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Search, Evaluate, and Read Evidence","\u002Fen\u002Facademic-writing\u002F02-reading-and-literature-matrix","en\u002Facademic-writing\u002F02-reading-and-literature-matrix",{"title":27,"path":28,"stem":29},"3. From Sources to Synthesis and Argument","\u002Fen\u002Facademic-writing\u002F03-arguments-outlines-and-paragraphs","en\u002Facademic-writing\u002F03-arguments-outlines-and-paragraphs",{"title":31,"path":32,"stem":33},"4. Literature Review and a Defensible Gap","\u002Fen\u002Facademic-writing\u002F04-writing-the-literature-review","en\u002Facademic-writing\u002F04-writing-the-literature-review",{"title":35,"path":36,"stem":37},"5. Research Design, Evidence, and Core Sections","\u002Fen\u002Facademic-writing\u002F05-core-sections-and-evidence","en\u002Facademic-writing\u002F05-core-sections-and-evidence",{"title":39,"path":40,"stem":41},"6. Citation, Paraphrasing, Integrity, and AI","\u002Fen\u002Facademic-writing\u002F06-citation-paraphrasing-and-integrity","en\u002Facademic-writing\u002F06-citation-paraphrasing-and-integrity",{"title":43,"path":44,"stem":45},"7. Revision, Review, and Submission","\u002Fen\u002Facademic-writing\u002F07-revision-style-and-submission","en\u002Facademic-writing\u002F07-revision-style-and-submission",{"title":47,"path":48,"stem":49},"8. Research Workbook","\u002Fen\u002Facademic-writing\u002F08-literature-review-checklist-and-template","en\u002Facademic-writing\u002F08-literature-review-checklist-and-template",{"title":51,"path":52,"stem":53},"9. Research Workflow and Tools","\u002Fen\u002Facademic-writing\u002F09-tools-for-academic-writing-and-literature-management","en\u002Facademic-writing\u002F09-tools-for-academic-writing-and-literature-management",{"title":55,"path":56,"stem":57},"10. Worked Project — From Question to Defensible Conclusion","\u002Fen\u002Facademic-writing\u002F10-worked-example-from-block-structure-to-question-chain","en\u002Facademic-writing\u002F10-worked-example-from-block-structure-to-question-chain",{"title":59,"path":60,"stem":61,"children":62,"page":249},"Accounting","\u002Fen\u002Faccounting","en\u002Faccounting",[63,69,87,93,193],{"title":64,"path":65,"stem":66,"children":67},"Accounting — From Evidence to Decisions","\u002Fen\u002Faccounting\u002F00-index","en\u002Faccounting\u002F00-index",[68],{"title":64,"path":65,"stem":66},{"title":70,"path":71,"stem":72,"children":73},"Accounting Appendix","\u002Fen\u002Faccounting\u002Fappendix","en\u002Faccounting\u002Fappendix\u002Findex",[74,75,79,83],{"title":70,"path":71,"stem":72},{"title":76,"path":77,"stem":78},"Worked Examples and Error Diagnosis","\u002Fen\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls","en\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls",{"title":80,"path":81,"stem":82},"Accounting Glossary","\u002Fen\u002Faccounting\u002Fappendix\u002F26-glossary","en\u002Faccounting\u002Fappendix\u002F26-glossary",{"title":84,"path":85,"stem":86},"Reading and Evidence Map","\u002Fen\u002Faccounting\u002Fappendix\u002F27-reading-map","en\u002Faccounting\u002Fappendix\u002F27-reading-map",{"title":88,"path":89,"stem":90,"children":91},"Northstar Record-to-Decision Capstone","\u002Fen\u002Faccounting\u002Fcapstone","en\u002Faccounting\u002Fcapstone\u002Findex",[92],{"title":88,"path":89,"stem":90},{"title":94,"path":95,"stem":96,"children":97},"Financial Accounting","\u002Fen\u002Faccounting\u002Ffinancial-accounting","en\u002Faccounting\u002Ffinancial-accounting\u002Findex",[98,99,117,131,165,179],{"title":94,"path":95,"stem":96},{"title":100,"path":101,"stem":102,"children":103},"1. Foundations","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002Findex",[104,105,109,113],{"title":100,"path":101,"stem":102},{"title":106,"path":107,"stem":108},"Objectives and Qualitative Characteristics","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics",{"title":110,"path":111,"stem":112},"Equation and Elements","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements",{"title":114,"path":115,"stem":116},"Accrual Basis, Estimates and Periods","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles",{"title":118,"path":119,"stem":120,"children":121},"2. Recording Transactions","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002Findex",[122,123,127],{"title":118,"path":119,"stem":120},{"title":124,"path":125,"stem":126},"Double-Entry and Debit\u002FCredit","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr",{"title":128,"path":129,"stem":130},"Accounting Cycle","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle",{"title":132,"path":133,"stem":134,"children":135},"3. Measurement and Adjustments","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002Findex",[136,137,141,145,149,153,157,161],{"title":132,"path":133,"stem":134},{"title":138,"path":139,"stem":140},"Revenue Recognition","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition",{"title":142,"path":143,"stem":144},"Inventory","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory",{"title":146,"path":147,"stem":148},"Receivables and Expected Credit Losses","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables",{"title":150,"path":151,"stem":152},"Property, Plant and Equipment","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe",{"title":154,"path":155,"stem":156},"Intangible Assets","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles",{"title":158,"path":159,"stem":160},"Leases","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases",{"title":162,"path":163,"stem":164},"Current and Deferred Income Tax","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax",{"title":166,"path":167,"stem":168,"children":169},"4. Reporting and Cash","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002Findex",[170,171,175],{"title":166,"path":167,"stem":168},{"title":172,"path":173,"stem":174},"Linked Financial Statements","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements",{"title":176,"path":177,"stem":178},"Cash, Reconciliation and Internal Control","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control",{"title":180,"path":181,"stem":182,"children":183},"5. Analysis and Comparison","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002Findex",[184,185,189],{"title":180,"path":181,"stem":182},{"title":186,"path":187,"stem":188},"Ratio Analysis","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis",{"title":190,"path":191,"stem":192},"IFRS versus US GAAP","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap",{"title":194,"path":195,"stem":196,"children":197},"Management Accounting","\u002Fen\u002Faccounting\u002Fmanagement-accounting","en\u002Faccounting\u002Fmanagement-accounting\u002Findex",[198,199,217,235],{"title":194,"path":195,"stem":196},{"title":200,"path":201,"stem":202,"children":203},"1. Cost Foundations","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002Findex",[204,205,209,213],{"title":200,"path":201,"stem":202},{"title":206,"path":207,"stem":208},"Cost Concepts and Behaviour","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts",{"title":210,"path":211,"stem":212},"Costing Systems","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems",{"title":214,"path":215,"stem":216},"Variable and Absorption Costing","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption",{"title":218,"path":219,"stem":220,"children":221},"2. Planning and Control","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002Findex",[222,223,227,231],{"title":218,"path":219,"stem":220},{"title":224,"path":225,"stem":226},"Cost–Volume–Profit Analysis","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis",{"title":228,"path":229,"stem":230},"Budgeting and Variance Analysis","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances",{"title":232,"path":233,"stem":234},"Performance Measurement","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement",{"title":236,"path":237,"stem":238,"children":239},"3. Decisions