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SQL Linear Regressor
This project is a Proof-of-Cocept that has the goal to demonstrate that SQL can be used to do really basic regression workloads that are barely useful for more complex scenarios, such as Linear Regression.
As linear regression technically counts as some very primitive sort of machine learning, this implies that pretty much every SQL database in production is able to do machine learning.
WITH R AS ( select <FIELD_X> AS x, <FIELD_Y> AS y from athlete_events ), T1 AS ( select x, y from R where x is not null and y is not null ), Txx AS ( select x*x AS xx from T1 ), Txy AS ( select x*y AS xy from T1 ), Tsumxx AS ( select SUM(xx) AS sumxx from Txx ), Tsumxy AS ( select SUM(xy) AS sumxy from Txy ), Tsumx AS ( select SUM(x) AS sumx from T1 ), Tsumy AS ( select SUM(y) AS sumy from T1 ), Tcnt AS ( select COUNT(1) AS cnt from T1 ), Tslope AS ( select ((cnt * sumxy) - (sumx * sumy)) / ((cnt * sumxx) - (sumx * sumx)) AS slope from Tcnt LEFT JOIN Tsumxx ON (1=1) LEFT JOIN Tsumxy ON (1=1) LEFT JOIN Tsumx ON (1=1) LEFT JOIN Tsumy ON (1=1) ), Tintercept AS ( select (sumy - (slope * sumx)) / cnt AS intercept from Tcnt LEFT JOIN Tsumx ON (1=1) LEFT JOIN Tsumy ON (1=1) LEFT JOIN Tslope ON (1=1) ) select slope, intercept from Tslope join Tintercept on (1=1) ;
<FIELD_Y> with the desired fields of a table.
In case you forgot, the formula is
y = slope * x + intercept, or
f(x) = slope * x + intercept.
Query performance complexity
It mainly depends on the number of lines in the table.
It calculates 5 "variables" at O(lines) cost, which can all be calculated in the same table scan if the query planner is competent enough, and then does some math (O(1) cost).
On SQLite, on my Ryzen 7900X with enough DDR5 3600 MT/s and BTRFS, timings were:
time sqlite3 db.sqlite3 < query1.sql real 0m0.321s user 0m0.048s sys 0m0.029s time sqlite3 db.sqlite3 < query2.sql real 0m0.248s user 0m0.053s sys 0m0.027s
For the 271116 rows of the dataset.
The sample code
It downloads a ZIP containing some olympics data, unzips a CSV, loads into a SQLite database, and correlates athletes' height and weight at a year to the year.
The output is the file
linear_regression.csv that is expected to contain: