MS SQL - 用户定义函数 - 斜率截距RSquare;如何按投资组合分组

Question

以下是我的数据示例，表RR_Linest：

投资组合---- Month_number ----收藏品 A --- --------- 1 --------------------- $ 100 -------------- -------------------------------------------------- --------------------- A -------------- 2 --------------------- $ 90
A ------------- 3 --------------------- $ 80 ------------- -------------------------------------------------- ----------------------- A ------------- 4 --------------------- $ 70 ------------- -------------------------------------------------- ----------------------- B ------------- 1 -------------------- $ 100 -------------- -------------------------------------------------- --------------------- B ---- -------- 2 ---------------------- $ 90 ------------- -------------------------------------------------- ---------------------- B - ------------ 3 --------------------- $ 80

我能够通过删除投资组合列并且仅为一个选定的投资组合选择month_Number（x）和集合数据（y）来弄清楚如何获得一个投资组合的斜率，截距，RSquare （我删除了投资组合B的数据）并运行下面的代码。

我一直在尝试更改功能，以便在运行时;它通过投资组合给出了斜率，截距和R平方。有人知道怎么做吗？我尝试了很多方法，但我无法弄清楚。

首先我创建了这个函数：

声明@RegressionInput_A [dbo]。[RegressionInput_A]

插入@RegressionInput_A（x，y） 选择 （[模型月份]），log（[collection $]） 来自[dbo]。[RR_Linest]

从[dbo] .LinearRegression_A

中选择*

GO

drop function dbo.LinearRegression_A

CREATE FUNCTION dbo.LinearRegression_A
( 
@RegressionInputs_A AS dbo.RegressionInput_A READONLY 
) 
RETURNS @RegressionOutput_A TABLE 
( 
Slope DECIMAL(18, 6), 
Intercept DECIMAL(18, 6), 
RSquare DECIMAL(18, 6) 
) 
AS
BEGIN 

DECLARE @Xaverage AS DECIMAL(18, 6)
DECLARE @Yaverage AS DECIMAL(18, 6)
DECLARE @slope AS DECIMAL(18, 6)
DECLARE @intercept AS DECIMAL(18, 6)
DECLARE @rSquare AS DECIMAL(18, 6)

SELECT
@Xaverage = AVG(x),
@Yaverage = AVG(y)
FROM
@RegressionInputs_A

SELECT
@slope = SUM((x - @Xaverage) * (y - @Yaverage))/SUM(POWER(x - @Xaverage, 2))
FROM
@RegressionInputs_A

SELECT
@intercept = @Yaverage - (@slope * @Xaverage) 

SELECT @rSquare = 1 - (SUM(POWER(y - (@intercept + @slope * x), 2))/(SUM(POWER(y - (@intercept + @slope * x), 2)) + SUM(POWER(((@intercept + @slope * x) - @Yaverage), 2))))
FROM
@RegressionInputs_A

INSERT INTO
@RegressionOutput_A
(
Slope,
Intercept,
RSquare
)
SELECT
@slope,
@intercept,
@rSquare

RETURN

END
GO

然后我运行功能

declare @RegressionInput_A  [dbo].[RegressionInput_A]

insert into @RegressionInput_A (x,y)
select
([model month]),log([collection $])
from [dbo].[RR_Linest]

select * from [dbo].[LinearRegression_A](@RegressionInput_A)

Answer 1

哇，这是如何在内联表值函数中使用嵌套CTE的一个很酷的例子。您想要使用ITVF，因为它们很快。请参阅韦恩谢菲尔德的blog文章，证明了这一事实。

我总是从一个示例数据库/表开始，如果它确实很复杂，以确保我给用户一个正确的解决方案。

让我们根据模型创建一个名为[test]的数据库。

--
-- Create a simple db
--

-- use master
use master;
go

-- delete existing databases
IF EXISTS (SELECT name FROM sys.databases WHERE name = N'Test')
DROP DATABASE Test
GO

-- simple db based on model
create database Test;
go

-- switch to new db
use [Test];
go

让我们创建一个名为[InputToLinearReg]的表类型。

--
-- Create table type to pass data
--

-- Delete the existing table type
IF  EXISTS (SELECT * FROM sys.systypes WHERE name = 'InputToLinearReg')
DROP TYPE dbo.InputToLinearReg
GO

--  Create the table type
CREATE TYPE InputToLinearReg AS TABLE
(
portfolio_cd char(1),
month_num int,
collections_amt money
);
go

好的，这是使用CTE的多层SELECT语句。查询分析器将此视为可以并行执行的SQL语句，而不是常规函数。请参阅Wayne文章的黑匣子部分。

--
-- Create in line table value function (fast)
--

-- Remove if it exists
IF OBJECT_ID('CalculateLinearReg') > 0
DROP FUNCTION CalculateLinearReg
GO

