{
  "title": "Logistic Regression Mastery: 100 MCQs",
  "description": "A comprehensive set of 100 multiple-choice questions designed to teach and test your understanding of Logistic Regression, from basic concepts to advanced topics like regularization, odds ratio, decision boundaries, and real-world scenario applications.",
  "questions": [
    {
      "id": 1,
      "questionText": "What is the main purpose of Logistic Regression?",
      "options": [
        "To cluster data points",
        "To predict binary or categorical outcomes",
        "To reduce dimensionality",
        "To predict a continuous outcome"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Logistic Regression models the probability of binary or categorical outcomes, not continuous values."
    },
    {
      "id": 2,
      "questionText": "Which function does Logistic Regression use to map predicted values to probabilities?",
      "options": [
        "Sigmoid function",
        "ReLU function",
        "Step function",
        "Linear function"
      ],
      "correctAnswerIndex": 0,
      "explanation": "The sigmoid function maps any real-valued number into the range 0 to 1, representing probabilities."
    },
    {
      "id": 3,
      "questionText": "In Logistic Regression, what does the odds ratio represent?",
      "options": [
        "The number of features in the model",
        "The error of the model",
        "The predicted probability itself",
        "The ratio of probability of success to failure"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Odds ratio = probability of success / probability of failure."
    },
    {
      "id": 4,
      "questionText": "What type of relationship does Logistic Regression model between input and output?",
      "options": [
        "Non-linear relationship between input and output",
        "Linear relationship between input and output",
        "Linear relationship between input and probability log-odds",
        "Polynomial relationship"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Logistic Regression models the log-odds (logit) as a linear combination of inputs."
    },
    {
      "id": 5,
      "questionText": "Which loss function is used in Logistic Regression?",
      "options": [
        "Hinge Loss",
        "Absolute Error",
        "Mean Squared Error",
        "Cross-Entropy / Log Loss"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Logistic Regression uses log loss (cross-entropy) to penalize incorrect probabilistic predictions."
    },
    {
      "id": 6,
      "questionText": "Scenario: A dataset has highly imbalanced classes. What is a good approach in Logistic Regression?",
      "options": [
        "Remove majority class",
        "Use class weights or resampling techniques",
        "Ignore imbalance and train directly",
        "Use Linear Regression instead"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Class imbalance can bias predictions; weighting or resampling helps model performance."
    },
    {
      "id": 7,
      "questionText": "Which metric is most appropriate for evaluating Logistic Regression?",
      "options": [
        "Mean Absolute Error",
        "Accuracy, Precision, Recall, F1-score",
        "R-squared",
        "Explained Variance"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Classification metrics like accuracy, precision, recall, and F1-score are used for Logistic Regression."
    },
    {
      "id": 8,
      "questionText": "Scenario: Logistic Regression model shows overfitting. Recommended solution?",
      "options": [
        "Reduce dataset size",
        "Apply regularization (L1 or L2)",
        "Increase learning rate",
        "Remove all features"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Regularization penalizes large coefficients, reducing overfitting."
    },
    {
      "id": 9,
      "questionText": "Which regularization is used in Logistic Regression to encourage sparsity in coefficients?",
      "options": [
        "L2 Regularization (Ridge)",
        "No regularization",
        "L1 Regularization (Lasso)",
        "ElasticNet only"
      ],
      "correctAnswerIndex": 2,
      "explanation": "L1 regularization encourages some coefficients to become exactly zero, promoting sparsity."
    },
    {
      "id": 10,
      "questionText": "Scenario: Logistic Regression is applied with two highly correlated features. Observation?",
      "options": [
        "Features ignored automatically",
        "Model always underfits",
        "Multicollinearity can inflate coefficient variance",
        "Coefficients are exact"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Highly correlated features lead to unstable coefficients due to multicollinearity."
    },
    {
      "id": 11,
      "questionText": "Which threshold is commonly used to convert probabilities into class predictions?",
      "options": [
        "1.0",
        "Negative values",
        "0.25",
        "0.5"
      ],
      "correctAnswerIndex": 3,
      "explanation": "By default, probabilities ≥0.5 are classified as 1, below 0.5 as 0."
    },
    {
      "id": 12,
      "questionText": "Scenario: Predicted probability = 0.8. What is predicted class (threshold=0.5)?",
      "options": [
        "Depends on dataset",
        "Undetermined",
        "Class 1",
        "Class 0"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Probability >0.5 is classified as Class 1 by default."
