Assessment of application of different model selection approaches in multiple regression.
", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "statement": "Consider the general multiple linear regression model:
\n\\[\\hat{y}=\\beta_0+\\beta_1x_1+ \\beta_2x_2+\\beta_3x_3+\\beta_4x_4 \\]
\n", "advice": "See literature on multiple regression, e.g., Section 9.2 of OpenIntro Statistics.
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\nFour models are then fitted, each excluding a different predictor, obtaining the following output:
\nR2 adj $=$ [[0]]
\n", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2.5", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "R2BEMax", "maxValue": "R2BEMax", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "Starting from a no-predictor model, we fit four models, each including a single predictor, obtaining the following (each row corresponds to a different model):
\n{table(dataFS,[\"Only predictor\",\"R2 adj\"])}
\nR2 adj $=$ [[0]]
\n", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2.5", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "R2FSMax", "maxValue": "R2FSMax", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "The full model is fitted to some data using a statistics software, obtaining this output:
\nStarting from a no-predictor model, we fit four models, each including a single predictor, obtaining the following (each row corresponds to a different model):
\n{table(dataFSp,[\"Parameter\",\"p-value\"])}
\nTo improve the no-predictor model, we want to add one predictor; identify such predictor and enter its p-value below:
\np-value $=$ [[0]]
\n\n", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2.5", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "pMin", "maxValue": "pMin", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "type": "question", "contributors": [{"name": "Mario Orsi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/427/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Mario Orsi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/427/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}