.rn=test.rn and test.rn>2;
 count |    regr_slope
-------+-------------------
   362 | 0.906861594725424
(1 row)

使用自变量44248推测因变量40145.

使用公式推测的结果为46401.062078405991152

digoal=> select 44248*0.906861594725424+6274.25023499543;
       ?column?
-----------------------
 46401.062078405991152
(1 row)

准确度 :

digoal=> select 40145/46401.062078405991152;
        ?column?
------------------------
 0.86517416200873079820
(1 row)

当我们使用另一组截距和斜率时, 准确度最低是0.32915622582628. 所以得到的预测结果可能不及以上的.

截距
digoal=> select count(*),regr_intercept(t.cnt,test.cnt) from
(select rn-1 as rn,cnt from test) as t,test where t.rn=test.rn and test.rn>1;
 count |  regr_intercept
-------+------------------
   363 | 49279.0342891155
(1 row)
斜率
digoal=> select count(*),regr_slope(t.cnt,test.cnt) from
(select rn-1 as rn,cnt from test) as t,test where t.rn=test.rn and test.rn>1;
 count |    regr_slope
-------+-------------------
   363 | 0.292250474909646
(1 row)
预测结果
digoal=> select 44248*0.292250474909646+49279.0342891155;
       ?column?
-----------------------
 62210.533302917516208
(1 row)
准确度
digoal=> select 40145/62210.533302917516208;
        ?column?
------------------------
 0.64530872616900233730
(1 row)

最后再提一下另外几个和回归相关的函数 :

`regr_avgx(Y, X)`	double precision	double precision	average of the independent variable (sum(X)/N)
`regr_avgy(Y, X)`	double precision	double precision	average of the dependent variable (sum(Y)/N)
`regr_count(Y, X)`	double precision	bigint	number of input rows in which both expressions are nonnull

`regr_sxx(Y, X)`	double precision	double precision	sum(X^2) - sum(X)^2/N ("sum of squares" of the independent variable)
`regr_sxy(Y, X)`	double precision	double precision	sum(XY) - sum(X) sum(Y)/N ("sum of products" of independent times dependent variable)
`regr_syy(Y, X)`	double precision	double precision	sum(Y^2) - sum(Y)^2/N ("sum of squares" of the dependent variable)

regr_avgx(y, x)其实就是算x的平均值(数学期望), y在这里没有任何作用.

regr_avgy(y, x)其实就是算y的平均值(数学期望), x在这里没有任何作用.

regr_count(y, x) 计算x和y都不是空的记录数.

另外三个是辅助函数, 计算诊断统计信息(总方差, 总协方差).

regr_sxx(y, x)  :  sum(X^2) - sum(X)^2/N
regr_sxy(y, x)  :  sum(X*Y) - sum(X) * sum(Y)/N
regr_syy(y, x)  :  sum(Y^2) - sum(Y)^2/N
REGR_SXY, REGR_SXX, REGR_SYY are auxiliary functions that are used to compute various diagnostic statistics.
REGR_SXX makes the following computation after the elimination of null (expr1, expr2) pairs:
REGR_COUNT(expr1, expr2) * VAR_POP(expr2)

REGR_SYY makes the following computation after the elimination of null (expr1, expr2) pairs:
REGR_COUNT(expr1, expr2) * VAR_POP(expr1)

REGR_SXY makes the following computation after the elimination of null (expr1, expr2) pairs:
REGR_COUNT(expr1, expr2) * COVAR_POP(expr1, expr2)

验证regr_sxx, sxy, syy.

postgres=# select regr_sxx(y,x), REGR_COUNT(y,x)*VAR_POP(x) from (values(2,400),(6,401),(7,400),(3,400),(1000,488)) as t(x,y);
 regr_sxx |      ?column?
----------+---------------------
 792833.2 | 792833.200000000000
(1 row)

postgres=# select regr_sxy(y,x), REGR_COUNT(y,x)*COVAR_POP(x,y) from (values(2,400),(6,401),(7,400),(3,400),(1000,488)) as t(x,y);
 regr_sxy | ?column?
----------+----------
  69885.6 |  69885.6
(1 row)

postgres=# select regr_syy(y,x), REGR_COUNT(y,x)*VAR_POP(y) from (values(2,400),(6,401),(7,400),(3,400),(1000,488)) as t(x,y);
 regr_syy |       ?column?
----------+-----------------------
   6160.8 | 6160.8000000000000000
(1 row)

好了, 先写到这里, 你还可以尝试更多的折腾玩法.

