// Numbas version: finer_feedback_settings
{"name": "Test Yourself Week 3", "metadata": {"description": "", "licence": "None specified"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Curve fitting practice", "extensions": ["linear-algebra", "stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Will Rushworth", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/20560/"}], "tags": [], "metadata": {"description": "<p>A random dataset given by a linear function with noise (gradient and y-intercept of the linear function are randomised as is distribution of x values).</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Suppose that you have recorded the following experimental data:</p>\n<p>{table(display,[\"Current, A,\", \"Voltage, V,\", \"Error, V\"])}</p>\n<p>Note that the button 'Try another question like this one' will provide a new dataset.</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"xs": {"name": "xs", "group": "Ungrouped variables", "definition": "repeat(precround(random(1..100#0),3), n)", "description": "<p>X values. Chosen uniformly at random within a range.</p>", "templateType": "anything", "can_override": false}, "ys": {"name": "ys", "group": "Ungrouped variables", "definition": "map(\n  precround(gradient*x + intercept + normalsample(0,noise_variance), 3),\n  x,\n  xs\n)", "description": "<p>Y values. They have a linear relationship with X, plus some normally-distributed noise. The values are rounded to 3 d.p.</p>", "templateType": "anything", "can_override": false}, "gradient": {"name": "gradient", "group": "Ungrouped variables", "definition": "random(1..4#0.1)", "description": "<p>The gradient of Y with respect to X.</p>", "templateType": "anything", "can_override": false}, "intercept": {"name": "intercept", "group": "Ungrouped variables", "definition": "random(30..50)", "description": "<p>The $y$-intercept of the line.</p>", "templateType": "anything", "can_override": false}, "noise_variance": {"name": "noise_variance", "group": "Ungrouped variables", "definition": "5^2", "description": "<p>The variance of the noise.</p>", "templateType": "anything", "can_override": false}, "es": {"name": "es", "group": "Ungrouped variables", "definition": "repeat(precround(random(1..10#0),3), n)", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "30", "description": "", "templateType": "anything", "can_override": false}, "display": {"name": "display", "group": "Ungrouped variables", "definition": "[xs[i], ys[i], es[i]] for: i of: 0..29", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["xs", "ys", "gradient", "intercept", "noise_variance", "es", "n", "display"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "information", "useCustomName": true, "customName": "1", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find a line of best fit for the dataset of the form $y = mx$, using only the independent and dependent variables (omitting the measurement error).</p>"}, {"type": "information", "useCustomName": true, "customName": "2", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find a line of best fit for the dataset of the form $y = mx + c$, using the independent and dependent variables and the measurement error.</p>"}, {"type": "information", "useCustomName": true, "customName": "3", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Plot both lines of best fit on the same axes, along with the dataset.</p>"}, {"type": "information", "useCustomName": true, "customName": "4", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Adding the option <code>p0 = [m_0, c_0]</code> to <code>curve_fit()</code>, where <code>m_0</code> and <code>c_0</code> are floats, will use these values as initial guesses for $m$ and $c$ in the line of best fit.</p>\n<p>How does inputting various initial guesses for the fitting parameters affect the line of best fit in this example?</p>"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", 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"showanswerstatewhen": "always", "showadvicewhen": "inreview"}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "type": "exam", "contributors": [{"name": "Will Rushworth", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/20560/"}], "extensions": ["linear-algebra", "stats"], "custom_part_types": [], "resources": []}