{
  "title": "Ridge Regression Mastery: 100 MCQs",
  "description": "A comprehensive set of multiple-choice questions designed to teach and test your understanding of Ridge Regression, starting from basic concepts to advanced scenario-based problems.",
  "questions": [
    {
      "id": 1,
      "questionText": "What is the main purpose of Ridge Regression?",
      "options": [
        "To reduce bias in predictions",
        "To prevent overfitting by adding L2 regularization",
        "To increase the complexity of the model",
        "To reduce the number of features"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Ridge Regression adds L2 regularization to penalize large coefficients, helping prevent overfitting."
    },
    {
      "id": 2,
      "questionText": "Which term is added to the loss function in Ridge Regression?",
      "options": [
        "Sum of squared residuals",
        "Sum of absolute values of coefficients",
        "Sum of squares of coefficients multiplied by alpha",
        "Log-likelihood term"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Ridge Regression adds alpha * sum of squared coefficients to the standard squared error loss."
    },
    {
      "id": 3,
      "questionText": "Ridge Regression is a type of:",
      "options": [
        "Linear Regression with L1 regularization",
        "Linear Regression with L2 regularization",
        "Logistic Regression",
        "Decision Tree Regression"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Ridge Regression is Linear Regression with L2 regularization to shrink coefficients."
    },
    {
      "id": 4,
      "questionText": "Which problem does Ridge Regression primarily address?",
      "options": [
        "Underfitting",
        "Overfitting due to multicollinearity",
        "Non-linear data",
        "Categorical features"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Ridge Regression reduces overfitting when features are highly correlated."
    },
    {
      "id": 5,
      "questionText": "How does Ridge Regression shrink coefficients?",
      "options": [
        "By adding noise to data",
        "By adding a penalty proportional to the square of coefficients",
        "By removing features randomly",
        "By using stepwise regression"
      ],
      "correctAnswerIndex": 1,
      "explanation": "The L2 penalty in Ridge Regression discourages large coefficients."
    },
    {
      "id": 6,
      "questionText": "What happens if alpha=0 in Ridge Regression?",
      "options": [
        "It becomes standard Linear Regression",
        "It becomes Lasso Regression",
        "It ignores the bias term",
        "It fails to converge"
      ],
      "correctAnswerIndex": 0,
      "explanation": "With alpha=0, the L2 penalty is removed, so Ridge Regression is equivalent to Linear Regression."
    },
    {
      "id": 7,
      "questionText": "Ridge Regression is particularly useful when:",
      "options": [
        "The dataset has multicollinearity among features",
        "The dataset has very few samples",
        "There is no noise in data",
        "You want sparse coefficients"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Ridge Regression handles multicollinearity by penalizing large correlated coefficients."
    },
    {
      "id": 8,
      "questionText": "Which metric is commonly used to select the optimal alpha in Ridge Regression?",
      "options": [
        "R-squared",
        "Mean Squared Error on cross-validation",
        "Correlation coefficient",
        "Number of features selected"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Cross-validation MSE is used to find the alpha that balances bias and variance."
    },
    {
      "id": 9,
      "questionText": "What effect does increasing the alpha parameter have?",
      "options": [
        "Increases overfitting",
        "Decreases coefficient values and reduces overfitting",
        "Increases model complexity",
        "Removes features automatically"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Higher alpha increases the penalty on large coefficients, which shrinks them and reduces overfitting."
    },
    {
      "id": 10,
      "questionText": "Why should features be standardized before applying Ridge Regression?",
      "options": [
        "To make computation faster",
        "To give all features equal importance in regularization",
        "To reduce number of samples",
        "To convert all values to integers"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Standardization ensures the penalty treats all features fairly, regardless of scale."
    },
    {
      "id": 11,
      "questionText": "Ridge Regression cannot produce sparse models because:",
      "options": [
        "It uses L1 penalty",
        "It uses L2 penalty which shrinks but does not set coefficients to zero",
        "It ignores regularization",
        "It only works with one feature"
      ],
      "correctAnswerIndex": 1,
      "explanation": "L2 penalty reduces coefficient magnitudes but does not eliminate features completely."
    },
    {
      "id": 12,
      "questionText": "Which scenario favors Ridge Regression over Lasso?",
      "options": [
        "You want feature selection",
        "All features are relevant and correlated",
        "You have very few samples",
        "Your target variable is categorical"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Ridge is better when all features contribute and are correlated; Lasso performs feature selection."
    },
    {
      "id": 13,
      "questionText": "Which of the following is a loss function of Ridge Regression?",
      "options": [
        "Sum of squared errors",
        "Sum of squared errors + alpha * sum of squared coefficients",
        "Sum of absolute errors",
        "Mean absolute percentage error"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Ridge adds the L2 penalty to the usual squared error loss function."
