// Numbas version: finer_feedback_settings
{"name": "Statistical Analysis of Production", "extensions": ["stats", "jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Statistical Analysis of Production", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>The data below corresponds to energy consumption (kWh) and units of production (tonnes) for a particular factory as it runs over a 10 week period.&nbsp;</p>\n<p>Copy the data from the table into (Microsoft Excel or similar) and plot the trendline as seen in the graph below.</p>\n<p></p>\n<table border=\"0\" cellpadding=\"0\" cellspacing=\"0\" width=\"192\" style=\"height: 220px; width: 166px;\"><colgroup><col width=\"64\" span=\"3\"/></colgroup>\n<tbody>\n<tr height=\"20\" style=\"height: 20px;\">\n<td height=\"20\" style=\"height: 20px; width: 38.125px; text-align: center;\">Week</td>\n<td style=\"height: 20px; width: 74.5156px; text-align: center;\">Production (tonnes)</td>\n<td style=\"height: 20px; width: 54.2656px; text-align: center;\">Energy (kWh)</td>\n</tr>\n<tr height=\"20\" style=\"height: 20px;\">\n<td height=\"20\" style=\"height: 20px; width: 38.125px; text-align: center;\">1</td>\n<td style=\"height: 20px; width: 74.5156px; text-align: center;\">{r1[0]}</td>\n<td style=\"height: 20px; width: 54.2656px; text-align: center;\">{r2[0]}</td>\n</tr>\n<tr height=\"20\" style=\"height: 20px;\">\n<td height=\"20\" style=\"height: 20px; width: 38.125px; text-align: center;\">2</td>\n<td style=\"height: 20px; width: 74.5156px; text-align: center;\">{r1[1]}</td>\n<td style=\"height: 20px; width: 54.2656px; text-align: center;\">{r2[1]}</td>\n</tr>\n<tr height=\"20\" style=\"height: 20px;\">\n<td height=\"20\" style=\"height: 20px; width: 38.125px; text-align: center;\">3</td>\n<td style=\"height: 20px; width: 74.5156px; text-align: center;\">{r1[2]}</td>\n<td style=\"height: 20px; width: 54.2656px; text-align: center;\">{r2[2]}</td>\n</tr>\n<tr height=\"20\" style=\"height: 20px;\">\n<td height=\"20\" style=\"height: 20px; width: 38.125px; text-align: center;\">4</td>\n<td style=\"height: 20px; width: 74.5156px; text-align: center;\">{r1[3]}</td>\n<td style=\"height: 20px; width: 54.2656px; text-align: center;\">{r2[3]}</td>\n</tr>\n<tr height=\"20\" style=\"height: 20px;\">\n<td height=\"20\" style=\"height: 20px; width: 38.125px; text-align: center;\">5</td>\n<td style=\"height: 20px; width: 74.5156px; text-align: center;\">{r1[4]}</td>\n<td style=\"height: 20px; width: 54.2656px; text-align: center;\">{r2[4]}</td>\n</tr>\n<tr height=\"20\" style=\"height: 20px;\">\n<td height=\"20\" style=\"height: 20px; width: 38.125px; text-align: center;\">6</td>\n<td style=\"height: 20px; width: 74.5156px; text-align: center;\">{r1[5]}</td>\n<td style=\"height: 20px; width: 54.2656px; text-align: center;\">{r2[5]}</td>\n</tr>\n<tr height=\"20\" style=\"height: 20px;\">\n<td height=\"20\" style=\"height: 20px; width: 38.125px; text-align: center;\">7</td>\n<td style=\"height: 20px; width: 74.5156px; text-align: center;\">{r1[6]}</td>\n<td style=\"height: 20px; width: 54.2656px; text-align: center;\">{r2[6]}</td>\n</tr>\n<tr height=\"20\" style=\"height: 20px;\">\n<td height=\"20\" style=\"height: 20px; width: 38.125px; text-align: center;\">8</td>\n<td style=\"height: 20px; width: 74.5156px; text-align: center;\">{r1[7]}</td>\n<td style=\"height: 20px; width: 54.2656px; text-align: center;\">{r2[7]}</td>\n</tr>\n<tr height=\"20\" style=\"height: 20px;\">\n<td height=\"20\" style=\"height: 20px; width: 38.125px; text-align: center;\">9</td>\n<td style=\"height: 20px; width: 74.5156px; text-align: center;\">{r1[8]}</td>\n<td style=\"height: 20px; width: 54.2656px; text-align: center;\">{r2[8]}</td>\n</tr>\n<tr height=\"20\" style=\"height: 20px;\">\n<td height=\"20\" style=\"height: 20px; width: 38.125px; text-align: center;\">10</td>\n<td style=\"height: 20px; width: 74.5156px; text-align: center;\">{r1[9]}</td>\n<td style=\"height: 20px; width: 54.2656px; text-align: center;\">{r2[9]}</td>\n</tr>\n</tbody>\n</table>\n<hr/>\n<table style=\"height: 259px;\" width=\"39\">\n<tbody>\n<tr style=\"height: 25px;\">\n<td style=\"height: 25px; width: 49.0469px;\">Energy (kWh)</td>\n<td style=\"height: 25px; width: 105.188px;\">{drawgraph()}</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 49.0469px;\"></td>\n<td style=\"height: 18px; width: 105.188px;\">Production (tonnes)</td>\n</tr>\n</tbody>\n</table>", "advice": "<p><strong>How much energy, in kWh, will likely be needed to produce {rand_units_of_product} tonnes of product?</strong></p>\n<p>Equation of a straight line: y = mx+c</p>\n<p><em>Where m is the gradient of the trendline and c is the y axis intercept.&nbsp;</em></p>\n<p><em></em></p>\n<p>m = {precround(m_hat,3)}, c = {precround(c_hat,3)}</p>\n<p>Energy = {precround(m_hat,3)} x {rand_units_of_product} + {precround(c_hat,3)}</p>\n<p>Energy = {precround(energy_required,3)}kWh</p>\n<p></p>\n<hr/>\n<p><strong></strong></p>\n<p><strong>If the factory is using {rand_units_of_energy}kWh of energy, estimate how many tonnes of product are being produced.