  We address the challenge of estimation in the context of constant linear
effect models with dense functional responses. In this framework, the
conditional expectation of the response curve is represented by a linear
combination of functional covariates with constant regression parameters. In
this paper, we present an alternative solution by employing the quadratic
inference approach, a well-established method for analyzing correlated data, to
estimate the regression coefficients. Our approach leverages non-parametrically
estimated basis functions, eliminating the need for choosing working
correlation structures. Furthermore, we demonstrate that our method achieves a
parametric $\sqrt{n}$-convergence rate, contingent on an appropriate choice of
bandwidth. This convergence is observed when the number of repeated
measurements per trajectory exceeds a certain threshold, specifically, when it
surpasses $n^{a_{0}}$, with $n$ representing the number of trajectories.
Additionally, we establish the asymptotic normality of the resulting estimator.
The performance of the proposed method is compared with that of existing
methods through extensive simulation studies, where our proposed method
outperforms. Real data analysis is also conducted to demonstrate the proposed
method.