    },
    {
      "id": 14,
      "questionText": "Scenario: Your data has 200 features and 50 samples. Linear Regression overfits. What should you do?",
      "options": [
        "Use Ridge Regression with appropriate alpha",
        "Use Linear Regression without changes",
        "Remove all features",
        "Use logistic regression"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Regularization like Ridge helps prevent overfitting when features outnumber samples."
    },
    {
      "id": 15,
      "questionText": "Scenario: Ridge Regression gives large coefficients even after standardization. Likely reason?",
      "options": [
        "Alpha is too small",
        "Data has no noise",
        "Features are uncorrelated",
        "Model is perfect"
      ],
      "correctAnswerIndex": 0,
      "explanation": "A small alpha means the penalty is weak, so coefficients remain large."
    },
    {
      "id": 16,
      "questionText": "Scenario: After increasing alpha, training error increased but test error decreased. This illustrates:",
      "options": [
        "Bias-variance tradeoff",
        "Overfitting",
        "Underfitting",
        "Multicollinearity"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Increasing alpha increases bias (higher training error) but reduces variance (lower test error)."
    },
    {
      "id": 17,
      "questionText": "Which Python library provides Ridge Regression?",
      "options": [
        "numpy",
        "pandas",
        "scikit-learn",
        "matplotlib"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Scikit-learn provides Ridge regression through sklearn.linear_model.Ridge."
    },
    {
      "id": 18,
      "questionText": "Which parameter in Ridge controls regularization strength?",
      "options": [
        "beta",
        "lambda",
        "alpha",
        "gamma"
      ],
      "correctAnswerIndex": 2,
      "explanation": "In scikit-learn's Ridge, alpha sets the L2 penalty strength."
    },
    {
      "id": 19,
      "questionText": "Ridge Regression reduces multicollinearity by:",
      "options": [
        "Shrinking correlated coefficients",
        "Eliminating features",
        "Adding noise",
        "Creating polynomial features"
      ],
      "correctAnswerIndex": 0,
      "explanation": "L2 regularization shrinks correlated coefficients to reduce instability."
    },
    {
      "id": 20,
      "questionText": "Ridge Regression can be used for:",
      "options": [
        "Regression only",
        "Classification only",
        "Clustering",
        "Principal Component Analysis"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Ridge is an extension of Linear Regression and is used for regression tasks."
    },
    {
      "id": 21,
      "questionText": "Standardizing features before Ridge is important because:",
      "options": [
        "It reduces alpha value automatically",
        "It ensures regularization treats all features equally",
        "It changes the target variable",
        "It creates sparse solutions"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Without standardization, features with larger scales are penalized more than smaller ones."
    },
    {
      "id": 22,
      "questionText": "Scenario: Alpha is set very high. Likely effect on model?",
      "options": [
        "Overfitting",
        "Underfitting",
        "Perfect fit",
        "No effect"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Very high alpha over-penalizes coefficients, increasing bias and underfitting the data."
    },
    {
      "id": 23,
      "questionText": "Which type of regularization does Ridge use?",
      "options": [
        "L1",
        "L2",
        "Elastic Net",
        "Dropout"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Ridge uses L2 regularization to shrink coefficients."
    },
    {
      "id": 24,
      "questionText": "Scenario: Two features are highly correlated. Ridge Regression will:",
      "options": [
        "Randomly select one feature",
        "Shrink their coefficients without eliminating either",
        "Eliminate both features",
        "Increase their coefficients"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Ridge shrinks correlated coefficients but keeps both in the model."
    },
    {
      "id": 25,
      "questionText": "Scenario: Dataset has noisy features. Ridge Regression helps by:",
      "options": [
        "Ignoring noise completely",
        "Reducing coefficient magnitudes to prevent overfitting",
        "Removing noisy features automatically",
        "Converting data to categorical"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Regularization reduces sensitivity to noise, helping the model generalize better."
    },
    {
      "id": 26,
      "questionText": "Scenario: You applied Ridge Regression but your test error is still high. What could help?",
      "options": [
        "Decrease alpha",
        "Increase alpha or try dimensionality reduction",
        "Remove the intercept",
        "Ignore standardization"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Increasing regularization or using PCA/PLS can help improve generalization when test error is high."
    },
    {
      "id": 27,
      "questionText": "Scenario: Two datasets have the same features, but one has highly correlated inputs. Ridge Regression will:",
      "options": [
        "Shrink coefficients more for correlated features",
        "Perform the same on both",
        "Eliminate correlated features",
        "Fail to converge"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Ridge handles multicollinearity by shrinking coefficients of correlated features."
