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are aggregation functions in SQL, one can easily implement the solution.I've done so in HIVE to do linear calibration of the scores of a Logistic model - amongst many advantages, one is that you can function entirely within HIVE without going out and back in from some scripting language.FN_Get Linear Regression [email protected],30); */ Here it is as a function that takes a table type of type: table (Y float, X double) which is called XYDouble Type and assumes our linear function is of the form AX B. I hope the following answer helps one understand where some of the solutions come from.It returns A and B a Table column just in case you want to have it in a join or something CREATE FUNCTION FN_Get ABFor Data( @XYData as XYDouble Type READONLY ) RETURNS @ABData TABLE( A FLOAT, B FLOAT, Rsquare FLOAT ) AS BEGIN DECLARE @sx FLOAT, @sy FLOAT DECLARE @sxx FLOAT,@syy FLOAT, @sxy FLOAT,@sxsy FLOAT, @sxsx FLOAT, @sysy FLOAT DECLARE @n FLOAT, @A FLOAT, @B FLOAT, @Rsq FLOAT SELECT @sx =SUM(D. I am going to illustrate it with a simple example, but the generalization to many variables is theoretically straightforward as long as you know how to use index notation or matrices.-- test data (Group IDs 1, 2 normal regressions, 3, 4 = no variance) WITH some_table(Group ID, x, y) AS ( SELECT 1, 1, 1 UNION SELECT 1, 2, 2 UNION SELECT 1, 3, 1.3 UNION SELECT 1, 4, 3.75 UNION SELECT 1, 5, 2.25 UNION SELECT 2, 95, 85 UNION SELECT 2, 85, 95 UNION SELECT 2, 80, 70 UNION SELECT 2, 70, 65 UNION SELECT 2, 60, 70 UNION SELECT 3, 1, 2 UNION SELECT 3, 1, 3 UNION SELECT 4, 1, 2 UNION SELECT 4, 2, 2), -- linear regression query /*WITH*/ mean_estimates AS ( SELECT Group ID , AVG(x * 1.) AS xmean , AVG(y * 1.) AS ymean FROM some_table GROUP BY Group ID ), stdev_estimates AS ( SELECT pd. Group ID, pm.xmean, pm.ymean ), standardized_data AS -- increases numerical stability ( SELECT pd. Group ID ,ymean - xmean * betastd * ystdev / xstdev AS Alpha ,betastd * ystdev / xstdev AS Beta FROM standardized_beta_estimates pb INNER JOIN stdev_estimates ps ON ps. Please be mindful of the precision of the data type used in your tables as the numerical stability can deteriorate quickly if the precision is not high enough relative to your data. I could improve stability by replacing my standard deviation with a numerically stable online algorithm, but this would complicate the implementation substantantially (and slow it down). Kahan(-Babuška-Neumaier) compensations for the gives you an integer if your input data has type integer.Group ID -- T-SQL STDEV() implementation is not numerically stable , CASE SUM(SQUARE(x - xmean)) WHEN 0 THEN 1 ELSE SQRT(SUM(SQUARE(x - xmean)) / (COUNT(*) - 1)) END AS xstdev , SQRT(SUM(SQUARE(y - ymean)) / (COUNT(*) - 1)) AS ystdev FROM some_table pd INNER JOIN mean_estimates pm ON pm. Group ID ,(x - xmean) / xstdev AS xstd , CASE ystdev WHEN 0 THEN 0 ELSE (y - ymean) / ystdev END AS ystd FROM some_table pd INNER JOIN stdev_estimates ps ON ps. EDIT: (in answer to Peter's question for additional statistics like R2 in the comments) You can easily calculate additional statistics using the same technique. Group ID ), standardized_beta_estimates AS ( SELECT Group ID , CASE WHEN SUM(xstd * xstd) = 0 THEN 0 ELSE SUM(xstd * ystd) / (COUNT(*) - 1) END AS betastd FROM standardized_data GROUP BY Group ID ) SELECT pb. But now for the real issue: your code is not numerically stable, see code comments and starting at "Edit 2".are integers; 2) the version in my answers standardizes the data which might help with some idiosyncrazies / edge-cases of floating-point arithmetics.

