As is well-known, the ordinary regression analysis method is confined to a simplified linear model of the estimation based on the Gaussian property and a least squares error criterion. Then, usually the prediction is done through the transformation based on this regression function. In this paper, a new trial for the regression analysis is proposed especially in the form matched to the complexity of physical phenomena and stochastic signal detection under the existence of background noise. Furthermore, the prediction of the output probability distribution is done based on the regression relationship with less information loss. Finally, the effectiveness of the proposed method is confirmed experimentally by applying it to the actual acoustic data.