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Adding multiple functional and scalar covariates, model ({{EquationNote|2}}) can be extended to
{{NumBlk|::|<math display="block">Y = \sum_{k=1}^q Z_k\alpha_k + \sum_{j=1}^p \int_{\mathcal{T}_j} X_j^c(t) \beta_j(t) dt + \epsilon,</math>|{{EquationRef|3}}}}
where <math>Z_1,\cdots,Z_q</math> are scalar covariates with <math>Z_1=1</math>, <math>\alpha_1,\cdots,\alpha_q</math> are the coefficients corresponding to <math>Z_1,\cdots,Z_q</math>, respectively, <math>X^c_j</math> is a centered functional covariate given by <math>X_j^c(\cdot) = X_j(\cdot) - \mathbb{E}(X_j(\cdot))</math>, <math>\beta_j</math> is the corresponding coefficient function, and <math>\mathcal{T}_j</math> is the ___domain of <math>X_j</math> and <math>\beta_j</math>, for <math>j=1,\cdots,p</math>. However, due to the parametric component <math>\alpha</math>, the estimation methods for model ({{EquationNote|2}}) cannot be used in this case<ref name=wang:16>Wang, Chiou and Müller (2016). "Functional data analysis". ''Annual Review of Statistics and Its Application''. '''3''':257–295. [[Digital object identifier|doi]]:[http://doi.org/10.1146/annurev-statistics-041715-033624 10.1146/annurev-statistics-041715-033624].</ref> and various estimation methods for model ({{EquationNote|3}}) are available<ref>Kong, Xue, Yao and Zhang (2016). "Partially functional linear regression in high dimensions". ''Biometrika''. '''103''' (1):147–159. [[Digital object identifier|doi]]:[http://doi.org/10.1093/biomet/asv062 10.1093/biomet/asv062]</ref><ref>Hu, Wang and Carroll (2004). "Profile-kernel versus backfitting in the partially linear models for longitudinal/clustered data". ''Biometrika''. '''91''' (2): 251–262. [[Digital object identifier|doi]]:[http://doi.org/10.1093/biomet/91.2.251 10.1093/biomet/91.2.251]</ref>.<br />
=== Functional linear models with functional responses ===
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