&nbsp;</strong></p>\n<p>Equation of a straight line: y = mx+c</p>\n<p><em>y is the energy usage, x is the factory production.&nbsp;</em></p>\n<p></p>\n<p><strong>Step 1</strong>, rearrange the equation.</p>\n<p>(y-c)/m = x</p>\n<p></p>\n<p><strong>Step 2</strong>, input values.&nbsp;</p>\n<p>({rand_units_of_energy}-{precround(c_hat,3)})/{precround(m_hat,3)} = x</p>\n<p>x = {product_tonnes_produced} tonnes</p>", "rulesets": {}, "extensions": ["jsxgraph", "stats"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"r1": {"name": "r1", "group": "Ungrouped variables", "definition": 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"description": "", "templateType": "anything", "can_override": false}, "rand_units_of_product": {"name": "rand_units_of_product", "group": "question variables", "definition": "abs(round(normalsample(1200,600)))", "description": "", "templateType": "anything", "can_override": false}, "rand_units_of_energy": {"name": "rand_units_of_energy", "group": "question variables", "definition": "round(c+m*abs(round(normalsample(1200,600)))+random(-5000..5000))", "description": "", "templateType": "anything", "can_override": false}, "energy_required": {"name": "energy_required", "group": "question variables", "definition": "(m_hat*rand_units_of_product)+c_hat", "description": "", "templateType": "anything", "can_override": false}, "product_tonnes_produced": {"name": "product_tonnes_produced", "group": "question variables", "definition": "(rand_units_of_energy-c_hat)/m_hat", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["r1", "m", "c", "r2", "n"], "variable_groups": [{"name": "Calculate line of best fit", "variables": ["spxy", "c_hat", "m_hat", "ss", "res", "ssq", "sxy", "t"]}, {"name": "Plotting", "variables": ["minx", "miny", "maxx", "maxy", "regy1", "regy2"]}, {"name": "question variables", "variables": ["rand_units_of_product", "rand_units_of_energy", "energy_required", "product_tonnes_produced"]}], "functions": {"drawgraph": {"parameters": [], "type": "html", "language": "javascript", "definition": "var miny = Numbas.jme.unwrapValue(scope.variables.miny);\nvar maxy = Numbas.jme.unwrapValue(scope.variables.maxy);\nvar minx = Numbas.jme.unwrapValue(scope.variables.minx);\nvar maxx = Numbas.jme.unwrapValue(scope.variables.maxx);\nvar r1 = Numbas.jme.unwrapValue(scope.variables.r1);\nvar r2 = Numbas.jme.unwrapValue(scope.variables.r2);\n\nvar m = Numbas.jme.unwrapValue(scope.variables.m_hat);\nvar c = Numbas.jme.unwrapValue(scope.variables.c_hat);\n\nvar regy1 = Numbas.jme.unwrapValue(scope.variables.regy1);\nvar regy2 = Numbas.jme.unwrapValue(scope.variables.regy2);\n\n// Ensure a reasonable margin for visibility\nvar x_margin = (maxx - minx) * 0.1; // 10% margin\nvar y_margin = (maxy - miny) * 0.1;\n\nvar div = Numbas.extensions.jsxgraph.makeBoard('400px','400px',\n{\n    boundingBox: [minx - x_margin, maxy + y_margin, maxx + x_margin, miny - y_margin],\n    axis: false,\n    showNavigation: true,\n    grid: true,\n    zoomX: true,\n    zoomY:true,\n    pan: {\n        enabled: true,  // Allow panning\n        needShift: false, // No need to hold Shift to pan\n        needTwoFingers: false // No need for two fingers on touch devices\n    }\n  \n});\n\nvar brd = div.board;  \n\n// Ensure axes extend fully\nvar xaxis = brd.create('axis', [[minx - x_margin, 0], [maxx + x_margin, 0]], { fixed: true });\nvar yaxis = brd.create('axis', [[0, miny - y_margin], [0, maxy + y_margin]], { fixed: true });\n\n// Regression line\nvar li1 = brd.create('line', [[minx, regy1], [maxx, regy2]], { fixed: true, withLabel: false });\n\n// Plot points\nfor (let i = 0; i < Math.min(10, r1.length, r2.length); i++) {\n    brd.create('point', [r1[i], r2[i]], { visible: true, withLabel: false, fixed: true });\n}\n\nreturn div;"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Predict the fixed energy cost in kWh to run the factory at idle (i.e. no production).</p>\n<p>Hint: Calculate the y-axis intercept of the trendline.</p>", "minValue": "c_hat", "maxValue": "c_hat", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>How much extra energy, in kWh, is needed to produce one additional tonne of product?&nbsp;</p>\n<p>Hint: Calculate the gradient of the trendline.</p>\n<p></p>", "minValue": "m_hat", "maxValue": "m_hat", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>How much energy, in kWh, will likely be needed to produce {rand_units_of_product} tonnes of product?&nbsp;</p>", "minValue": "energy_required", "maxValue": "energy_required", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If the factory is using {rand_units_of_energy}kWh of energy, estimate how many tonnes of product are being produced.&nbsp;</p>", "minValue": "product_tonnes_produced", "maxValue": "product_tonnes_produced", 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