    },
    {
      "id": 13,
      "questionText": "Scenario: Logistic Regression applied to a dataset with 3 classes. Which extension is required?",
      "options": [
        "Binary Logistic Regression",
        "Ridge Regression",
        "Linear Regression",
        "Multinomial Logistic Regression (Softmax)"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Multinomial logistic regression generalizes to multi-class problems using softmax function."
    },
    {
      "id": 14,
      "questionText": "What does the coefficient in Logistic Regression represent?",
      "options": [
        "Predicted probability",
        "Change in log-odds per unit change in feature",
        "Mean of feature",
        "Error term"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Each coefficient measures the impact of its feature on log-odds of the outcome."
    },
    {
      "id": 15,
      "questionText": "Scenario: Logistic Regression is applied with L2 regularization. Observation?",
      "options": [
        "Coefficients become exactly zero",
        "Model ignores features",
        "Training fails",
        "Coefficients shrink, helps reduce overfitting"
      ],
      "correctAnswerIndex": 3,
      "explanation": "L2 penalizes large coefficients, reducing variance without forcing zeros."
    },
    {
      "id": 16,
      "questionText": "Which function converts log-odds to probability in Logistic Regression?",
      "options": [
        "ReLU",
        "Linear",
        "Tanh",
        "Sigmoid"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Sigmoid maps log-odds to probability between 0 and 1."
    },
    {
      "id": 17,
      "questionText": "Scenario: Dataset has 100 features, 10,000 samples. Regularization needed?",
      "options": [
        "No, model will generalize automatically",
        "Yes, to prevent overfitting and reduce coefficient variance",
        "Remove samples instead",
        "Use only linear regression"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Regularization is important when features are many relative to samples to improve generalization."
    },
    {
      "id": 18,
      "questionText": "Scenario: Logistic Regression shows poor recall for minority class. Solution?",
      "options": [
        "Remove majority class",
        "Ignore minority class",
        "Increase learning rate",
        "Adjust decision threshold or use class weights"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Threshold adjustment or class weighting helps improve minority class prediction."
    },
    {
      "id": 19,
      "questionText": "Which optimization method is commonly used to train Logistic Regression?",
      "options": [
        "Random Forest",
        "Gradient Descent / Newton-Raphson",
        "PCA",
        "K-Means"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Gradient-based optimization (like gradient descent or Newton-Raphson) is used to minimize log-loss."
    },
    {
      "id": 20,
      "questionText": "Scenario: Logistic Regression applied with perfect separation. Observation?",
      "options": [
        "Model ignores features",
        "Coefficients can go to infinity; regularization needed",
        "Model works fine without issues",
        "Training error is high"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Perfect separation leads to extremely large coefficients; L1/L2 regularization stabilizes estimates."
    },
    {
      "id": 21,
      "questionText": "Scenario: Logistic Regression applied to highly imbalanced dataset. Metric to monitor?",
      "options": [
        "R-squared",
        "Precision, Recall, F1-score",
        "Explained Variance",
        "Mean Absolute Error"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Classification metrics like precision, recall, and F1 are more appropriate than regression metrics."
    },
    {
      "id": 22,
      "questionText": "Scenario: Model predicts 0.49 for minority class with threshold=0.5. Observation?",
      "options": [
        "Prediction invalid",
        "Class predicted as 0; threshold can be adjusted",
        "Model underfits",
        "Class predicted as 1"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Probability <0.5 leads to class 0; threshold adjustment can improve minority class recall."
    },
    {
      "id": 23,
      "questionText": "Scenario: Logistic Regression with correlated inputs. Potential issue?",
      "options": [
        "Model ignores correlated features automatically",
        "Multicollinearity inflates variance of coefficients",
        "Training fails",
        "Model underfits"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Multicollinearity leads to unstable coefficient estimates."
    },
    {
      "id": 24,
      "questionText": "Scenario: Logistic Regression used for spam email detection. What is the output?",
      "options": [
        "Continuous score unrelated to probability",
        "Distance from origin",
        "Probability of spam",
        "Exact class label only"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Logistic Regression outputs the probability of the positive class (spam)."
    },
    {
      "id": 25,
      "questionText": "Scenario: Logistic Regression applied with L1 regularization. Observation?",
      "options": [
        "Training fails",
        "Model ignores features",
        "Some coefficients may become exactly zero, feature selection happens",
        "All coefficients increase"
      ],
      "correctAnswerIndex": 2,
      "explanation": "L1 regularization shrinks some coefficients to zero, effectively performing feature selection."