自动选择最优相关的例子如下 .

=> select * from test order by to_char desc limit 10;
  to_char   | count
------------+--------
 2015030123 | 149496
 2015030122 | 165320
 2015030121 | 167663
 2015030120 | 161071
 2015030119 | 145570
 2015030118 | 133155
 2015030117 | 133962
 2015030116 | 130484
 2015030115 | 126182
 2015030114 | 122998
(10 rows)

=> do language plpgsql $$
declare
  r2_1 numeric := 0;
  r2_2 numeric := 0;
  var int;
  inter numeric;
  slope numeric;
  inter_2 numeric;
  slope_2 numeric;
  realv numeric;
  predicv numeric;
  offset_var int := 0; -- 最后一个值的预测值
begin
  for i in 1..450 loop
    with t1 as (select row_number() over(order by to_char) as rn,count from test order by to_char desc offset offset_var),
         t2 as (select row_number() over(order by to_char)-1 as rn,count from test order by to_char desc offset offset_var)
      select regr_intercept(t2.count,t1.count),regr_slope(t2.count,t1.count),regr_r2(t1.count,t2.count) into inter,slope,r2_1 from t1,t2 where t1.rn=t2.rn and t1.rn>i;
    if r2_1>r2_2 then
      inter_2:=inter;
      slope_2:=slope;
      r2_2:=r2_1;
      var:=i;
    end if;
  end loop; 

  raise notice '%, %, %, %', var, inter_2,slope_2,r2_2;
  select slope_2*count+inter_2 into predicv from test order by to_char desc offset offset_var+1 limit 1;
  select count into realv from test order by to_char desc offset offset_var limit 1;
  raise notice '%, %', realv, predicv;
end;
$$;
NOTICE:  436, 16599.0041292694, 0.896184690654355, 0.925125327496365
NOTICE:  149496, 164756.257188247368600
DO

=> select 149496/164756.2;
        ?column?
------------------------
 0.90737708201572990880
(1 row)

=> do language plpgsql $$
declare
  r2_1 numeric := 0; -- 相关性
  r2_2 numeric := 0; -- 最大相关性
  var int;  --  样本数量
  inter_1 numeric;  --  截距
  slope_1 numeric;  --  斜率
  inter_2 numeric;  --  最大相关性截距
  slope_2 numeric;  --  最大相关性斜率
  realv numeric;    --  真实数据
  predicv numeric;  --  预测数据
  offset_var int := 1;   -- 倒数第二个值的预测值, 不停迭代, 最后计算所有的实际值和预测值的corr, 看看相似度如何?
begin
  for i in 1..450 loop
    with t1 as (select row_number() over(order by to_char) as rn,count from test order by to_char desc offset offset_var),
         t2 as (select row_number() over(order by to_char)-1 as rn,count from test order by to_char desc offset offset_var)
      select regr_intercept(t2.count,t1.count),regr_slope(t2.count,t1.count),regr_r2(t1.count,t2.count) into inter_1,slope_1,r2_1 from t1,t2 where t1.rn=t2.rn and t1.rn>i;
    if r2_1>r2_2 then
      inter_2 := inter_1;
      slope_2 := slope_1;
      r2_2 := r2_1;
      var := i;
    end if;
  end loop;

  raise notice '样本数量%, 截距%, 斜率%, 相关性%', var, round(inter_2,4), round(slope_2,4), round(r2_2,4);
  select slope_2*count+inter_2 into predicv from test order by to_char desc offset offset_var+1 limit 1;
  select count into realv from test order by to_char desc offset offset_var limit 1;
  raise notice '真实数据%, 预测数据%, 本次预测偏差,%%%', realv, round(predicv), abs(1-round(predicv/realv,4))*100;
end;
$$;
NOTICE:  样本数量436, 截距10109.8500, 斜率0.9573, 相关性0.9476
NOTICE:  真实数据165320, 预测数据170611, 本次预测偏差,%3.2000
DO

