{
  "title": "Lasso Regression Mastery: 100 MCQs",
  "description": "A comprehensive set of 100 multiple-choice questions designed to teach and test your understanding of Lasso Regression, from basic linear regression concepts to advanced feature selection, sparsity, regularization, and real-world scenarios.",
  "questions": [
    {
      "id": 1,
      "questionText": "What is the main goal of Lasso Regression?",
      "options": [
        "To predict categories",
        "To find a straight-line relationship and perform feature selection",
        "To compress the data",
        "To find clusters in data"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Lasso Regression adds an L1 penalty, which can shrink some coefficients to exactly zero, performing feature selection while modeling relationships."
    },
    {
      "id": 2,
      "questionText": "Lasso Regression differs from Ridge Regression because it:",
      "options": [
        "Uses L1 penalty instead of L2",
        "Does not require standardization",
        "Cannot handle multicollinearity",
        "Always increases training error"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Lasso uses L1 regularization, which can shrink some coefficients to zero, unlike Ridge which uses L2 and shrinks all coefficients."
    },
    {
      "id": 3,
      "questionText": "Scenario: You have a dataset with 20 features, some irrelevant. Which regression is suitable for automatic feature selection?",
      "options": [
        "Ridge Regression",
        "Linear Regression",
        "Lasso Regression",
        "Polynomial Regression"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Lasso’s L1 penalty can zero out irrelevant features, performing automatic feature selection."
    },
    {
      "id": 4,
      "questionText": "In Lasso Regression, increasing the alpha parameter will:",
      "options": [
        "Ignore correlated features",
        "Shrink more coefficients to zero",
        "Decrease training error and increase test error",
        "Remove the intercept automatically"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Higher alpha strengthens the L1 penalty, increasing sparsity and setting more coefficients exactly to zero."
    },
    {
      "id": 5,
      "questionText": "Why is feature standardization important in Lasso Regression?",
      "options": [
        "It removes noise automatically",
        "Alpha is irrelevant",
        "Intercept is ignored otherwise",
        "L1 penalty depends on coefficient magnitude, which depends on feature scale"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Without standardization, features with large scales dominate the penalty, leading to unfair coefficient shrinkage."
    },
    {
      "id": 6,
      "questionText": "Scenario: Two features are highly correlated. Lasso Regression may:",
      "options": [
        "Select one feature and zero the other",
        "Ignore both",
        "Shrink both equally like Ridge",
        "Fail to converge"
      ],
      "correctAnswerIndex": 0,
      "explanation": "L1 penalty tends to pick one correlated feature and set the other to zero, performing feature selection."
    },
    {
      "id": 7,
      "questionText": "Scenario: Lasso Regression applied with alpha=0. Result?",
      "options": [
        "Removes multicollinearity",
        "Performs feature selection",
        "Reduces variance",
        "Behaves like Linear Regression"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Alpha=0 removes the L1 penalty, reducing Lasso to standard Linear Regression."
    },
    {
      "id": 8,
      "questionText": "Scenario: Lasso Regression applied to polynomial features with high degree. Main effect?",
      "options": [
        "Eliminates low-degree terms automatically",
        "Increases training error only",
        "Removes intercept",
        "Controls overfitting by zeroing some coefficients"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Lasso shrinks some high-degree term coefficients to zero, reducing overfitting."
    },
    {
      "id": 9,
      "questionText": "Scenario: Lasso Regression applied on dataset with missing values. Action?",
      "options": [
        "Remove alpha",
        "Impute missing values before Lasso",
        "L1 penalty handles missing automatically",
        "Ignore missing values"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Lasso requires complete data; missing values should be imputed or removed first."
    },
    {
      "id": 10,
      "questionText": "Scenario: Lasso Regression applied on standardized dataset. Alpha too high. Result?",
      "options": [
        "Intercept removed automatically",
        "Coefficients remain unchanged",
        "Low training error, high variance",
        "Many coefficients set to zero, potential underfitting"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Excessive regularization shrinks many coefficients to zero, increasing bias."
    },
    {
      "id": 11,
      "questionText": "Scenario: Lasso vs Ridge on dataset with irrelevant features. Observation?",
      "options": [
        "Ridge eliminates features; Lasso does not",
        "Ridge shrinks coefficients but keeps them non-zero; Lasso may zero irrelevant features",
        "Both produce identical results",
        "Alpha irrelevant"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Lasso performs feature selection while Ridge shrinks coefficients but retains all features."
    },
    {
      "id": 12,
      "questionText": "Scenario: Lasso Regression applied to time-series data with lag features. Standardization importance?",
      "options": [
        "Ensures fair penalty for all lag features",
        "Alpha irrelevant",
        "Intercept ignored otherwise",
        "Training error minimized automatically"
      ],
      "correctAnswerIndex": 0,
      "explanation": "L1 penalty affects coefficients fairly only if features are standardized."
