why sigmoid function is used in logistic regression instead of a simple x intercept?

Sigmoid has the nice concept of outputting a value between 0 and 1, which can be interpreted as a probability.

It is also critical for the logistic cost function, which is designed to create a boundary between two classes. This is different than linear regression, where the model is trying to predict the values.

Because you need a loss function that has good behavior in order to drive your back propagation. Sigmoid is paired with cross entropy loss, which expects an input that looks like a probability.

If you just use distance as your loss metric, it doesn’t work well because classification problems have fundamentally different properties than regression problems.

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