In this paper we present a novel approach of face identification by formulating the pattern recognition problem in terms of linear regression. Using a fundamental concept that patterns from a single object class lie on a linear subspace, we develop a linear model representing a probe image as a linear combination of class specific galleries. The inverse problem is solved using the least squares method and the decision is ruled in favor of the class with the minimum reconstruction error. The algorithm is extensively evaluated using two standard databases, a comparative study with the benchmark algorithms clearly reflects the efficacy of the proposed approach.