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Glossary math Term Page

Residual

The unexplained difference vector

residual #math#linear-algebra
Korean version

Aliases

residual

Prerequisites

Vector

Related Concepts

ProjectionOrthogonalityLeast SquaresLinear Regression

Core Idea

A residual is the leftover difference between a target vector and its model-based or projected approximation. In least squares, the residual is the quantity whose size we try to make as small as possible.

Role In This Blog

In Mathbong, residuals are central to projection, least squares, normal equations, and linear regression.

Posts Mentioning This Concept

[Linear Algebra Series Part 17] Orthogonality and Projection: Finding the Closest Point Use [[orthogonality|orthogonality]] and [[projection|projection]] to understand best approximation and residual error.[선형대수 시리즈 17편] 직교와 정사영: 가장 가까운 점 찾기 직교와 정사영을 통해 벡터를 기준 공간에 가장 가깝게 맞추는 방법을 설명합니다.[Linear Algebra Series Part 18] Least Squares and the Basics of Linear Regression Use [[least-squares|least squares]] and [[linear-regression|linear regression]] to find the best approximate solution when `Ax = b` has no exact answer.