{ "title": "Polynomial Regression Mastery: 100 MCQs", "description": "A comprehensive set of 100 multiple-choice questions designed to teach and test your understanding of Polynomial Regression, starting from basic Linear Regression concepts to advanced ideas like model evaluation, bias-variance tradeoff, and overfitting.", "questions": [ { "id": 1, "questionText": "What is the main goal of Linear Regression?", "options": [ "To find clusters in data", "To compress the data", "To find a straight-line relationship between variables", "To predict categories" ], "correctAnswerIndex": 2, "explanation": "Linear Regression tries to find the best straight line that shows the relationship between input and output variables." }, { "id": 2, "questionText": "In Linear Regression, what kind of relationship is modeled between X and Y?", "options": [ "Polynomial", "Linear", "Circular", "Exponential" ], "correctAnswerIndex": 1, "explanation": "Linear Regression assumes a straight-line (linear) relationship between the independent and dependent variables." }, { "id": 3, "questionText": "What does the slope in Linear Regression represent?", "options": [ "The change in Y for a one-unit change in X", "The error of the model", "The average of all Y values", "The value of Y when X is 0" ], "correctAnswerIndex": 0, "explanation": "The slope tells us how much Y changes when X increases by 1 unit." }, { "id": 4, "questionText": "What is the intercept in a Linear Regression equation?", "options": [ "The number of data points", "The steepness of the line", "The point where the line crosses the Y-axis", "The residual value" ], "correctAnswerIndex": 2, "explanation": "The intercept is the Y value when X equals 0. It’s where the line meets the Y-axis." }, { "id": 5, "questionText": "What does a residual represent in regression?", "options": [ "The slope of the line", "The average of predictions", "Difference between actual and predicted values", "The standard deviation" ], "correctAnswerIndex": 2, "explanation": "A residual is the difference between the actual value and the predicted value. It shows how far the model’s prediction is from reality." }, { "id": 6, "questionText": "What method is commonly used to fit a Linear Regression line?", "options": [ "Gradient Ascent", "Residual Addition", "Ordinary Least Squares", "Mean Minimization" ], "correctAnswerIndex": 2, "explanation": "Ordinary Least Squares (OLS) minimizes the sum of squared residuals to find the best-fitting line." }, { "id": 7, "questionText": "What happens if residuals are not randomly distributed?", "options": [ "There may be a pattern not captured by the model", "It increases accuracy", "The slope becomes 0", "The model is perfect" ], "correctAnswerIndex": 0, "explanation": "If residuals show a pattern, it means the model missed some relationship in the data." }, { "id": 8, "questionText": "What type of variable does Linear Regression predict?", "options": [ "Continuous", "Integer only", "Categorical", "Binary" ], "correctAnswerIndex": 0, "explanation": "Linear Regression is used for predicting continuous numerical values like height, weight, or prices." }, { "id": 9, "questionText": "Which assumption is true for Linear Regression?", "options": [ "All features are independent", "Residuals are normally distributed", "Data must be categorical", "Output is binary" ], "correctAnswerIndex": 1, "explanation": "One assumption of Linear Regression is that residuals should follow a normal distribution." }, { "id": 10, "questionText": "What problem occurs when data is not linear?", "options": [ "Lower variance", "Perfect prediction", "Poor model fit", "Balanced output" ], "correctAnswerIndex": 2, "explanation": "Linear Regression works best for linear data. If data is curved, it won’t fit well, leading to high error." }, { "id": 11, "questionText": "What is Polynomial Regression used for?", "options": [ "Modeling curved relationships", "Modeling straight-line relationships", "Finding clusters", "Reducing dimensionality" ], "correctAnswerIndex": 0, "explanation": "Polynomial Regression models non-linear or curved relationships between input and output variables." }, { "id": 12, "questionText": "Polynomial Regression is an extension of which model?", "options": [ "Decision Tree", "Linear Regression", "Logistic Regression", "Naive