Relationship between VC dimension and degrees of freedom
As stated by Prof Yaser Abu-Mostafa-


  Degrees of freedom are an abstraction of the effective number of parameters. The effective number is based on how many dichotomies one can get, rather than how many real-valued parameters are used. In the case of 2-dimensional perceptron, one can think of slope and intercept (plus a binary degree of freedom for which region goes to +1), or one can think of 3 parameters w_0,w_1,w_2 (though the weights can be simultaneously scaled up or down without affecting the resulting hypothesis). The degrees of freedom, however, are 3 because we have the flexibility to shatter 3 points, not because of one way or another of counting the number of parameters.