  This paper introduces the problem of coresets for regression problems to
panel data settings. We first define coresets for several variants of
regression problems with panel data and then present efficient algorithms to
construct coresets of size that depend polynomially on 1/$\varepsilon$ (where
$\varepsilon$ is the error parameter) and the number of regression parameters -
independent of the number of individuals in the panel data or the time units
each individual is observed for. Our approach is based on the Feldman-Langberg
framework in which a key step is to upper bound the "total sensitivity" that is
roughly the sum of maximum influences of all individual-time pairs taken over
all possible choices of regression parameters. Empirically, we assess our
approach with synthetic and real-world datasets; the coreset sizes constructed
using our approach are much smaller than the full dataset and coresets indeed
accelerate the running time of computing the regression objective.