    },
    {
      "id": 13,
      "questionText": "Scenario: Lasso Regression applied to one-hot encoded categorical variables. Concern?",
      "options": [
        "May zero some dummy variables while keeping others",
        "Intercept removed automatically",
        "No need for scaling",
        "Alpha irrelevant"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Lasso may select one dummy feature and set others to zero, performing feature selection."
    },
    {
      "id": 14,
      "questionText": "Scenario: Lasso Regression applied to high-dimensional dataset (features > samples). Advantage?",
      "options": [
        "Training error minimal",
        "Can produce sparse model, eliminating irrelevant features",
        "Cannot converge",
        "Removes intercept"
      ],
      "correctAnswerIndex": 1,
      "explanation": "L1 penalty creates sparsity, which is helpful in high-dimensional problems."
    },
    {
      "id": 15,
      "questionText": "Scenario: Lasso Regression applied with cross-validation. Purpose of cross-validation?",
      "options": [
        "Eliminate correlated features",
        "Always minimize training error",
        "Select optimal alpha to balance bias-variance tradeoff",
        "Ignore feature scaling"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Cross-validation identifies alpha that minimizes validation/test error for better generalization."
    },
    {
      "id": 16,
      "questionText": "Scenario: Lasso Regression applied to noisy dataset. Observed smaller coefficients than Linear Regression. Why?",
      "options": [
        "Alpha zero",
        "Noise ignored automatically",
        "L1 penalty shrinks some coefficients to zero, reducing variance",
        "Intercept removed"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Regularization reduces sensitivity to noise, shrinking coefficients and improving generalization."
    },
    {
      "id": 17,
      "questionText": "Scenario: Lasso Regression vs Elastic Net. Main difference?",
      "options": [
        "Elastic Net ignores feature selection",
        "Lasso uses L2",
        "Elastic Net uses L1 only",
        "Elastic Net combines L1 and L2, useful when correlated features exist"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Elastic Net combines L1 and L2 penalties, balancing feature selection and coefficient shrinkage."
    },
    {
      "id": 18,
      "questionText": "Scenario: Lasso Regression applied to correlated features. Observation?",
      "options": [
        "Shrinks coefficients equally",
        "Tends to select one and zero others",
        "Fails to converge",
        "Removes intercept"
      ],
      "correctAnswerIndex": 1,
      "explanation": "L1 penalty promotes sparsity, often selecting one feature from correlated groups."
    },
    {
      "id": 19,
      "questionText": "Scenario: Lasso Regression applied with very small alpha. Effect?",
      "options": [
        "High sparsity",
        "Fails to converge",
        "Minimal regularization, behaves like Linear Regression",
        "Intercept removed"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Small alpha means weak L1 penalty; model behaves like Linear Regression with minimal feature selection."
    },
    {
      "id": 20,
      "questionText": "Scenario: Lasso Regression applied to polynomial features. High-degree coefficients are large. Solution?",
      "options": [
        "Increase alpha to shrink some coefficients to zero",
        "Ignore intercept",
        "Decrease alpha",
        "Remove low-degree terms"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Higher alpha reduces overfitting by zeroing some large coefficients from high-degree terms."
    },
    {
      "id": 21,
      "questionText": "Scenario: Lasso Regression applied to dataset with irrelevant features. Test error high. Solution?",
      "options": [
        "Ignore irrelevant features",
        "Increase alpha excessively",
        "Alpha tuning via cross-validation, or consider Elastic Net",
        "Decrease alpha to zero"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Cross-validation or Elastic Net can select relevant features and improve generalization."
    },
    {
      "id": 22,
      "questionText": "Scenario: Lasso Regression applied to dataset with standardized features. Correlated features coefficients?",
      "options": [
        "One selected, others may be zero",
        "Fails to converge",
        "All coefficients equal",
        "Intercept removed automatically"
      ],
      "correctAnswerIndex": 0,
      "explanation": "L1 penalty often selects one correlated feature and zeros others."
    },
    {
      "id": 23,
      "questionText": "Scenario: Lasso Regression applied on large dataset. Why standardize features?",
      "options": [
        "Data shrunk automatically",
        "Alpha irrelevant",
        "Intercept removed otherwise",
        "L1 penalty treats all features fairly only if scaled"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Without standardization, large-scale features dominate the penalty."
    },
    {
      "id": 24,
      "questionText": "Scenario: Lasso Regression applied to dataset with missing values. Action?",
      "options": [
        "Remove alpha",
        "Ignore missing values",
        "Impute missing values first",
        "L1 handles missing automatically"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Lasso cannot handle missing values; imputation or removal is required."
    },
    {
      "id": 25,
      "questionText": "Scenario: Lasso Regression applied with high alpha. Many coefficients zero. Risk?",
      "options": [
        "Intercept ignored",
        "Underfitting due to excessive sparsity",
        "Overfitting",
        "Training error minimized"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Too high alpha increases bias and underfits the data."
