Logistic Regression

Question 1

What function maps the output to a probability between 0 and 1?

Accepted Answer

A sigmoid-style function — The Sigmoid function takes any real value and squashes it to the range [0, 1], making it suitable for probability estimation.

Question 2

What is the key difference between logistic and linear regression?

Accepted Answer

Logistic squashes the linear score into a (0,1) probability — Unlike linear regression, which predicts an unbounded score, logistic regression passes w·x+b through sigmoid to produce a probability — enabling classification by thresholding at 0.5.

Question 3

Logistic regression is used for…

Accepted Answer

Binary classification — Despite its name, it predicts class probabilities, making it a classification algorithm — the linear model's output is squashed to [0,1].

Question 4

The sigmoid function σ(z) = 1/(1+e⁻ᶻ) maps any real number to…

Accepted Answer

A probability strictly between 0 and 1 — The sigmoid squashes the linear score w·x+b into (0,1), giving P(y=1|x).

Question 5

Logistic regression is trained by minimizing…

Accepted Answer

Minimizing binary cross-entropy — Log loss is the negative log-likelihood under the Bernoulli model; it's convex in the weights and penalizes confident wrong predictions heavily.

Question 6

Why is MSE a poor loss for logistic regression?

Accepted Answer

It creates a non-convex surface with vanishing gradients — MSE+sigmoid yields a non-convex surface with vanishing gradients at the extremes; cross-entropy is convex and gives strong gradients.

Question 7

The decision boundary of logistic regression is…

Accepted Answer

Linear — It's a linear hyperplane; the sigmoid is monotonic, so the boundary occurs where the linear score is zero (p=0.5).

Question 8

The 'logit' (log-odds) modeled linearly by logistic regression is…

Accepted Answer

The value log(p/(1−p)), equal to w·x + b — Logistic regression assumes the log-odds of the positive class is a linear function of the features.

Question 9

A coefficient wᵢ in logistic regression affects the odds by a factor of…

Accepted Answer

A multiplicative factor equal to e raised to wᵢ — Exponentiating a coefficient gives the odds ratio: each unit increase in feature i multiplies the odds by e^{wᵢ}.

Question 10

For MULTICLASS classification, logistic regression generalizes via…

Accepted Answer

Via the softmax function — Softmax outputs a probability distribution over k classes; cross-entropy is the corresponding loss.

Logistic Regression

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