-- Create the function
CREATE FUNCTION CalculateLinearReg
( 
    @ParmInTable AS dbo.InputToLinearReg READONLY 
) 
RETURNS TABLE 
AS
RETURN
(

  WITH cteRawData as
  (
    SELECT
        T.portfolio_cd,
        CAST(T.month_num as decimal(18, 6)) as x,
        LOG(CAST(T.collections_amt as decimal(18, 6))) as y
    FROM
        @ParmInTable as T
  ),

  cteAvgByPortfolio as
  (
    SELECT
        portfolio_cd,
        AVG(x) as xavg,
        AVG(y) as yavg
    FROM
        cteRawData 
    GROUP BY 
        portfolio_cd
  ),

  cteSlopeByPortfolio as
  (
    SELECT
        R.portfolio_cd,
        SUM((R.x - A.xavg) * (R.y - A.yavg)) / SUM(POWER(R.x - A.xavg, 2)) as slope
    FROM
        cteRawData as R 
    INNER JOIN 
        cteAvgByPortfolio A
    ON 
        R.portfolio_cd = A.portfolio_cd
    GROUP BY 
        R.portfolio_cd
  ),

  cteInterceptByPortfolio as
  (
    SELECT
        A.portfolio_cd,
        (A.yavg - (S.slope * A.xavg)) as intercept
    FROM
        cteAvgByPortfolio as A
    INNER JOIN 
        cteSlopeByPortfolio S
    ON 
        A.portfolio_cd = S.portfolio_cd

  )

  SELECT 
      A.portfolio_cd,
      A.xavg,
      A.yavg,
      S.slope,
      I.intercept,
      1 - (SUM(POWER(R.y - (I.intercept + S.slope * R.x), 2)) /
      (SUM(POWER(R.y - (I.intercept + S.slope * R.x), 2)) + 
      SUM(POWER(((I.intercept + S.slope * R.x) - A.yavg), 2)))) as rsquared
  FROM
      cteRawData as R 
        INNER JOIN 
      cteAvgByPortfolio as A ON R.portfolio_cd = A.portfolio_cd
        INNER JOIN 
      cteSlopeByPortfolio S ON A.portfolio_cd = S.portfolio_cd
        INNER JOIN 
      cteInterceptByPortfolio I ON S.portfolio_cd = I.portfolio_cd
  GROUP BY 
      A.portfolio_cd,
      A.xavg,
      A.yavg,
      S.slope,
      I.intercept
);

最后但并非最不重要的是，设置表变量并获得答案。与您上面的解决方案不同，它按产品组ID进行分组。

-- Load data into variable
DECLARE @InTable AS InputToLinearReg;

-- insert data
insert into @InTable
values
('A', 1, 100.00),
('A', 2, 90.00),
('A', 3, 80.00),
('A', 4, 70.00),
('B', 1, 100.00),
('B', 2, 90.00),
('B', 3, 80.00);

-- show data
select * from CalculateLinearReg(@InTable)
go

以下是使用您的数据的结果图片。

Answer 2

CREATE FUNCTION dbo.LinearRegression 
( 
  @RegressionInputs AS dbo.RegressionInput READONLY 
) 
RETURNS TABLE AS
RETURN
(
  WITH
    t1 AS ( --calculate averages
      SELECT portfolio, x, y,
        AVG(x) OVER(PARTITION BY portfolio) Xaverage,
        AVG(y) OVER(PARTITION BY portfolio) Yaverage
      FROM @RegressionInputs
    ),
    t2 AS ( --calculate slopes
      SELECT portfolio, Xaverage, Yaverage,
        SUM((x - Xaverage) * (y - Yaverage))/SUM(POWER(x - Xaverage, 2)) slope
      FROM t1
      GROUP BY portfolio, Xaverage, Yaverage
    ),
    t3 AS ( --calculate intercepts
      SELECT portfolio, slope,
        (Yaverage - (slope * Xaverage) ) AS intercept
      FROM t2
    ),
    t4 AS ( --calculate rSquare
      SELECT t1.portfolio, slope, intercept,
        1 - (SUM(POWER(y - (intercept + slope * x), 2))/(SUM(POWER(y - (intercept + slope * x), 2)) + SUM(POWER(((intercept + slope * x) - Yaverage), 2)))) AS rSquare
      FROM t1
      INNER JOIN t3 ON (t1.portfolio = t3.portfolio)
      GROUP BY t1.portfolio
    )
  SELECT portfolio, slope, intercept, rSquare FROM t4
)