Bayes" ], "correctAnswerIndex": 1, "explanation": "Polynomial Regression is an extension of Linear Regression where input features are raised to powers." }, { "id": 13, "questionText": "In Polynomial Regression, we add what kind of terms to the model?", "options": [ "Cubic roots only", "Squared and higher power terms of input", "Logarithmic terms", "Exponential terms" ], "correctAnswerIndex": 1, "explanation": "Polynomial Regression includes higher power terms like x², x³, etc., to capture curves in the data." }, { "id": 14, "questionText": "What shape can a second-degree Polynomial Regression model represent?", "options": [ "Circle", "Parabola", "Zigzag", "Straight line" ], "correctAnswerIndex": 1, "explanation": "A second-degree polynomial creates a parabola-shaped curve, allowing the model to fit U-shaped data." }, { "id": 15, "questionText": "What is the general form of a Polynomial Regression equation with one variable?", "options": [ "y = b0 + b1x + b2x² + ... + bkx^k", "y = mx + b", "y = b0 + b1x", "y = bx + c" ], "correctAnswerIndex": 0, "explanation": "Polynomial Regression includes terms of increasing power: x, x², x³, etc., up to the desired degree k." }, { "id": 16, "questionText": "What happens when you increase the degree of a polynomial too much?", "options": [ "The model becomes linear", "The model may overfit the data", "The model becomes simpler", "The error increases on training data" ], "correctAnswerIndex": 1, "explanation": "A high-degree polynomial can overfit by fitting noise in the training data rather than the true pattern." }, { "id": 17, "questionText": "Overfitting in Polynomial Regression leads to what?", "options": [ "Lower variance", "Simpler equations", "Better generalization", "Poor performance on new data" ], "correctAnswerIndex": 3, "explanation": "Overfitting means the model performs well on training data but fails to generalize to unseen data." }, { "id": 18, "questionText": "What is underfitting?", "options": [ "When the model is too simple to capture patterns", "When training accuracy is 100%", "When residuals are 0", "When the model is too complex" ], "correctAnswerIndex": 0, "explanation": "Underfitting happens when the model is too simple and cannot capture the underlying structure of the data." }, { "id": 19, "questionText": "Which term describes the trade-off between bias and variance in a polynomial model?", "options": [ "Regularization", "Feature Scaling", "Gradient Descent", "Bias-Variance Tradeoff" ], "correctAnswerIndex": 3, "explanation": "Bias-Variance Tradeoff explains how increasing model complexity reduces bias but increases variance." }, { "id": 20, "questionText": "What is the degree of a polynomial?", "options": [ "Number of variables", "Highest power of the input variable", "Sum of all coefficients", "Number of residuals" ], "correctAnswerIndex": 1, "explanation": "The degree of a polynomial is the highest exponent of the input variable in the equation." }, { "id": 21, "questionText": "Which type of relationship can Polynomial Regression handle that Linear Regression cannot?", "options": [ "Categorical", "Binary", "Constant", "Non-linear" ], "correctAnswerIndex": 3, "explanation": "Polynomial Regression can model curved, non-linear relationships, unlike simple linear regression." }, { "id": 22, "questionText": "What does increasing the polynomial degree do?", "options": [ "Simplifies computation", "Decreases coefficients", "Removes noise", "Adds more curve flexibility" ], "correctAnswerIndex": 3, "explanation": "A higher degree polynomial gives the model more flexibility to follow the data's shape." }, { "id": 23, "questionText": "What kind of curve does a third-degree polynomial create?", "options": [ "Straight line", "S-shape", "U-shape", "Flat line" ], "correctAnswerIndex": 1, "explanation": "A cubic polynomial (degree 3) can create an S-shaped curve that changes direction once." }, { "id": 24, "questionText": "Which library in Python is commonly used to create polynomial features?", "options": [ "NumPy", "scikit-learn", "Pandas", "Matplotlib" ], "correctAnswerIndex": 1, "explanation": "The PolynomialFeatures class from scikit-learn is used to generate higher-degree input features." }, { "id": 25, "questionText": "What function in scikit-learn is used to transform data into polynomial features?", "options": [ "create_poly_data()", "PolynomialFeatures()", "poly_transform()", "make_polynomial()" ], "correctAnswerIndex": 1, "explanation": "The PolynomialFeatures() function expands input features into polynomial combinations." }, { "id": 26, "questionText": "Which of the following problems is Polynomial Regression best suited for?", "options": [ "Linear relationships only", "Categorical output prediction", "Curved relationships between variables", "Time series forecasting only" ], "correctAnswerIndex": 2, "explanation": "Polynomial Regression is best used when data shows a curved or non-linear pattern between input and output." }, { "id": 27, "questionText": "If the degree of the polynomial is 1, what does Polynomial Regression become?", "options": [ "Logistic Regression", "Linear Regression", "Decision Tree", "Ridge Regression" ], "correctAnswerIndex": 1, "explanation": "When the degree is 1, Polynomial Regression is the same as simple Linear Regression." }, { "id": 28, "questionText": "What happens when you use a degree that is too low for Polynomial Regression?", "options": [ "No bias", "Underfitting", "Perfect fit", "Overfitting" ], "correctAnswerIndex": 1, "explanation": "Using a degree that is too low may cause the model to miss patterns, leading to underfitting." }, { "id": 29, "questionText": "What kind of error increases with a high-degree polynomial?", "options": [ "Noise", "Correlation", "Bias", "Variance" ], "correctAnswerIndex": 3, "explanation": "High-degree polynomials often increase variance, meaning the model becomes sensitive to small data changes." }, { "id": 30, "questionText": "What is the main goal when choosing the degree of a polynomial?", "options": [ "To balance bias and variance", "To reduce coefficients", "To fit as many points as possible", "To maximize error" ], "correctAnswerIndex": 0, "explanation": "The degree should be chosen to balance bias (simplicity) and variance (complexity) for good generalization." }, { "id": 31, "questionText": "What technique can help prevent overfitting in Polynomial Regression?", "options": [ "Adding more features", "Increasing polynomial degree", "Removing training data", "Regularization" ], "correctAnswerIndex": 3, "explanation": "Regularization methods like Ridge or Lasso Regression can reduce overfitting by penalizing large coefficients." }, { "id": 32, "questionText": "What is Ridge Regression also known as?", "options": [ "Variance Reduction", "L2 Regularization", "Elastic Net", "L1 Regularization" ], "correctAnswerIndex": 1, "explanation": "Ridge Regression uses L2 Regularization, which penalizes the sum of squared coefficients." }, { "id": 33, "questionText": "What is Lasso Regression also known as?", "options": [ "L1 Regularization", "Bias Correction", "L2 Regularization", "Polynomial Fitting" ], "correctAnswerIndex": 0, "explanation": "Lasso Regression uses L1 Regularization, which penalizes the absolute values of coefficients." }, { "id": 34, "questionText": "What is the main difference between Ridge and Lasso?", "options": [ "Ridge can remove features, Lasso cannot", "Ridge uses L1, Lasso uses L2", "Both remove coefficients equally", "Lasso can make some coefficients zero, Ridge cannot" ], "correctAnswerIndex": 3, "explanation": "Lasso can shrink some coefficients to exactly zero, performing feature selection, while Ridge cannot." }, { "id": 35, "questionText": "What evaluation metric measures how well the model explains the variance of the data?", "options": [ "Mean Absolute Error", "Mean Squared Error", "R-squared", "Root Mean Square Deviation" ], "correctAnswerIndex": 2, "explanation": "R-squared measures the proportion of variance in the target variable explained by the model." }, { "id": 36, "questionText": "What is the range of R-squared values?", "options": [ "0 to 1", "1 to infinity", "0 to 100", "-1 to 1" ], "correctAnswerIndex": 0, "explanation": "R-squared ranges from 0 to 1, where 1 means perfect prediction and 0 means no predictive power." }, { "id": 37, "questionText": "Which error metric squares the difference between actual and predicted values?", "options": [ "Correlation Coefficient", "R-squared", "Mean Absolute Error", "Mean Squared Error" ], "correctAnswerIndex": 3, "explanation": "Mean Squared Error (MSE) calculates the average of squared prediction errors." }, { "id": 38, "questionText": "Why is