Identifying trend with SQL query

Question

I have a table (let\'s call it Data) with a set of object IDs, numeric values and dates. I would like to identify the objects whose values had a positive trend over the last X m

Answer 1

You inspired me to go and implement linear regression in SQL Server. This could be modified for MySQL/Oracle/Whatever without too much trouble. It's the mathematically best way of determining the trend over the hour for each entity_id and it will select out only the ones with a positive trend.

It implements the formula for calculating B1hat listed here: https://en.wikipedia.org/wiki/Regression_analysis#Linear_regression

create table #temp
(
    entity_id int,
    value int,
    [date] datetime
)

insert into #temp (entity_id, value, [date])
values
(1,10,'20140102 07:00:00 AM'),
(1,20,'20140102 07:15:00 AM'),
(1,30,'20140102 07:30:00 AM'),
(2,50,'20140102 07:00:00 AM'),
(2,20,'20140102 07:47:00 AM'),
(3,40,'20140102 07:00:00 AM'),
(3,40,'20140102 07:52:00 AM')

select entity_id, 1.0*sum((x-xbar)*(y-ybar))/sum((x-xbar)*(x-xbar)) as Beta
from
(
    select entity_id,
        avg(value) over(partition by entity_id) as ybar,
        value as y,
        avg(datediff(second,'20140102 07:00:00 AM',[date])) over(partition by entity_id) as xbar,
        datediff(second,'20140102 07:00:00 AM',[date]) as x
    from #temp
    where [date]>='20140102 07:00:00 AM' and [date]<'20140102 08:00:00 AM'
) as Calcs
group by entity_id
having 1.0*sum((x-xbar)*(y-ybar))/sum((x-xbar)*(x-xbar))>0