This paper presents a linear regression based back-end for speaker verification. Linear regression is a simple linear model that minimizes the mean squared estimation error between the target and its estimate with a closed form solution, where the target is defined as the ground-truth indicator vectors of utterances. We use the linear regression model to learn speaker models from a front-end, and verify the similarity of two speaker models by a cosine similarity scoring classifier. To evaluate the effectiveness of the linear regression model, we construct three speaker verification systems that use the Gaussian mixture model and identity-vector (GMM/i-vector) front-end, deep neural network and i-vector (DNN/i-vector) front-end, and deep vector (d-vector) front-end as their front-ends, respectively. Our empirical comparison results on the NIST speaker recognition evaluation data sets show that the proposed method outperforms within-class covariance normalization, linear discriminant analysis, and probabilistic linear discriminant analysis, given any of the three front-ends.