    },
    {
      "id": 26,
      "questionText": "Scenario: Lasso Regression applied to dataset with 100 features, many irrelevant. Observation: only 20 features have non-zero coefficients. Reason?",
      "options": [
        "Alpha too small",
        "Training error minimized",
        "Intercept removed",
        "L1 penalty induces sparsity, zeroing irrelevant features"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Lasso’s L1 penalty shrinks some coefficients to exactly zero, effectively performing feature selection."
    },
    {
      "id": 27,
      "questionText": "Scenario: Lasso Regression applied to highly correlated features. Observation: model selects some features and zeros others. Advantage?",
      "options": [
        "Intercept removed automatically",
        "All features retained",
        "Reduces multicollinearity impact and produces sparse model",
        "Increases variance"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Lasso selects one feature from a correlated group, reducing multicollinearity and producing a simpler model."
    },
    {
      "id": 28,
      "questionText": "Scenario: Lasso Regression applied with cross-validation on dataset with noisy features. Best practice?",
      "options": [
        "Always use alpha=1",
        "Select alpha minimizing validation/test error",
        "Remove polynomial terms",
        "Ignore feature scaling"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Cross-validation finds alpha that balances bias and variance, improving generalization on noisy data."
    },
    {
      "id": 29,
      "questionText": "Scenario: Lasso Regression applied to polynomial regression of degree 8. Observation: some high-degree term coefficients zeroed. Why?",
      "options": [
        "Intercept removed",
        "Training error minimized",
        "Polynomial terms ignored automatically",
        "L1 penalty shrinks less important coefficients to zero, controlling overfitting"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Lasso penalizes large coefficients, eliminating less important high-degree terms to prevent overfitting."
    },
    {
      "id": 30,
      "questionText": "Scenario: Lasso Regression applied to dataset with one-hot encoded categorical features. Observation: some dummy variables zeroed. Effect?",
      "options": [
        "Training error increases",
        "All features retained",
        "Automatic feature selection among categorical levels",
        "Intercept removed"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Lasso can zero some dummy variables, selecting the most predictive categories."
    },
    {
      "id": 31,
      "questionText": "Scenario: Lasso Regression applied to dataset with features in different units. Observation: large coefficients for small-scale features. Cause?",
      "options": [
        "Data uncorrelated",
        "Intercept removed",
        "Alpha too low",
        "L1 penalty is unfair without standardization"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Without standardization, features with small scales are penalized less, leading to larger coefficients."
    },
    {
      "id": 32,
      "questionText": "Scenario: Lasso Regression applied to time-series lag features. Standardization importance?",
      "options": [
        "Intercept ignored",
        "Training error minimized automatically",
        "Alpha irrelevant",
        "Ensures fair L1 penalty across features"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Standardization ensures all features contribute fairly to the penalty."
    },
    {
      "id": 33,
      "questionText": "Scenario: Lasso Regression applied with alpha too small. Observation?",
      "options": [
        "Fails to converge",
        "Many coefficients zero",
        "Minimal sparsity, behaves like Linear Regression",
        "Intercept removed"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Small alpha provides weak L1 penalty; few or no coefficients are zeroed."
    },
    {
      "id": 34,
      "questionText": "Scenario: Lasso Regression applied to dataset with missing values. Observation: model cannot train. Solution?",
      "options": [
        "Increase alpha",
        "Ignore missing values",
        "Impute missing values before Lasso",
        "Decrease alpha"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Lasso requires complete data; missing values must be imputed or removed before training."
    },
    {
      "id": 35,
      "questionText": "Scenario: Lasso Regression applied to dataset with highly noisy features. Observation: fewer non-zero coefficients than Ridge. Why?",
      "options": [
        "Alpha irrelevant",
        "Intercept removed",
        "L1 penalty zeroes some coefficients, reducing variance",
        "Training error minimized"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Lasso induces sparsity by zeroing less important coefficients, effectively reducing variance."
    },
    {
      "id": 36,
      "questionText": "Scenario: Lasso Regression applied to dataset with polynomial features of degree 10. Observation: high-degree terms zeroed. Effect?",
      "options": [
        "Intercept removed",
        "Training error minimized",
        "Low-degree terms ignored",
        "Controls overfitting by eliminating less important terms"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Lasso shrinks high-degree coefficients to zero, reducing overfitting and model complexity."
    },
    {
      "id": 37,
      "questionText": "Scenario: Lasso Regression applied to dataset with 1000 features, alpha tuned via cross-validation. Observation: 200 features non-zero. Interpretation?",
      "options": [
        "Intercept removed",
        "Model underfits",
        "Optimal alpha balances sparsity and generalization",
        "Training error high"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Cross-validation selects alpha that keeps predictive features while zeroing irrelevant ones."
