Virtual Labs

Binary Classification and Decision Boundary Analysis using Logistic Regression

Logistic regression is primarily used for which type of task?

a: Dimensionality reduction Explanation

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b: Binary classification Explanation

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c: Clustering Explanation

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d: Continuous value prediction Explanation

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Logistic regression belongs to which category of machine learning?

a: Supervised learning Explanation

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b: Unsupervised learning Explanation

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c: Reinforcement learning Explanation

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d: Semi-supervised learning Explanation

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In logistic regression, the linear combination z is passed through which activation function to obtain a probability?

a: Hyperbolic tangent (tanh) Explanation

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b: Rectified Linear Unit (ReLU) Explanation

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c: Sigmoid (logistic) function Explanation

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d: Softmax function Explanation

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The output range of the sigmoid function σ(z) = 11 + e^−z is:

a: (-1,+1) Explanation

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b: (-∞,+∞) Explanation

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c: [0,+∞) Explanation

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d: (0,1) Explanation

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In the linear equation z = w · x + b, what role does the bias term b play?

a: It controls the learning rate during training Explanation

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b: It normalizes the input features Explanation

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c: It shifts the decision boundary independently of the input features Explanation

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d: It regularizes the model to prevent overfitting Explanation

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Why is the default classification threshold in logistic regression set at 0.5?

a: It always maximises classification accuracy Explanation

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b: It corresponds to the midpoint of the sigmoid curve where z = 0 Explanation

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c: It is selected randomly and has no mathematical justification Explanation

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d: It minimises the log-loss function Explanation

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Which loss function is minimised during the training of a logistic regression model?

a: Mean Squared Error (MSE) Explanation

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b: Hinge loss Explanation

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c: Binary Cross-Entropy (Log Loss) Explanation

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d: Huber loss Explanation

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What is the key property of the sigmoid function that makes it suitable for gradient-based optimisation in logistic regression?

a: It is a periodic function Explanation

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b: It is differentiable everywhere and its derivative can be expressed in terms of itself Explanation

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c: It produces unbounded outputs Explanation

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d: It is a piecewise linear function Explanation

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What does the log-odds (logit) represent in logistic regression?

a: The probability of the positive class Explanation

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b: The natural logarithm of the ratio of the probability of the positive class to the probability of the negative class Explanation

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c: The squared error between predicted and actual values Explanation

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d: The Euclidean distance between data points Explanation

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In logistic regression, what is the effect of applying L2 regularization (Ridge penalty) on the weight coefficients?

a: It sets some coefficients exactly to zero, performing feature selection Explanation

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b: It penalises the sum of squared weights, shrinking all coefficients toward zero to reduce overfitting Explanation

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c: It increases the model complexity to fit the training data more closely Explanation

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d: It replaces the sigmoid function with a linear activation Explanation

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