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The functional linear regression model with points of impact is a recentaugmentation of the classical functional linear model with many practicallyimportant applications. In this work, however, we demonstrate that the existingdata-driven procedure for estimating the parameters of this regression modelcan be very instable and inaccurate. The tendency to omit relevant points ofimpact is a particularly problematic aspect resulting in omitted-variablebiases. We explain the theoretical reason for this problem and propose a newsequential estimation algorithm that leads to significantly improved estimationresults. Our estimation algorithm is compared with the existing estimationprocedure using an in-depth simulation study. The applicability is demonstratedusing data from Google AdWords, today's most important platform for onlineadvertisements. The \textsf{R}-package \texttt{FunRegPoI} and additional\textsf{R}-codes are provided in the online supplementary material.

Improving Estimation in Functional Linear Regression with Points of Impact: Insights into Google AdWords