    },
    {
      "id": 38,
      "questionText": "Scenario: Lasso Regression vs Ridge on dataset with correlated features. Observation?",
      "options": [
        "Ridge eliminates features; Lasso does not",
        "Lasso selects some features and zeros others; Ridge shrinks all coefficients",
        "Alpha irrelevant",
        "Both produce sparse models"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Lasso promotes sparsity and feature selection; Ridge keeps all correlated features."
    },
    {
      "id": 39,
      "questionText": "Scenario: Lasso Regression applied to dataset with irrelevant features. Test error high. Recommended solution?",
      "options": [
        "Increase alpha excessively",
        "Ignore irrelevant features",
        "Decrease alpha to zero",
        "Adjust alpha via cross-validation or use Elastic Net"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Cross-validation tuning or Elastic Net can remove irrelevant features while balancing regularization."
    },
    {
      "id": 40,
      "questionText": "Scenario: Lasso Regression applied on standardized features. Observation: correlated feature coefficients? ",
      "options": [
        "Intercept removed",
        "One selected, others zeroed",
        "Fail to converge",
        "All coefficients equal"
      ],
      "correctAnswerIndex": 1,
      "explanation": "L1 penalty selects one correlated feature and zeros the others."
    },
    {
      "id": 41,
      "questionText": "Scenario: Lasso Regression applied to high-dimensional dataset (features > samples). Advantage?",
      "options": [
        "Produces sparse model, eliminating irrelevant features",
        "Intercept removed",
        "Cannot converge",
        "Training error minimal"
      ],
      "correctAnswerIndex": 0,
      "explanation": "L1 penalty shrinks unimportant coefficients to zero, useful in high-dimensional problems."
    },
    {
      "id": 42,
      "questionText": "Scenario: Lasso Regression applied with very high alpha. Observation?",
      "options": [
        "High variance",
        "Intercept ignored",
        "Many coefficients zeroed, possible underfitting",
        "Training error minimized"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Excessive regularization increases bias, underfitting the model."
    },
    {
      "id": 43,
      "questionText": "Scenario: Lasso Regression applied with cross-validation. Purpose?",
      "options": [
        "Always minimize training error",
        "Ignore standardization",
        "Select alpha that minimizes validation/test error",
        "Remove correlated features"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Cross-validation identifies alpha that optimally balances bias and variance."
    },
    {
      "id": 44,
      "questionText": "Scenario: Lasso Regression applied to polynomial regression. Observation: low-degree term coefficients non-zero, high-degree zero. Effect?",
      "options": [
        "Low-degree terms ignored",
        "Training error minimized",
        "Reduces overfitting by removing less important high-degree terms",
        "Intercept removed"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Lasso controls overfitting by penalizing and zeroing high-degree terms."
    },
    {
      "id": 45,
      "questionText": "Scenario: Lasso Regression applied to dataset with missing values. Recommended practice?",
      "options": [
        "Increase alpha",
        "Impute missing values before training",
        "Ignore missing values",
        "Decrease alpha"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Lasso cannot handle missing data; it must be imputed or cleaned first."
    },
    {
      "id": 46,
      "questionText": "Scenario: Lasso Regression applied on dataset with noisy features. Observation: fewer non-zero coefficients than Ridge. Why?",
      "options": [
        "Intercept removed",
        "Training error minimized",
        "L1 penalty zeroes some coefficients, reducing variance",
        "Alpha irrelevant"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Lasso induces sparsity, setting some coefficients to zero, which reduces variance in noisy datasets."
    },
    {
      "id": 47,
      "questionText": "Scenario: Lasso Regression applied to dataset with one-hot encoded features. Observation: some dummy variables zeroed. Effect?",
      "options": [
        "Intercept removed",
        "Feature selection among categories",
        "All features retained",
        "Training error increased"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Lasso may zero less predictive categories, retaining only important levels."
    },
    {
      "id": 48,
      "questionText": "Scenario: Lasso Regression applied to polynomial features of degree 12. Observation: high-degree coefficients zeroed. Effect?",
      "options": [
        "Reduces overfitting and model complexity",
        "Intercept removed",
        "Low-degree terms ignored",
        "Training error minimized"
      ],
      "correctAnswerIndex": 0,
      "explanation": "High-degree coefficients are penalized, reducing model complexity and overfitting."
    },
    {
      "id": 49,
      "questionText": "Scenario: Lasso Regression applied to dataset with highly correlated features. Observation: some features zeroed. Advantage?",
      "options": [
        "Reduces multicollinearity and simplifies model",
        "Fails to converge",
        "Increases variance",
        "Intercept removed"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Lasso selects one feature from correlated group, producing a simpler, less collinear model."
    },
    {
      "id": 50,
      "questionText": "Scenario: Lasso Regression applied with small alpha. Observation?",
      "options": [
        "Minimal feature selection; behaves like Linear Regression",
        "Fails to converge",
        "Many coefficients zeroed",
        "Intercept removed"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Small alpha provides weak L1 penalty; the model retains most features with minimal sparsity."
