In lossless image coding, it has been demonstrated that using the method of ordinary least squares (OLS) to design a linear predictor for each pixel results in better compression performance than that of the state-of-the-art. In previous studies, the order of the predictor is chosen empirically and fixed for the whole image. Since images are nonstationary signals, the order should be adapted to the local characteristics of the image. In this paper, we tackle this problem by using a model averaging approach. We show that by averaging over a group of OLS predictors, the effective number of parameter of the resultant predictor is adjusted adaptively. We show that the proposed method is robust to changes in the size of the training block. It also leads to better performance than the OLS predictor.