postgresql – 使用postgres进行线性回归

我使用Postgres,我有大量的行,每个站点有值和日期.
(日期可以分开几天.)

id      | value | idstation | udate
--------+-------+-----------+-----
1       |  5    | 12        | 1984-02-11 00:00:00
2       |  7    | 12        | 1984-02-17 00:00:00
3       |  8    | 12        | 1984-02-21 00:00:00
4       |  9    | 12        | 1984-02-23 00:00:00
5       |  4    | 12        | 1984-02-24 00:00:00
6       |  8    | 12        | 1984-02-28 00:00:00
7       |  9    | 14        | 1984-02-21 00:00:00
8       |  15   | 15        | 1984-02-21 00:00:00
9       |  14   | 18        | 1984-02-21 00:00:00
10      |  200  | 19        | 1984-02-21 00:00:00

原谅可能是一个愚蠢的问题,但我不是一个数据库大师.

是否可以直接输入一个SQL查询,该查询将计算每个日期的每个日期的线性回归,知道回归必须只计算实际的ID日期,前一个id日期和下一个id日期？

例如,id 2的线性回归必须以值7(实际),5(上一个),8(下一个)计算日期1984-02-17,1984-02-11和1984-02-21

编辑：我必须使用regr_intercept(value,udate)但我真的不知道如何执行此操作,如果我必须只使用每行的实际,上一个和下一个值/日期.

Edit2：将3行添加到idstation(12); ID和日期编号已更改

希望你能帮助我,谢谢！

这是Joop的统计数据和Denis的窗口函数的组合：

WITH num AS (
        SELECT id,idstation,(udate - '1984-01-01'::date) as idate -- count in dayse since jan 1984,value AS value
        FROM thedata
        )
        -- id + the ids of the {prev,next} records
        --  within the same idstation group,drag AS (
        SELECT id AS center,LAG(id) OVER www AS prev,LEAD(id) OVER www AS next
        FROM thedata
        WINDOW www AS (partition by idstation ORDER BY id)
        )
        -- junction CTE between ID and its three Feeders,tri AS (
                  SELECT center AS this,center AS that FROM drag
        UNION ALL SELECT center AS this,prev AS that FROM drag
        UNION ALL SELECT center AS this,next AS that FROM drag
        )
SELECT  t.this,n.idstation,regr_intercept(value,idate) AS intercept,regr_slope(value,idate) AS slope,regr_r2(value,idate) AS rsq,regr_avgx(value,idate) AS avgx,regr_avgy(value,idate) AS avgy
FROM num n
JOIN tri t ON t.that = n.id
GROUP BY t.this,n.idstation
        ;

结果：

INSERT 0 7
 this | idstation |     intercept     |       slope       |        rsq        |       avgx       |       avgy       
------+-----------+-------------------+-------------------+-------------------+------------------+------------------
    1 |        12 |               -46 |                 1 |                 1 |               52 |                6
    2 |        12 | -24.2105263157895 | 0.578947368421053 | 0.909774436090226 | 53.3333333333333 | 6.66666666666667
    3 |        12 | -10.6666666666667 | 0.333333333333333 |                 1 |             54.5 |              7.5
    4 |        14 |                   |                   |                   |               51 |                9
    5 |        15 |                   |                   |                   |               51 |               15
    6 |        18 |                   |                   |                   |               51 |               14
    7 |        19 |                   |                   |                   |               51 |              200
(7 rows)

使用rank()或row_number()函数可以更优雅地完成三组的聚类,这也允许使用更大的滑动窗口.