    },
    {
      "id": 51,
      "questionText": "Scenario: Lasso Regression applied to a medical dataset with 500 features. Many coefficients zeroed. Interpretation?",
      "options": [
        "Training error is zero",
        "L1 penalty removed irrelevant features, simplifying the model",
        "Model underfits due to small dataset",
        "Intercept removed automatically"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Lasso shrinks less important features to zero, keeping only predictive variables, which is useful in high-dimensional data."
    },
    {
      "id": 52,
      "questionText": "Scenario: Lasso Regression applied with correlated features. Observation: only one feature from each correlated group selected. Advantage?",
      "options": [
        "Reduces multicollinearity and produces sparse solution",
        "All features retained",
        "Intercept removed",
        "Model overfits"
      ],
      "correctAnswerIndex": 0,
      "explanation": "L1 penalty selects one feature and zeros others, reducing multicollinearity and simplifying interpretation."
    },
    {
      "id": 53,
      "questionText": "Scenario: Lasso Regression applied with cross-validation. Optimal alpha minimizes:",
      "options": [
        "Validation/test error",
        "Training error",
        "Intercept value",
        "Number of non-zero features only"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Cross-validation selects the alpha that balances bias-variance and gives best generalization on unseen data."
    },
    {
      "id": 54,
      "questionText": "Scenario: Lasso Regression applied on polynomial regression of degree 12. Observation: high-degree terms zeroed. Effect?",
      "options": [
        "Low-degree terms ignored",
        "Reduces overfitting by eliminating less important terms",
        "Training error minimized",
        "Intercept removed"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Lasso penalizes high-degree coefficients, zeroing unimportant terms to prevent overfitting."
    },
    {
      "id": 55,
      "questionText": "Scenario: Lasso Regression applied to time-series dataset with lag features. Importance of feature standardization?",
      "options": [
        "Alpha irrelevant",
        "Training error minimized automatically",
        "Ensures fair L1 penalty across all lag features",
        "Intercept ignored"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Standardization ensures features on different scales are penalized fairly."
    },
    {
      "id": 56,
      "questionText": "Scenario: Lasso Regression applied to dataset with one-hot encoded categorical features. Observation: some dummy variables zeroed. Effect?",
      "options": [
        "Intercept removed",
        "Training error increased",
        "Automatic feature selection among categories",
        "All features retained"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Lasso may zero less predictive categories, keeping only important levels."
    },
    {
      "id": 57,
      "questionText": "Scenario: Lasso Regression applied to high-dimensional dataset (features > samples). Advantage?",
      "options": [
        "Intercept removed",
        "Cannot converge",
        "Produces sparse model, eliminating irrelevant features",
        "Training error minimal"
      ],
      "correctAnswerIndex": 2,
      "explanation": "L1 penalty zeros unimportant coefficients, which is effective in high-dimensional settings."
    },
    {
      "id": 58,
      "questionText": "Scenario: Lasso Regression applied with alpha too high. Observation?",
      "options": [
        "Training error minimized",
        "High variance",
        "Many coefficients zeroed, potential underfitting",
        "Intercept ignored"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Excessive regularization increases bias, underfitting the model."
    },
    {
      "id": 59,
      "questionText": "Scenario: Lasso Regression vs Ridge Regression. Observation: Lasso zeros some coefficients, Ridge does not. Implication?",
      "options": [
        "Both behave identically",
        "Ridge produces sparse model",
        "Lasso performs feature selection; Ridge does not",
        "Alpha irrelevant"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Lasso can zero out coefficients, effectively performing feature selection; Ridge shrinks coefficients but keeps all features."
    },
    {
      "id": 60,
      "questionText": "Scenario: Lasso Regression applied to dataset with noisy features. Observation: fewer non-zero coefficients than Ridge. Why?",
      "options": [
        "Intercept removed",
        "Alpha irrelevant",
        "L1 penalty zeroes less important coefficients, reducing variance",
        "Training error minimized"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Lasso induces sparsity and reduces variance by eliminating less predictive/noisy features."
    },
    {
      "id": 61,
      "questionText": "Scenario: Lasso Regression applied on dataset with highly correlated features. Observation: some features zeroed. Advantage?",
      "options": [
        "Increases variance",
        "Fails to converge",
        "Intercept removed",
        "Reduces multicollinearity and simplifies model"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Lasso selects one feature from correlated group, producing a simpler, less collinear model."
    },
    {
      "id": 62,
      "questionText": "Scenario: Lasso Regression applied to dataset with missing values. Observation: model cannot train. Recommended solution?",
      "options": [
        "Impute missing values before training",
        "Increase alpha",
        "Decrease alpha",
        "Ignore missing values"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Lasso requires complete data; missing values must be imputed or removed."
