As machine learning becomes widely used for automated decisions, attackers have strong incentives to manipulate the results and models generated by machine learning algorithms. In this paper, we perform the first systematic study of poisoning attacks and their countermeasures for linear regression models. In poisoning attacks, attackers deliberately influence the training data to manipulate the results of a predictive model. We propose a theoretically-grounded optimization framework specifically designed for linear regression and demonstrate its effectiveness on a range of datasets and models. We also introduce a fast statistical attack that requires limited knowledge of the training process. Finally, we design a new principled defense method that is highly resilient against all poisoning attacks. We provide formal guarantees about its convergence and an upper bound on the effect of poisoning attacks when the defense is deployed. We evaluate extensively our attacks and defenses on three realistic datasets from health care, loan assessment, and real estate domains.