// Numbas version: finer_feedback_settings {"name": "SA13 Correlation", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "SA13 Correlation", "tags": [], "metadata": {"description": "
Tests understanding of scatter plots and related concepts.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "The scatter plot below shows the relationship between an employee’s height in centimetres and how long it takes them to walk to work in minutes.
\ntime (mins) | \n{drawgraph()} | \n
\n | height (cm) | \n
The graph shows that there is a positive correlation between a person's height and how long it takes them to walk to work.
\nA postive correlation is a relationship between two variables where both variables move in the same diection.
\nThis tells us that as a person's height increases, the time it takes to walk to work increases.
\nUse this link to find some resources which will help you revise this topic
", "rulesets": {}, "extensions": ["jsxgraph"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"slope": {"name": "slope", "group": "Regression variables", "definition": "(6*sumxy-sumx*sumy)/(6*sumxx-(sumx)^2)", "description": "s
", "templateType": "anything", "can_override": false}, "timemax": {"name": "timemax", "group": "Calculation variables", "definition": "max([p1y,p2y,p3y,p4y,p5y,p6y])", "description": "", "templateType": "anything", "can_override": false}, "minx": {"name": "minx", "group": "Graph Limits", "definition": "140", "description": "", "templateType": "anything", "can_override": false}, "miny": {"name": "miny", "group": "Graph Limits", "definition": "-10", "description": "", "templateType": "anything", "can_override": false}, "p3x": {"name": "p3x", "group": "Points", "definition": "random(166..175)", "description": "", "templateType": "anything", "can_override": false}, "p3y": {"name": "p3y", "group": "Points", "definition": "random(26..35)", "description": "", "templateType": "anything", "can_override": false}, "p5x": {"name": "p5x", "group": "Points", "definition": "random(146..155 except p1x)", "description": "", "templateType": "anything", "can_override": false}, "p5y": {"name": "p5y", "group": "Points", "definition": "random(6..15)", "description": "", "templateType": "anything", "can_override": false}, "p1x": {"name": "p1x", "group": "Points", "definition": "random(146..155)", "description": "", "templateType": "anything", "can_override": false}, "p1y": {"name": "p1y", "group": "Points", "definition": "random(6..15)", "description": "", "templateType": "anything", "can_override": false}, "timediff": {"name": "timediff", "group": "Calculation variables", "definition": "timemax-timemin", "description": "", "templateType": "anything", "can_override": false}, "maxx": {"name": "maxx", "group": "Graph Limits", "definition": "188", "description": "", "templateType": "anything", "can_override": false}, "maxy": {"name": "maxy", "group": "Graph Limits", "definition": "63", "description": "", "templateType": "anything", "can_override": false}, "roundedslope": {"name": "roundedslope", "group": "Regression variables", "definition": "precround(slope,2)", "description": "", "templateType": "anything", "can_override": false}, "yintercept": {"name": "yintercept", "group": "Regression variables", "definition": "(sumy-slope*sumx)/6", "description": "", "templateType": "anything", "can_override": false}, "timemin": {"name": "timemin", "group": "Calculation variables", "definition": "min([p1y,p2y,p3y,p4y,p5y,p6y])", "description": "", "templateType": "anything", "can_override": false}, "tallest": {"name": "tallest", "group": "Calculation variables", "definition": "max([p1x,p2x,p3x,p4x,p5x,p6x])", "description": "", "templateType": "anything", "can_override": false}, "regy1": {"name": "regy1", "group": "Regression variables", "definition": "slope*minx+yintercept", "description": "", "templateType": "anything", "can_override": false}, "regy2": {"name": "regy2", "group": "Regression variables", "definition": "slope*maxx+yintercept", "description": "", "templateType": "anything", "can_override": false}, "sumy": {"name": "sumy", "group": "Regression variables", "definition": "p1y+p2y+p3y+p4y+p5y+p6y", "description": "", "templateType": "anything", "can_override": false}, "sumx": {"name": "sumx", "group": "Regression variables", "definition": "p1x+p2x+p3x+p4x+p5x+p6x", "description": "", "templateType": "anything", "can_override": false}, "p6y": {"name": "p6y", "group": "Points", "definition": "random(46..55)", "description": "p6y