    },
    {
      "id": 63,
      "questionText": "Scenario: Lasso Regression applied to polynomial features of degree 10. Observation: high-degree term coefficients zeroed. Effect?",
      "options": [
        "Training error minimized",
        "Low-degree terms ignored",
        "Reduces overfitting and model complexity",
        "Intercept removed"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Lasso shrinks unimportant high-degree coefficients to zero, preventing overfitting."
    },
    {
      "id": 64,
      "questionText": "Scenario: Lasso Regression applied to a dataset with many irrelevant features. Observation: test error high. Recommended solution?",
      "options": [
        "Increase alpha excessively",
        "Decrease alpha to zero",
        "Ignore irrelevant features",
        "Adjust alpha via cross-validation or use Elastic Net"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Cross-validation tuning or Elastic Net helps remove irrelevant features and improves generalization."
    },
    {
      "id": 65,
      "questionText": "Scenario: Lasso Regression applied to standardized features. Observation: correlated feature coefficients?",
      "options": [
        "One selected, others zeroed",
        "All coefficients equal",
        "Intercept removed",
        "Fails to converge"
      ],
      "correctAnswerIndex": 0,
      "explanation": "L1 penalty selects one correlated feature and zeros the others."
    },
    {
      "id": 66,
      "questionText": "Scenario: Lasso Regression applied to high-dimensional data (features > samples). Observation: model converges with sparse solution. Why?",
      "options": [
        "L1 penalty promotes sparsity, retaining only important features",
        "Training error minimized",
        "Intercept removed",
        "Model underfits"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Lasso shrinks less important coefficients to zero, allowing sparse solution even in high-dimensional datasets."
    },
    {
      "id": 67,
      "questionText": "Scenario: Lasso Regression applied to noisy features. Observation: model zeroed several noisy features. Effect?",
      "options": [
        "Reduces variance and improves generalization",
        "Intercept removed",
        "Training error minimized",
        "Alpha irrelevant"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Lasso zeros noisy features, reducing variance and improving generalization."
    },
    {
      "id": 68,
      "questionText": "Scenario: Lasso Regression applied to polynomial features. Observation: only low-degree coefficients retained. Reason?",
      "options": [
        "High-degree coefficients penalized and zeroed by L1",
        "Training error minimized",
        "Intercept removed",
        "Low-degree terms ignored"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Lasso penalizes high-degree coefficients, shrinking unimportant terms to zero."
    },
    {
      "id": 69,
      "questionText": "Scenario: Lasso Regression applied to dataset with one-hot encoded categorical features. Observation: some levels zeroed. Effect?",
      "options": [
        "Feature selection among categories",
        "All levels retained",
        "Intercept removed",
        "Training error increased"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Lasso may zero less predictive categories, retaining only important levels."
    },
    {
      "id": 70,
      "questionText": "Scenario: Lasso Regression applied with alpha too small. Observation?",
      "options": [
        "Few coefficients zeroed; model behaves like Linear Regression",
        "Many coefficients zeroed",
        "Intercept removed",
        "Fails to converge"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Small alpha provides weak L1 penalty; model retains most features with minimal sparsity."
    },
    {
      "id": 71,
      "questionText": "Scenario: Lasso Regression applied to dataset with highly correlated features. Observation: some features zeroed. Effect?",
      "options": [
        "Simplifies model and reduces multicollinearity",
        "Increases variance",
        "Intercept removed",
        "Fails to converge"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Lasso selects one feature from correlated groups, simplifying the model and reducing multicollinearity."
    },
    {
      "id": 72,
      "questionText": "Scenario: Lasso Regression applied with cross-validation on dataset with noisy features. Observation: alpha selected?",
      "options": [
        "Minimizes validation/test error, balances sparsity and generalization",
        "Maximizes training error",
        "Removes correlated features automatically",
        "Intercept ignored"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Cross-validation selects alpha for optimal bias-variance tradeoff."
    },
    {
      "id": 73,
      "questionText": "Scenario: Lasso Regression applied on polynomial features. Observation: high-degree coefficients zeroed. Reason?",
      "options": [
        "L1 penalty shrinks less important terms to zero",
        "Intercept removed",
        "Training error minimized",
        "Low-degree terms ignored"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Lasso controls overfitting by penalizing and zeroing high-degree terms."
    },
    {
      "id": 74,
      "questionText": "Scenario: Lasso Regression applied to high-dimensional dataset. Observation: sparse solution. Advantage?",
      "options": [
        "Improves interpretability and reduces overfitting",
        "Training error minimized",
        "Intercept removed",
        "Model underfits always"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Sparse solution keeps only important features, enhancing interpretability and generalization."
    },
    {
      "id": 75,
      "questionText": "Scenario: Lasso Regression applied with standardized features. Observation: correlated features handled by sparsity. Benefit?",
      "options": [
        "Simpler model with reduced multicollinearity",
        "Training error minimized",
        "Intercept removed",
        "Fails to converge"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Lasso selects only one feature from correlated groups, simplifying the model."