In the following, yv should be replaced by [email protected] Y select 1-sum(power(err,2))/sum(power(yv,2)) from I have translated the Linear Regression Function used in the funcion Forecast in Excel, and created an SQL function that returns a,b, and the Forecast.

My primary source is Elements of Statistical Learning (2008) by Hastie, Tibshirni and Friedman.

--Create a table of data create table #rawdata (id int,area float, rooms float, odd float, price float) insert into #rawdata select 1, 2201,3,1,400 insert into #rawdata select 2, 1600,3,0,330 insert into #rawdata select 3, 2400,3,1,369 insert into #rawdata select 4, 1416,2,1,232 insert into #rawdata select 5, 3000,4,0,540 --Insert the data into x & y vectors select id xid, 0 xn,1 xv into #x from #rawdata union all select id, 1,rooms from #rawdata union all select id, 2,area from #rawdata union all select id, 3,odd from #rawdata select id yid, 0 yn, price yv into #y from #rawdata --create a residuals table and insert the intercept (1) create table #z (zid int, zn int, zv float) insert into #z select id , 0 zn,1 zv from #rawdata --create a table for the orthoganal (#c) & regression(#b) parameters create table #c(cxn int, czn int, cv float) create table #b(bn int, bv float) [email protected] is the number of independent variables including the intercept (@p = 0) declare @p int set @p = 1 --Loop through each independent variable and estimate the orthagonal parameter (#c) -- then estimate the residuals and insert into the residuals table (#z) while @p =0 begin insert into #b select zn, sum(yv*zv)/ sum(zv*zv) from #z join (select yid, yv-isnull(sum(bv*xv),0) yv from #x join #y on xid = yid left join #b on xn=bn group by yid, yv) y on zid = yid where zn = @p group by zn set @p = @p-1 end --The regression parameters select * from #b --Actual vs.

CREATE TABLE vote_count ( submit_date DATE NOT NULL, num_votes NUMBER NOT NULL); INSERT INTO vote_count VALUES (TRUNC(SYSDATE)-4, 100); INSERT INTO vote_count VALUES (TRUNC(SYSDATE)-3, 150); INSERT INTO vote_count VALUES (TRUNC(SYSDATE)-2, 75); INSERT INTO vote_count VALUES (TRUNC(SYSDATE)-3, 25); INSERT INTO vote_count VALUES (TRUNC(SYSDATE)-1, 50); COMMIT; SELECT * FROM vote_count; SELECT submit_date, num_votes, TRUNC(CREATE TABLE myprods ( prod1 NUMBER(3), prod2 NUMBER(3), prod3 NUMBER(3)); INSERT INTO myprods VALUES (34,23,45); INSERT INTO myprods VALUES (34,22,34); INSERT INTO myprods VALUES (54,44,45); INSERT INTO myprods VALUES (23,22,45); INSERT INTO myprods VALUES (45,22,34); SELECT prod1, CREATE TABLE t1 ( row_num NUMBER(3), col1 VARCHAR2(15), col2 VARCHAR2(15)); INSERT INTO t1 VALUES (6, NULL, NULL); INSERT INTO t1 VALUES (1, 'Category 1', 'Mango'); INSERT INTO t1 VALUES (2, NULL, NULL); INSERT INTO t1 VALUES (3, NULL, NULL); INSERT INTO t1 VALUES (4, NULL, 'Banana'); INSERT INTO t1 VALUES (5, NULL, NULL); INSERT INTO t1 VALUES (6, NULL, NULL); INSERT INTO t1 VALUES (7, 'Category 2', 'Vanilla'); INSERT INTO t1 VALUES (8, NULL, NULL); INSERT INTO t1 VALUES (9, 'Category 3', 'Strawberry'); COMMIT; SELECT * FROM t1; SELECT row_num, LAST_VALUE(col1 LAG provides access to more than one row of a table at the same time without a self-join.

Given a series of rows returned from a query and a position of the cursor, LAG provides access to a row at a given physical offset prior to that position.

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You can use this function to predict future sales, inventory requirements, or consumer trends. I included the unstable versions to warn you against those.

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