quiz.json

[
  {
    "id": "biasvar-pre-1",
    "stage": "pre",
    "question": "A linear model is used to fit a clearly curved (quadratic) relationship. Which error component dominates?",
    "options": [
      "Variance: the model changes too much with different training data",
      "Bias: the model is too rigid to capture the true nonlinear pattern",
      "Irreducible noise: the data is too noisy",
      "None: the model should fit perfectly"
    ],
    "correct": 1,
    "explanation": "A linear model cannot capture a quadratic curve no matter how much data it sees. This systematic error from wrong model assumptions is bias. The model underfits."
  },
  {
    "id": "biasvar-pre-2",
    "stage": "pre",
    "question": "The bias-variance decomposition of expected error has three terms. Which one cannot be reduced by any model?",
    "options": [
      "Bias squared",
      "Variance",
      "Irreducible noise (sigma squared)",
      "All three can be reduced to zero"
    ],
    "correct": 2,
    "explanation": "Irreducible noise comes from randomness in the data itself (measurement error, missing variables). No model can predict noise. Expected error = bias^2 + variance + irreducible noise."
  },
  {
    "id": "biasvar-post-1",
    "stage": "post",
    "question": "Adding L2 regularization to a model increases bias and decreases variance. Why is this useful?",
    "options": [
      "It always improves both training and test accuracy",
      "The reduction in variance can outweigh the increase in bias, lowering total error",
      "L2 regularization eliminates irreducible noise",
      "It makes the model faster to train"
    ],
    "correct": 1,
    "explanation": "Regularization trades a small increase in bias for a larger decrease in variance. When a model is overfitting (high variance), this tradeoff reduces total error even though bias goes up slightly."
  },
  {
    "id": "biasvar-post-2",
    "stage": "post",
    "question": "A model has training error = 2% and test error = 25%. What is the most likely diagnosis?",
    "options": [
      "High bias (underfitting): the model is too simple",
      "High variance (overfitting): the model memorized training data and fails to generalize",
      "High irreducible noise: the data is too noisy",
      "The model is perfectly calibrated"
    ],
    "correct": 1,
    "explanation": "Low training error + high test error + large gap = high variance (overfitting). The model fits training-specific noise. Remedies: regularize, reduce complexity, get more data."
  },
  {
    "id": "biasvar-post-3",
    "stage": "post",
    "question": "You train the same model architecture on 50 different random training subsets and observe that predictions vary wildly between them. What does this indicate?",
    "options": [
      "High bias: the model consistently misses the true pattern",
      "High variance: the model is sensitive to which specific training data it sees",
      "High irreducible noise: the target variable is random",
      "The learning rate is too high"
    ],
    "correct": 1,
    "explanation": "Variance measures how much predictions change when trained on different data subsets. Wildly different predictions across subsets is the definition of high variance."
  }
]