# Regression and Linear Combinations

DevFeed: [Regression and Linear Combinations](<https://devfeed.tech/articles/regression-and-linear-combinations-40446.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2021/03/29/regression-and-linear-combinations/>)

Published: 2021-03-29T09:00:00Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [linear-regression](<https://devfeed.tech/topics/linear-regression.md>), [math](<https://devfeed.tech/topics/math.md>), [Optimization](<https://devfeed.tech/topics/optimization.md>), [Algorithms, Complexity](<https://devfeed.tech/topics/algorithms-complexity.md>)

Tags: [data](<https://devfeed.tech/tags/data.md>), [gradient-descent](<https://devfeed.tech/tags/gradient-descent.md>), [kernelization](<https://devfeed.tech/tags/kernelization.md>), [linear-algebra](<https://devfeed.tech/tags/linear-algebra.md>), [linear-combination](<https://devfeed.tech/tags/linear-combination.md>), [linear-regression](<https://devfeed.tech/tags/linear-regression.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [optimization](<https://devfeed.tech/tags/optimization.md>), [programming](<https://devfeed.tech/tags/programming.md>), [regression](<https://devfeed.tech/tags/regression.md>)

## AI overview

The article explains why linear combinations matter to programmers, using linear regression as a practical example. It describes representing inputs and weights as vectors, incorporating an intercept into the input vector, and formulating regression as a least-squares optimization problem. The supplied excerpt then begins introducing basis functions for modeling nonlinearity.

## Source excerpt

Recently I've been helping out with a linear algebra course organized by Tai-Danae Bradley and Jack Hidary, and one of the questions that came up a few times was, "why should programmers care about the concept of a linear combination?" For those who don't know, given vectors $ v_1, \dots, v_n$, a linear combination of the vectors is a choice of some coefficients $ a_i$ with which to weight the vectors in a sum $ v = \sum_{i=1}^n a_i v_i$.