    },
    {
      "id": 28,
      "questionText": "How can you choose the optimal alpha in Ridge Regression?",
      "options": [
        "Random guess",
        "Cross-validation on a range of alpha values",
        "Using R-squared only",
        "Using the number of features"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Cross-validation is used to evaluate model performance for different alpha values and select the best one."
    },
    {
      "id": 29,
      "questionText": "Ridge Regression vs Linear Regression: which statement is true?",
      "options": [
        "Ridge ignores some features",
        "Ridge always has lower training error",
        "Ridge adds L2 penalty to reduce coefficient magnitude",
        "Ridge cannot handle more features than samples"
      ],
      "correctAnswerIndex": 2,
      "explanation": "The L2 penalty in Ridge helps shrink coefficients to reduce overfitting."
    },
    {
      "id": 30,
      "questionText": "Scenario: You have standardized features and apply Ridge Regression with alpha=0.1. Increasing alpha to 10 will:",
      "options": [
        "Increase training error and may decrease test error",
        "Decrease both training and test errors",
        "Have no effect",
        "Eliminate some features automatically"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Higher alpha increases bias (training error) but can reduce variance (improve test error)."
    },
    {
      "id": 31,
      "questionText": "Why is Ridge Regression sensitive to feature scaling?",
      "options": [
        "L2 penalty depends on coefficient magnitude, which depends on feature scale",
        "It uses absolute values",
        "It ignores intercept",
        "It only works with integers"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Without scaling, large-scale features are penalized more than small-scale features."
    },
    {
      "id": 32,
      "questionText": "Scenario: You have a polynomial dataset. Ridge Regression helps by:",
      "options": [
        "Eliminating polynomial terms",
        "Reducing overfitting caused by high-degree terms",
        "Making all coefficients equal",
        "Removing intercept automatically"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Ridge shrinks coefficients of high-degree polynomial terms, reducing overfitting."
    },
    {
      "id": 33,
      "questionText": "Scenario: Ridge Regression and Lasso applied on same dataset. Lasso gives some zero coefficients while Ridge does not. Why?",
      "options": [
        "Ridge uses L1 penalty",
        "Ridge uses L2 penalty which shrinks but doesn’t eliminate coefficients",
        "Lasso ignores correlated features",
        "Ridge ignores alpha"
      ],
      "correctAnswerIndex": 1,
      "explanation": "L2 penalty in Ridge shrinks coefficients, while L1 penalty in Lasso can set them exactly to zero."
    },
    {
      "id": 34,
      "questionText": "Scenario: Your dataset has features with very different scales. What should you do before Ridge Regression?",
      "options": [
        "Normalize or standardize features",
        "Leave features as they are",
        "Add noise to smaller features",
        "Remove largest features"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Standardizing ensures the penalty treats all features equally."
    },
    {
      "id": 35,
      "questionText": "Scenario: You applied Ridge Regression on noisy data. The coefficients are smaller than in Linear Regression. Why?",
      "options": [
        "Ridge ignores noise",
        "L2 penalty shrinks coefficients to reduce overfitting",
        "Noise is removed automatically",
        "Training error increases"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Regularization shrinks coefficients, making the model less sensitive to noise."
    },
    {
      "id": 36,
      "questionText": "Scenario: You have highly correlated features and want some coefficients exactly zero. What should you use?",
      "options": [
        "Ridge Regression",
        "Lasso Regression",
        "Linear Regression",
        "Polynomial Regression"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Lasso uses L1 penalty which can set some coefficients exactly to zero, performing feature selection."
    },
    {
      "id": 37,
      "questionText": "Scenario: Ridge Regression shows underfitting. What adjustment can help?",
      "options": [
        "Decrease alpha",
        "Increase alpha",
        "Remove standardization",
        "Add noise"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Lowering alpha reduces regularization, allowing coefficients to fit data better."
    },
    {
      "id": 38,
      "questionText": "Scenario: Two Ridge models with different alpha are trained. Model A (low alpha) has low training error, high test error. Model B (high alpha) has higher training error, lower test error. This illustrates:",
      "options": [
        "Bias-variance tradeoff",
        "Underfitting",
        "Multicollinearity",
        "Polynomial expansion"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Increasing alpha increases bias (higher training error) but reduces variance (better generalization)."
    },
    {
      "id": 39,
      "questionText": "Scenario: Ridge Regression on dataset with 10,000 features. Most features are irrelevant. Which is better?",
      "options": [
        "Ridge Regression",
        "Lasso Regression",
        "Standard Linear Regression",
        "Decision Tree"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Lasso can eliminate irrelevant features via L1 penalty, producing sparse coefficients."