    },
    {
      "id": 26,
      "questionText": "Scenario: Logistic Regression applied to dataset with outliers. Observation?",
      "options": [
        "Model underfits",
        "Training fails",
        "Outliers have no effect",
        "Coefficients may be skewed by outliers"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Outliers can distort the logistic regression coefficients, affecting predictions."
    },
    {
      "id": 27,
      "questionText": "Scenario: Logistic Regression with L2 regularization on small dataset. Observation?",
      "options": [
        "Model ignores features",
        "Coefficients become exactly zero",
        "Coefficients shrink, improving generalization",
        "Training fails"
      ],
      "correctAnswerIndex": 2,
      "explanation": "L2 regularization penalizes large coefficients, stabilizing them for small datasets."
    },
    {
      "id": 28,
      "questionText": "Scenario: Logistic Regression applied with highly correlated features. Observation?",
      "options": [
        "Model underfits",
        "Model ignores correlated features automatically",
        "Training fails",
        "Multicollinearity inflates variance of coefficients"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Highly correlated features lead to unstable coefficient estimates, increasing variance."
    },
    {
      "id": 29,
      "questionText": "Scenario: Logistic Regression used for credit default prediction. Output?",
      "options": [
        "Distance from origin",
        "Exact class label only",
        "Continuous score unrelated to probability",
        "Probability of default"
      ],
      "correctAnswerIndex": 3,
      "explanation": "The model outputs probabilities, which can then be converted to class labels using a threshold."
    },
    {
      "id": 30,
      "questionText": "Scenario: Logistic Regression trained with balanced class weights. Observation?",
      "options": [
        "All probabilities are 0.5",
        "Model ignores minority class",
        "Minority class predictions improve",
        "Training fails"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Class weights balance the loss function, improving minority class prediction."
    },
    {
      "id": 31,
      "questionText": "Scenario: Logistic Regression applied with feature scaling. Observation?",
      "options": [
        "Scaling changes predicted classes",
        "Scaling reduces number of features",
        "Scaling is required to make model work",
        "Scaling helps optimization but does not affect model predictions"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Feature scaling speeds up convergence but does not change final probabilities."
    },
    {
      "id": 32,
      "questionText": "Scenario: Logistic Regression applied with perfect separation. Observation?",
      "options": [
        "Coefficients may become infinite",
        "Training fails automatically",
        "Model ignores features",
        "Model underfits"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Perfect separation leads to very large coefficients; regularization stabilizes estimates."
    },
    {
      "id": 33,
      "questionText": "Scenario: Logistic Regression applied with threshold=0.7. Observation?",
      "options": [
        "Predictions become stricter for positive class",
        "Model underfits",
        "Threshold does not affect predictions",
        "Predictions become more lenient"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Higher threshold means a higher probability is required to classify as positive, reducing false positives but increasing false negatives."
    },
    {
      "id": 34,
      "questionText": "Scenario: Logistic Regression applied with L1 regularization. Observation?",
      "options": [
        "Training fails",
        "All coefficients increase",
        "Some coefficients shrink to zero",
        "Model ignores features"
      ],
      "correctAnswerIndex": 2,
      "explanation": "L1 encourages sparsity; some features are removed automatically."
    },
    {
      "id": 35,
      "questionText": "Scenario: Logistic Regression applied to multiclass problem. Observation?",
      "options": [
        "Binary logistic regression works fine",
        "Model ignores extra classes",
        "Use multinomial logistic regression with softmax",
        "Training fails"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Binary logistic regression cannot handle more than two classes without modification."
    },
    {
      "id": 36,
      "questionText": "Scenario: Logistic Regression applied to imbalanced dataset. Observation?",
      "options": [
        "Minority class predictions improve automatically",
        "Majority class dominates predictions",
        "Training fails",
        "Model ignores majority class"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Without adjustments, logistic regression may predict majority class most of the time."
    },
    {
      "id": 37,
      "questionText": "Scenario: Logistic Regression applied with gradient descent optimizer. Observation?",
      "options": [
        "Coefficients are updated iteratively to minimize log-loss",
        "Training fails",
        "Model overfits automatically",
        "Predictions remain constant"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Gradient descent iteratively updates weights to minimize cross-entropy loss."
    },
    {
      "id": 38,
      "questionText": "Scenario: Logistic Regression applied to dataset with categorical features. Observation?",
      "options": [
        "Model ignores categorical features",
        "Categorical features must be encoded (e.g., one-hot)",
        "Training fails",
        "Model handles categories directly"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Logistic Regression requires numeric input; categorical variables must be encoded."