and Investment","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002Findex",[240,241,245],{"title":236,"path":237,"stem":238},{"title":242,"path":243,"stem":244},"Short-Term Decisions","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions",{"title":246,"path":247,"stem":248},"Capital Budgeting","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting",false,{"title":251,"path":252,"stem":253,"children":254,"page":249},"Business Analytics","\u002Fen\u002Fbusiness-analytics","en\u002Fbusiness-analytics",[255,261,279,305,335,365,383,400],{"title":256,"path":257,"stem":258,"children":259},"Business Analytics — From Data to Defensible Action","\u002Fen\u002Fbusiness-analytics\u002F00-index","en\u002Fbusiness-analytics\u002F00-index",[260],{"title":256,"path":257,"stem":258},{"title":262,"path":263,"stem":264,"children":265},"0. Decision and Data Foundations","\u002Fen\u002Fbusiness-analytics\u002F00-intro","en\u002Fbusiness-analytics\u002F00-intro\u002Findex",[266,267,271,275],{"title":262,"path":263,"stem":264},{"title":268,"path":269,"stem":270},"Decision Framing","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F01-decision-framing","en\u002Fbusiness-analytics\u002F00-intro\u002F01-decision-framing",{"title":272,"path":273,"stem":274},"Data Contracts","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F02-data-contracts","en\u002Fbusiness-analytics\u002F00-intro\u002F02-data-contracts",{"title":276,"path":277,"stem":278},"Reproducible Analytics Workflow","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F03-reproducible-workflow","en\u002Fbusiness-analytics\u002F00-intro\u002F03-reproducible-workflow",{"title":280,"path":281,"stem":282,"children":283},"1. Descriptive Analytics","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive","en\u002Fbusiness-analytics\u002F01-descriptive\u002Findex",[284,285,289,293,297,301],{"title":280,"path":281,"stem":282},{"title":286,"path":287,"stem":288},"Distributions and Exploratory Data Analysis","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F04-distributions-eda","en\u002Fbusiness-analytics\u002F01-descriptive\u002F04-distributions-eda",{"title":290,"path":291,"stem":292},"KPIs and Denominators","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F05-kpis-denominators","en\u002Fbusiness-analytics\u002F01-descriptive\u002F05-kpis-denominators",{"title":294,"path":295,"stem":296},"Segments, Cohorts and Funnels","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F06-segmentation-cohorts-funnels","en\u002Fbusiness-analytics\u002F01-descriptive\u002F06-segmentation-cohorts-funnels",{"title":298,"path":299,"stem":300},"Visual Evidence and Data Stories","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F07-visualisation-story","en\u002Fbusiness-analytics\u002F01-descriptive\u002F07-visualisation-story",{"title":302,"path":303,"stem":304},"Experiments and Causal Boundaries","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F08-experiments-causal-boundary","en\u002Fbusiness-analytics\u002F01-descriptive\u002F08-experiments-causal-boundary",{"title":306,"path":307,"stem":308,"children":309},"2. Predictive Analytics","\u002Fen\u002Fbusiness-analytics\u002F02-predictive","en\u002Fbusiness-analytics\u002F02-predictive\u002Findex",[310,311,315,319,323,327,331],{"title":306,"path":307,"stem":308},{"title":312,"path":313,"stem":314},"Validation, Baselines and Leakage","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F09-validation-leakage","en\u002Fbusiness-analytics\u002F02-predictive\u002F09-validation-leakage",{"title":316,"path":317,"stem":318},"Regression and Forecasting","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F10-regression-forecasting","en\u002Fbusiness-analytics\u002F02-predictive\u002F10-regression-forecasting",{"title":320,"path":321,"stem":322},"Classification and Calibration","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F11-classification-calibration","en\u002Fbusiness-analytics\u002F02-predictive\u002F11-classification-calibration",{"title":324,"path":325,"stem":326},"Trees and Ensembles","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F12-trees-ensembles","en\u002Fbusiness-analytics\u002F02-predictive\u002F12-trees-ensembles",{"title":328,"path":329,"stem":330},"Decision Metrics and Thresholds","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F13-decision-metrics-thresholds","en\u002Fbusiness-analytics\u002F02-predictive\u002F13-decision-metrics-thresholds",{"title":332,"path":333,"stem":334},"Explainability, Monitoring and Drift","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F14-explainability-drift","en\u002Fbusiness-analytics\u002F02-predictive\u002F14-explainability-drift",{"title":336,"path":337,"stem":338,"children":339},"3. Prescriptive Analytics","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive","en\u002Fbusiness-analytics\u002F03-prescriptive\u002Findex",[340,341,345,349,353,357,361],{"title":336,"path":337,"stem":338},{"title":342,"path":343,"stem":344},"Decision-Making under Uncertainty","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F15-decision-uncertainty","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F15-decision-uncertainty",{"title":346,"path":347,"stem":348},"Linear Optimisation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F16-linear-optimization","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F16-linear-optimization",{"title":350,"path":351,"stem":352},"Inventory and Allocation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F17-inventory-allocation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F17-inventory-allocation",{"title":354,"path":355,"stem":356},"Queueing and Simulation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F18-queueing-simulation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F18-queueing-simulation",{"title":358,"path":359,"stem":360},"Pricing and Revenue Management","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F19-pricing-experimentation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F19-pricing-experimentation",{"title":362,"path":363,"stem":364},"Causal Targeting and Policy Learning","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F20-causal-targeting","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F20-causal-targeting",{"title":366,"path":367,"stem":368,"children":369},"4. Deployment and Governance","\u002Fen\u002Fbusiness-analytics\u002F04-deployment","en\u002Fbusiness-analytics\u002F04-deployment\u002Findex",[370,371,375,379],{"title":366,"path":367,"stem":368},{"title":372,"path":373,"stem":374},"Data Products and Monitoring","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F21-data-products-monitoring","en\u002Fbusiness-analytics\u002F04-deployment\u002F21-data-products-monitoring",{"title":376,"path":377,"stem":378},"Governance, Fairness and Privacy","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F22-governance-fairness-privacy","en\u002Fbusiness-analytics\u002F04-deployment\u002F22-governance-fairness-privacy",{"title":380,"path":381,"stem":382},"Adoption and Business Value","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F23-adoption-value","en\u002Fbusiness-analytics\u002F04-deployment\u002F23-adoption-value",{"title":384,"path":385,"stem":386,"children":387},"Appendix and Revision Tools","\u002Fen\u002Fbusiness-analytics\u002Fappendix","en\u002Fbusiness-analytics\u002Fappendix\u002Findex",[388,389,393,397],{"title":384,"path":385,"stem":386},{"title":390,"path":391,"stem":392},"Formula and Decision Map","\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F24-formula-map","en\u002Fbusiness-analytics\u002Fappendix\u002F24-formula-map",{"title":394,"path":395,"stem":396},"Worked Examples and Pitfalls","\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F25-worked-examples-pitfalls","en\u002Fbusiness-analytics\u002Fappendix\u002F25-worked-examples-pitfalls",{"title":84,"path":398,"stem":399},"\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F26-reading-map","en\u002Fbusiness-analytics\u002Fappendix\u002F26-reading-map",{"title":401,"path":402,"stem":403,"children":404},"Capstone — The Evening Delivery Promise","\u002Fen\u002Fbusiness-analytics\u002Fcapstone","en\u002Fbusiness-analytics\u002Fcapstone\u002Findex",[405],{"title":401,"path":402,"stem":403},{"title":407,"path":408,"stem":409,"children":410,"page":249},"Financial Economic Time Series","\u002Fen\u002Ffinancial-economic-time-series","en\u002Ffinancial-economic-time-series",[411,417,423,429,435,441,447,453,459,465,471],{"title":412,"path":413,"stem":414,"children":415},"Financial and Economic Time Series — Course Guide","\u002Fen\u002Ffinancial-economic-time-series\u002F00-intro","en\u002Ffinancial-economic-time-series\u002F00-intro\u002Findex",[416],{"title":412,"path":413,"stem":414},{"title":418,"path":419,"stem":420,"children":421},"Three Versions of Time Series","\u002Fen\u002Ffinancial-economic-time-series\u002F01-bridge","en\u002Ffinancial-economic-time-series\u002F01-bridge\u002Findex",[422],{"title":418,"path":419,"stem":420},{"title":424,"path":425,"stem":426,"children":427},"Data, Clocks, and Transformations","\u002Fen\u002Ffinancial-economic-time-series\u002F02-data-transformations","en\u002Ffinancial-economic-time-series\u002F02-data-transformations\u002Findex",[428],{"title":424,"path":425,"stem":426},{"title":430,"path":431,"stem":432,"children":433},"Predictive Regressions and Persistent Predictors","\u002Fen\u002Ffinancial-economic-time-series\u002F03-predictive-regressions","en\u002Ffinancial-economic-time-series\u002F03-predictive-regressions\u002Findex",[434],{"title":430,"path":431,"stem":432},{"title":436,"path":437,"stem":438,"children":439},"Volatility, Tails, and Financial Risk","\u002Fen\u002Ffinancial-economic-time-series\u002F04-volatility-risk","en\u002Ffinancial-economic-time-series\u002F04-volatility-risk\u002Findex",[440],{"title":436,"path":437,"stem":438},{"title":442,"path":443,"stem":444,"children":445},"Unit Roots, Cointegration, and Error Correction","\u002Fen\u002Ffinancial-economic-time-series\u002F05-unit-roots-cointegration","en\u002Ffinancial-economic-time-series\u002F05-unit-roots-cointegration\u002Findex",[446],{"title":442,"path":443,"stem":444},{"title":448,"path":449,"stem":450,"children":451},"VAR, Structural Identification, and Local Projections","\u002Fen\u002Ffinancial-economic-time-series\u002F06-var-identification","en\u002Ffinancial-economic-time-series\u002F06-var-identification\u002Findex",[452],{"title":448,"path":449,"stem":450},{"title":454,"path":455,"stem":456,"children":457},"State Space, Mixed Frequency, and Nowcasting","\u002Fen\u002Ffinancial-economic-time-series\u002F07-state-space-nowcasting","en\u002Ffinancial-economic-time-series\u002F07-state-space-nowcasting\u002Findex",[458],{"title":454,"path":455,"stem":456},{"title":460,"path":461,"stem":462,"children":463},"Forecast Evaluation for Decisions","\u002Fen\u002Ffinancial-economic-time-series\u002F08-forecast-evaluation","en\u002Ffinancial-economic-time-series\u002F08-forecast-evaluation\u002Findex",[464],{"title":460,"path":461,"stem":462},{"title":466,"path":467,"stem":468,"children":469},"Integrated R Laboratory","\u002Fen\u002Ffinancial-economic-time-series\u002F09-r-laboratory","en\u002Ffinancial-economic-time-series\u002F09-r-laboratory\u002Findex",[470],{"title":466,"path":467,"stem":468},{"title":472,"path":473,"stem":474,"children":475},"Capstones, Data, and Reading Ladder","\u002Fen\u002Ffinancial-economic-time-series\u002F10-capstone-readings","en\u002Ffinancial-economic-time-series\u002F10-capstone-readings\u002Findex",[476],{"title":472,"path":473,"stem":474},{"title":478,"path":479,"stem":480,"children":481,"page":249},"Intro To Economics","\u002Fen\u002Fintro-to-economics","en\u002Fintro-to-economics",[482,486,490,494,498,502,506,510,514,518,522,526,530],{"title":483,"path":484,"stem":485},"Introduction to Economics — Decisions, Markets, and the Macroeconomy","\u002Fen\u002Fintro-to-economics\u002F00-intro","en\u002Fintro-to-economics\u002F00-intro",{"title":487,"path":488,"stem":489},"Chapter 1 — Choice, Opportunity Cost, and Trade","\u002Fen\u002Fintro-to-economics\u002F01-foundations","en\u002Fintro-to-economics\u002F01-foundations",{"title":491,"path":492,"stem":493},"Chapter 2 — Demand, Supply, Equilibrium, and Welfare","\u002Fen\u002Fintro-to-economics\u002F02-demand-and-supply","en\u002Fintro-to-economics\u002F02-demand-and-supply",{"title":495,"path":496,"stem":497},"Chapter 3 — Elasticity, Revenue, and Tax Incidence","\u002Fen\u002Fintro-to-economics\u002F03-elasticity","en\u002Fintro-to-economics\u002F03-elasticity",{"title":499,"path":500,"stem":501},"Chapter 4 — Firms, Market Power, and Market Failure","\u002Fen\u002Fintro-to-economics\u002F04-market-structures","en\u002Fintro-to-economics\u002F04-market-structures",{"title":503,"path":504,"stem":505},"Chapter 5 — GDP, Income, Wealth, and Welfare","\u002Fen\u002Fintro-to-economics\u002F05-gdp-and-wealth","en\u002Fintro-to-economics\u002F05-gdp-and-wealth",{"title":507,"path":508,"stem":509},"Chapter 6 — Inflation, Purchasing Power, and Labour Markets","\u002Fen\u002Fintro-to-economics\u002F06-inflation-and-unemployment","en\u002Fintro-to-economics\u002F06-inflation-and-unemployment",{"title":511,"path":512,"stem":513},"Chapter 7 — Productivity, Technology, and Economic Growth","\u002Fen\u002Fintro-to-economics\u002F07-economic-growth","en\u002Fintro-to-economics\u002F07-economic-growth",{"title":515,"path":516,"stem":517},"Chapter 8 — Money, Credit, and Banking","\u002Fen\u002Fintro-to-economics\u002F08-money-and-banking","en\u002Fintro-to-economics\u002F08-money-and-banking",{"title":519,"path":520,"stem":521},"Chapter 9 — Business Cycles, AD–AS, and Monetary Policy","\u002Fen\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as","en\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as",{"title":523,"path":524,"stem":525},"Chapter 10 — Fiscal Policy, Distribution, and Public Debt","\u002Fen\u002Fintro-to-economics\u002F10-fiscal-policy","en\u002Fintro-to-economics\u002F10-fiscal-policy",{"title":527,"path":528,"stem":529},"Chapter 11 — Trade, Capital Flows, and Exchange Rates","\u002Fen\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates","en\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates",{"title":531,"path":532,"stem":533},"Chapter 12 — Integrated Economic Analysis Studio","\u002Fen\u002Fintro-to-economics\u002F12-review-and-case-studies","en\u002Fintro-to-economics\u002F12-review-and-case-studies",{"title":535,"path":536,"stem":537,"children":538,"page":249},"Microeconometrics","\u002Fen\u002Fmicroeconometrics","en\u002Fmicroeconometrics",[539,557,563,581,603,629,651,673,691,709],{"title":540,"path":541,"stem":542,"children":543},"0. Causal Questions and Designs","\u002Fen\u002Fmicroeconometrics\u002F00-foundations","en\u002Fmicroeconometrics\u002F00-foundations\u002Findex",[544,545,549,553],{"title":540,"path":541,"stem":542},{"title":546,"path":547,"stem":548},"Causal Questions and Estimands","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F01-causal-question-estimands","en\u002Fmicroeconometrics\u002F00-foundations\u002F01-causal-question-estimands",{"title":550,"path":551,"stem":552},"Potential Outcomes and Experiments","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F02-potential-outcomes-experiments","en\u002Fmicroeconometrics\u002F00-foundations\u002F02-potential-outcomes-experiments",{"title":554,"path":555,"stem":556},"Causal Diagrams and Controls","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F03-dags-controls","en\u002Fmicroeconometrics\u002F00-foundations\u002F03-dags-controls",{"title":558,"path":559,"stem":560,"children":561},"Microeconometrics — Designing Credible