    },
    {
      "id": 40,
      "questionText": "Scenario: After Ridge Regression, coefficients of correlated features are close but non-zero. This is expected because:",
      "options": [
        "Ridge ignores correlation",
        "L2 penalty shrinks correlated coefficients equally",
        "L1 penalty would do the same",
        "Model is underfitting"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Ridge shrinks coefficients of correlated features similarly, avoiding instability."
    },
    {
      "id": 41,
      "questionText": "Scenario: You want Ridge Regression but with some feature selection. Which method combines L1 and L2 penalties?",
      "options": [
        "Lasso",
        "Elastic Net",
        "Linear Regression",
        "Polynomial Regression"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Elastic Net combines L1 (feature selection) and L2 (shrinkage) penalties."
    },
    {
      "id": 42,
      "questionText": "Scenario: Ridge Regression applied without standardization. What can happen?",
      "options": [
        "Features with larger scale get larger penalties",
        "All coefficients shrink equally",
        "Training error drops",
        "Alpha becomes irrelevant"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Without scaling, features with larger magnitude are penalized more, biasing the model."
    },
    {
      "id": 43,
      "questionText": "Scenario: Ridge Regression applied to high-degree polynomial features. Main risk:",
      "options": [
        "Underfitting",
        "Overfitting due to many terms",
        "Alpha is too low",
        "Features become sparse"
      ],
      "correctAnswerIndex": 1,
      "explanation": "High-degree polynomial features increase model complexity; Ridge shrinks coefficients to control overfitting."
    },
    {
      "id": 44,
      "questionText": "Scenario: You want to compare Ridge Regression performance with different alpha. Best approach?",
      "options": [
        "Single train-test split",
        "K-fold cross-validation",
        "Use R-squared only",
        "Ignore alpha values"
      ],
      "correctAnswerIndex": 1,
      "explanation": "K-fold CV allows evaluating different alpha values reliably and selecting the optimal one."
    },
    {
      "id": 45,
      "questionText": "Scenario: Ridge Regression model has high training error and high test error. What’s happening?",
      "options": [
        "Underfitting due to too high alpha",
        "Overfitting",
        "Model perfect",
        "Features irrelevant"
      ],
      "correctAnswerIndex": 0,
      "explanation": "High alpha over-penalizes coefficients, increasing bias and underfitting the data."
    },
    {
      "id": 46,
      "questionText": "Scenario: Dataset has multicollinearity. Which regression reduces variance without eliminating features?",
      "options": [
        "Ridge Regression",
        "Lasso Regression",
        "Linear Regression",
        "Polynomial Regression"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Ridge reduces coefficient magnitude for correlated features, lowering variance without zeroing coefficients."
    },
    {
      "id": 47,
      "questionText": "Scenario: Ridge Regression on noisy data. Coefficients are smaller than Linear Regression. Why?",
      "options": [
        "Noise removed automatically",
        "L2 penalty shrinks coefficients",
        "Model ignores target variable",
        "Alpha is zero"
      ],
      "correctAnswerIndex": 1,
      "explanation": "L2 penalty makes the model less sensitive to noise by shrinking coefficients."
    },
    {
      "id": 48,
      "questionText": "Scenario: Ridge Regression applied to dataset with features on vastly different scales. Outcome?",
      "options": [
        "Some features penalized more than others",
        "All coefficients equal",
        "Alpha becomes zero",
        "Model fails"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Without scaling, large-scale features incur larger penalties than small-scale features."
    },
    {
      "id": 49,
      "questionText": "Scenario: Ridge Regression used for dataset with correlated inputs. What happens to their coefficients?",
      "options": [
        "Shrink similarly, remain non-zero",
        "Zeroed out automatically",
        "Become negative",
        "Removed from model"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Ridge shrinks correlated coefficients together without eliminating them."
    },
    {
      "id": 50,
      "questionText": "Scenario: You need Ridge Regression but also want feature selection. Best choice?",
      "options": [
        "Increase alpha",
        "Use Elastic Net combining L1 and L2",
        "Decrease alpha",
        "Ignore multicollinearity"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Elastic Net allows both shrinkage (L2) and feature selection (L1)."
    },
    {
      "id": 51,
      "questionText": "Scenario: Ridge Regression is applied to a dataset with 5000 features, most of which are correlated. What is the main advantage?",
      "options": [
        "Eliminates irrelevant features",
        "Reduces coefficient variance without removing features",
        "Always decreases bias to zero",
        "Removes noise automatically"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Ridge shrinks correlated feature coefficients to reduce variance, maintaining all features in the model."
    },
    {
      "id": 52,
      "questionText": "Scenario: After Ridge Regression, test error is still high. Possible solution?",
      "options": [
        "Increase alpha further",
        "Use dimensionality reduction like PCA before Ridge",
        "Remove standardization",
        "Reduce training samples"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Dimensionality reduction can remove redundant features and improve generalization."
