how to do a linear regression in SQL

linear_regression.sql

drop table if exists linear_test;

create table linear_test (
    x numeric(19,4),
    y numeric(19,4),
    workspace_id text
);

insert into linear_test (x,y, workspace_id) values (1, 10, 'a'), (2, 20, 'a'), (3, 30, 'a'), (4, 40, 'a'), (5, 50, 'a');
insert into linear_test (x,y, workspace_id) values (5, 10, 'b'), (6, 20, 'b'), (7, 30, 'b'), (8, 40, 'b'), (9, 50, 'b');
insert into linear_test (x,y, workspace_id) values (1, -1, 'c'), (2, -2, 'c'), (3, -3, 'c'), (4, -4, 'c'), (5, -5, 'c');

select * from linear_test;

with base_table as (
select 
    workspace_id,
    x as x_axis,
    y
from linear_test
),

sums_table as (select distinct
    workspace_id,
    sum(x_axis) over (partition by workspace_id) as sum_x, 
    sum(x_axis * x_axis) over (partition by workspace_id) as sum_x2, 
    sum(y) over (partition by workspace_id) as sum_y,
    sum(x_axis * y) over (partition by workspace_id) as sum_x_y,
    COUNT(x_axis) over (partition by workspace_id) as num_rows
from base_table
)

select 
    workspace_id,
    num_rows,
    sum_x,
    sum_x2,
    sum_y,
    sum_x_y,
    ((sum_y * sum_x2) - (sum_x * sum_x_y)) / nullif((num_rows * sum_x2) - (sum_x * sum_x),0) as a_order_count, 
    ((num_rows * sum_x_y ) - (sum_x * sum_y ))  / nullif((num_rows * sum_x2) - (sum_x * sum_x),0) as b_order_count
from sums_table
order by workspace_id