Linear regression classification (LRC) has proven to be a successful recognition tool in recent years. LRC depends on using the least square algorithm to get the solution of the linear regression equation. To improve the performance of the LRC algorithm, in this paper, we extend the LRC strategy to both quaternion and reduced biquaternion domains to consider image color information. We derive closed-form solutions from the properties of both domains . We also improve on the accuracy of the closed-form solutions using nonlinear optimization. Our experiments on three benchmark color face recognition databases demonstrate the effectiveness of the proposed methods for recognizing color faces.