    },
    {
      "id": 53,
      "questionText": "Scenario: Ridge Regression applied to dataset with polynomial features. Observed very high coefficients for high-degree terms. Best approach?",
      "options": [
        "Increase alpha",
        "Decrease alpha",
        "Remove intercept",
        "Ignore polynomial terms"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Increasing alpha penalizes large coefficients, controlling overfitting in polynomial terms."
    },
    {
      "id": 54,
      "questionText": "Scenario: Ridge Regression on dataset with noisy inputs and high multicollinearity. Observed stable coefficients. Why?",
      "options": [
        "L2 penalty reduces sensitivity to noise and stabilizes correlated coefficients",
        "Training error is minimized",
        "Alpha is zero",
        "Model ignores correlated features"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Ridge shrinks coefficients to stabilize model against noise and multicollinearity."
    },
    {
      "id": 55,
      "questionText": "Scenario: You perform Ridge Regression with alpha=1 and 10-fold cross-validation. Best alpha is found to be 5. Interpretation?",
      "options": [
        "Model underfits with alpha=1, alpha=5 improves generalization",
        "Model overfits with alpha=5",
        "Cross-validation is irrelevant",
        "Training error is minimal at alpha=1"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Higher alpha increases bias slightly but reduces variance, improving test performance."
    },
    {
      "id": 56,
      "questionText": "Scenario: Ridge Regression applied to standardized features. Coefficients of two correlated features are nearly equal. This occurs because:",
      "options": [
        "Alpha is too high",
        "L2 penalty shrinks correlated coefficients similarly",
        "Features are independent",
        "Standardization is not needed"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Ridge shrinks correlated coefficients together, leading to similar values."
    },
    {
      "id": 57,
      "questionText": "Scenario: You applied Ridge Regression with alpha=0. Ridge behaves like:",
      "options": [
        "Lasso Regression",
        "Linear Regression",
        "Elastic Net",
        "Polynomial Regression"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Alpha=0 removes the L2 penalty, reducing Ridge to standard Linear Regression."
    },
    {
      "id": 58,
      "questionText": "Scenario: Ridge Regression applied on dataset with 1000 features, many irrelevant. Which method could improve sparsity?",
      "options": [
        "Increase alpha",
        "Switch to Lasso or Elastic Net",
        "Decrease alpha",
        "Use standardization only"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Lasso (L1) or Elastic Net can set irrelevant coefficients to zero, creating sparse models."
    },
    {
      "id": 59,
      "questionText": "Scenario: Ridge Regression used for a dataset with missing values. Best approach?",
      "options": [
        "Ridge handles missing automatically",
        "Impute missing values before applying Ridge",
        "Remove alpha",
        "Ignore missing values"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Ridge requires complete data; missing values should be imputed or removed first."
    },
    {
      "id": 60,
      "questionText": "Scenario: Ridge Regression on standardized dataset shows training error slightly higher than Linear Regression but test error lower. Reason?",
      "options": [
        "Bias-variance tradeoff: Ridge increased bias slightly but reduced variance",
        "Model underfits completely",
        "Alpha is zero",
        "Data is too small"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Regularization increases bias but reduces variance, improving test performance."
    },
    {
      "id": 61,
      "questionText": "Scenario: Ridge Regression applied with high alpha and low alpha. Observed training and test errors: High alpha → high training, low test; Low alpha → low training, high test. This illustrates:",
      "options": [
        "Bias-variance tradeoff",
        "Overfitting",
        "Multicollinearity",
        "Polynomial expansion"
      ],
      "correctAnswerIndex": 0,
      "explanation": "This is the classic bias-variance tradeoff scenario."
    },
    {
      "id": 62,
      "questionText": "Scenario: Ridge Regression on dataset with categorical variables encoded as one-hot vectors. Main concern?",
      "options": [
        "High multicollinearity due to dummy variables",
        "Alpha selection irrelevant",
        "Scaling not required",
        "Target variable changes"
      ],
      "correctAnswerIndex": 0,
      "explanation": "One-hot encoding can produce correlated dummy features; Ridge helps reduce coefficient variance."
    },
    {
      "id": 63,
      "questionText": "Scenario: Ridge Regression applied on a time-series dataset with lag features. Why standardization is important?",
      "options": [
        "Alpha only applies to standardized features",
        "Regularization penalizes coefficients fairly only if features are on same scale",
        "Intercept is ignored otherwise",
        "Time index must be normalized"
      ],
      "correctAnswerIndex": 1,
      "explanation": "L2 penalty shrinks coefficients fairly only when all features are standardized."