校验函数

=> create or replace function check_predict(IN ov int, OUT rv numeric, OUT pv numeric, OUT dev numeric) returns record as $$
declare
  r2_1 numeric := 0; -- 相关性
  r2_2 numeric := 0; -- 最大相关性
  var int;  --  样本数量
  inter_1 numeric;  --  截距
  slope_1 numeric;  --  斜率
  inter_2 numeric;  --  最大相关性截距
  slope_2 numeric;  --  最大相关性斜率
  realv numeric;    --  真实数据
  predicv numeric;  --  预测数据
  offset_var int := ov;   -- 倒数第二个值的预测值, 不停迭代, 最后计算所有的实际值和预测值的corr, 看看相似度如何?
  lps int := 0;
begin
  select count(*)-offset_var-4 into lps from test;  --  循环不要超过总样本数, 同时至少给2个样本.
  for i in 1..lps loop
    with t1 as (select row_number() over(order by to_char) as rn,to_char,count from test order by to_char desc offset offset_var),
         t2 as (select row_number() over(order by to_char)-1 as rn,to_char,count from test order by to_char desc offset offset_var)
      select regr_intercept(t2.count,t1.count),regr_slope(t2.count,t1.count),regr_r2(t1.count,t2.count) into inter_1,slope_1,r2_1 from t1,t2 where t1.rn=t2.rn and t1.rn>i;
    if r2_1>r2_2 then
      inter_2 := inter_1;
      slope_2 := slope_1;
      r2_2 := r2_1;
      var := i;
    end if;
  end loop;

  raise notice '样本数量%, 截距%, 斜率%, 相关性%', var, round(inter_2,4), round(slope_2,4), round(r2_2,4);
  select slope_2*count+inter_2 into predicv from test order by to_char desc offset offset_var+1 limit 1;
  select count into realv from test order by to_char desc offset offset_var limit 1;
  raise notice '真实数据%, 预测数据%, 本次预测偏差%%%', realv, round(predicv), abs(1-round(predicv/realv,4))*100;

  rv := realv;
  pv := round(predicv);
  dev := abs(1-round(predicv/realv,4));
  return;
end;
$$ language plpgsql;

校验测试 :

