  The age of big data has produced data sets that are computationally expensive
to analyze and store. Algorithmic leveraging proposes that we sample
observations from the original data set to generate a representative data set
and then perform analysis on the representative data set. In this paper, we
present efficient algorithms for constructing finite sample confidence
intervals for each algorithmic leveraging estimated regression coefficient,
with asymptotic coverage guarantees. In simulations, we confirm empirically
that the confidence intervals have the desired coverage probabilities, while
bootstrap confidence intervals may not.
