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Adding multiple functional and scalar covariates, the FLR can be extended as
<math display="block">Y = \langle\mathbf{Z},\alpha\rangle + \sum_{j=1}^p \int_{\mathcal{T}_j} X_j^c(t) \beta_j(t) dt + \epsilon</math>
where <math>\mathbf{Z}=(Z_1,\cdots,Z_q)^T</math> with <math>Z_1=1</math> is a vector of scalar covariates, <math>\alpha=(\alpha_1,\cdots,\alpha_q)^T</math> is a vector of coefficients corresponding to <math>\mathbf{Z}</math>, <math>\langle\cdot,\cdot\rangle</math> denotes the inner product in Euclidean space, <math>X^c_1,\cdots,X^c_p</math> are multiple centered functional covariates given by <math>X_j^c(\cdot) = X_j(\cdot) - \mathbb{E}(X_j(\cdot))</math>, and <math>\mathcal{T}_j</math> is the [[Domain of a function|___domain]] of <math>X_j(\cdot)</math>. However, due to the parametric component <math>\alpha</math>, the estimation of this model is different from that of the FLR. General estimation approaches have been proposed<ref>Yao, Müller and Wang (2005). "Functional linear regression analysis for longitudinal data". ''The Annals of Statistics''. '''33''' (6):2873–2903. [[Digital object identifier|doi]]:[http://
=== Functional linear models with functional response ===
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