    },
    {
      "id": 39,
      "questionText": "Scenario: Logistic Regression applied with very few samples. Observation?",
      "options": [
        "Training fails",
        "Model ignores features",
        "Regularization is critical to prevent overfitting",
        "Model always underfits"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Small datasets can lead to high variance; regularization helps stabilize coefficients."
    },
    {
      "id": 40,
      "questionText": "Scenario: Logistic Regression applied to text classification using TF-IDF features. Observation?",
      "options": [
        "Training error is zero",
        "Model fails automatically",
        "Model can handle high-dimensional sparse data with regularization",
        "Model ignores sparse features"
      ],
      "correctAnswerIndex": 2,
      "explanation": "With regularization, logistic regression works well on high-dimensional sparse data like TF-IDF vectors."
    },
    {
      "id": 41,
      "questionText": "Scenario: Logistic Regression applied to dataset with missing values. Observation?",
      "options": [
        "Training fails",
        "Imputation required before training",
        "Model ignores missing values automatically",
        "Model underfits"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Logistic Regression cannot handle missing values directly; preprocessing like imputation is required."
    },
    {
      "id": 42,
      "questionText": "Scenario: Logistic Regression applied with regularization strength very high. Observation?",
      "options": [
        "Training fails",
        "Model ignores features",
        "Coefficients increase automatically",
        "Coefficients shrink drastically, model may underfit"
      ],
      "correctAnswerIndex": 3,
      "explanation": "High regularization penalizes coefficients heavily, potentially underfitting the data."
    },
    {
      "id": 43,
      "questionText": "Scenario: Logistic Regression applied with learning rate too high. Observation?",
      "options": [
        "Optimization may diverge",
        "Training fails silently",
        "Predictions remain perfect",
        "Model always converges"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Too high learning rate can make gradient descent overshoot, preventing convergence."
    },
    {
      "id": 44,
      "questionText": "Scenario: Logistic Regression applied with L1 and L2 regularization combined. Observation?",
      "options": [
        "Training fails",
        "ElasticNet combines both, balancing sparsity and coefficient shrinkage",
        "All coefficients go to zero",
        "Model ignores features"
      ],
      "correctAnswerIndex": 1,
      "explanation": "ElasticNet uses a weighted combination of L1 and L2 to balance sparsity and shrinkage."
    },
    {
      "id": 45,
      "questionText": "Scenario: Logistic Regression applied with non-linear patterns in features. Observation?",
      "options": [
        "Model ignores non-linear features",
        "Training fails",
        "Model captures non-linearities automatically",
        "Linear decision boundary may underfit; feature engineering or polynomial expansion needed"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Logistic Regression assumes linear relationship between log-odds and features; non-linearities require feature transformations."
    },
    {
      "id": 46,
      "questionText": "Scenario: Logistic Regression applied to probability output. Which method can calibrate probabilities?",
      "options": [
        "StandardScaler",
        "PCA",
        "Platt Scaling or Isotonic Regression",
        "Ridge Regression"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Platt scaling or isotonic regression adjusts predicted probabilities for better calibration."
    },
    {
      "id": 47,
      "questionText": "Scenario: Logistic Regression applied with many irrelevant features. Observation?",
      "options": [
        "Training fails",
        "Regularization can reduce effect of irrelevant features",
        "Model ignores irrelevant features automatically",
        "Model overfits regardless"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Regularization reduces coefficients of uninformative features, improving generalization."
    },
    {
      "id": 48,
      "questionText": "Scenario: Logistic Regression applied to dataset with 3 classes. Threshold method?",
      "options": [
        "Model fails",
        "Softmax probabilities used for multiclass prediction",
        "Binary logistic regression applies",
        "Single threshold 0.5 used for all classes"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Multinomial logistic regression uses softmax to handle multiple classes."
    },
    {
      "id": 49,
      "questionText": "Scenario: Logistic Regression applied to dataset with skewed classes. Observation?",
      "options": [
        "Minority class ignored automatically",
        "Class weighting or resampling improves minority prediction",
        "Model fails",
        "All predictions become majority class"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Class weighting or resampling is needed to handle skewed datasets effectively."
    },
    {
      "id": 50,
      "questionText": "Scenario: Logistic Regression applied with early stopping during optimization. Observation?",
      "options": [
        "Coefficients go to zero",
        "Model always underfits",
        "Prevents overfitting and reduces training time",
        "Training fails"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Early stopping halts training when improvement slows, helping avoid overfitting."