=> select check_predict(i) from generate_series(1,100) t(i);
NOTICE:  样本数量436, 截距10109.8500, 斜率0.9573, 相关性0.9476
NOTICE:  真实数据165320, 预测数据170611, 本次预测偏差%3.2000
NOTICE:  样本数量436, 截距6909.3635, 斜率0.9872, 相关性0.9419
NOTICE:  真实数据167663, 预测数据165922, 本次预测偏差%1.0400
NOTICE:  样本数量436, 截距8151.8730, 斜率0.9754, 相关性0.9249
NOTICE:  真实数据161071, 预测数据150145, 本次预测偏差%6.7800
NOTICE:  样本数量436, 截距14388.5296, 斜率0.9135, 相关性0.9275
NOTICE:  真实数据145570, 预测数据136026, 本次预测偏差%6.5600
NOTICE:  样本数量437, 截距30451.0167, 斜率0.7726, 相关性0.9570
NOTICE:  真实数据133155, 预测数据133953, 本次预测偏差%0.6000
NOTICE:  样本数量446, 截距343.4262, 斜率1.0262, 相关性0.9785
NOTICE:  真实数据133962, 预测数据134241, 本次预测偏差%0.2100
NOTICE:  样本数量437, 截距31491.5019, 斜率0.7616, 相关性0.9494
NOTICE:  真实数据130484, 预测数据127596, 本次预测偏差%2.2100
NOTICE:  样本数量438, 截距48512.9273, 斜率0.6126, 相关性0.9484
NOTICE:  真实数据126182, 预测数据123864, 本次预测偏差%1.8400
NOTICE:  样本数量438, 截距50299.8161, 斜率0.5940, 相关性0.9526
NOTICE:  真实数据122998, 预测数据124578, 本次预测偏差%1.2800
NOTICE:  样本数量442, 截距33561.3690, 斜率0.7444, 相关性0.9983
NOTICE:  真实数据125052, 预测数据125119, 本次预测偏差%0.0500
NOTICE:  样本数量438, 截距50126.2968, 斜率0.5954, 相关性0.9475
NOTICE:  真实数据123000, 预测数据121572, 本次预测偏差%1.1600
NOTICE:  样本数量438, 截距52640.6564, 斜率0.5687, 相关性0.9400
NOTICE:  真实数据119991, 预测数据118710, 本次预测偏差%1.0700
NOTICE:  样本数量438, 截距55198.2911, 斜率0.5404, 相关性0.9301
NOTICE:  真实数据116182, 预测数据118363, 本次预测偏差%1.8800
NOTICE:  样本数量438, 截距43721.8498, 斜率0.6665, 相关性0.9845
NOTICE:  真实数据116887, 预测数据116082, 本次预测偏差%0.6900
NOTICE:  样本数量1, 截距4661.3951, 斜率0.9464, 相关性0.8978
NOTICE:  真实数据108562, 预测数据98517, 本次预测偏差%9.2500
NOTICE:  样本数量1, 截距4675.5276, 斜率0.9460, 相关性0.8979
NOTICE:  真实数据99168, 预测数据82725, 本次预测偏差%16.5800
NOTICE:  样本数量432, 截距39520.3078, 斜率0.4823, 相关性0.9201
NOTICE:  真实数据82505, 预测数据74942, 本次预测偏差%9.1700
NOTICE:  样本数量432, 截距31502.3387, 斜率0.5457, 相关性0.9985
NOTICE:  真实数据73450, 预测数据72804, 本次预测偏差%0.8800
NOTICE:  样本数量432, 截距30417.7790, 斜率0.5542, 相关性0.9989
NOTICE:  真实数据75681, 预测数据76143, 本次预测偏差%0.6100
NOTICE:  样本数量432, 截距31775.6232, 斜率0.5440, 相关性0.9992
NOTICE:  真实数据82509, 预测数据82187, 本次预测偏差%0.3900
NOTICE:  样本数量1, 截距4622.2503, 斜率0.9465, 相关性0.8993
NOTICE:  真实数据92670, 预测数据111447, 本次预测偏差%20.2600
NOTICE:  样本数量1, 截距4531.6850, 斜率0.9481, 相关性0.9003
NOTICE:  真实数据112865, 预测数据145539, 本次预测偏差%28.9500
NOTICE:  样本数量412, 截距19211.5611, 斜率0.8778, 相关性0.9590
NOTICE:  真实数据148731, 预测数据150848, 本次预测偏差%1.4200
NOTICE:  样本数量412, 截距18806.5399, 斜率0.8820, 相关性0.9580
NOTICE:  真实数据149961, 预测数据156169, 本次预测偏差%4.1400
NOTICE:  样本数量412, 截距17050.6057, 斜率0.8991, 相关性0.9603