Root Mean Squared Error (RMSE) preferred over MSE?", "options": [ "It gives larger values", "It reduces overfitting", "It is in the same units as the target variable", "It lowers variance" ], "correctAnswerIndex": 2, "explanation": "RMSE is the square root of MSE, giving error values in the same unit as the dependent variable." }, { "id": 39, "questionText": "What can be a sign of overfitting when comparing training and test errors?", "options": [ "Training error is low but test error is high", "Both errors are low", "Both errors are high", "Test error is lower than training error" ], "correctAnswerIndex": 0, "explanation": "If the training error is much lower than test error, it indicates the model has memorized the training data." }, { "id": 40, "questionText": "Which plot is useful to visualize Polynomial Regression fit?", "options": [ "Scatter plot with curve", "Line plot", "Bar plot", "Pie chart" ], "correctAnswerIndex": 0, "explanation": "Scatter plots with a fitted curve help visualize how well the polynomial model fits the data." }, { "id": 41, "questionText": "How can you check if adding polynomial terms improves your model?", "options": [ "By visualizing the curve", "By comparing R-squared values", "By adding random features", "By increasing degree blindly" ], "correctAnswerIndex": 1, "explanation": "Comparing R-squared and validation errors helps decide if extra polynomial terms improve model accuracy." }, { "id": 42, "questionText": "What is multicollinearity in Polynomial Regression?", "options": [ "When residuals are independent", "When regularization is applied", "When output is non-linear", "When input features are highly correlated" ], "correctAnswerIndex": 3, "explanation": "Polynomial features (x, x², x³, etc.) are often correlated, causing multicollinearity, which affects coefficient stability." }, { "id": 43, "questionText": "Which method can help reduce multicollinearity in polynomial models?", "options": [ "Adding noise", "Increasing degree", "Regularization", "Ignoring correlations" ], "correctAnswerIndex": 2, "explanation": "Regularization (Ridge or Lasso) reduces coefficient sensitivity caused by multicollinearity." }, { "id": 44, "questionText": "What is the purpose of feature scaling in Polynomial Regression?", "options": [ "To make data categorical", "To prevent large coefficient values", "To remove outliers", "To increase variance" ], "correctAnswerIndex": 1, "explanation": "Feature scaling ensures that polynomial features with large values do not dominate during training." }, { "id": 45, "questionText": "Which scaling method is commonly used before Polynomial Regression?", "options": [ "Min-Max Scaling", "Text Vectorization", "One-Hot Encoding", "Label Encoding" ], "correctAnswerIndex": 0, "explanation": "Min-Max Scaling is often used to bring features within a small range, improving numerical stability." }, { "id": 46, "questionText": "What is the main advantage of Polynomial Regression over Linear Regression?", "options": [ "Faster computation", "Easier interpretation", "Ability to fit curved patterns", "Less data needed" ], "correctAnswerIndex": 2, "explanation": "Polynomial Regression can model curved, non-linear data patterns that linear models cannot handle." }, { "id": 47, "questionText": "Which curve fitting problem can Polynomial Regression solve?", "options": [ "Fitting U-shaped and S-shaped data", "Fitting straight lines", "Finding text patterns", "Classifying images" ], "correctAnswerIndex": 0, "explanation": "Polynomial Regression is effective for U-shaped or S-shaped curves that need flexibility in fitting." }, { "id": 48, "questionText": "Which of these statements about high-degree polynomials is true?", "options": [ "They are simple to interpret", "They generalize well", "They may oscillate wildly between points", "They reduce variance" ], "correctAnswerIndex": 2, "explanation": "High-degree polynomials may fluctuate too much between data points, reducing stability." }, { "id": 49, "questionText": "What type of regularization combines L1 and L2?", "options": [ "Ridge", "Dropout", "Elastic Net", "Lasso" ], "correctAnswerIndex": 2, "explanation": "Elastic Net combines both L1 (Lasso) and L2 (Ridge) regularization techniques." }, { "id": 50, "questionText": "What does the alpha parameter control in Ridge and Lasso Regression?", "options": [ "The learning rate", "The model degree", "The regularization strength", "The intercept" ], "correctAnswerIndex": 2, "explanation": "Alpha controls how strongly the model penalizes large coefficient values. Higher alpha means stronger regularization." }, { "id": 51, "questionText": "What happens if the polynomial degree is set too high on a small dataset?", "options": [ "Perfect fitting always", "Underfitting", "Overfitting", "No change in accuracy" ], "correctAnswerIndex": 2, "explanation": "A high-degree polynomial can memorize the training data, leading to overfitting and poor generalization." }, { "id": 52, "questionText": "Which of the following helps reduce overfitting in Polynomial Regression?", "options": [ "Using regularization", "Using fewer data points", "Adding noise to labels", "Increasing polynomial degree" ], "correctAnswerIndex": 0, "explanation": "Regularization penalizes large coefficients, which helps reduce overfitting." }, { "id": 53, "questionText": "What does feature scaling do before applying polynomial features?", "options": [ "Ensures all features contribute equally", "Removes outliers", "Increases model degree", "Makes coefficients smaller" ], "correctAnswerIndex": 0, "explanation": "Feature scaling ensures all input features have similar ranges, preventing domination by one feature." }, { "id": 54, "questionText": "Why is Polynomial Regression still considered a linear model?", "options": [ "Because it ignores nonlinear patterns", "Because coefficients are linear in parameters", "Because data must be linear", "Because it uses straight lines" ], "correctAnswerIndex": 1, "explanation": "Despite nonlinear features, the model remains linear in terms of its coefficients." }, { "id": 55, "questionText": "Which sklearn class is used to generate polynomial features?", "options": [ "PolynomialFeatures", "PolyScaler", "FeatureGenerator", "PolynomialModel" ], "correctAnswerIndex": 0, "explanation": "PolynomialFeatures from sklearn.preprocessing expands input data to include polynomial terms." }, { "id": 56, "questionText": "What is the main disadvantage of using very high-degree polynomials?", "options": [ "Simpler model", "Overfitting and numerical instability", "Lower computation time", "Underfitting" ], "correctAnswerIndex": 1, "explanation": "High-degree polynomials can overfit and suffer from large coefficient swings causing instability." }, { "id": 57, "questionText": "In Polynomial Regression, which term represents the intercept?", "options": [ "x^n term", "x^1 term", "x^0 term", "x^2 term" ], "correctAnswerIndex": 2, "explanation": "The x^0 term represents the constant (intercept) of the polynomial equation." }, { "id": 58, "questionText": "What will happen if we skip PolynomialFeatures but use degree > 1 in LinearRegression?", "options": [ "It will use polynomial terms automatically", "The model will fail", "It will regularize coefficients", "It will behave like linear regression" ], "correctAnswerIndex": 3, "explanation": "LinearRegression does not create polynomial terms automatically. Without PolynomialFeatures, it stays linear." }, { "id": 59, "questionText": "Which cross-validation technique is useful to choose polynomial degree?", "options": [ "Train-Test Split only", "Random Sampling", "Leave-One-Out CV", "No validation needed" ], "correctAnswerIndex": 2, "explanation": "Leave-One-Out Cross Validation works well to find the optimal polynomial degree for small datasets." }, { "id": 60, "questionText": "How does increasing polynomial degree affect bias and variance?", "options": [ "Increases bias and decreases variance", "Decreases bias and increases variance", "Increases both", "Decreases both" ], "correctAnswerIndex": 1, "explanation": "Higher degrees reduce bias (fit training data better) but increase variance (sensitive to noise)." }, { "id": 61, "questionText": "What does the term 'interaction features' mean in Polynomial Regression?", "options": [ "Features multiplied together", "Random noise features", "Unrelated features", "Features added together" ], "correctAnswerIndex": 0, "explanation": "Interaction features are created by multiplying original features, capturing combined effects." }, { "id": 62, "questionText": "What happens to training error as we increase polynomial degree?", "options": [ "Always increases", "Usually