    },
    {
      "id": 51,
      "questionText": "Scenario: Logistic Regression applied to dataset with nonlinear boundaries. Observation?",
      "options": [
        "Model perfectly separates classes",
        "Training fails",
        "Model ignores features",
        "Linear decision boundary may underfit; feature engineering needed"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Logistic Regression assumes linear decision boundary on log-odds; nonlinear relationships require transformations."
    },
    {
      "id": 52,
      "questionText": "Scenario: Logistic Regression applied to high-dimensional sparse data like text. Observation?",
      "options": [
        "Training fails automatically",
        "Model ignores sparse features",
        "Model always underfits",
        "Regularization is essential to prevent overfitting"
      ],
      "correctAnswerIndex": 3,
      "explanation": "L1 or L2 regularization stabilizes coefficients in high-dimensional sparse datasets."
    },
    {
      "id": 53,
      "questionText": "Scenario: Logistic Regression applied to highly imbalanced dataset. Best practice?",
      "options": [
        "Increase learning rate",
        "Use class weighting or resampling techniques",
        "Ignore imbalance and train directly",
        "Remove minority class"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Adjusting for class imbalance helps improve minority class predictions."
    },
    {
      "id": 54,
      "questionText": "Scenario: Logistic Regression model shows large coefficients for correlated features. Observation?",
      "options": [
        "Model ignores correlated features automatically",
        "Coefficients are perfect",
        "Training fails",
        "Multicollinearity inflates variance of coefficients"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Highly correlated inputs can lead to unstable coefficient estimates."
    },
    {
      "id": 55,
      "questionText": "Scenario: Logistic Regression applied with threshold=0.3. Observation?",
      "options": [
        "Threshold has no effect",
        "Predictions become stricter",
        "Model underfits",
        "Predictions become more lenient for positive class"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Lowering threshold increases positive predictions, improving recall but may reduce precision."
    },
    {
      "id": 56,
      "questionText": "Scenario: Logistic Regression applied with very small L2 regularization. Observation?",
      "options": [
        "Training fails",
        "Model underfits automatically",
        "Coefficients shrink to zero",
        "Coefficients may be large, risk of overfitting"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Small regularization may allow large coefficients, increasing variance."
    },
    {
      "id": 57,
      "questionText": "Scenario: Logistic Regression applied with L1 regularization. Observation?",
      "options": [
        "Some coefficients shrink to zero, performing feature selection",
        "Training fails",
        "All coefficients increase",
        "Model ignores features"
      ],
      "correctAnswerIndex": 0,
      "explanation": "L1 regularization promotes sparsity, setting some coefficients exactly to zero."
    },
    {
      "id": 58,
      "questionText": "Scenario: Logistic Regression applied to multiclass problem. Observation?",
      "options": [
        "Training fails",
        "Binary logistic regression works fine",
        "Use multinomial logistic regression with softmax",
        "Model ignores extra classes"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Binary logistic regression cannot handle more than two classes without modification."
    },
    {
      "id": 59,
      "questionText": "Scenario: Logistic Regression applied to dataset with missing values. Observation?",
      "options": [
        "Training fails automatically",
        "Model ignores missing values automatically",
        "Model underfits",
        "Imputation required before training"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Logistic Regression cannot handle missing values directly; preprocessing is needed."
    },
    {
      "id": 60,
      "questionText": "Scenario: Logistic Regression applied to text classification with TF-IDF features. Observation?",
      "options": [
        "Training error is zero",
        "Model fails automatically",
        "All sparse features are ignored",
        "Regularization prevents overfitting in high-dimensional sparse features"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Regularization stabilizes coefficients and improves generalization on sparse datasets."
    },
    {
      "id": 61,
      "questionText": "Scenario: Logistic Regression applied with gradient descent and large learning rate. Observation?",
      "options": [
        "Model converges perfectly",
        "Optimization may diverge",
        "Model ignores features",
        "Predictions remain constant"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Too high learning rate can cause gradient descent to overshoot and fail to converge."
    },
    {
      "id": 62,
      "questionText": "Scenario: Logistic Regression applied with perfect separation in classes. Observation?",
      "options": [
        "Model underfits",
        "Training fails automatically",
        "Coefficients may become extremely large",
        "Model ignores features"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Perfect separation leads to very large coefficients; regularization helps stabilize the model."
