Glossary

Why the sigmoid works:

When $b_0 + b_1 x$ is a large positive number (say, +10), $e^{-10}$ is tiny, so $P \approx \frac{1}{1+0} \approx 1$ - When $b_0 + b_1 x$ is a large negative number (say, -10), $e^{10}$ is huge, so $P \approx \frac{1}{1+22026} \approx 0$ - When $b_0 + b_1 x = 0$, $e^0 = 1$, so $P = \frac{1}{1+1} = 0.

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