The signed regressor (SR) algorithm employs one bit quantization on the input regressor (or tap input) in such a way that the quantized input sequences become +1 or -1. The algorithm is computationally more efficient by nature than the popular least mean square (LMS) algorithm. The behavior of the SR algorithm unfortunately is heavily dependent on the characteristics of the input signal, and there are some Inputs for which the SR algorithm becomes unstable. It is known, however, that such a stability problem does not take place with the SR algorithm when the input signal is Gaussian, such as in the case of speech processing. In this paper, we explore a statistical analysis of the SR algorithm. Under the assumption that signals involved are zero-mean and Gaussian, and further employing the commonly used independence assumption, we derive a set of nonlinear evolution equations that characterizes the mean and mean-squared behavior of the SR algorithm. Experimental results that show very good agreement with our theoretical derivations are also presented.