decreases", "Becomes random", "Stays constant" ], "correctAnswerIndex": 1, "explanation": "A higher-degree polynomial fits the training data better, reducing training error." }, { "id": 63, "questionText": "Which step comes immediately after generating polynomial features?", "options": [ "Scaling", "Model fitting", "Data shuffling", "Feature selection" ], "correctAnswerIndex": 1, "explanation": "After generating polynomial features, the next step is fitting the regression model." }, { "id": 64, "questionText": "What is a typical symptom of overfitting in Polynomial Regression?", "options": [ "Identical train and test results", "Low training accuracy", "High training accuracy but low test accuracy", "High test accuracy" ], "correctAnswerIndex": 2, "explanation": "Overfitting happens when a model performs very well on training data but poorly on unseen data." }, { "id": 65, "questionText": "How can we make polynomial regression less sensitive to outliers?", "options": [ "Use regularization", "Add more noise", "Ignore scaling", "Increase degree" ], "correctAnswerIndex": 0, "explanation": "Regularization like Ridge or Lasso limits large coefficient values, making the model less sensitive to outliers." }, { "id": 66, "questionText": "Which metric is least suitable for measuring polynomial regression performance?", "options": [ "R-squared", "Confusion Matrix", "Mean Absolute Error", "Mean Squared Error" ], "correctAnswerIndex": 1, "explanation": "Confusion Matrix is used for classification problems, not regression." }, { "id": 67, "questionText": "What is the shape of the curve in quadratic regression?", "options": [ "Circle", "Parabola", "Hyperbola", "Line" ], "correctAnswerIndex": 1, "explanation": "A second-degree polynomial forms a parabola." }, { "id": 68, "questionText": "What does PolynomialFeatures(degree=3) generate for input x?", "options": [ "x^2 only", "x^3 only", "x, x^2, x^3", "x" ], "correctAnswerIndex": 2, "explanation": "It expands the feature set to include x, x^2, and x^3 terms." }, { "id": 69, "questionText": "When should we use Polynomial Regression over Linear Regression?", "options": [ "When relationship is clearly nonlinear", "When slope is constant", "When data has many missing values", "When data is categorical" ], "correctAnswerIndex": 0, "explanation": "Polynomial Regression captures nonlinear relationships between input and output." }, { "id": 70, "questionText": "Why does feature scaling matter more for higher-degree polynomials?", "options": [ "Because it reduces intercept", "Because it helps visualization", "Because polynomial terms grow rapidly", "Because it ignores bias" ], "correctAnswerIndex": 2, "explanation": "High-degree terms like x^5 or x^6 can produce large numeric values; scaling keeps them manageable." }, { "id": 71, "questionText": "What is the main effect of high-degree polynomials on model complexity?", "options": [ "Increases complexity", "Keeps complexity same", "Removes features", "Reduces complexity" ], "correctAnswerIndex": 0, "explanation": "High-degree polynomials add more terms, increasing model complexity and flexibility." }, { "id": 72, "questionText": "Which method helps select the optimal polynomial degree?", "options": [ "Cross-validation", "Using only training error", "Trial and error", "Random selection" ], "correctAnswerIndex": 0, "explanation": "Cross-validation evaluates model performance on unseen data to choose the best polynomial degree." }, { "id": 73, "questionText": "What is bias in the context of polynomial regression?", "options": [ "Error due to noise", "Error due to large coefficients", "Error due to model simplicity", "Random fluctuation" ], "correctAnswerIndex": 2, "explanation": "Bias measures the error caused by approximating a complex relationship with a simple model." }, { "id": 74, "questionText": "What is variance in the context of polynomial regression?", "options": [ "Error due to bias", "Error due to sensitivity to training data", "Error due to model simplicity", "Error due to missing features" ], "correctAnswerIndex": 1, "explanation": "Variance is the error caused when the model changes too much with small changes in the training data." }, { "id": 75, "questionText": "Which combination of bias and variance is ideal?", "options": [ "High bias, low variance", "Low bias, high variance", "High