Counterfactuals","\u002Fen\u002Fmicroeconometrics\u002F00-index","en\u002Fmicroeconometrics\u002F00-index",[562],{"title":558,"path":559,"stem":560},{"title":564,"path":565,"stem":566,"children":567},"1. Regression and Inference","\u002Fen\u002Fmicroeconometrics\u002F01-regression","en\u002Fmicroeconometrics\u002F01-regression\u002Findex",[568,569,573,577],{"title":564,"path":565,"stem":566},{"title":570,"path":571,"stem":572},"OLS as a Projection","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F04-ols-projection","en\u002Fmicroeconometrics\u002F01-regression\u002F04-ols-projection",{"title":574,"path":575,"stem":576},"FWL, Selection and Controls","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F05-fwl-selection-controls","en\u002Fmicroeconometrics\u002F01-regression\u002F05-fwl-selection-controls",{"title":578,"path":579,"stem":580},"Inference and Clustering","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F06-inference-clustering","en\u002Fmicroeconometrics\u002F01-regression\u002F06-inference-clustering",{"title":582,"path":583,"stem":584,"children":585},"2. Instruments and Panel Data","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel","en\u002Fmicroeconometrics\u002F02-iv-panel\u002Findex",[586,587,591,595,599],{"title":582,"path":583,"stem":584},{"title":588,"path":589,"stem":590},"Instrumental Variables","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F07-iv-identification","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F07-iv-identification",{"title":592,"path":593,"stem":594},"Weak Instruments and LATE","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F08-weak-iv-late","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F08-weak-iv-late",{"title":596,"path":597,"stem":598},"Panel Fixed Effects","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F09-panel-fixed-effects","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F09-panel-fixed-effects",{"title":600,"path":601,"stem":602},"Dynamic Panels and Limits","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F10-dynamic-panel","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F10-dynamic-panel",{"title":604,"path":605,"stem":606,"children":607},"3. Policy Evaluation Designs","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs","en\u002Fmicroeconometrics\u002F03-policy-designs\u002Findex",[608,609,613,617,621,625],{"title":604,"path":605,"stem":606},{"title":610,"path":611,"stem":612},"Difference-in-Differences","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F11-did-core","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F11-did-core",{"title":614,"path":615,"stem":616},"Staggered DID and Event Studies","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F12-staggered-event-studies","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F12-staggered-event-studies",{"title":618,"path":619,"stem":620},"Regression Discontinuity","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F13-rdd","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F13-rdd",{"title":622,"path":623,"stem":624},"Matching, Weighting and Overlap","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F14-matching-weighting","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F14-matching-weighting",{"title":626,"path":627,"stem":628},"Synthetic Control","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F15-synthetic-control","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F15-synthetic-control",{"title":630,"path":631,"stem":632,"children":633},"Module 4 — Choice and Limited Outcomes","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002Findex",[634,635,639,643,647],{"title":630,"path":631,"stem":632},{"title":636,"path":637,"stem":638},"Binary Choice","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F16-binary-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F16-binary-choice",{"title":640,"path":641,"stem":642},"Multinomial and Ordered Choice","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F17-multinomial-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F17-multinomial-choice",{"title":644,"path":645,"stem":646},"Count Outcomes","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F18-count-outcomes","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F18-count-outcomes",{"title":648,"path":649,"stem":650},"Censoring, Truncation and Selection","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F19-censoring-selection","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F19-censoring-selection",{"title":652,"path":653,"stem":654,"children":655},"Module 5 — Modern Causal Analysis","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal","en\u002Fmicroeconometrics\u002F05-modern-causal\u002Findex",[656,657,661,665,669],{"title":652,"path":653,"stem":654},{"title":658,"path":659,"stem":660},"Double Machine Learning","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F20-dml","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F20-dml",{"title":662,"path":663,"stem":664},"Heterogeneity and Policy Learning","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F21-heterogeneity-policy","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F21-heterogeneity-policy",{"title":666,"path":667,"stem":668},"Sensitivity and Partial Identification","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F22-sensitivity-partial-id","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F22-sensitivity-partial-id",{"title":670,"path":671,"stem":672},"External Validity and Transport","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F23-external-validity","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F23-external-validity",{"title":674,"path":675,"stem":676,"children":677},"Module 6 — From Data to Auditable Evidence","\u002Fen\u002Fmicroeconometrics\u002F06-workflow","en\u002Fmicroeconometrics\u002F06-workflow\u002Findex",[678,679,683,687],{"title":674,"path":675,"stem":676},{"title":680,"path":681,"stem":682},"Data Provenance","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F24-data-provenance","en\u002Fmicroeconometrics\u002F06-workflow\u002F24-data-provenance",{"title":684,"path":685,"stem":686},"Reproducibility and Reporting","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F25-reproducibility-reporting","en\u002Fmicroeconometrics\u002F06-workflow\u002F25-reproducibility-reporting",{"title":688,"path":689,"stem":690},"Paper and Evidence Audit","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F26-paper-audit","en\u002Fmicroeconometrics\u002F06-workflow\u002F26-paper-audit",{"title":692,"path":693,"stem":694,"children":695},"Appendix — Revision and Evidence Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix","en\u002Fmicroeconometrics\u002Fappendix\u002Findex",[696,697,701,705],{"title":692,"path":693,"stem":694},{"title":698,"path":699,"stem":700},"Formula and Design Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F27-formula-design-map","en\u002Fmicroeconometrics\u002Fappendix\u002F27-formula-design-map",{"title":702,"path":703,"stem":704},"Ten Worked Microeconometric Pitfalls","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F28-worked-pitfalls","en\u002Fmicroeconometrics\u002Fappendix\u002F28-worked-pitfalls",{"title":706,"path":707,"stem":708},"Reading and Software Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F29-reading-software-map","en\u002Fmicroeconometrics\u002Fappendix\u002F29-reading-software-map",{"title":710,"path":711,"stem":712,"children":713},"Capstone — Should Northbridge Expand Pathways?","\u002Fen\u002Fmicroeconometrics\u002Fcapstone","en\u002Fmicroeconometrics\u002Fcapstone\u002Findex",[714],{"title":710,"path":711,"stem":712},{"title":716,"path":717,"stem":718,"children":719,"page":249},"Microeconomics","\u002Fen\u002Fmicroeconomics","en\u002Fmicroeconomics",[720,726,732,738,744,750,756,762,768,774,780,786,792],{"title":721,"path":722,"stem":723,"children":724},"Advanced Microeconomics — Course Guide","\u002Fen\u002Fmicroeconomics\u002F00-intro","en\u002Fmicroeconomics\u002F00-intro\u002Findex",[725],{"title":721,"path":722,"stem":723},{"title":727,"path":728,"stem":729,"children":730},"Module 