The dual-beta model is a generalization of the CAPM model. In the dual-beta model, separate beta estimates are provided for up-market and down-market days. This paper uses the historical "Anscombe quartet" results which illustrated how very different datasets can produce the same regression coefficients to motivate a discussion of the dual-beta model. Using data from 39 mutual funds, it is shown how very different dual-beta models can lead to the same CAPM beta estimates, much like the Anscombe quartet scenarios.