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A student stated: I fail to see why the response function needs to be constrained between 0 and 1 when the response variable is binary

A student stated: "I fail to see why the response function needs to be constrained between 0 and 1 when the response variable is binary and has a Bernoulli distribution. The fit to 0, 1 data will take care of this problem for any response function." Comment.

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