# Using the Frisch-Waugh-Lovell Theorem to Improve CUPED Variance Reduction in Online Experiments

DevFeed: [Using the Frisch-Waugh-Lovell Theorem to Improve CUPED Variance Reduction in Online Experiments](<https://devfeed.tech/articles/you-can-t-spell-cuped-without-frisch-waugh-lovell-37906.md>)

Original publisher: [Read original article](<https://www.evanmiller.org/you-cant-spell-cuped-without-frisch-waugh-lovell.html>)

Author: Evan Miller

Published: 2022-07-15T00:35:00Z

Content type: tutorial

Language: en

Sources: [Evan Miller](<https://devfeed.tech/sources/evan-miller.md>)

Topics: [experiments](<https://devfeed.tech/topics/experiments.md>), [math](<https://devfeed.tech/topics/math.md>), [data](<https://devfeed.tech/topics/data.md>)

Tags: [analysis](<https://devfeed.tech/tags/analysis.md>), [experiments](<https://devfeed.tech/tags/experiments.md>), [math](<https://devfeed.tech/tags/math.md>), [reduction](<https://devfeed.tech/tags/reduction.md>), [variance](<https://devfeed.tech/tags/variance.md>)

## AI overview

This tutorial explains the mathematical connection between CUPED and partial linear regression through the Frisch-Waugh-Lovell Theorem. It discusses how variance reduction can decrease experiment sample sizes and proposes including a vector of treatments in CUPED regressions for additional variance reduction.

## Source excerpt

A/B tests run faster with CUPED. Here I explain the underlying math, and use it to invent an even better variance-reduction technique for online experiments: You Can't Spell CUPED Without Frisch-Waugh-Lovell