1 — Choice, Duality, and Revealed Preference","\u002Fen\u002Fmicroeconomics\u002F01-fundations","en\u002Fmicroeconomics\u002F01-fundations\u002Findex",[731],{"title":727,"path":728,"stem":729},{"title":733,"path":734,"stem":735,"children":736},"Module 2 — Comparative Statics and Welfare Measurement","\u002Fen\u002Fmicroeconomics\u002F02-comparative-statics","en\u002Fmicroeconomics\u002F02-comparative-statics\u002Findex",[737],{"title":733,"path":734,"stem":735},{"title":739,"path":740,"stem":741,"children":742},"Module 3 — Choice under Risk and Insurance","\u002Fen\u002Fmicroeconomics\u002F03-uncertainty","en\u002Fmicroeconomics\u002F03-uncertainty\u002Findex",[743],{"title":739,"path":740,"stem":741},{"title":745,"path":746,"stem":747,"children":748},"Module 4 — General Equilibrium and Welfare","\u002Fen\u002Fmicroeconomics\u002F04-general-equilibrium","en\u002Fmicroeconomics\u002F04-general-equilibrium\u002Findex",[749],{"title":745,"path":746,"stem":747},{"title":751,"path":752,"stem":753,"children":754},"Module 5 — Static, Dynamic, and Repeated Games","\u002Fen\u002Fmicroeconomics\u002F05-game-theory","en\u002Fmicroeconomics\u002F05-game-theory\u002Findex",[755],{"title":751,"path":752,"stem":753},{"title":757,"path":758,"stem":759,"children":760},"Module 6 — Oligopoly, Entry, and Algorithmic Pricing","\u002Fen\u002Fmicroeconomics\u002F06-oligopoly","en\u002Fmicroeconomics\u002F06-oligopoly\u002Findex",[761],{"title":757,"path":758,"stem":759},{"title":763,"path":764,"stem":765,"children":766},"Module 7 — Information Economics and Contracts","\u002Fen\u002Fmicroeconomics\u002F07-information-economics","en\u002Fmicroeconomics\u002F07-information-economics\u002Findex",[767],{"title":763,"path":764,"stem":765},{"title":769,"path":770,"stem":771,"children":772},"Module 8 — Mechanism Design and Auctions","\u002Fen\u002Fmicroeconomics\u002F08-mechanism-design","en\u002Fmicroeconomics\u002F08-mechanism-design\u002Findex",[773],{"title":769,"path":770,"stem":771},{"title":775,"path":776,"stem":777,"children":778},"Module 9 — Behavioural and Experimental Microeconomics","\u002Fen\u002Fmicroeconomics\u002F09-behavioural-economics","en\u002Fmicroeconomics\u002F09-behavioural-economics\u002Findex",[779],{"title":775,"path":776,"stem":777},{"title":781,"path":782,"stem":783,"children":784},"Module 10 — Externalities, Public Goods, and Collective Action","\u002Fen\u002Fmicroeconomics\u002F10-externalities-public-goods","en\u002Fmicroeconomics\u002F10-externalities-public-goods\u002Findex",[785],{"title":781,"path":782,"stem":783},{"title":787,"path":788,"stem":789,"children":790},"Module 11 — Matching and Market Design","\u002Fen\u002Fmicroeconomics\u002F11-market-design","en\u002Fmicroeconomics\u002F11-market-design\u002Findex",[791],{"title":787,"path":788,"stem":789},{"title":793,"path":794,"stem":795,"children":796},"Module 12 — Integrated Microeconomic Design Studio","\u002Fen\u002Fmicroeconomics\u002F12-review","en\u002Fmicroeconomics\u002F12-review\u002Findex",[797],{"title":793,"path":794,"stem":795},{"title":799,"path":800,"stem":801,"children":802},"Playground","\u002Fen\u002Fplayground","en\u002Fplayground\u002Findex",[803,804,808,812,816,820],{"title":799,"path":800,"stem":801},{"title":805,"path":806,"stem":807},"Typst Plugin Playground","\u002Fen\u002Fplayground\u002F01-typstex","en\u002Fplayground\u002F01-typstex",{"title":809,"path":810,"stem":811},"Citation Plugin Test","\u002Fen\u002Fplayground\u002F02-citation","en\u002Fplayground\u002F02-citation",{"title":813,"path":814,"stem":815},"Pyodide Playground","\u002Fen\u002Fplayground\u002F03-pyodide","en\u002Fplayground\u002F03-pyodide",{"title":817,"path":818,"stem":819},"WebR Playground","\u002Fen\u002Fplayground\u002F04-webr","en\u002Fplayground\u002F04-webr",{"title":821,"path":822,"stem":823},"Chart.js 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文献综述的构建与写作","\u002Fzh\u002Facademic-writing\u002F04-writing-the-literature-review","zh\u002Facademic-writing\u002F04-writing-the-literature-review",{"title":1056,"path":1057,"stem":1058},"8. 文献综述清单与模板","\u002Fzh\u002Facademic-writing\u002F08-literature-review-checklist-and-template","zh\u002Facademic-writing\u002F08-literature-review-checklist-and-template",{"title":1060,"path":1061,"stem":1062},"10. 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",[1831,1832,1835,1866],"span",{"className":1833},[1834],"katex",[1831,1836,1839],{"className":1837},[1838],"katex-mathml",[1840,1841,1843],"math",{"xmlns":1842},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[1844,1845,1846,1861],"semantics",{},[1847,1848,1849],"mrow",{},[1850,1851,1853,1857],"mover",{"accent":1852},"true",[1854,1855,1856],"mi",{},"β",[1858,1859,1860],"mo",{},"^",[1862,1863,1865],"annotation",{"encoding":1864},"application\u002Fx-tex","\\hat\\beta",[1831,1867,1870],{"className":1868,"ariaHidden":1852},[1869],"katex-html",[1831,1871,1874,1879],{"className":1872},[1873],"base",[1831,1875],{"className":1876,"style":1878},[1877],"strut","height:1.1523em;vertical-align:-0.1944em;",[1831,1880,1884],{"className":1881},[1882,1883],"mord","accent",[1831,1885,1889,1930],{"className":1886},[1887,1888],"vlist-t","vlist-t2",[1831,1890,1893,1925],{"className":1891},[1892],"vlist-r",[1831,1894,1898,1911],{"className":1895,"style":1897},[1896],"vlist","height:0.9579em;",[1831,1899,1901,1906],{"style":1900},"top:-3em;",[1831,1902],{"className":1903,"style":1905},[1904],"pstrut","height:3em;",[1831,1907,1856],{"className":1908,"style":1910},[1882,1909],"mathnormal","margin-right:0.0528em;",[1831,1912,1914,1917],{"style":1913},"top:-3.2634em;",[1831,1915],{"className":1916,"style":1905},[1904],[1831,1918,1922],{"className":1919,"style":1921},[1920],"accent-body","left:-0.1667em;",[1831,1923,1860],{"className":1924},[1882],[1831,1926,1929],{"className":1927},[1928],"vlist-s","​",[1831,1931,1933],{"className":1932},[1892],[1831,1934,1937],{"className":1935,"style":1936},[1896],"height:0.1944em;",[1831,1938],{},"，这些估计值的分布就是抽样分布。标准误是其标准差的估计。样本量增大通常让估计更集中，但前提是样本和估计过程仍然针对同一目标。",[1798,1941,1942],{},"大样本近似常写为：",[1831,1944,1947],{"className":1945},[1946],"katex-display",[1831,1948,1950,2022],{"className":1949},[1834],[1831,1951,1953],{"className":1952},[1838],[1840,1954,1956],{"xmlns":1842,"display":1955},"block",[1844,1957,1958,2019],{},[1847,1959,1960,1966,1970,1976,1979,1981,1984,1998,2001,2003,2007,2010,2013,2015],{},[1961,1962,1963],"msqrt",{},[1854,1964,1965],{},"n",[1858,1967,1969],{"stretchy":1968},"false","(",[1850,1971,1972,1974],{"accent":1852},[1854,1973,1856],{},[1858,1975,1860],{},[1858,1977,1978],{},"−",[1854,1980,1856],{},[1858,1982,1983],{"stretchy":1968},")",[1850,1985,1986,1990],{},[1858,1987,1989],{"stretchy":1852,"minsize":1988},"3.0em","→",[1991,1992,1995],"mpadded",{"width":1993,"lspace":1994},"+0.6em","0.3em",[1854,1996,1997],{},"d",[1854,1999,2000],{},"N",[1858,2002,1969],{"stretchy":1968},[2004,2005,2006],"mn",{},"0",[1858,2008,2009],{"separator":1852},",",[1854,2011,2012],{},"V",[1858,2014,1983],{"stretchy":1968},[1854,2016,2018],{"mathvariant":2017},"normal",".",[1862,2020,2021],{"encoding":1864},"\\sqrt{n}(\\hat\\beta-\\beta)\\xrightarrow{d}N(0,V).",[1831,2023,2025,2153,2241],{"className":2024,"ariaHidden":1852},[1869],[1831,2026,2028,2032,2095,2099,2141,2146,2150],{"className":2027},[1873],[1831,2029],{"className":2030,"style":2031},[1877],"height:1.2079em;vertical-align:-0.25em;",[1831,2033,2036],{"className":2034},[1882,2035],"sqrt",[1831,2037,2039,2086],{"className":2038},[1887,1888],[1831,2040,2042,2083],{"className":2041},[1892],[1831,2043,2046,2060],{"className":2044,"style":2045},[1896],"height:0.8492em;",[1831,2047,2050,2053],{"className":2048,"style":1900},[2049],"svg-align",[1831,2051],{"className":2052,"style":1905},[1904],[1831,2054,2057],{"className":2055,"style":2056},[1882],"padding-left:0.833em;",[1831,2058,1965],{"className":2059},[1882,1909],[1831,2061,2063,2066],{"style":2062},"top:-2.8092em;",[1831,2064],{"className":2065,"style":1905},[1904],[1831,2067,2071],{"className":2068,"style":2070},[2069],"hide-tail","min-width:0.853em;height:1.08em;",[2072,2073,2079],"svg",{"xmlns":2074,"width":2075,"height":2076,"viewBox":2077,"preserveAspectRatio":2078},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 