    },
    {
      "id": 63,
      "questionText": "Scenario: Logistic Regression applied with early stopping. Observation?",
      "options": [
        "Training fails",
        "Coefficients go to zero",
        "Prevents overfitting and reduces training time",
        "Model always underfits"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Early stopping halts training when loss improvement slows, improving generalization."
    },
    {
      "id": 64,
      "questionText": "Scenario: Logistic Regression applied to dataset with skewed target. Observation?",
      "options": [
        "Use class weights or resampling to balance predictions",
        "Minority class ignored automatically",
        "All predictions become majority class",
        "Model fails"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Adjusting for skewed targets helps prevent biased predictions toward majority class."
    },
    {
      "id": 65,
      "questionText": "Scenario: Logistic Regression applied with categorical features. Observation?",
      "options": [
        "Model ignores categorical features",
        "Training fails",
        "Categorical features must be encoded numerically",
        "Model handles categories automatically"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Logistic Regression requires numeric input, so categories need encoding (e.g., one-hot)."
    },
    {
      "id": 66,
      "questionText": "Scenario: Logistic Regression applied with too many irrelevant features. Observation?",
      "options": [
        "Model ignores irrelevant features automatically",
        "Model overfits regardless",
        "Training fails",
        "Regularization reduces effect of irrelevant features"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Regularization helps suppress coefficients of uninformative features."
    },
    {
      "id": 67,
      "questionText": "Scenario: Logistic Regression applied with L1 and L2 combined. Observation?",
      "options": [
        "ElasticNet balances sparsity and shrinkage",
        "All coefficients become zero",
        "Model ignores features",
        "Training fails"
      ],
      "correctAnswerIndex": 0,
      "explanation": "ElasticNet combines L1 and L2 penalties to balance feature selection and coefficient shrinkage."
    },
    {
      "id": 68,
      "questionText": "Scenario: Logistic Regression applied with adjusted threshold for minority class. Observation?",
      "options": [
        "Precision decreases automatically",
        "Recall of minority class improves",
        "All predictions become majority class",
        "Model fails"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Lowering threshold increases positive predictions, improving recall for minority class."
    },
    {
      "id": 69,
      "questionText": "Scenario: Logistic Regression applied with small dataset. Observation?",
      "options": [
        "Model underfits automatically",
        "Training fails",
        "Regularization stabilizes coefficients and reduces variance",
        "Model ignores features"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Small datasets are prone to overfitting; regularization improves generalization."
    },
    {
      "id": 70,
      "questionText": "Scenario: Logistic Regression applied with non-linear feature transformations. Observation?",
      "options": [
        "Training fails",
        "Model ignores non-linear features",
        "Non-linear terms help model complex relationships",
        "Predictions remain linear"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Polynomial or interaction terms allow Logistic Regression to capture non-linear relationships."
    },
    {
      "id": 71,
      "questionText": "Scenario: Logistic Regression applied with continuous target mistakenly. Observation?",
      "options": [
        "Model ignores continuous targets",
        "Model works fine",
        "Training fails",
        "Logistic Regression is inappropriate; should use Linear Regression"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Logistic Regression predicts probabilities for categorical outcomes, not continuous values."
    },
    {
      "id": 72,
      "questionText": "Scenario: Logistic Regression applied with L2 regularization too strong. Observation?",
      "options": [
        "Training fails",
        "Model ignores features",
        "Coefficients increase automatically",
        "Model may underfit due to overly shrunk coefficients"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Excessive regularization reduces coefficient magnitude, potentially underfitting."
    },
    {
      "id": 73,
      "questionText": "Scenario: Logistic Regression applied to imbalanced multiclass problem. Observation?",
      "options": [
        "Training fails",
        "Class weighting or resampling recommended for each class",
        "All predictions go to majority class",
        "Model ignores minority classes"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Balanced weighting improves prediction performance for minority classes."
    },
    {
      "id": 74,
      "questionText": "Scenario: Logistic Regression applied with very high learning rate. Observation?",
      "options": [
        "Gradient descent may diverge",
        "Model ignores features",
        "Predictions remain constant",
        "Model converges perfectly"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Too high learning rate causes optimization to overshoot, preventing convergence."
    },
    {
      "id": 75,
      "questionText": "Scenario: Logistic Regression applied with probability calibration methods. Observation?",
      "options": [
        "Training fails",
        "Calibration has no effect",
        "Platt scaling or isotonic regression improves predicted probabilities",
        "Model ignores calibration"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Probability calibration aligns predicted probabilities with true outcomes, improving reliability."
