File size: 48,073 Bytes
0d00d62 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 |
{
"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."
}
]
}
|