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0 400000 522","xMaxYMin slice",[2080,2224],{"d":2225},"M0 241v40h399891c-47.3 35.3-84 78-110 128\n-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20\n 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7\n 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85\n-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5\n-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67\n 151.7 139 205zm0 0v40h399900v-40z",[1831,2227,1929],{"className":2228},[1928],[1831,2230,2232],{"className":2231},[1892],[1831,2233,2236],{"className":2234,"style":2235},[1896],"height:0.011em;",[1831,2237],{},[1831,2239],{"className":2240,"style":2170},[2144],[1831,2242,2244,2248,2252,2255,2258,2262,2266,2269,2272],{"className":2243},[1873],[1831,2245],{"className":2246,"style":2247},[1877],"height:1em;vertical-align:-0.25em;",[1831,2249,2000],{"className":2250,"style":2251},[1882,1909],"margin-right:0.109em;",[1831,2253,1969],{"className":2254},[2098],[1831,2256,2006],{"className":2257},[1882],[1831,2259,2009],{"className":2260},[2261],"mpunct",[1831,2263],{"className":2264,"style":2265},[2144],"margin-right:0.1667em;",[1831,2267,2012],{"className":2268,"style":2145},[1882,1909],[1831,2270,1983],{"className":2271},[2166],[1831,2273,2018],{"className":2274},[1882],[1798,2276,2277,2278,2307],{},"推断需要估计 ",[1831,2279,2281,2294],{"className":2280},[1834],[1831,2282,2284],{"className":2283},[1838],[1840,2285,2286],{"xmlns":1842},[1844,2287,2288,2292],{},[1847,2289,2290],{},[1854,2291,2012],{},[1862,2293,2012],{"encoding":1864},[1831,2295,2297],{"className":2296,"ariaHidden":1852},[1869],[1831,2298,2300,2304],{"className":2299},[1873],[1831,2301],{"className":2302,"style":2303},[1877],"height:0.6833em;",[1831,2305,2012],{"className":2306,"style":2145},[1882,1909],"。如果误差具有异方差或组内相关，使用错误的方差公式会让置信区间过窄，t 统计量过大。",[1793,2309,2311],{"id":2310},"_3-t-检验与置信区间","3. t 检验与置信区间",[1798,2313,2314,2315,2542],{},"检验 ",[1831,2316,2318,2363],{"className":2317},[1834],[1831,2319,2321],{"className":2320},[1838],[1840,2322,2323],{"xmlns":1842},[1844,2324,2325,2360],{},[1847,2326,2327,2335,2338,2345,2348],{},[2328,2329,2330,2333],"msub",{},[1854,2331,2332],{},"H",[2004,2334,2006],{},[1858,2336,2337],{},":",[2328,2339,2340,2342],{},[1854,2341,1856],{},[1854,2343,2344],{},"j",[1858,2346,2347],{},"=",[2328,2349,2350,2352],{},[1854,2351,1856],{},[1847,2353,2354,2356,2358],{},[1854,2355,2344],{},[1858,2357,2009],{"separator":1852},[2004,2359,2006],{},[1862,2361,2362],{"encoding":1864},"H_0:\\beta_j=\\beta_{j,0}",[1831,2364,2366,2427,2487],{"className":2365,"ariaHidden":1852},[1869],[1831,2367,2369,2373,2418,2421,2424],{"className":2368},[1873],[1831,2370],{"className":2371,"style":2372},[1877],"height:0.8333em;vertical-align:-0.15em;",[1831,2374,2376,2380],{"className":2375},[1882],[1831,2377,2332],{"className":2378,"style":2379},[1882,1909],"margin-right:0.0813em;",[1831,2381,2384],{"className":2382},[2383],"msupsub",[1831,2385,2387,2409],{"className":2386},[1887,1888],[1831,2388,2390,2406],{"className":2389},[1892],[1831,2391,2394],{"className":2392,"style":2393},[1896],"height:0.3011em;",[1831,2395,2397,2400],{"style":2396},"top:-2.55em;margin-left:-0.0813em;margin-right:0.05em;",[1831,2398],{"className":2399,"style":2192},[1904],[1831,2401,2403],{"className":2402},[2196,2197,2198,2199],[1831,2404,2006],{"className":2405},[1882,2199],[1831,2407,1929],{"className":2408},[1928],[1831,2410,2412],{"className":2411},[1892],[1831,2413,2416],{"className":2414,"style":2415},[1896],"height:0.15em;",[1831,2417],{},[1831,2419],{"className":2420,"style":2170},[2144],[1831,2422,2337],{"className":2423},[2174],[1831,2425],{"className":2426,"style":2170},[2144],[1831,2428,2430,2434,2478,2481,2484],{"className":2429},[1873],[1831,2431],{"className":2432,"style":2433},[1877],"height:0.9805em;vertical-align:-0.2861em;",[1831,2435,2437,2440],{"className":2436},[1882],[1831,2438,1856],{"className":2439,"style":1910},[1882,1909],[1831,2441,2443],{"className":2442},[2383],[1831,2444,2446,2469],{"className":2445},[1887,1888],[1831,2447,2449,2466],{"className":2448},[1892],[1831,2450,2453],{"className":2451,"style":2452},[1896],"height:0.3117em;",[1831,2454,2456,2459],{"style":2455},"top:-2.55em;margin-left:-0.0528em;margin-right:0.05em;",[1831,2457],{"className":2458,"style":2192},[1904],[1831,2460,2462],{"className":2461},[2196,2197,2198,2199],[1831,2463,2344],{"className":2464,"style":2465},[1882,1909,2199],"margin-right:0.0572em;",[1831,2467,1929],{"className":2468},[1928],[1831,2470,2472],{"className":2471},[1892],[1831,2473,2476],{"className":2474,"style":2475},[1896],"height:0.2861em;",[1831,2477],{},[1831,2479],{"className":2480,"style":2170},[2144],[1831,2482,2347],{"className":2483},[2174],[1831,2485],{"className":2486,"style":2170},[2144],[1831,2488,2490,2493],{"className":2489},[1873],[1831,2491],{"className":2492,"style":2433},[1877],[1831,2494,2496,2499],{"className":2495},[1882],[1831,2497,1856],{"className":2498,"style":1910},[1882,1909],[1831,2500,2502],{"className":2501},[2383],[1831,2503,2505,2534],{"className":2504},[1887,1888],[1831,2506,2508,2531],{"className":2507},[1892],[1831,2509,2511],{"className":2510,"style":2452},[1896],[1831,2512,2513,2516],{"style":2455},[1831,2514],{"className":2515,"style":2192},[1904],[1831,2517,2519],{"className":2518},[2196,2197,2198,2199],[1831,2520,2522,2525,2528],{"className":2521},[1882,2199],[1831,2523,2344],{"className":2524,"style":2465},[1882,1909,2199],[1831,2526,2009],{"className":2527},[2261,2199],[1831,2529,2006],{"className":2530},[1882,2199],[1831,2532,1929],{"className":2533},[1928],[1831,2535,2537],{"className":2536},[1892],[1831,2538,2540],{"className":2539,"style":2475},[1896],[1831,2541],{}," 的统计量为：",[1831,2544,2546],{"className":2545},[1946],[1831,2547,2549,2619],{"className":2548},[1834],[1831,2550,2552],{"className":2551},[1838],[1840,2553,2554],{"xmlns":1842,"display":1955},[1844,2555,2556,2616],{},[1847,2557,2558,2561,2563,2614],{},[1854,2559,2560],{},"t",[1858,2562,2347],{},[2564,2565,2566,2592],"mfrac",{},[1847,2567,2568,2578,2580],{},[2328,2569,2570,2576],{},[1850,2571,2572,2574],{"accent":1852},[1854,2573,1856],{},[1858,2575,1860],{},[1854,2577,2344],{},[1858,2579,1978],{},[2328,2581,2582,2584],{},[1854,2583,1856],{},[1847,2585,2586,2588,2590],{},[1854,2587,2344],{},[1858,2589,2009],{"separator":1852},[2004,2591,2006],{},[1847,2593,2594,2597,2600,2602,2612],{},[1854,2595,2596],{},"S",[1854,2598,2599],{},"E",[1858,2601,1969],{"stretchy":1968},[2328,2603,2604,2610],{},[1850,2605,2606,2608],{"accent":1852},[1854,2607,1856],{},[1858,2609,1860],{},[1854,2611,2344],{},[1858,2613,1983],{"stretchy":1968},[1854,2615,2018],{"mathvariant":2017},[1862,2617,2618],{"encoding":1864},"t=\\frac{\\hat\\beta_j-\\beta_{j,0}}{SE(\\hat\\beta_j)}.",[1831,2620,2622,2641],{"className":2621,"ariaHidden":1852},[1869],[1831,2623,2625,2629,2632,2635,2638],{"className":2624},[1873],[1831,2626],{"className":2627,"style":2628},[1877],"height:0.6151em;",[1831,2630,2560],{"className":2631},[1882,1909],[1831,2633],{"className":2634,"style":2170},[2144],[1831,2636,2347],{"className":2637},[2174],[1831,2639],{"className":2640,"style":2170},[2144],[1831,2642,2644,2648,2941],{"className":2643},[1873],[1831,2645],{"className":2646,"style":2647},[1877],"height:2.7689em;vertical-align:-1.134em;",[1831,2649,2651,2655,2938],{"className":2650},[1882],[1831,2652],{"className":2653},[2098,2654],"nulldelimiter",[1831,2656,2658],{"className":2657},[2564],[1831,2659,2661,2929],{"className":2660},[1887