    },
    {
      "id": 76,
      "questionText": "Scenario: Lasso Regression applied to a genomics dataset with 20,000 features and 500 samples. Observation: only 150 features non-zero. Benefit?",
      "options": [
        "Reduces dimensionality and improves interpretability",
        "Training error minimized",
        "Intercept removed",
        "All features retained"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Lasso’s sparsity selects only the most predictive genes, reducing dimensionality and simplifying interpretation."
    },
    {
      "id": 77,
      "questionText": "Scenario: Lasso Regression applied on dataset with highly correlated financial indicators. Observation: only one indicator from each group retained. Advantage?",
      "options": [
        "Reduces multicollinearity and simplifies model",
        "Increases variance",
        "All features retained",
        "Intercept removed"
      ],
      "correctAnswerIndex": 0,
      "explanation": "L1 penalty selects one feature from correlated groups, producing a simpler, less collinear model."
    },
    {
      "id": 78,
      "questionText": "Scenario: Lasso Regression applied with cross-validation. Observation: optimal alpha very high. Effect?",
      "options": [
        "Many coefficients zeroed, risk of underfitting",
        "All coefficients retained",
        "Intercept removed",
        "Training error minimized"
      ],
      "correctAnswerIndex": 0,
      "explanation": "High alpha increases regularization, shrinking many coefficients to zero and potentially underfitting the model."
    },
    {
      "id": 79,
      "questionText": "Scenario: Lasso Regression applied to polynomial regression (degree 15). Observation: high-degree coefficients zeroed. Benefit?",
      "options": [
        "Controls overfitting and reduces model complexity",
        "Training error minimized",
        "Intercept removed",
        "Low-degree terms ignored"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Lasso penalizes high-degree terms, shrinking less important coefficients to zero and preventing overfitting."
    },
    {
      "id": 80,
      "questionText": "Scenario: Lasso Regression applied to dataset with missing values. Action required?",
      "options": [
        "Impute missing values before training",
        "Ignore missing values",
        "Decrease alpha",
        "Increase alpha"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Lasso cannot handle missing data; it must be imputed or removed first."
    },
    {
      "id": 81,
      "questionText": "Scenario: Lasso Regression applied on standardized one-hot encoded categorical features. Observation: some dummy variables zeroed. Effect?",
      "options": [
        "Feature selection among categories",
        "All dummy variables retained",
        "Intercept removed",
        "Training error increased"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Lasso may zero less predictive categories, retaining only important levels."
    },
    {
      "id": 82,
      "questionText": "Scenario: Lasso Regression applied to a noisy dataset. Observation: fewer non-zero coefficients than Ridge. Why?",
      "options": [
        "L1 penalty zeroes less important coefficients, reducing variance",
        "Training error minimized",
        "Intercept removed",
        "Alpha irrelevant"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Lasso induces sparsity, setting some coefficients to zero, which reduces variance in noisy datasets."
    },
    {
      "id": 83,
      "questionText": "Scenario: Lasso Regression vs Elastic Net. When is Elastic Net preferred?",
      "options": [
        "When correlated features need to be retained and feature selection is desired",
        "Always",
        "When features are uncorrelated",
        "When alpha=0"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Elastic Net combines L1 and L2 penalties, balancing sparsity and correlated feature retention."
    },
    {
      "id": 84,
      "questionText": "Scenario: Lasso Regression applied with very small alpha. Observation?",
      "options": [
        "Minimal feature selection; behaves like Linear Regression",
        "Many coefficients zeroed",
        "Intercept removed",
        "Fails to converge"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Small alpha provides weak regularization, retaining most coefficients and minimal sparsity."
    },
    {
      "id": 85,
      "questionText": "Scenario: Lasso Regression applied to polynomial regression with high-degree terms dominating. Observation: high-degree terms zeroed. Benefit?",
      "options": [
        "Reduces overfitting by removing less important terms",
        "Training error minimized",
        "Intercept removed",
        "Low-degree terms ignored"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Lasso penalizes high-degree coefficients, reducing overfitting and improving generalization."
    },
    {
      "id": 86,
      "questionText": "Scenario: Lasso Regression applied to a dataset with 10,000 features, 1,000 samples. Observation: sparse solution. Advantage?",
      "options": [
        "Improves interpretability and reduces computational cost",
        "Training error minimized",
        "Intercept removed",
        "Fails to converge"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Sparse solution retains only important features, improving interpretability and computational efficiency."
    },
    {
      "id": 87,
      "questionText": "Scenario: Lasso Regression applied to dataset with correlated features. Observation: some coefficients zeroed. Effect?",
      "options": [
        "Simplifies model and reduces multicollinearity",
        "Increases variance",
        "Intercept removed",
        "Training error minimized"
      ],
      "correctAnswerIndex": 0,
      "explanation": "L1 penalty selects one feature from correlated groups, producing a simpler, more stable model."