    },
    {
      "id": 76,
      "questionText": "Scenario: Logistic Regression applied with small training data and no regularization. Observation?",
      "options": [
        "Model may overfit due to high variance",
        "Training fails",
        "Model underfits automatically",
        "Model ignores features"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Small datasets can cause overfitting; regularization helps stabilize coefficients."
    },
    {
      "id": 77,
      "questionText": "Scenario: Logistic Regression applied with a feature highly correlated with target. Observation?",
      "options": [
        "Model ignores the feature",
        "Training fails",
        "Model coefficient will likely be significant",
        "Regularization removes feature automatically"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Highly predictive features typically get larger coefficients, unless heavily regularized."
    },
    {
      "id": 78,
      "questionText": "Scenario: Logistic Regression applied with overcomplete features (more features than samples). Observation?",
      "options": [
        "Training fails automatically",
        "Regularization is essential to prevent overfitting",
        "Model always underfits",
        "All features ignored"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Too many features relative to samples increase overfitting risk; regularization stabilizes model."
    },
    {
      "id": 79,
      "questionText": "Scenario: Logistic Regression applied with extreme class imbalance. Observation?",
      "options": [
        "Minority class predictions improve automatically",
        "Predictions dominated by majority class without class weighting",
        "Training fails",
        "All probabilities become 0.5"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Without adjustments, the model predicts the majority class most of the time."
    },
    {
      "id": 80,
      "questionText": "Scenario: Logistic Regression applied to multiclass problem using one-vs-rest. Observation?",
      "options": [
        "Binary logistic regression fails automatically",
        "Training fails",
        "Each class is treated as positive against all others",
        "Only majority class is predicted"
      ],
      "correctAnswerIndex": 2,
      "explanation": "One-vs-rest handles multiclass by training separate classifiers for each class."
    },
    {
      "id": 81,
      "questionText": "Scenario: Logistic Regression applied with very high regularization. Observation?",
      "options": [
        "Predictions become perfect",
        "Coefficients shrink too much; model may underfit",
        "Coefficients increase automatically",
        "Training fails"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Strong regularization reduces coefficient magnitude excessively, potentially underfitting."
    },
    {
      "id": 82,
      "questionText": "Scenario: Logistic Regression applied with a categorical feature incorrectly encoded as ordinal. Observation?",
      "options": [
        "Model ignores feature automatically",
        "Training fails",
        "Model may misinterpret ordering; predictions may be biased",
        "Predictions remain correct"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Ordinal encoding imposes an artificial order; one-hot encoding is better for nominal features."
    },
    {
      "id": 83,
      "questionText": "Scenario: Logistic Regression applied with overlapping class distributions. Observation?",
      "options": [
        "Training fails",
        "Model may have misclassifications; probabilities indicate uncertainty",
        "Model ignores overlapping features",
        "All predictions are correct"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Overlap leads to inherent classification errors; logistic regression outputs probability estimates reflecting uncertainty."
    },
    {
      "id": 84,
      "questionText": "Scenario: Logistic Regression applied with threshold set very high (0.9). Observation?",
      "options": [
        "Few positives predicted; recall decreases",
        "Training fails",
        "All predictions become positive",
        "Model underfits automatically"
      ],
      "correctAnswerIndex": 0,
      "explanation": "High threshold reduces positive predictions, improving precision but lowering recall."
    },
    {
      "id": 85,
      "questionText": "Scenario: Logistic Regression applied with L1 regularization on sparse dataset. Observation?",
      "options": [
        "All coefficients increase",
        "Model ignores sparse features",
        "Training fails automatically",
        "Some coefficients shrink to zero, performing feature selection"
      ],
      "correctAnswerIndex": 3,
      "explanation": "L1 encourages sparsity, zeroing out uninformative features."
    },
    {
      "id": 86,
      "questionText": "Scenario: Logistic Regression applied with feature scaling not applied. Observation?",
      "options": [
        "Model fails automatically",
        "Optimization may be slower but predictions unaffected",
        "Predictions become invalid",
        "Coefficients ignored"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Scaling affects optimization speed, not the final probability outputs."
    },
    {
      "id": 87,
      "questionText": "Scenario: Logistic Regression applied with learning rate too low. Observation?",
      "options": [
        "Predictions remain constant",
        "Training fails",
        "Model underfits automatically",
        "Convergence is slow but eventual solution correct"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Small learning rate slows gradient descent but does not prevent eventual convergence."