NOTICE:  真实数据155748, 预测数据161289, 本次预测偏差%3.5600
NOTICE:  样本数量412, 截距14830.5241, 斜率0.9202, 相关性0.9607
NOTICE:  真实数据160430, 预测数据155939, 本次预测偏差%2.8000
NOTICE:  样本数量412, 截距16540.9704, 斜率0.9034, 相关性0.9574
NOTICE:  真实数据153344, 预测数据150240, 本次预测偏差%2.0200
NOTICE:  样本数量412, 截距17692.1060, 斜率0.8917, 相关性0.9532
NOTICE:  真实数据147997, 预测数据140772, 本次预测偏差%4.8800
NOTICE:  样本数量414, 截距41717.5731, 斜率0.6980, 相关性0.9736
NOTICE:  真实数据138023, 预测数据137013, 本次预测偏差%0.7300
NOTICE:  样本数量414, 截距42191.4454, 斜率0.6933, 相关性0.9722
NOTICE:  真实数据136535, 预测数据135075, 本次预测偏差%1.0700
NOTICE:  样本数量414, 截距42836.5141, 斜率0.6866, 相关性0.9716
NOTICE:  真实数据133978, 预测数据133909, 本次预测偏差%0.0500
NOTICE:  样本数量414, 截距42868.4919, 斜率0.6863, 相关性0.9698
NOTICE:  真实数据132634, 预测数据136891, 本次预测偏差%3.2100
NOTICE:  样本数量414, 截距39356.6117, 斜率0.7213, 相关性0.9849
NOTICE:  真实数据136998, 预测数据137674, 本次预测偏差%0.4900
NOTICE:  样本数量418, 截距-98886.5041, 斜率1.7965, 相关性0.9925
NOTICE:  真实数据136303, 预测数据136431, 本次预测偏差%0.0900
NOTICE:  样本数量414, 截距41274.0892, 斜率0.7011, 相关性0.9848
NOTICE:  真实数据130987, 预测数据130817, 本次预测偏差%0.1300
NOTICE:  样本数量414, 截距41537.1100, 斜率0.6983, 相关性0.9803
NOTICE:  真实数据127722, 预测数据129731, 本次预测偏差%1.5700
NOTICE:  样本数量414, 截距35567.9284, 斜率0.7625, 相关性0.9901
NOTICE:  真实数据126303, 预测数据124949, 本次预测偏差%1.0700
NOTICE:  样本数量414, 截距41599.7365, 斜率0.6944, 相关性0.9993
NOTICE:  真实数据117218, 预测数据117405, 本次预测偏差%0.1600
NOTICE:  样本数量413, 截距1686.3033, 斜率1.1262, 相关性0.8957
NOTICE:  真实数据109160, 预测数据110726, 本次预测偏差%1.4300
NOTICE:  样本数量412, 截距-126088.7154, 斜率2.7998, 相关性0.9671
NOTICE:  真实数据96823, 预测数据97097, 本次预测偏差%0.2800
NOTICE:  样本数量408, 截距36426.6219, 斜率0.5003, 相关性0.9205
NOTICE:  真实数据79716, 预测数据72776, 本次预测偏差%8.7100
NOTICE:  样本数量408, 截距29915.3284, 斜率0.5522, 相关性0.9813
NOTICE:  真实数据72658, 预测数据69530, 本次预测偏差%4.3100
NOTICE:  样本数量409, 截距30542.2158, 斜率0.5286, 相关性0.9970
NOTICE:  真实数据71739, 预测数据71377, 本次预测偏差%0.5100
NOTICE:  样本数量408, 截距21294.1724, 斜率0.6206, 相关性0.9985
NOTICE:  真实数据77243, 预测数据76786, 本次预测偏差%0.5900
NOTICE:  样本数量1, 截距4921.7169, 斜率0.9414, 相关性0.8898
NOTICE:  真实数据89412, 预测数据109386, 本次预测偏差%22.3400
NOTICE:  样本数量406, 截距-771730.9711, 斜率6.1383, 相关性0.9650
NOTICE:  真实数据110972, 预测数据112269, 本次预测偏差%1.1700
NOTICE:  样本数量388, 截距15580.3852, 斜率0.9001, 相关性0.9520
NOTICE:  真实数据144014, 预测数据149237, 本次预测偏差%3.6300
NOTICE:  样本数量388, 截距14377.9729, 斜率0.9129, 相关性0.9524
NOTICE:  真实数据148483, 预测数据151688, 本次预测偏差%2.1600
NOTICE:  样本数量388, 截距13455.2553, 斜率0.9226, 相关性0.9497
NOTICE:  真实数据150405, 预测数据156324, 本次预测偏差%3.9400
NOTICE:  样本数量402, 截距71505.3386, 斜率0.5561, 相关性0.9759
