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== Functional linear models (FLMs) ==
Functional linear models (FLMs) are an extension of [[Linear regression|traditional multivariate linear models]] with scalar response <math>Y\in\mathbb{R}</math> and scalar covariates <math>\mathbf{X}\in\mathbb{R}^p</math>, which can be written as
<math display="block">Y = \beta_0 + \langle\mathbf{X},\beta\rangle + \epsilon</math>,▼
▲<math>Y = \beta_0 + \langle\mathbf{X},\beta\rangle + \epsilon</math>
where <math>\langle\cdot,\cdot\rangle</math> denotes the [[Inner product space|inner product]] in [[Euclidean space|Euclidean space]], <math>\beta_0\in\mathbb{R}</math> and <math>\beta\in\mathbb{R}^p</math> denote the regression coefficients, and <math>\epsilon</math> is a random error with [[Expected value|mean]] zero and [[Variance|variance]] finite. FLMs can be divided into three types based on responses and covariates.
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