// Numbas version: exam_results_page_options
{"name": "Identifying Parts of Equations: R^2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["changes", "r", "wrong_answer"], "name": "Identifying Parts of Equations: R^2", "tags": [], "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>What is $\\hat{y}_i$?</p>", "matrix": ["1", 0, 0, 0], "shuffleChoices": true, "marks": 0, "variableReplacements": [], "choices": ["<p>The model's prediction&nbsp;of $y_i$.</p>", "<p>The mean of $y_i$.</p>", "<p>The $i^{\\text{th}}$ $y$ value.</p>", "<p>The variance of the $y$ values.</p>"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": 0, "scripts": {}, "distractors": ["", "", "", ""], "displayColumns": "2", "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}, {"prompt": "<p>What can the formula be rearranged to?</p>", "matrix": ["1", 0, 0, 0], "shuffleChoices": true, "marks": 0, "variableReplacements": [], "choices": ["<p>$R^2 = \\dfrac{\\sum(y_i-\\bar{y})^2-(y_i-\\hat{y}_i)^2}{\\sum(y_i-\\bar{y})^2}$</p>", "<p>$R = 1 - \\dfrac{\\sum(y_i-\\hat{y}_i)}{\\sum(y_i - \\bar{y})}$</p>", "<p>$R^2 = 1 - \\dfrac{\\sum(\\hat{y}_i-\\bar{y})^2}{\\sum(y_i-\\bar{y})^2}$</p>", "<p>$R^2 = 1 - \\dfrac{\\sum\\hat{y}_i^2}{\\sum\\bar{y}^2}$</p>"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": 0, "scripts": {}, "distractors": ["", "", "", ""], "displayColumns": "1", "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}, {"prompt": "<p>What is the largest value $R$ can take?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "1", "minValue": "1", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": false, "scripts": {}, "marks": "1", "type": "numberentry", "showPrecisionHint": false}], "statement": "<p>Given the formula for the coefficient of determination of a regression model,</p>\n<p>\\[ R^2 = 1 - \\dfrac{\\sum(y_i-\\hat{y}_i)^2}{\\sum(y_i-\\bar{y})^2}, \\]</p>\n<p>answer the following questions</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"wrong_answer": {"definition": "reverse(changes)", "templateType": "anything", "group": "Ungrouped variables", "name": "wrong_answer", "description": ""}, "r": {"definition": "random(0,1)", "templateType": "anything", "group": "Ungrouped variables", "name": "r", "description": ""}, "changes": {"definition": "[ \"increases\", \"decreases\" ]", "templateType": "list of strings", "group": "Ungrouped variables", "name": "changes", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Hayley Moore", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/495/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Hayley Moore", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/495/"}]}