NOTICE:  真实数据154850, 预测数据155607, 本次预测偏差%0.4900
NOTICE:  样本数量388, 截距11270.4334, 斜率0.9451, 相关性0.9387
NOTICE:  真实数据151244, 预测数据144638, 本次预测偏差%4.3700
NOTICE:  样本数量388, 截距14060.3682, 斜率0.9147, 相关性0.9332
NOTICE:  真实数据141118, 预测数据129415, 本次预测偏差%8.2900
NOTICE:  样本数量390, 截距36957.1231, 斜率0.7099, 相关性0.9656
NOTICE:  真实数据126106, 预测数据125617, 本次预测偏差%0.3900
NOTICE:  样本数量390, 截距37150.1505, 斜率0.7077, 相关性0.9636
NOTICE:  真实数据124896, 预测数据128489, 本次预测偏差%2.8800
NOTICE:  样本数量390, 截距34760.7660, 斜率0.7330, 相关性0.9714
NOTICE:  真实数据129061, 预测数据128477, 本次预测偏差%0.4500
NOTICE:  样本数量390, 截距35229.1317, 斜率0.7280, 相关性0.9667
NOTICE:  真实数据127849, 预测数据128208, 本次预测偏差%0.2800
NOTICE:  样本数量392, 截距4342.9938, 斜率1.0018, 相关性0.9702
NOTICE:  真实数据127715, 预测数据129117, 本次预测偏差%1.1000
NOTICE:  样本数量393, 截距-32076.9878, 斜率1.3312, 相关性0.9964
NOTICE:  真实数据124554, 预测数据124206, 本次预测偏差%0.2800
NOTICE:  样本数量393, 截距-19541.0766, 斜率1.2152, 相关性1.0000
NOTICE:  真实数据117397, 预测数据117404, 本次预测偏差%0.0100
NOTICE:  样本数量390, 截距47549.0400, 斜率0.5872, 相关性0.9902
NOTICE:  真实数据112693, 预测数据111435, 本次预测偏差%1.1200
NOTICE:  样本数量390, 截距50098.4943, 斜率0.5560, 相关性0.9977
NOTICE:  真实数据108804, 预测数据108821, 本次预测偏差%0.0200
NOTICE:  样本数量390, 截距50042.2813, 斜率0.5567, 相关性0.9964
NOTICE:  真实数据105623, 预测数据105973, 本次预测偏差%0.3300
NOTICE:  样本数量1, 截距5273.1579, 斜率0.9358, 相关性0.8782
NOTICE:  真实数据100474, 预测数据89115, 本次预测偏差%11.3100
NOTICE:  样本数量1, 截距5280.4763, 斜率0.9354, 相关性0.8785
NOTICE:  真实数据89591, 预测数据72087, 本次预测偏差%19.5400
NOTICE:  样本数量384, 截距30325.0273, 斜率0.5354, 相关性0.9387
NOTICE:  真实数据71422, 预测数据64918, 本次预测偏差%9.1100
NOTICE:  样本数量386, 截距37631.4820, 斜率0.4029, 相关性0.9941
NOTICE:  真实数据64616, 预测数据64377, 本次预测偏差%0.3700
NOTICE:  样本数量384, 截距20707.7226, 斜率0.6191, 相关性0.9961
NOTICE:  真实数据66389, 预测数据65428, 本次预测偏差%1.4500
NOTICE:  样本数量384, 截距17341.5766, 斜率0.6472, 相关性0.9978
NOTICE:  真实数据72238, 预测数据72772, 本次预测偏差%0.7400
NOTICE:  样本数量1, 截距5202.6036, 斜率0.9363, 相关性0.8805
NOTICE:  真实数据85644, 预测数据102774, 本次预测偏差%20.0000
NOTICE:  样本数量382, 截距-211937.8855, 斜率2.3700, 相关性0.9232
NOTICE:  真实数据104207, 预测数据107341, 本次预测偏差%3.0100
NOTICE:  样本数量363, 截距10473.2297, 斜率0.9328, 相关性0.9381
NOTICE:  真实数据134716, 预测数据144319, 本次预测偏差%7.1300
NOTICE:  样本数量363, 截距8082.7467, 斜率0.9608, 相关性0.9426
NOTICE:  真实数据143484, 预测数据153571, 本次预测偏差%7.0300
NOTICE:  样本数量379, 截距90033.9242, 斜率0.4106, 相关性0.9539
NOTICE:  真实数据151426, 预测数据150648, 本次预测偏差%0.5100
NOTICE:  样本数量363, 截距3555.4288, 斜率1.0121, 相关性0.9344
NOTICE:  真实数据147628, 预测数据148068, 本次预测偏差%0.3000
NOTICE:  样本数量377, 截距-22855.0642, 斜率1.3040, 相关性0.9608