    },
    {
      "id": 64,
      "questionText": "Scenario: Ridge Regression and OLS applied on small dataset with multicollinearity. Observed unstable coefficients with OLS, stable with Ridge. Why?",
      "options": [
        "Ridge reduces coefficient variance through regularization",
        "Ridge increases training error",
        "OLS ignores multicollinearity",
        "Alpha is zero"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Regularization stabilizes coefficients for correlated features."
    },
    {
      "id": 65,
      "questionText": "Scenario: Ridge Regression applied after PCA. Advantage?",
      "options": [
        "Reduces dimensionality, coefficients shrunk on principal components",
        "Eliminates intercept",
        "No need for alpha",
        "Features become sparse"
      ],
      "correctAnswerIndex": 0,
      "explanation": "PCA reduces dimensionality; Ridge shrinks coefficients on principal components to control overfitting."
    },
    {
      "id": 66,
      "questionText": "Scenario: Ridge Regression applied with alpha very large. Observed training and test errors both high. Reason?",
      "options": [
        "Underfitting due to over-penalization",
        "Overfitting",
        "Alpha too small",
        "Data not standardized"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Excessive alpha causes high bias, leading to underfitting."
    },
    {
      "id": 67,
      "questionText": "Scenario: Ridge Regression applied to polynomial regression with degree 10. Why use Ridge?",
      "options": [
        "Prevent overfitting from high-degree polynomial terms",
        "Increase training error",
        "Eliminate low-degree terms",
        "Remove intercept automatically"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Ridge penalizes large coefficients from high-degree terms, reducing overfitting."
    },
    {
      "id": 68,
      "questionText": "Scenario: Ridge Regression applied to features with different units. Observed coefficients of small-scale features larger than large-scale ones. Reason?",
      "options": [
        "L2 penalty uneven due to lack of standardization",
        "Alpha is zero",
        "Model overfits",
        "Data too small"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Without standardization, penalty is unfair; features with small scale are penalized less."
    },
    {
      "id": 69,
      "questionText": "Scenario: Ridge Regression applied with cross-validation. Optimal alpha selected minimizes:",
      "options": [
        "Training error only",
        "Test error on validation folds",
        "Number of features",
        "Intercept value"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Cross-validation selects alpha that minimizes validation/test error, improving generalization."
    },
    {
      "id": 70,
      "questionText": "Scenario: Ridge Regression applied to dataset with multicollinearity. Coefficients are shrunk but all non-zero. Implication?",
      "options": [
        "Variance reduced, all features retained",
        "Model overfits",
        "Features eliminated automatically",
        "Model fails"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Ridge reduces variance without eliminating correlated features."
    },
    {
      "id": 71,
      "questionText": "Scenario: Ridge Regression applied to large-scale dataset. Alpha tuning via grid search. Why important?",
      "options": [
        "Different alphas balance bias and variance for optimal performance",
        "Alpha irrelevant",
        "Alpha only affects training error",
        "Regularization unnecessary"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Alpha controls regularization strength; tuning balances bias and variance."
    },
    {
      "id": 72,
      "questionText": "Scenario: Ridge Regression applied with very small alpha. Observed high variance. Why?",
      "options": [
        "L2 penalty too weak to control overfitting",
        "Alpha too large",
        "Data unstandardized",
        "Intercept ignored"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Small alpha provides minimal regularization, leaving high-variance coefficients unchecked."
    },
    {
      "id": 73,
      "questionText": "Scenario: Ridge Regression vs Lasso on highly correlated features. Expected result?",
      "options": [
        "Ridge shrinks coefficients similarly; Lasso selects one and zeroes others",
        "Both eliminate all correlated features",
        "Ridge produces sparse solution; Lasso does not",
        "Alpha irrelevant"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Ridge keeps all correlated features with smaller coefficients; Lasso may zero some."
    },
    {
      "id": 74,
      "questionText": "Scenario: Ridge Regression applied with alpha=0. Model behaves like:",
      "options": [
        "Linear Regression",
        "Lasso",
        "Elastic Net",
        "Polynomial Regression"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Alpha=0 removes L2 penalty, reducing Ridge to standard Linear Regression."
    },
    {
      "id": 75,
      "questionText": "Scenario: Ridge Regression applied to a dataset with 1000 features, some irrelevant. How to reduce irrelevant features?",
      "options": [
        "Switch to Lasso or Elastic Net",
        "Increase alpha excessively",
        "Decrease alpha to zero",
        "Ignore standardization"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Lasso or Elastic Net can remove irrelevant features via L1 regularization."