bias, high variance", "Low bias, low variance" ], "correctAnswerIndex": 3, "explanation": "The ideal model has low bias (accurate on training) and low variance (stable on new data)." }, { "id": 76, "questionText": "How can we detect overfitting visually?", "options": [ "By examining coefficients only", "By looking at training vs test error", "By plotting residuals", "By plotting polynomial degree only" ], "correctAnswerIndex": 1, "explanation": "Overfitting is indicated when training error is very low but test error is high." }, { "id": 77, "questionText": "Which method reduces model complexity while keeping fit reasonable?", "options": [ "Regularization", "Adding more polynomial terms", "Ignoring validation data", "Increasing dataset noise" ], "correctAnswerIndex": 0, "explanation": "Regularization penalizes large coefficients, simplifying the model and reducing overfitting." }, { "id": 78, "questionText": "Why is L1 regularization useful in polynomial regression?", "options": [ "Increases variance", "Makes polynomial degree higher", "Removes features automatically", "Decreases bias only" ], "correctAnswerIndex": 2, "explanation": "L1 regularization (Lasso) can shrink some coefficients to zero, effectively selecting important features." }, { "id": 79, "questionText": "Why is L2 regularization useful in polynomial regression?", "options": [ "Removes features", "Reduces large coefficient impact", "Increases polynomial degree", "Increases training error only" ], "correctAnswerIndex": 1, "explanation": "L2 regularization (Ridge) penalizes large coefficients to make the model more stable." }, { "id": 80, "questionText": "Which visualization helps check polynomial fit?", "options": [ "Histogram", "Box plot", "Scatter plot with fitted curve", "Bar chart" ], "correctAnswerIndex": 2, "explanation": "Scatter plots with fitted curves show how well the polynomial captures data patterns." }, { "id": 81, "questionText": "What does R-squared indicate in polynomial regression?", "options": [ "Mean squared error", "Training time", "Number of features", "Proportion of variance explained" ], "correctAnswerIndex": 3, "explanation": "R-squared measures how much of the target variance is captured by the model." }, { "id": 82, "questionText": "Which error metric gives average magnitude of prediction errors?", "options": [ "Mean Absolute Error", "Variance", "R-squared", "Mean Squared Error" ], "correctAnswerIndex": 0, "explanation": "Mean Absolute Error calculates the average absolute difference between predicted and actual values." }, { "id": 83, "questionText": "Which metric penalizes large errors more heavily?", "options": [ "MSE", "MAE", "R-squared", "Correlation coefficient" ], "correctAnswerIndex": 0, "explanation": "MSE squares the errors, giving higher weight to large deviations." }, { "id": 84, "questionText": "Why is cross-validation important in polynomial regression?", "options": [ "To ignore overfitting", "To fit data perfectly", "To evaluate model on unseen data", "To increase polynomial degree" ], "correctAnswerIndex": 2, "explanation": "Cross-validation tests model performance on unseen data, helping select optimal degree and reduce overfitting." }, { "id": 85, "questionText": "Which technique can combine multiple polynomial models for better prediction?", "options": [ "Single model fitting", "L1 regularization only", "Feature scaling", "Bagging" ], "correctAnswerIndex": 3, "explanation": "Bagging combines predictions from multiple models to reduce variance and improve accuracy." }, { "id": 86, "questionText": "Which problem arises if polynomial degree is too low?", "options": [ "Feature scaling", "Underfitting", "Regularization", "Overfitting" ], "correctAnswerIndex": 1, "explanation": "A low-degree polynomial may fail to capture data patterns, causing underfitting." }, { "id": 87, "questionText": "Which method automatically selects important polynomial terms?", "options": [ "Lasso Regression", "Ridge Regression", "Cross-validation only", "Standard Linear Regression" ], "correctAnswerIndex": 0, "explanation": "Lasso regression can shrink some coefficients to zero, selecting the most important features." }, { "id": 88, "questionText": "Which is a symptom of multicollinearity in polynomial regression?", "options": [ "Low variance", "High R-squared always", "Unstable