This letter proposes a regression model for nonnegative signals. The proposed regression estimates the mean of Rayleigh distributed signals by a structure which includes a set of regressors and a link function. For the proposed model, we present: 1) parameter estimation; 2) large data record results; and 3) a detection technique. In this letter, we present closed-form expressions for the score vector and Fisher information matrix. The proposed model is submitted to extensive Monte Carlo simulations and to the measured data. The Monte Carlo simulations are used to evaluate the performance of maximum likelihood estimators. Also, an application is performed comparing the detection results of the proposed model with Gaussian-, Gamma-, and Weibull-based regression models in synthetic aperture radar (SAR) images.