", "templateType": "anything", "can_override": false}, "p6x": {"name": "p6x", "group": "Points", "definition": "random(176..185 except p4x)", "description": "", "templateType": "anything", "can_override": false}, "p4y": {"name": "p4y", "group": "Points", "definition": "random(36..45)", "description": "", "templateType": "anything", "can_override": false}, "p4x": {"name": "p4x", "group": "Points", "definition": "random(176..185)", "description": "", "templateType": "anything", "can_override": false}, "p2y": {"name": "p2y", "group": "Points", "definition": "random(16..25)", "description": "", "templateType": "anything", "can_override": false}, "p2x": {"name": "p2x", "group": "Points", "definition": "random(156..165)", "description": "", "templateType": "anything", "can_override": false}, "sumxx": {"name": "sumxx", "group": "Regression variables", "definition": "p1x^2+p2x^2+p3x^2+p4x^2+p5x^2+p6x^2", "description": "", "templateType": "anything", "can_override": false}, "sumxy": {"name": "sumxy", "group": "Regression variables", "definition": "p1x*p1y+p2x*p2y+p3x*p3y+p4x*p4y+p5x*p5y+p6x*p6y", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Graph Limits", "variables": ["minx", "maxx", "miny", "maxy"]}, {"name": "Points", "variables": ["p1x", "p1y", "p2x", "p2y", "p3x", "p3y", "p4x", "p4y", "p5x", "p5y", "p6x", "p6y"]}, {"name": "Calculation variables", "variables": ["tallest", "timemax", "timemin", "timediff"]}, {"name": "Regression variables", "variables": ["sumx", "sumy", "sumxy", "sumxx", "slope", "yintercept", "regy1", "regy2", "roundedslope"]}], "functions": {"drawgraph": {"parameters": [], "type": "html", "language": "javascript", "definition": " var miny = Numbas.jme.unwrapValue(scope.variables.miny);\n var maxy = Numbas.jme.unwrapValue(scope.variables.maxy);\n var minx = Numbas.jme.unwrapValue(scope.variables.minx);\n var maxx = Numbas.jme.unwrapValue(scope.variables.maxx);\n var regy1 = Numbas.jme.unwrapValue(scope.variables.regy1);\n var regy2 = Numbas.jme.unwrapValue(scope.variables.regy2);\n\n var p1x = Numbas.jme.unwrapValue(scope.variables.p1x);\n var p1y = Numbas.jme.unwrapValue(scope.variables.p1y);\n var p2x = Numbas.jme.unwrapValue(scope.variables.p2x);\n var p2y= Numbas.jme.unwrapValue(scope.variables.p2y);\n var p3x = Numbas.jme.unwrapValue(scope.variables.p3x);\n var p3y= Numbas.jme.unwrapValue(scope.variables.p3y);\n var p4x = Numbas.jme.unwrapValue(scope.variables.p4x);\n var p4y= Numbas.jme.unwrapValue(scope.variables.p4y);\n var p5x = Numbas.jme.unwrapValue(scope.variables.p5x);\n var p5y= Numbas.jme.unwrapValue(scope.variables.p5y);\n var p6x = Numbas.jme.unwrapValue(scope.variables.p6x);\n var p6y= Numbas.jme.unwrapValue(scope.variables.p6y);\n \n var div = Numbas.extensions.jsxgraph.makeBoard('400px','400px',\n {boundingBox:[minx,maxy,maxx,miny],\n axis:false,\n showNavigation:false,\n grid:true});\n var brd = div.board; \n var xaxis=brd.createElement('axis', [[minx,0],[maxx,0]]);\n var yaxis=brd.createElement('axis', [[minx+5,miny],[minx+5,maxy]]);\n var li1=brd.create('line',[[minx,regy1],[maxx,regy2]],{fixed:true,withLabel:false});\n var pt1=brd.create('point',[p1x,p1y],{visible:true,withLabel:false}); \n var pt2=brd.create('point',[p2x,p2y],{visible:true,withLabel:false}); \n var pt3=brd.create('point',[p3x,p3y],{visible:true,withLabel:false}); \n var pt4=brd.create('point',[p4x,p4y],{visible:true,withLabel:false}); \n var pt5=brd.create('point',[p5x,p5y],{visible:true,withLabel:false}); \n var pt6=brd.create('point',[p6x,p6y],{visible:true,withLabel:false}); \nreturn div;\n "}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Mark the statement that best describes what this scatter plot shows.
", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["In general, there is a positive correlation between a person's height and how long it takes them to walk to work.
", "In general, there is a negative correlation between a person's height and how long it takes them to walk to work.
", "In general, there is a no correlation between a person's height and how long it takes them to walk to work.
"], "matrix": ["1", 0, 0], "distractors": ["", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Richard Miles", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/882/"}, {"name": "Lauren Desoysa", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21504/"}, {"name": "Upuli Wickramaarachchi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23527/"}]}]}], "contributors": [{"name": "Richard Miles", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/882/"}, {"name": "Lauren Desoysa", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21504/"}, {"name": "Upuli Wickramaarachchi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23527/"}]}