  We begin the study of list-decodable linear regression using batches. In this
setting only an $\alpha \in (0,1]$ fraction of the batches are genuine. Each
genuine batch contains $\ge n$ i.i.d. samples from a common unknown
distribution and the remaining batches may contain arbitrary or even
adversarial samples. We derive a polynomial time algorithm that for any $n\ge
\tilde \Omega(1/\alpha)$ returns a list of size $\mathcal O(1/\alpha^2)$ such
that one of the items in the list is close to the true regression parameter.
The algorithm requires only $\tilde{\mathcal{O}}(d/\alpha^2)$ genuine batches
and works under fairly general assumptions on the distribution.
  The results demonstrate the utility of batch structure, which allows for the
first polynomial time algorithm for list-decodable regression, which may be
impossible for the non-batch setting, as suggested by a recent SQ lower bound
\cite{diakonikolas2021statistical} for the non-batch setting.