    },
    {
      "id": 76,
      "questionText": "Scenario: Ridge Regression applied on medical dataset with 500 features, many correlated. Goal: predict patient outcome. Best approach?",
      "options": [
        "Use Ridge Regression with cross-validated alpha",
        "Use standard Linear Regression",
        "Use Lasso only",
        "Ignore multicollinearity"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Ridge handles correlated features effectively and cross-validation selects optimal alpha."
    },
    {
      "id": 77,
      "questionText": "Scenario: Ridge Regression applied to dataset with outliers. Observation: coefficients not extremely affected. Why?",
      "options": [
        "L2 penalty shrinks coefficients, reducing sensitivity to outliers",
        "Training error minimized",
        "Model ignores target variable",
        "Alpha is zero"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Regularization prevents large coefficients, making the model less sensitive to outliers."
    },
    {
      "id": 78,
      "questionText": "Scenario: Ridge Regression applied with alpha very small, results similar to Linear Regression. Interpretation?",
      "options": [
        "L2 penalty is too weak to control overfitting",
        "Model underfits",
        "Coefficients are zero",
        "Training error very high"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Small alpha means minimal regularization; Ridge behaves like Linear Regression with potential overfitting."
    },
    {
      "id": 79,
      "questionText": "Scenario: Ridge Regression on dataset with 2000 features, many irrelevant. Test error high. Recommended?",
      "options": [
        "Switch to Lasso or Elastic Net",
        "Increase alpha excessively",
        "Decrease alpha",
        "Ignore irrelevant features"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Lasso or Elastic Net can remove irrelevant features, improving generalization."
    },
    {
      "id": 80,
      "questionText": "Scenario: Ridge Regression applied on highly noisy dataset. Observed smaller coefficients than Linear Regression. Why?",
      "options": [
        "L2 penalty shrinks coefficients to reduce variance",
        "Model ignores noise",
        "Training error drops to zero",
        "Alpha is zero"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Regularization reduces sensitivity to noise, shrinking coefficients."
    },
    {
      "id": 81,
      "questionText": "Scenario: Ridge Regression applied to polynomial features with high degree. Observation: large coefficients for high-degree terms. Best solution?",
      "options": [
        "Increase alpha to penalize large coefficients",
        "Decrease alpha",
        "Remove intercept",
        "Ignore polynomial terms"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Higher alpha controls overfitting from high-degree polynomial terms."
    },
    {
      "id": 82,
      "questionText": "Scenario: Ridge Regression applied to dataset with categorical features encoded as one-hot vectors. Concern?",
      "options": [
        "Multicollinearity due to dummy variables",
        "Alpha irrelevant",
        "Scaling not required",
        "Target variable changes"
      ],
      "correctAnswerIndex": 0,
      "explanation": "One-hot encoding creates correlated dummy features; Ridge shrinks their coefficients."
    },
    {
      "id": 83,
      "questionText": "Scenario: Ridge Regression applied to time-series dataset with lag features. Why standardization important?",
      "options": [
        "L2 penalty penalizes coefficients fairly only if features are on same scale",
        "Intercept ignored otherwise",
        "Time index must be normalized",
        "Alpha irrelevant"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Standardizing features ensures L2 penalty treats all lag features fairly."
    },
    {
      "id": 84,
      "questionText": "Scenario: Ridge Regression applied on dataset with missing values. Action required?",
      "options": [
        "Impute missing values before applying Ridge",
        "Remove alpha",
        "Ignore missing values",
        "L2 penalty handles missing automatically"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Ridge requires complete data; missing values must be imputed first."
    },
    {
      "id": 85,
      "questionText": "Scenario: Ridge Regression with very high alpha. Observed high training and test errors. Reason?",
      "options": [
        "Underfitting due to over-penalization",
        "Overfitting",
        "Alpha too small",
        "Data not standardized"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Excessive alpha increases bias, causing underfitting."
    },
    {
      "id": 86,
      "questionText": "Scenario: Ridge Regression applied on dataset with highly correlated features. Coefficients shrunk but non-zero. Implication?",
      "options": [
        "Variance reduced, features retained",
        "Overfitting",
        "Features eliminated",
        "Model fails"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Ridge reduces variance without removing correlated features."
    },
    {
      "id": 87,
      "questionText": "Scenario: Ridge Regression applied on large-scale dataset. Why tune alpha via grid search?",
      "options": [
        "Alpha balances bias-variance tradeoff for optimal performance",
        "Alpha irrelevant",
        "Alpha only affects training error",
        "Regularization unnecessary"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Grid search finds alpha that provides the best tradeoff between bias and variance."
    },
    {
      "id": 88,
      "questionText": "Scenario: Ridge Regression applied to dataset with polynomial features. High-degree terms dominate coefficients. Solution?",
      "options": [
        "Increase alpha to control large coefficients",
        "Decrease alpha",
        "Remove polynomial terms",
        "Ignore coefficients"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Higher alpha penalizes large coefficients, reducing overfitting."