    },
    {
      "id": 88,
      "questionText": "Scenario: Logistic Regression applied to dataset with multicollinearity. Observation?",
      "options": [
        "Coefficients unstable; variance inflated",
        "Training fails",
        "Model ignores correlated features automatically",
        "Predictions unaffected"
      ],
      "correctAnswerIndex": 0,
      "explanation": "High correlation among features inflates coefficient variance, making estimates unstable."
    },
    {
      "id": 89,
      "questionText": "Scenario: Logistic Regression applied with probability calibration. Observation?",
      "options": [
        "Platt scaling or isotonic regression improves probability estimates",
        "Calibration has no effect",
        "Training fails",
        "Model ignores calibration"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Probability calibration aligns predicted probabilities with actual outcomes."
    },
    {
      "id": 90,
      "questionText": "Scenario: Logistic Regression applied with interaction terms added. Observation?",
      "options": [
        "Training fails",
        "Model can capture combined effect of features",
        "Model ignores interactions",
        "Predictions become random"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Interaction terms allow logistic regression to model dependencies between features."
    },
    {
      "id": 91,
      "questionText": "Scenario: Logistic Regression applied to dataset with outliers. Observation?",
      "options": [
        "Training fails",
        "Predictions unaffected",
        "Model ignores outliers automatically",
        "Outliers may distort coefficients; regularization helps"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Outliers can skew estimates; regularization stabilizes coefficients."
    },
    {
      "id": 92,
      "questionText": "Scenario: Logistic Regression applied with small sample size and large number of features. Observation?",
      "options": [
        "Model underfits automatically",
        "High risk of overfitting; regularization essential",
        "Predictions remain perfect",
        "Training fails"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Many features relative to samples increase variance; regularization prevents overfitting."
    },
    {
      "id": 93,
      "questionText": "Scenario: Logistic Regression applied with multiclass softmax. Observation?",
      "options": [
        "Model ignores extra classes",
        "Training fails",
        "Binary thresholding works automatically",
        "Softmax outputs probabilities for each class"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Softmax generalizes logistic regression to multiple classes, outputting probabilities."
    },
    {
      "id": 94,
      "questionText": "Scenario: Logistic Regression applied with polynomial features. Observation?",
      "options": [
        "Predictions remain linear",
        "Model ignores polynomial terms",
        "Training fails",
        "Can model non-linear relationships between features"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Polynomial terms allow logistic regression to capture non-linear effects."
    },
    {
      "id": 95,
      "questionText": "Scenario: Logistic Regression applied with overfitting on training set. Observation?",
      "options": [
        "Training fails automatically",
        "Model ignores training data",
        "Predictions perfect on test set",
        "Apply regularization or reduce features"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Regularization or feature selection reduces overfitting and improves generalization."
    },
    {
      "id": 96,
      "questionText": "Scenario: Logistic Regression applied to dataset with skewed class distribution. Observation?",
      "options": [
        "Training fails",
        "Predictions always majority class",
        "Use class weights or resampling",
        "Model ignores minority class automatically"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Adjusting for imbalance improves minority class prediction performance."
    },
    {
      "id": 97,
      "questionText": "Scenario: Logistic Regression applied with continuous predictors on very different scales. Observation?",
      "options": [
        "Model fails automatically",
        "Training error zero",
        "Predictions invalid",
        "Scaling helps optimization; predictions unchanged"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Scaling speeds convergence but does not affect model predictions."
    },
    {
      "id": 98,
      "questionText": "Scenario: Logistic Regression applied with threshold adjustment. Observation?",
      "options": [
        "Threshold has no effect",
        "Changing threshold trades off precision and recall",
        "Training fails",
        "Predictions remain constant"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Adjusting threshold changes classification cutoff, affecting false positives and negatives."
    },
    {
      "id": 99,
      "questionText": "Scenario: Logistic Regression applied with noisy data. Observation?",
      "options": [
        "Noise is ignored automatically",
        "Model may misclassify; regularization improves stability",
        "Predictions perfect",
        "Training fails"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Noise affects coefficient estimation; regularization improves generalization."
    },
    {
      "id": 100,
      "questionText": "Scenario: Logistic Regression applied with missing categorical features. Observation?",
      "options": [
        "Model ignores missing categories automatically",
        "Training fails",
        "Predictions unaffected",
        "Imputation or encoding needed before training"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Missing categorical data must be imputed or encoded for logistic regression to work."
    }
  ]
}