    },
    {
      "id": 88,
      "questionText": "Scenario: Lasso Regression applied with cross-validation. Observation: alpha selected minimizes:",
      "options": [
        "Validation/test error",
        "Training error",
        "Number of features",
        "Intercept value"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Cross-validation selects alpha to balance bias-variance and achieve optimal generalization."
    },
    {
      "id": 89,
      "questionText": "Scenario: Lasso Regression applied on standardized features with highly correlated groups. Observation: some features zeroed. Reason?",
      "options": [
        "L1 penalty favors sparsity, selecting one feature from each correlated group",
        "Intercept removed",
        "Training error minimized",
        "All coefficients retained"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Lasso promotes sparsity, zeroing less important features in correlated groups."
    },
    {
      "id": 90,
      "questionText": "Scenario: Lasso Regression applied on dataset with polynomial features. Observation: only low-degree coefficients retained. Why?",
      "options": [
        "High-degree coefficients penalized and zeroed",
        "Training error minimized",
        "Intercept removed",
        "Low-degree terms ignored"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Lasso penalizes less important high-degree coefficients, preventing overfitting."
    },
    {
      "id": 91,
      "questionText": "Scenario: Lasso Regression applied to dataset with missing values. Observation: model fails. Action required?",
      "options": [
        "Impute missing values first",
        "Ignore missing values",
        "Decrease alpha",
        "Increase alpha"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Lasso requires complete data; missing values must be imputed or removed."
    },
    {
      "id": 92,
      "questionText": "Scenario: Lasso Regression applied with alpha very high. Observation: almost all coefficients zeroed. Risk?",
      "options": [
        "Underfitting due to excessive sparsity",
        "Overfitting",
        "Intercept removed",
        "Training error minimized"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Excessive alpha increases bias and underfits the model."
    },
    {
      "id": 93,
      "questionText": "Scenario: Lasso Regression applied to standardized one-hot encoded categorical variables. Observation: some levels zeroed. Effect?",
      "options": [
        "Simplifies categorical feature selection",
        "Intercept removed",
        "All levels retained",
        "Training error increased"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Lasso zeros less predictive categories, keeping only important levels."
    },
    {
      "id": 94,
      "questionText": "Scenario: Lasso Regression applied to dataset with 100 correlated features. Observation: only a few selected. Advantage?",
      "options": [
        "Reduces multicollinearity and simplifies interpretation",
        "Increases variance",
        "Intercept removed",
        "Training error minimized"
      ],
      "correctAnswerIndex": 0,
      "explanation": "L1 penalty selects a subset of features from correlated groups, reducing complexity."
    },
    {
      "id": 95,
      "questionText": "Scenario: Lasso Regression applied to polynomial features of degree 20. Observation: only low-degree terms retained. Reason?",
      "options": [
        "High-degree terms penalized and zeroed",
        "Intercept removed",
        "Training error minimized",
        "Low-degree terms ignored"
      ],
      "correctAnswerIndex": 0,
      "explanation": "L1 penalty zeroes less important high-degree coefficients to control overfitting."
    },
    {
      "id": 96,
      "questionText": "Scenario: Lasso Regression applied to high-dimensional sparse data. Observation: sparse solution obtained. Benefit?",
      "options": [
        "Interpretability and reduced computational cost",
        "Training error minimized",
        "Intercept removed",
        "Model fails to converge"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Sparse solution retains only relevant features, improving interpretability and efficiency."
    },
    {
      "id": 97,
      "questionText": "Scenario: Lasso Regression applied to dataset with noisy features. Observation: model zeroed some noisy features. Effect?",
      "options": [
        "Reduces variance and improves generalization",
        "Intercept removed",
        "Training error minimized",
        "All features retained"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Lasso removes less predictive/noisy features, reducing variance and improving generalization."
    },
    {
      "id": 98,
      "questionText": "Scenario: Lasso Regression applied with cross-validation. Observation: alpha selected reduces validation error. Advantage?",
      "options": [
        "Balances bias-variance tradeoff and improves generalization",
        "Minimizes training error only",
        "Removes correlated features automatically",
        "Intercept removed"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Cross-validation selects alpha that optimally balances bias and variance for unseen data."
    },
    {
      "id": 99,
      "questionText": "Scenario: Lasso Regression applied to one-hot encoded dataset with missing values. Recommended action?",
      "options": [
        "Impute missing values before training",
        "Ignore missing values",
        "Decrease alpha",
        "Increase alpha"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Lasso cannot handle missing data; it must be imputed or removed first."
    },
    {
      "id": 100,
      "questionText": "Scenario: Lasso Regression applied to dataset with high multicollinearity, noisy features, and many irrelevant variables. Best approach?",
      "options": [
        "Standardize features, tune alpha via cross-validation, consider Elastic Net if feature selection needed",
        "Use Linear Regression",
        "Ignore alpha",
        "Remove L1 penalty"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Standardization, cross-validated Lasso, or Elastic Net handles noise, multicollinearity, and feature selection effectively."
    }
  ]
}