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For Simple Linear/Polynomial regression, we can choose hypothesis equation based on data shape, eg degree-1 for linear data shape, degree-2 for parabolic data shape etc.

But how do we choose the hypothesis equation degree for logistic regression? Is it also based on data shape?

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Looking at the data to determine what the functional form of the conditional mean should be is an example of testing hypothesis suggested by the data. If your goal is inference of a particular type, you should be going into the experiment with an idea of what the functional form should look like and not consult the data.

If instead your goal is to build a predictive model, for example, you might benefit from using something like a spline rather than specifying polynomial terms in your fit. Splines allow for a much wider class of functions to be fit as compared to polynomials, and if you use something like a natural spline (a.k.a. restricted cubic spline) then the estimates are linear in the tails of the predictor.

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