coefficients", "Zero training error" ], "correctAnswerIndex": 2, "explanation": "Polynomial terms are often correlated, making coefficients unstable and sensitive to small data changes." }, { "id": 89, "questionText": "Which of these is an advantage of polynomial regression?", "options": [ "Fits linear data only", "Can fit nonlinear patterns", "Removes outliers automatically", "Reduces training data needed" ], "correctAnswerIndex": 1, "explanation": "Polynomial regression captures nonlinear relationships between variables." }, { "id": 90, "questionText": "Which is a common step before polynomial regression on real data?", "options": [ "Removing target variable", "Feature scaling", "Increasing polynomial degree blindly", "Random noise addition" ], "correctAnswerIndex": 1, "explanation": "Feature scaling ensures all polynomial terms are on a similar scale for stable model training." }, { "id": 91, "questionText": "Which model would you choose for a U-shaped data trend?", "options": [ "Linear Regression", "Logistic Regression", "Quadratic Polynomial Regression", "Cubic Regression" ], "correctAnswerIndex": 2, "explanation": "Quadratic (degree 2) polynomial regression is ideal for U-shaped patterns." }, { "id": 92, "questionText": "Which model would you choose for an S-shaped trend?", "options": [ "Quadratic Regression", "Cubic Regression", "Linear Regression", "Logistic Regression" ], "correctAnswerIndex": 1, "explanation": "Cubic (degree 3) polynomial regression can fit S-shaped trends with one inflection point." }, { "id": 93, "questionText": "Which is an indicator of underfitting in polynomial regression?", "options": [ "Low bias", "High variance", "Low training error and high test error", "High training error and high test error" ], "correctAnswerIndex": 3, "explanation": "Underfitting shows both training and test errors are high due to a too-simple model." }, { "id": 94, "questionText": "What is the effect of regularization on polynomial coefficients?", "options": [ "Increases bias only", "Reduces magnitude of coefficients", "Increases all coefficients", "Removes training data" ], "correctAnswerIndex": 1, "explanation": "Regularization penalizes large coefficients to reduce overfitting." }, { "id": 95, "questionText": "Which method can evaluate polynomial regression stability across datasets?", "options": [ "Only visualization", "Train-test split", "Cross-validation", "Random coefficient assignment" ], "correctAnswerIndex": 2, "explanation": "Cross-validation tests the model on multiple data splits to check stability and generalization." }, { "id": 96, "questionText": "Why should we avoid excessively high-degree polynomials?", "options": [ "They increase overfitting", "They always improve R-squared", "They reduce bias", "They remove noise automatically" ], "correctAnswerIndex": 0, "explanation": "Excessively high-degree polynomials may fit noise rather than the actual pattern, causing overfitting." }, { "id": 97, "questionText": "Which method can simplify a polynomial regression model?", "options": [ "Ignoring validation", "Increasing degree", "Adding noise", "Regularization" ], "correctAnswerIndex": 3, "explanation": "Regularization reduces large coefficients and can simplify the model." }, { "id": 98, "questionText": "Which of the following is true about polynomial regression predictions?", "options": [ "Always linear", "Independent of input", "Always quadratic", "Can be nonlinear even with linear coefficients" ], "correctAnswerIndex": 3, "explanation": "Predictions can be nonlinear because the input features are polynomial terms, even if the model is linear in coefficients." }, { "id": 99, "questionText": "Which is a good strategy for selecting polynomial degree?", "options": [ "Ignoring training error", "Always using degree 5", "Using cross-validation", "Trial and error without validation" ], "correctAnswerIndex": 2, "explanation": "Cross-validation helps find a degree that balances underfitting and overfitting." }, { "id": 100, "questionText": "What is the final goal of polynomial regression?", "options": [ "To remove features", "To increase variance", "To predict continuous values with nonlinear patterns", "To classify data" ], "correctAnswerIndex": 2, "explanation": "Polynomial regression aims to predict continuous outcomes while capturing nonlinear relationships." } ] }