NOTICE:  真实数据142781, 预测数据143858, 本次预测偏差%0.7500
NOTICE:  样本数量363, 截距8135.3139, 斜率0.9564, 相关性0.9081
NOTICE:  真实数据127852, 预测数据116232, 本次预测偏差%9.0900
NOTICE:  样本数量363, 截距11650.2051, 斜率0.9095, 相关性0.9209
NOTICE:  真实数据113022, 预测数据107993, 本次预测偏差%4.4500
NOTICE:  样本数量366, 截距43850.9025, 斜率0.5911, 相关性0.9231
NOTICE:  真实数据105932, 预测数据109352, 本次预测偏差%3.2300
NOTICE:  样本数量366, 截距41459.4112, 斜率0.6193, 相关性0.9421
NOTICE:  真实数据110807, 预测数据111147, 本次预测偏差%0.3100
NOTICE:  样本数量366, 截距41099.7207, 斜率0.6234, 相关性0.9330
NOTICE:  真实数据112531, 预测数据107192, 本次预测偏差%4.7400
NOTICE:  样本数量366, 截距45144.8340, 斜率0.5733, 相关性0.9910
NOTICE:  真实数据106011, 预测数据105444, 本次预测偏差%0.5400
NOTICE:  样本数量366, 截距45652.0542, 斜率0.5670, 相关性0.9907
NOTICE:  真实数据105170, 预测数据104365, 本次预测偏差%0.7600
NOTICE:  样本数量368, 截距57233.9599, 斜率0.4495, 相关性0.9969
NOTICE:  真实数据103554, 预测数据103401, 本次预测偏差%0.1500
NOTICE:  样本数量368, 截距58816.4609, 斜率0.4327, 相关性0.9999
NOTICE:  真实数据102706, 预测数据102719, 本次预测偏差%0.0100
NOTICE:  样本数量366, 截距45837.1316, 斜率0.5648, 相关性0.9874
NOTICE:  真实数据101460, 预测数据101473, 本次预测偏差%0.0100
NOTICE:  样本数量366, 截距45788.3201, 斜率0.5655, 相关性0.9787
NOTICE:  真实数据98505, 预测数据97660, 本次预测偏差%0.8600
NOTICE:  样本数量1, 截距5430.0126, 斜率0.9322, 相关性0.8723
NOTICE:  真实数据91734, 预测数据83227, 本次预测偏差%9.2700
NOTICE:  样本数量1, 截距5423.3347, 斜率0.9320, 相关性0.8726
NOTICE:  真实数据83453, 预测数据66847, 本次预测偏差%19.9000
NOTICE:  样本数量360, 截距30435.2931, 斜率0.4928, 相关性0.9223
NOTICE:  真实数据65904, 预测数据59957, 本次预测偏差%9.0200
NOTICE:  样本数量360, 截距25313.6494, 斜率0.5394, 相关性0.9738
NOTICE:  真实数据59911, 预测数据58046, 本次预测偏差%3.1100
NOTICE:  样本数量360, 截距22789.5261, 斜率0.5623, 相关性0.9761
NOTICE:  真实数据60677, 预测数据57848, 本次预测偏差%4.6600
NOTICE:  样本数量360, 截距14289.6380, 斜率0.6383, 相关性1.0000
NOTICE:  真实数据62350, 预测数据62309, 本次预测偏差%0.0700
NOTICE:  样本数量1, 截距5349.6991, 斜率0.9328, 相关性0.8743
NOTICE:  真实数据75224, 预测数据94495, 本次预测偏差%25.6200
NOTICE:  样本数量1, 截距5276.8974, 斜率0.9345, 相关性0.8761
NOTICE:  真实数据95563, 预测数据124211, 本次预测偏差%29.9800
NOTICE:  样本数量339, 截距10611.8990, 斜率0.9248, 相关性0.9273
NOTICE:  真实数据127277, 预测数据132503, 本次预测偏差%4.1100
NOTICE:  样本数量339, 截距9346.7583, 斜率0.9398, 相关性0.9270
NOTICE:  真实数据131802, 预测数据141158, 本次预测偏差%7.1000
NOTICE:  样本数量354, 截距45602.8301, 斜率0.6964, 相关性0.9378
NOTICE:  真实数据140259, 预测数据142531, 本次预测偏差%1.6200
NOTICE:  样本数量354, 截距22118.2940, 斜率0.8984, 相关性0.9995
NOTICE:  真实数据139179, 预测数据139044, 本次预测偏差%0.1000
NOTICE:  样本数量339, 截距7066.6202, 斜率0.9646, 相关性0.9085
NOTICE:  真实数据130151, 预测数据123330, 本次预测偏差%5.2400
NOTICE:  样本数量352, 截距788258.5127, 斜率-6.1054, 相关性0.9259