,1888],[1831,2662,2664,2926],{"className":2663},[1892],[1831,2665,2668,2769,2780],{"className":2666,"style":2667},[1896],"height:1.6349em;",[1831,2669,2671,2674],{"style":2670},"top:-2.1521em;",[1831,2672],{"className":2673,"style":1905},[1904],[1831,2675,2677,2681,2684,2687,2766],{"className":2676},[1882],[1831,2678,2596],{"className":2679,"style":2680},[1882,1909],"margin-right:0.0576em;",[1831,2682,2599],{"className":2683,"style":2680},[1882,1909],[1831,2685,1969],{"className":2686},[2098],[1831,2688,2690,2732],{"className":2689},[1882],[1831,2691,2693],{"className":2692},[1882,1883],[1831,2694,2696,2724],{"className":2695},[1887,1888],[1831,2697,2699,2721],{"className":2698},[1892],[1831,2700,2702,2710],{"className":2701,"style":1897},[1896],[1831,2703,2704,2707],{"style":1900},[1831,2705],{"className":2706,"style":1905},[1904],[1831,2708,1856],{"className":2709,"style":1910},[1882,1909],[1831,2711,2712,2715],{"style":1913},[1831,2713],{"className":2714,"style":1905},[1904],[1831,2716,2718],{"className":2717,"style":1921},[1920],[1831,2719,1860],{"className":2720},[1882],[1831,2722,1929],{"className":2723},[1928],[1831,2725,2727],{"className":2726},[1892],[1831,2728,2730],{"className":2729,"style":1936},[1896],[1831,2731],{},[1831,2733,2735],{"className":2734},[2383],[1831,2736,2738,2758],{"className":2737},[1887,1888],[1831,2739,2741,2755],{"className":2740},[1892],[1831,2742,2744],{"className":2743,"style":2452},[1896],[1831,2745,2746,2749],{"style":2455},[1831,2747],{"className":2748,"style":2192},[1904],[1831,2750,2752],{"className":2751},[2196,2197,2198,2199],[1831,2753,2344],{"className":2754,"style":2465},[1882,1909,2199],[1831,2756,1929],{"className":2757},[1928],[1831,2759,2761],{"className":2760},[1892],[1831,2762,2764],{"className":2763,"style":2475},[1896],[1831,2765],{},[1831,2767,1983],{"className":2768},[2166],[1831,2770,2772,2775],{"style":2771},"top:-3.23em;",[1831,2773],{"className":2774,"style":1905},[1904],[1831,2776],{"className":2777,"style":2779},[2778],"frac-line","border-bottom-width:0.04em;",[1831,2781,2783,2786],{"style":2782},"top:-3.677em;",[1831,2784],{"className":2785,"style":1905},[1904],[1831,2787,2789,2868,2871,2874,2877],{"className":2788},[1882],[1831,2790,2792,2834],{"className":2791},[1882],[1831,2793,2795],{"className":2794},[1882,1883],[1831,2796,2798,2826],{"className":2797},[1887,1888],[1831,2799,2801,2823],{"className":2800},[1892],[1831,2802,2804,2812],{"className":2803,"style":1897},[1896],[1831,2805,2806,2809],{"style":1900},[1831,2807],{"className":2808,"style":1905},[1904],[1831,2810,1856],{"className":2811,"style":1910},[1882,1909],[1831,2813,2814,2817],{"style":1913},[1831,2815],{"className":2816,"style":1905},[1904],[1831,2818,2820],{"className":2819,"style":1921},[1920],[1831,2821,1860],{"className":2822},[1882],[1831,2824,1929],{"className":2825},[1928],[1831,2827,2829],{"className":2828},[1892],[1831,2830,2832],{"className":2831,"style":1936},[1896],[1831,2833],{},[1831,2835,2837],{"className":2836},[2383],[1831,2838,2840,2860],{"className":2839},[1887,1888],[1831,2841,2843,2857],{"className":2842},[1892],[1831,2844,2846],{"className":2845,"style":2452},[1896],[1831,2847,2848,2851],{"style":2455},[1831,2849],{"className":2850,"style":2192},[1904],[1831,2852,2854],{"className":2853},[2196,2197,2198,2199],[1831,2855,2344],{"className":2856,"style":2465},[1882,1909,2199],[1831,2858,1929],{"className":2859},[1928],[1831,2861,2863],{"className":2862},[1892],[1831,2864,2866],{"className":2865,"style":2475},[1896],[1831,2867],{},[1831,2869],{"className":2870,"style":2145},[2144],[1831,2872,1978],{"className":2873},[2149],[1831,2875],{"className":2876,"style":2145},[2144],[1831,2878,2880,2883],{"className":2879},[1882],[1831,2881,1856],{"className":2882,"style":1910},[1882,1909],[1831,2884,2886],{"className":2885},[2383],[1831,2887,2889,2918],{"className":2888},[1887,1888],[1831,2890,2892,2915],{"className":2891},[1892],[1831,2893,2895],{"className":2894,"style":2452},[1896],[1831,2896,2897,2900],{"style":2455},[1831,2898],{"className":2899,"style":2192},[1904],[1831,2901,2903],{"className":2902},[2196,2197,2198,2199],[1831,2904,2906,2909,2912],{"className":2905},[1882,2199],[1831,2907,2344],{"className":2908,"style":2465},[1882,1909,2199],[1831,2910,2009],{"className":2911},[2261,2199],[1831,2913,2006],{"className":2914},[1882,2199],[1831,2916,1929],{"className":2917},[1928],[1831,2919,2921],{"className":2920},[1892],[1831,2922,2924],{"className":2923,"style":2475},[1896],[1831,2925],{},[1831,2927,1929],{"className":2928},[1928],[1831,2930,2932],{"className":2931},[1892],[1831,2933,2936],{"className":2934,"style":2935},[1896],"height:1.134em;",[1831,2937],{},[1831,2939],{"className":2940},[2166,2654],[1831,2942,2018],{"className":2943},[1882],[1798,2945,2946],{},"95% 置信区间近似为：",[1831,2948,2950],{"className":2949},[1946],[1831,2951,2953,3005],{"className":2952},[1834],[1831,2954,2956],{"className":2955},[1838],[1840,2957,2958],{"xmlns":1842,"display":1955},[1844,2959,2960,3002],{},[1847,2961,2962,2972,2975,2978,2982,2984,2986,2988,2998,3000],{},[2328,2963,2964,2970],{},[1850,2965,2966,2968],{"accent":1852},[1854,2967,1856],{},[1858,2969,1860],{},[1854,2971,2344],{},[1858,2973,2974],{},"±",[2004,2976,2977],{},"1.96",[2979,2980,2981],"mtext",{}," ",[1854,2983,2596],{},[1854,2985,2599],{},[1858,2987,1969],{"stretchy":1968},[2328,2989,2990,2996],{},[1850,2991,2992,2994],{"accent":1852},[1854,2993,1856],{},[1858,2995,1860],{},[1854,2997,2344],{},[1858,2999,1983],{"stretchy":1968},[1854,3001,2018],{"mathvariant":2017},[1862,3003,3004],{"encoding":1864},"\\hat\\beta_j\\pm1.96\\,SE(\\hat\\beta_j).",[1831,3006,3008,3103],{"className":3007,"ariaHidden":1852},[1869],[1831,3009,3011,3015,3094,3097,3100],{"className":3010},[1873],[1831,3012],{"className":3013,"style":3014},[1877],"height:1.244em;vertical-align:-0.2861em;",[1831,3016,3018,3060],{"className":3017},[1882],[1831,3019,3021],{"className":3020},[1882,1883],[1831,3022,3024,3052],{"className":3023},[1887,1888],[1831,3025,3027,3049],{"className":3026},[1892],[1831,3028,3030,3038],{"className":3029,"style":1897},[1896],[1831,3031,3032,3035],{"style":1900},[1831,3033],{"className":3034,"style":1905},[1904],[1831,3036,1856],{"className":3037,"style":1910},[1882,1909],[1831,3039,3040,3043],{"style":1913},[1831,3041],{"className":3042,"style":1905},[1904],[1831,3044,3046],{"className":3045,"style":1921},[1920],[1831,3047,1860],{"className":3048},[1882],[1831,3050,1929],{"className":3051},[1928],[1831,3053,3055],{"className":3054},[1892],[1831,3056,3058],{"className":3057,"style":1936},[1896],[1831,3059],{},[1831,3061,3063],{"className":3062},[2383],[1831,3064,3066,3086],{"className":3065},[1887,1888],[1831,3067,3069,3083],{"className":3068},[1892],[1831,3070,3072],{"className":3071,"style":2452},[1896],[1831,3073,3074,3077],{"style":2455},[1831,3075],{"className":3076,"style":2192},[1904],[1831,3078,3080],{"className":3079},[2196,2197,2198,2199],[1831,3081,2344],{"className":3082,"style":2465},[1882,1909,2199],[1831,3084,1929],{"className":3085},[1928],[1831,3087,3089],{"className":3088},[1892],[1831,3090,3092],{"className":3091,"style":2475},[1896],[1831,3093],{},[1831,3095],{"className":3096,"style":2145},[2144],[1831,3098,2974],{"className":3099},[2149],[1831,3101],{"className":3102,"style":2145},[2144],[1831,3104,3106,3109,3112,3115,3118,3121,3124,3203,3206],{"className":3105},[1873],[1831,3107],{"className":3108,"style":3014},[1877],[1831,3110,2977],{"className":3111},[1882],[1831,3113],{"className":3114,"style":2265},[2144],[1831,3116,2596],{"className":3117,"style":2680},[1882,1909],[1831,3119,2599],{"className":3120,"style":2680},[1882,1909],[1831,3122,1969],{"className":3123},[2098],[1831,3125,3127,3169],{"className":3126},[1882],[1831,3128,3130],{"className":3129},[1882,1883],[1831,3131,3133,3161],{"className":3132},[1887,1888],[1831,3134,3136,3158],{"className":3135},[1892],[1831,3137,3139,3147],{"className