皮尔逊相关SQL Server

我有两张桌子：

ID、YRMO、计数

2013年12月1日，4

2014年1月1日，6

2014年2月1日，7

2014年1月2日，6

2014年2月2日，8

ID、YRMO、计数

2013年12月1日，10

2014年1月1日，8

2014年3月1日，12

2014年1月2日，6

2014年2月2日，10

我想找出每一组ID的pearson相关系数。大约有200多个不同的ID

皮尔逊相关性是两个变量X和Y之间线性相关性（相关性）的度量，给出的值介于+1和+1之间−1包括在内

更多信息可在此处找到：

---

在计算相关部分

计算皮尔逊相关系数；您需要首先计算

平均值

，然后计算

标准偏差

，然后计算

相关系数

，如下所述

1.计算平均数 2.计算标准差 3.最后

Pearson相关系数

在您发布的数据中，哪些会导致

这里有小提琴演示吗

编辑：

有点精致。您可以使用下面的函数获取PCC，但我没有得到与您的完全相同的结果，而是得到

ID=1

的

0.99990000000

这对你来说可能是一个很好的切入点。您可以从此处进一步细化计算

create function calculate_PCC(@id int)
returns decimal(16,15)
as
begin
declare @mean numeric(16,5);
declare @stddev numeric(16,5);
declare @count numeric(16,5);
declare @pcc numeric(16,12);
declare @store numeric(16,7);
select @count = CONVERT(numeric(16,5), count(case when Id=@id then 1 end)) from tab1;
select @mean = convert(numeric(16,5),sum([Counts])) / @count
from tab1 WHERE ID = @id;
select @store = (sum(counts * counts) / @count) from tab1 WHERE ID = @id;
set @stddev = sqrt(@store - (@mean * @mean)); 
set @pcc = ((@store - (@mean * @mean)) / (@stddev * @stddev)); 

return @pcc;
end

调用如下函数

select db_name.dbo.calculate_PCC(1)

单程解决方案： 皮尔逊相关系数有两种类型，一种用于样本，另一种用于整个人群。这些都是简单的单程公式，我相信这两个公式都是正确的：

-- Methods for calculating the two Pearson correlation coefficients
SELECT  
        -- For Population
        (avg(x * y) - avg(x) * avg(y)) / 
        (sqrt(avg(x * x) - avg(x) * avg(x)) * sqrt(avg(y * y) - avg(y) * avg(y))) 
        AS correlation_coefficient_population,
        -- For Sample
        (count(*) * sum(x * y) - sum(x) * sum(y)) / 
        (sqrt(count(*) * sum(x * x) - sum(x) * sum(x)) * sqrt(count(*) * sum(y * y) - sum(y) * sum(y))) 
        AS correlation_coefficient_sample
    FROM (
        -- The following generates a table of sample data containing two columns with a luke-warm and tweakable correlation 
        -- y = x for 0 thru 99, y = x - 100 for 100 thru 199, etc.  Execute it as a stand-alone to see for yourself
        -- x and y are CAST as DECIMAL to avoid integer math, you should definitely do the same
        -- Try TOP 100 or less for full correlation (y = x for all cases), TOP 200 for a PCC of 0.5, TOP 300 for one near 0.33, etc.
        -- The superfluous "+ 0" is where you could apply various offsets to see that they have no effect on the results
        SELECT TOP 200
                CAST(ROW_NUMBER() OVER (ORDER BY [object_id]) - 1 + 0 AS DECIMAL) AS x, 
                CAST((ROW_NUMBER() OVER (ORDER BY [object_id]) - 1) % 100 AS DECIMAL) AS y 
            FROM sys.all_objects
    ) AS a

正如我在评论中所指出的，您可以尝试前100名或以下的示例，以获得完全相关性（所有情况下y=x）；前200名产生的相关性非常接近0.5；前300名，约0.33；等。如果您愿意，有一个地方（“+0”）可以添加偏移量；扰流板警报，它没有效果。确保将值强制转换为十进制-整数数学可以显著影响这些计算

create function calculate_PCC(@id int)
returns decimal(16,15)
as
begin
declare @mean numeric(16,5);
declare @stddev numeric(16,5);
declare @count numeric(16,5);
declare @pcc numeric(16,12);
declare @store numeric(16,7);
select @count = CONVERT(numeric(16,5), count(case when Id=@id then 1 end)) from tab1;
select @mean = convert(numeric(16,5),sum([Counts])) / @count
from tab1 WHERE ID = @id;
select @store = (sum(counts * counts) / @count) from tab1 WHERE ID = @id;
set @stddev = sqrt(@store - (@mean * @mean)); 
set @pcc = ((@store - (@mean * @mean)) / (@stddev * @stddev)); 

return @pcc;
end

select db_name.dbo.calculate_PCC(1)

-- Methods for calculating the two Pearson correlation coefficients
SELECT  
        -- For Population
        (avg(x * y) - avg(x) * avg(y)) / 
        (sqrt(avg(x * x) - avg(x) * avg(x)) * sqrt(avg(y * y) - avg(y) * avg(y))) 
        AS correlation_coefficient_population,
        -- For Sample
        (count(*) * sum(x * y) - sum(x) * sum(y)) / 
        (sqrt(count(*) * sum(x * x) - sum(x) * sum(x)) * sqrt(count(*) * sum(y * y) - sum(y) * sum(y))) 
        AS correlation_coefficient_sample
    FROM (
        -- The following generates a table of sample data containing two columns with a luke-warm and tweakable correlation 
        -- y = x for 0 thru 99, y = x - 100 for 100 thru 199, etc.  Execute it as a stand-alone to see for yourself
        -- x and y are CAST as DECIMAL to avoid integer math, you should definitely do the same
        -- Try TOP 100 or less for full correlation (y = x for all cases), TOP 200 for a PCC of 0.5, TOP 300 for one near 0.33, etc.
        -- The superfluous "+ 0" is where you could apply various offsets to see that they have no effect on the results
        SELECT TOP 200
                CAST(ROW_NUMBER() OVER (ORDER BY [object_id]) - 1 + 0 AS DECIMAL) AS x, 
                CAST((ROW_NUMBER() OVER (ORDER BY [object_id]) - 1) % 100 AS DECIMAL) AS y 
            FROM sys.all_objects
    ) AS a