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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 + \varepsilon,</math>|{{EquationRef|3}}}}
where <math>Z_1,\ldots,Z_q</math> are scalar covariates with <math>Z_1=1</math>, <math>\alpha_1,\ldots,\alpha_q</math> are regression coefficients for <math>Z_1,\ldots,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 regression coefficient function for <math>X_j^c(\cdot)</math>, and <math>\mathcal{T}_j</math> is the ___domain of <math>X_j</math> and <math>\beta_j</math>, for <math>j=1,\ldots,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>{{cite journal|doi=10.1146/annurev-statistics-041715-033624|title=Functional Data Analysis|year=2016|last1=Wang|first1=Jane-Ling|last2=Chiou|first2=Jeng-Min|last3=Müller|first3=Hans-Georg|journal=[[Annual Review of Statistics and Its Application]]|volume=3|issue=1|pages=257–295|bibcode=2016AnRSA...3..257W|url=https://zenodo.org/record/895750|doi-access=free}}</ref> and alternative estimation methods for model ({{EquationNote|3}}) are available.<ref>{{Cite journal |last=Kong |first=Dehan |last2=Xue |first2=Kaijie |last3=Yao |first3=Fang |last4=Zhang |first4=Hao H. |date= |title=Partially functional linear regression in high dimensions |url=https://academic.oup.com/biomet/article-lookup/doi/10.1093/biomet/asv062 |journal=Biometrika |language=en |volume=103 |issue=1 |pages=147–159 |doi=10.1093/biomet/asv062 |issn=0006-3444}}</ref><ref>
=== Functional linear models with functional responses ===
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