NOTICE:  真实数据120531, 预测数据120243, 本次预测偏差%0.2400
     check_predict
------------------------
 (165320,170611,0.0320)
 (167663,165922,0.0104)
 (161071,150145,0.0678)
 (145570,136026,0.0656)
 (133155,133953,0.0060)
 (133962,134241,0.0021)
 (130484,127596,0.0221)
 (126182,123864,0.0184)
 (122998,124578,0.0128)
 (125052,125119,0.0005)
 (123000,121572,0.0116)
 (119991,118710,0.0107)
 (116182,118363,0.0188)
 (116887,116082,0.0069)
 (108562,98517,0.0925)
 (99168,82725,0.1658)
 (82505,74942,0.0917)
 (73450,72804,0.0088)
 (75681,76143,0.0061)
 (82509,82187,0.0039)
 (92670,111447,0.2026)
 (112865,145539,0.2895)
 (148731,150848,0.0142)
 (149961,156169,0.0414)
 (155748,161289,0.0356)
 (160430,155939,0.0280)
 (153344,150240,0.0202)
 (147997,140772,0.0488)
 (138023,137013,0.0073)
 (136535,135075,0.0107)
 (133978,133909,0.0005)
 (132634,136891,0.0321)
 (136998,137674,0.0049)
 (136303,136431,0.0009)
 (130987,130817,0.0013)
 (127722,129731,0.0157)
 (126303,124949,0.0107)
 (117218,117405,0.0016)
 (109160,110726,0.0143)
 (96823,97097,0.0028)
 (79716,72776,0.0871)
 (72658,69530,0.0431)
 (71739,71377,0.0051)
 (77243,76786,0.0059)
 (89412,109386,0.2234)
 (110972,112269,0.0117)
 (144014,149237,0.0363)
 (148483,151688,0.0216)
 (150405,156324,0.0394)
 (154850,155607,0.0049)
 (151244,144638,0.0437)
 (141118,129415,0.0829)
 (126106,125617,0.0039)
 (124896,128489,0.0288)
 (129061,128477,0.0045)
 (127849,128208,0.0028)
 (127715,129117,0.0110)
 (124554,124206,0.0028)
 (117397,117404,0.0001)
 (112693,111435,0.0112)
 (108804,108821,0.0002)
 (105623,105973,0.0033)
 (100474,89115,0.1131)
 (89591,72087,0.1954)
 (71422,64918,0.0911)
 (64616,64377,0.0037)
 (66389,65428,0.0145)
 (72238,72772,0.0074)
 (85644,102774,0.2000)
 (104207,107341,0.0301)
 (134716,144319,0.0713)
 (143484,153571,0.0703)
 (151426,150648,0.0051)
 (147628,148068,0.0030)
 (142781,143858,0.0075)
 (127852,116232,0.0909)
 (113022,107993,0.0445)
 (105932,109352,0.0323)
 (110807,111147,0.0031)
 (112531,107192,0.0474)
 (106011,105444,0.0054)
 (105170,104365,0.0076)
 (103554,103401,0.0015)
 (102706,102719,0.0001)
 (101460,101473,0.0001)
 (98505,97660,0.0086)
 (91734,83227,0.0927)
 (83453,66847,0.1990)
 (65904,59957,0.0902)
 (59911,58046,0.0311)
 (60677,57848,0.0466)
 (62350,62309,0.0007)
 (75224,94495,0.2562)
 (95563,124211,0.2998)
 (127277,132503,0.0411)
 (131802,141158,0.0710)
 (140259,142531,0.0162)
 (139179,139044,0.0010)
 (130151,123330,0.0524)
 (120531,120243,0.0024)
(100 rows)

预测曲线 :