Linear Regression in SQL: A Practical Guide for Data Engineers

Overview

Linear regression is one of the most widely used statistical techniques for predicting a continuous target based on one or more explanatory variables. While data scientists often perform regression in Python or R, modern analytical databases expose functions—such as LINEAR_REG_SLOPE, window aggregates, and matrix utilities—that let you fit models in-database with plain SQL. This article explains why, when, and how to run linear regression in SQL, outlines best practices, and shows complete working examples.

Why Run Linear Regression Inside the Database?

Eliminate Data Movement

Moving large datasets out of your warehouse to a notebook can be slow, costly, and insecure. Executing regression where the data already lives avoids serialization overhead and governance concerns.

Leverage MPP Engines

Distributed warehouses (Snowflake, BigQuery, Redshift, DuckDB, PostgreSQL with Citus, etc.) parallelize aggregations and matrix math, allowing regressions on billions of rows in seconds.

Atomic, Reproducible Pipelines

Storing both feature engineering and model training logic in version-controlled SQL keeps analytics and predictive steps in one place—easy to review, schedule, and re-run.

SQL Approaches to Linear Regression

1. Built-in Regression Functions

Several databases expose scalar or aggregate functions that calculate coefficients directly.

• BigQuery: ML.EXPLAIN_LINEAR_REG, ML.PREDICT
• Snowflake: LINEAR_REG_SLOPE, LINEAR_REG_INTERCEPT, LINEAR_REG_R2
• PostgreSQL: extensions like regr_slope, regr_intercept

These functions implement Ordinary Least Squares (OLS) under the hood. You supply a target and predictor; the database returns the best-fit coefficients.

2. Matrix Decomposition via Window Functions

If your engine lacks high-level regression helpers, you can compute normal equations (XᵀX and Xᵀy) with aggregations, then solve for β using matrix inversion utilities. DuckDB’s row_number() + array_agg() combo is a popular pattern.

3. SQL-to-ML Bridges

Tools like Vertica’s in-database machine learning or PostgreSQL’s MADlib ship pre-built procedures (madlib.linregr_train()) that accept a table name and output a model artifact.

Step-by-Step Example: Snowflake Simple Linear Regression

Assume we have a sales table:

CREATE OR REPLACE TABLE sales (
day DATE,
ads_spend NUMBER(12,2),
revenue NUMBER(12,2)
);

Goal: predict revenue from ads_spend.

Compute Coefficients

WITH stats AS (
SELECT
LINEAR_REG_SLOPE(revenue, ads_spend) AS slope,
LINEAR_REG_INTERCEPT(revenue, ads_spend) AS intercept,
LINEAR_REG_R2(revenue, ads_spend) AS r_squared
FROM sales
)
SELECT * FROM stats;

The query returns:

• slope – how much revenue increases per $1 in ad spend
• intercept – baseline revenue with $0 spend
• r_squared – goodness-of-fit (0-1)

Make Predictions

WITH coeffs AS (
SELECT
LINEAR_REG_SLOPE(revenue, ads_spend) AS m,
LINEAR_REG_INTERCEPT(revenue, ads_spend) AS b
FROM sales
)
SELECT
s.*, -- original row
(c.m * ads_spend + c.b) AS predicted_revenue,
(revenue - (c.m * ads_spend + c.b)) AS residual
FROM sales s
CROSS JOIN coeffs c;

Because everything is a SQL statement, you can chain this logic into dashboards, ETL, or Galaxy Collections for team reuse.

Multivariate Regression

Databases supporting matrix operations allow multiple predictors. For instance, BigQuery ML:

CREATE OR REPLACE MODEL `my_project.my_dataset.sales_model`
OPTIONS(model_type = 'linear_reg') AS
SELECT revenue AS label,
ads_spend,
site_visits,
promo_discount
FROM `my_project.my_dataset.sales`;

Once trained, call ML.PREDICT to score new data:

SELECT * FROM ML.PREDICT(MODEL `my_project.my_dataset.sales_model`,
(SELECT * FROM `my_project.my_dataset.future_spend`));

Best Practices

• Feature Scaling: Even though OLS is scale-invariant, some numerical functions overflow on extreme ranges. Normalize heavy-tailed features.
• Train/Test Split: Use SQL’s RANDOM() or TABLESAMPLE to create hold-out sets and avoid overfitting.
• Model Persistence: Store coefficients in a dedicated models.linear_regression table for lineage and auditing.
• Incremental Retraining: For time-series data, retrain on rolling windows (WHERE date >= CURRENT_DATE - INTERVAL '90' DAY).
• Explainability: Capture R², p-values (if available), and confidence intervals to document model quality.

Common Misconceptions

1. “SQL can’t do real ML.” Modern warehouses implement the same linear algebra kernels as Python libs.
2. “In-database regression is slower.” On large data, pushing compute to a distributed engine is usually faster than exporting to Pandas.
3. “You lose flexibility.” While complex neural nets need external tools, linear models—with transformations—are fully expressible in SQL.

Galaxy Integration

Galaxy’s context-aware AI copilot auto-completes analytical functions like LINEAR_REG_SLOPE and can refactor queries when your column names change. Store your regression script in a Galaxy Collection, endorse it, and teammates can reuse the vetted model logic without copy-pasting SQL in Slack.

When to Leave SQL

If you need:

• Non-linear kernels or regularization (Lasso, Ridge)
• Cross-validation across tens of hyper-parameters
• Deep learning

then export a sample to Python/R. But start with SQL for transparency and speed.

Conclusion

Yes—you can (and often should) run linear regression directly in SQL. With built-in analytical functions, you avoid data egress, exploit the power of MPP engines, and maintain auditable pipelines. Whether you are fitting a single-feature trend line or a multivariate sales forecast, today’s SQL engines—and developer-focused editors like Galaxy—make in-database modeling both practical and performant.