True/false question type to assess knowledge of the basics of linear correlation and regression.

", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "statement": "Identify each of the following statements as true or false in relation to linear regression:

", "advice": "Review linear regression (e.g., Chapter 8 in OpenIntro Statistics).

\n", "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "extensions": [], "variables": {"choices": {"name": "choices", "group": "Statements", "definition": "shuffle(0..len(statements)-1)[0..6]", "description": "", "templateType": "anything"}, "t_statements": {"name": "t_statements", "group": "Statements", "definition": "[ \"If the observed response is $\\\\var{y1}$ and the model prediction is $\\\\var{y1hat}$, the residual is $\\\\var{e1}$.\", \"If the observed response is $\\\\var{y2}$ and the residual is $\\\\var{e2}$, the model prediction is $\\\\var{y2hat}$.\", \"If a model underestimates an observation, the residual is positive.\", \"If a model overestimates an observation, the residual is negative.\", \"If a residual plot shows a random distribution around a horizontal line, it is reasonable to fit a linear model to the data.\", \"The correlation statistic $R$ quantifies the strength of the linear relationship between two variables. \", \"For a strong and positive correlation, $R$ will be near +1.\", \"For a strong and negative correlation, $R$ will be near -1.\", \"If there is no apparent correlation, $R$ will be near 0.\", \"$R=\\\\var{Rminus}$ indicates a stronger linear relationship than $R=\\\\var{Rplus}$.\", \"$R^2$ quantifies the amount of variation in the response that is explained by the model.\", \"In a model predicting weight (in kg) from height (in cm) in adult males, $R$ is dimensionless (no units).\", \"In a model predicting weight (in kg) from height (in cm) in adult males, the intercept is in kg.\", \"In a model predicting weight (in kg) from height (in cm) in adult males, the slope is in kg/cm.\", \"The uncertainty associated with the slope estimate ($b_1$) is higher when there is a lot of scatter around the regression line.\", \"The correlation coefficient is always unitless.\", \"If $R=\\\\var{R}$, the amount of variation in the response that is explained by the model is $\\\\var{R2pc}\\\\%$ (rounded to the nearest percentage point).\" ]", "description": "", "templateType": "list of strings"}, "statements": {"name": "statements", "group": "Statements", "definition": "t_statements+f_statements", "description": "", "templateType": "anything"}, "statement_marks": {"name": "statement_marks", "group": "Statements", "definition": "map([2,0],x,t_statements)+map([0,2],x,f_statements)", "description": "", "templateType": "anything"}, "f_statements": {"name": "f_statements", "group": "Statements", "definition": "[ \"If the observed response is $\\\\var{y1}$ and the model prediction is $\\\\var{y1hat}$, the residual is $\\\\var{e1false}$.\", \"If a model underestimate an observation, the residual is negative.\", \"If a model overestimates an observation, the residual is positive.\", \"If the observed response is $\\\\var{y2}$ and the residual is $\\\\var{e2}$, the model prediction is $\\\\var{y2hatfalse}$.\", \"If a residual plot shows a curvature, it is reasonable to fit a linear model to the data.\", \"The correlation statistic $R$ quantifies the slope of the linear relationship between two variables. \", \"For a strong and positive correlation, $R$ will be near 0.\", \"For a strong and negative correlation, $R$ will be near 0.\", \"If there is no apparent correlation, $R$ will be near -1.\", \"$R=\\\\var{Rminus}$ indicates a weaker linear relationship than $R=\\\\var{Rplus}$.\", \"$R^2$ quantifies the amount of variation in the explanatory variable that is explained by the response.\", \"In a model predicting weight (in kg) from height (in cm) in adult males, $R$ is in kg/cm.\", \"In a model predicting weight (in kg) from height (in cm) in adult males, the intercept is in cm.\", \"In a model predicting weight (in kg) from height (in cm) in adult males, the slope is dimensionless (no units).\", \"The uncertainty associated with the slope estimate ($b_1$) is higher when there is very little scatter around the regression line.\", \"The correlation coefficient has units given by the ratio between the units of $y$ and $x$.\", \"If $R=\\\\var{R}$, the amount of variation in the response that is explained by the model is $\\\\var{Rpc}\\\\%$ (rounded to the nearest percentage point).\" ]", "description": "", "templateType": "list of strings"}, "y1": {"name": "y1", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything"}, "y1hat": {"name": "y1hat", "group": "Ungrouped variables", "definition": "random(1..9 except y1)", "description": "", "templateType": "anything"}, "e1": {"name": "e1", "group": "Ungrouped variables", "definition": "y1-y1hat", "description": "", "templateType": "anything"}, "e1false": {"name": "e1false", "group": "Ungrouped variables", "definition": "y1hat-y1", "description": "", "templateType": "anything"}, "y2": {"name": "y2", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything"}, "e2": {"name": "e2", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything"}, "y2hat": {"name": "y2hat", "group": "Ungrouped variables", "definition": "y2-e2", "description": "", "templateType": "anything"}, "y2hatfalse": {"name": "y2hatfalse", "group": "Ungrouped variables", "definition": "e2+y2", "description": "", "templateType": "anything"}, "Rplus": {"name": "Rplus", "group": "Ungrouped variables", "definition": "random(0.5..0.75#0.01)", "description": "", "templateType": "anything"}, "Rminus": {"name": "Rminus", "group": "Ungrouped variables", "definition": "random(-0.80..-0.99#0.01)", "description": "", "templateType": "anything"}, "R": {"name": "R", "group": "Ungrouped variables", "definition": "random(0.4..0.9#0.01)", "description": "", "templateType": "anything"}, "R2": {"name": "R2", "group": "Ungrouped variables", "definition": "siground(R^2,3)", "description": "R squared.

", "templateType": "anything"}, "Rpc": {"name": "Rpc", "group": "Ungrouped variables", "definition": "precround(R*100,0)", "description": "R as pecentage.

", "templateType": "anything"}, "R2pc": {"name": "R2pc", "group": "Ungrouped variables", "definition": "precround(R2*100,0)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["y1", "y1hat", "e1", "e1false", "y2", "e2", "y2hat", "y2hatfalse", "Rplus", "Rminus", "R", "R2", "Rpc", "R2pc"], "variable_groups": [{"name": "Statements", "variables": ["t_statements", "f_statements", "statements", "statement_marks", "choices"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "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": "\n \n \n[[0]]

\n \n \n ", "gaps": [{"type": "m_n_x", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "minAnswers": 0, "maxAnswers": 0, "shuffleChoices": true, "shuffleAnswers": false, "displayType": "radiogroup", "warningType": "none", "showCellAnswerState": true, "choices": ["{statements[choices[0]]}", "{statements[choices[1]]}", "{statements[choices[2]]}", "{statements[choices[3]]}", "{statements[choices[4]]}"], "matrix": "map(statement_marks[choices[j]],j,0..4)", "layout": {"type": "all", "expression": ""}, "answers": ["True", "False"]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "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/"}, {"name": "Mario Orsi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/427/"}]}]}], "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/"}, {"name": "Mario Orsi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/427/"}]}