Discussion
Consider the following statements :
Statement (1) : In the logistic regression model we pass the values of W. x + b (for every x in the dot set) through a sigmoid function to return a probabilistic class label.
Statement (2) : In the logistic regression model, if the value (W. x + b) given to the sigmoid function in close to zero. Then the class label predicted (with a 0.5 threashold) is very certain and reliable.
Answer: A
Only statement (1) is correct.
Logistic regression computes \(z = W \cdot x + b\) and passes it through the sigmoid \(\sigma(z) = 1/(1 + e^{-z})\) to obtain a probability for the positive class, as statement (1) says.
Statement (2) is wrong. When z is close to zero, \(\sigma(z)\) is close to 0.5, right at the threshold, so the predicted label is the least certain; confident predictions come from large positive or negative z, where the probability is near 1 or 0.
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