With the use of the shrinked-map principle, we obtain a more general condition of the stability in cobweb model, where the usually cited linear hypothesis is canceled.

If that probability is low, then you can reject the null hypothesis that the mean is the best predictor and, correspondingly, gain confidence that a simple linear model offers a good fit for the data.

In a research context, the alternative hypothesis of a linear model needs to be established by theoretical and statistical arguments.