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In logistic regression, z = 2x − 4 is passed through the sigmoid function σ(z) = 1 ÷ (1 + e^(−z)) and the result is output as the probability of being positive. What is the output when x = 2?

  1. A0
  2. B0.5
  3. C1
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Answer: B. 0.5

When x = 2, z = 2 × 2 − 4 = 0, so σ(0) = 1 ÷ (1 + e⁰) = 1 ÷ 2 = 0.5. The sigmoid function maps any real number to a value between 0 and 1, approaching 1 as z grows and 0 as z falls. Logistic regression treats this value as the probability of being positive and splits items into two classes with a threshold such as 0.5; despite "regression" in its name, it is a model for classification.

  • A. This is the value of z, before it is passed through the sigmoid function.
  • B. Correct. σ(0) = 1 ÷ 2 = 0.5.
  • C. This is the value approached when z is large enough; at z = 0 the output is 0.5.
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