    },
    {
      "id": 89,
      "questionText": "Scenario: Ridge Regression applied on dataset with features in different units. Observation: large coefficients for small-scale features. Reason?",
      "options": [
        "L2 penalty uneven due to lack of standardization",
        "Alpha too high",
        "Data uncorrelated",
        "Training error minimal"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Without standardization, small-scale features are penalized less, leading to larger coefficients."
    },
    {
      "id": 90,
      "questionText": "Scenario: Ridge Regression applied with k-fold cross-validation. Optimal alpha minimizes:",
      "options": [
        "Validation/test error",
        "Training error",
        "Number of features",
        "Intercept value"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Cross-validation selects alpha that minimizes test error for better generalization."
    },
    {
      "id": 91,
      "questionText": "Scenario: Ridge Regression applied with very small alpha. Observed high variance. Reason?",
      "options": [
        "L2 penalty too weak to control overfitting",
        "Alpha too large",
        "Data unstandardized",
        "Intercept ignored"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Minimal regularization leaves coefficients unchecked, causing high variance."
    },
    {
      "id": 92,
      "questionText": "Scenario: Ridge Regression applied alongside Lasso on same dataset. Expected difference?",
      "options": [
        "Ridge shrinks coefficients; Lasso may zero some",
        "Both produce sparse solutions",
        "Ridge eliminates features; Lasso does not",
        "Alpha irrelevant"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Ridge keeps all coefficients small but non-zero; Lasso can perform feature selection."
    },
    {
      "id": 93,
      "questionText": "Scenario: Ridge Regression applied to dataset with irrelevant features. Test error high. Solution?",
      "options": [
        "Switch to Lasso or Elastic Net",
        "Increase alpha excessively",
        "Decrease alpha",
        "Ignore irrelevant features"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Lasso or Elastic Net can remove irrelevant features to improve performance."
    },
    {
      "id": 94,
      "questionText": "Scenario: Ridge Regression applied with standardized features. Coefficients for correlated features similar. Reason?",
      "options": [
        "L2 penalty shrinks correlated coefficients similarly",
        "Alpha too low",
        "Features independent",
        "Data too small"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Ridge shrinks correlated coefficients together, producing similar values."
    },
    {
      "id": 95,
      "questionText": "Scenario: Ridge Regression applied to dataset with noisy features. Coefficients smaller than Linear Regression. Why?",
      "options": [
        "Regularization reduces sensitivity to noise",
        "Training error minimized",
        "Alpha zero",
        "Noise ignored"
      ],
      "correctAnswerIndex": 0,
      "explanation": "L2 penalty shrinks coefficients, making model less sensitive to noise."
    },
    {
      "id": 96,
      "questionText": "Scenario: Ridge Regression applied to polynomial regression of degree 12. High-degree terms produce large coefficients. Solution?",
      "options": [
        "Increase alpha",
        "Decrease alpha",
        "Remove intercept",
        "Ignore coefficients"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Higher alpha controls overfitting by shrinking large coefficients from high-degree terms."
    },
    {
      "id": 97,
      "questionText": "Scenario: Ridge Regression applied on dataset with one-hot encoded features. Concern?",
      "options": [
        "Multicollinearity due to dummy variables",
        "Alpha irrelevant",
        "Scaling not needed",
        "Intercept ignored"
      ],
      "correctAnswerIndex": 0,
      "explanation": "One-hot encoding creates correlated dummy variables; Ridge shrinks their coefficients."
    },
    {
      "id": 98,
      "questionText": "Scenario: Ridge Regression applied on dataset with missing values. Action required?",
      "options": [
        "Impute missing values first",
        "Ignore missing values",
        "Remove alpha",
        "L2 penalty handles missing automatically"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Ridge requires complete data; missing values must be imputed or removed."
    },
    {
      "id": 99,
      "questionText": "Scenario: Ridge Regression applied with cross-validation. Selected alpha minimizes:",
      "options": [
        "Validation/test error",
        "Training error only",
        "Number of features",
        "Intercept value"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Cross-validation selects alpha that minimizes validation error for optimal generalization."
    },
    {
      "id": 100,
      "questionText": "Scenario: Ridge Regression applied to real-world dataset with high multicollinearity, noisy features, and high-dimensionality. Best approach?",
      "options": [
        "Standardize features, tune alpha via cross-validation, consider Elastic Net if feature selection needed",
        "Use Linear Regression",
        "Ignore alpha",
        "Remove L2 penalty"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Standardization and cross-validated Ridge handle noise and multicollinearity; Elastic Net adds feature selection."
    }
  ]
}