The estimation of abundance coefficients, or unmixing, of hyperspectral data is important in a wide variety of applications. Assuming the major constituents, or endmembers, of a scene are known, the unmixing problem is relatively straightforward and easily solved using least-squares techniques. What is less well understood, however, is how error in the original data affects the final solution. This error generally takes two forms: measurement error introduced by the sensor, and modeling error that arises from the assumption of linear mixing. In this paper, we investigate how the unmixing process propagates error that arises from sensor noise. In particular, we derive statistical bounds on how much error can be expected in the estimation of abundance coefficients due to measurement error. We also discuss how this error may affect post-processing algorithms such as subpixel target detection, and consider ways to validate the noise model through the use of residuals.