":3138,"style":1897},[1896],[1831,3140,3141,3144],{"style":1900},[1831,3142],{"className":3143,"style":1905},[1904],[1831,3145,1856],{"className":3146,"style":1910},[1882,1909],[1831,3148,3149,3152],{"style":1913},[1831,3150],{"className":3151,"style":1905},[1904],[1831,3153,3155],{"className":3154,"style":1921},[1920],[1831,3156,1860],{"className":3157},[1882],[1831,3159,1929],{"className":3160},[1928],[1831,3162,3164],{"className":3163},[1892],[1831,3165,3167],{"className":3166,"style":1936},[1896],[1831,3168],{},[1831,3170,3172],{"className":3171},[2383],[1831,3173,3175,3195],{"className":3174},[1887,1888],[1831,3176,3178,3192],{"className":3177},[1892],[1831,3179,3181],{"className":3180,"style":2452},[1896],[1831,3182,3183,3186],{"style":2455},[1831,3184],{"className":3185,"style":2192},[1904],[1831,3187,3189],{"className":3188},[2196,2197,2198,2199],[1831,3190,2344],{"className":3191,"style":2465},[1882,1909,2199],[1831,3193,1929],{"className":3194},[1928],[1831,3196,3198],{"className":3197},[1892],[1831,3199,3201],{"className":3200,"style":2475},[1896],[1831,3202],{},[1831,3204,1983],{"className":3205},[2166],[1831,3207,2018],{"className":3208},[1882],[1798,3210,3211],{},"置信区间不是“参数有 95% 概率在这个固定区间内”的贝叶斯陈述，而是重复抽样程序长期覆盖真参数约 95% 的频率学派解释。",[1793,3213,3215],{"id":3214},"_4-异方差","4. 异方差",[1798,3217,3218],{},"如果：",[1831,3220,3222],{"className":3221},[1946],[1831,3223,3225,3265],{"className":3224},[1834],[1831,3226,3228],{"className":3227},[1838],[1840,3229,3230],{"xmlns":1842,"display":1955},[1844,3231,3232,3262],{},[1847,3233,3234,3237,3240,3242,3250,3253,3260],{},[1854,3235,3236],{"mathvariant":2017},"Var",[1858,3238,3239],{},"⁡",[1858,3241,1969],{"stretchy":1968},[2328,3243,3244,3247],{},[1854,3245,3246],{},"u",[1854,3248,3249],{},"i",[1858,3251,3252],{},"∣",[2328,3254,3255,3258],{},[1854,3256,3257],{},"X",[1854,3259,3249],{},[1858,3261,1983],{"stretchy":1968},[1862,3263,3264],{"encoding":1864},"\\operatorname{Var}(u_i\\mid X_i)",[1831,3266,3268,3335],{"className":3267,"ariaHidden":1852},[1869],[1831,3269,3271,3274,3282,3285,3326,3329,3332],{"className":3270},[1873],[1831,3272],{"className":3273,"style":2247},[1877],[1831,3275,3278],{"className":3276},[3277],"mop",[1831,3279,3236],{"className":3280},[1882,3281],"mathrm",[1831,3283,1969],{"className":3284},[2098],[1831,3286,3288,3291],{"className":3287},[1882],[1831,3289,3246],{"className":3290},[1882,1909],[1831,3292,3294],{"className":3293},[2383],[1831,3295,3297,3318],{"className":3296},[1887,1888],[1831,3298,3300,3315],{"className":3299},[1892],[1831,3301,3303],{"className":3302,"style":2452},[1896],[1831,3304,3306,3309],{"style":3305},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1831,3307],{"className":3308,"style":2192},[1904],[1831,3310,3312],{"className":3311},[2196,2197,2198,2199],[1831,3313,3249],{"className":3314},[1882,1909,2199],[1831,3316,1929],{"className":3317},[1928],[1831,3319,3321],{"className":3320},[1892],[1831,3322,3324],{"className":3323,"style":2415},[1896],[1831,3325],{},[1831,3327],{"className":3328,"style":2170},[2144],[1831,3330,3252],{"className":3331},[2174],[1831,3333],{"className":3334,"style":2170},[2144],[1831,3336,3338,3341,3383],{"className":3337},[1873],[1831,3339],{"className":3340,"style":2247},[1877],[1831,3342,3344,3348],{"className":3343},[1882],[1831,3345,3257],{"className":3346,"style":3347},[1882,1909],"margin-right:0.0785em;",[1831,3349,3351],{"className":3350},[2383],[1831,3352,3354,3375],{"className":3353},[1887,1888],[1831,3355,3357,3372],{"className":3356},[1892],[1831,3358,3360],{"className":3359,"style":2452},[1896],[1831,3361,3363,3366],{"style":3362},"top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;",[1831,3364],{"className":3365,"style":2192},[1904],[1831,3367,3369],{"className":3368},[2196,2197,2198,2199],[1831,3370,3249],{"className":3371},[1882,1909,2199],[1831,3373,1929],{"className":3374},[1928],[1831,3376,3378],{"className":3377},[1892],[1831,3379,3381],{"className":3380,"style":2415},[1896],[1831,3382],{},[1831,3384,1983],{"className":3385},[2166],[1798,3387,3388,3389,3459],{},"随 ",[1831,3390,3392,3410],{"className":3391},[1834],[1831,3393,3395],{"className":3394},[1838],[1840,3396,3397],{"xmlns":1842},[1844,3398,3399,3407],{},[1847,3400,3401],{},[2328,3402,3403,3405],{},[1854,3404,3257],{},[1854,3406,3249],{},[1862,3408,3409],{"encoding":1864},"X_i",[1831,3411,3413],{"className":3412,"ariaHidden":1852},[1869],[1831,3414,3416,3419],{"className":3415},[1873],[1831,3417],{"className":3418,"style":2372},[1877],[1831,3420,3422,3425],{"className":3421},[1882],[1831,3423,3257],{"className":3424,"style":3347},[1882,1909],[1831,3426,3428],{"className":3427},[2383],[1831,3429,3431,3451],{"className":3430},[1887,1888],[1831,3432,3434,3448],{"className":3433},[1892],[1831,3435,3437],{"className":3436,"style":2452},[1896],[1831,3438,3439,3442],{"style":3362},[1831,3440],{"className":3441,"style":2192},[1904],[1831,3443,3445],{"className":3444},[2196,2197,2198,2199],[1831,3446,3249],{"className":3447},[1882,1909,2199],[1831,3449,1929],{"className":3450},[1928],[1831,3452,3454],{"className":3453},[1892],[1831,3455,3457],{"className":3456,"style":2415},[1896],[1831,3458],{}," 改变，就存在异方差。OLS 点估计在外生性成立时仍可能一致，但同方差标准误不再可靠。Huber–White 三明治方差估计为：",[1831,3461,3463],{"className":3462},[1946],[1831,3464,3466,3583],{"className":3465},[1834],[1831,3467,3469],{"className":3468},[1838],[1840,3470,3471],{"xmlns":1842,"display":1955},[1844,3472,3473,3580],{},[1847,3474,3475,3490,3492,3494,3503,3505,3516,3558,3560,3566,3568,3578],{},[2328,3476,3477,3483],{},[1850,3478,3479,3481],{"accent":1852},[1854,3480,2012],{},[1858,3482,1860],{"stretchy":1852},[1847,3484,3485,3487],{},[1854,3486,2332],{},[1854,3488,3489],{},"C",[1858,3491,2347],{},[1858,3493,1969],{"stretchy":1968},[3495,3496,3497,3499],"msup",{},[1854,3498,3257],{},[1858,3500,3502],{"mathvariant":2017,"lspace":3501,"rspace":3501},"0em","′",[1854,3504,3257],{},[3495,3506,3507,3509],{},[1858,3508,1983],{"stretchy":1968},[1847,3510,3511,3513],{},[1858,3512,1978],{},[2004,3514,3515],{},"1",[1847,3517,3518,3520,3528,3542,3548,3556],{},[1858,3519,1969],{"fence":1852},[3521,3522,3523,3526],"munder",{},[1858,3524,3525],{},"∑",[1854,3527,3249],{},[3529,3530,3531,3537,3539],"msubsup",{},[1850,3532,3533,3535],{"accent":1852},[1854,3534,3246],{},[1858,3536,1860],{},[1854,3538,3249],{},[2004,3540,3541],{},"2",[2328,3543,3544,3546],{},[1854,3545,3257],{},[1854,3547,3249],{},[3529,3549,3550,3552,3554],{},[1854,3551,3257],{},[1854,3553,3249],{},[1858,3555,3502],{"mathvariant":2017,"lspace":3501,"rspace":3501},[1858,3557,1983],{"fence":1852},[1858,3559,1969],{"stretchy":1968},[3495,3561,3562,3564],{},[1854,3563,3257],{},[1858,3565,3502],{"mathvariant":2017,"lspace":3501,"rspace":3501},[1854,3567,3257],{},[3495,3569,3570,3572],{},[1858,3571,1983],{"stretchy":1968},[1847,3573,3574,3576],{},[1858,3575,1978],{},[2004,3577,3515],{},[1854,3579,2018],{"mathvariant":2017},[1862,3581,3582],{"encoding":1864},"\\widehat V_{HC}\n=(X'X)^{-1}\\left(\\sum_i\\hat u_i^2X_iX_i'\\right)(X'X)^{-1}.",[1831,3584,3586,3688],{"className":3585,"ariaHidden":1852},[1869],[1831,3587,3589,3593,3679,3682,3685],{"className":3588},[1873],[1831,3590],{"className":3591,"style":3592},[1877],"height:1.0733em;vertical-align:-0.15em;",[1831,3594,3596,3636],{"className":3595},[1882],[1831,3597,3599],{"className":3598},[1882,1883],[1831,3600,3602],{"className":3601},[1887],[1831,3603,3605],{"className":3604},[1892],[1831,3606,3609,3617],{"className":3607,"style":3608},[1896],"height:0.9233em;",[1831,3610,3611,3614],{"style":1900},[1831,3612],{"className":3613,"style":1905},[1904],[1831,3615,2012],{"className":3616,"style":2145},[1882,1909],[1831,3618,3621,3624],{"className":3619,"style":3620},[2049],"top:-3.6833em;",[1831,3622],{"className":3623,"style":1905},[1904],[1831,3625,3627],{"style":3626},"height:0.24em;",[2072,3628,3633],{"xmlns":2074,"width":3629,"height":3630,"viewBox":3631,"preserveAspectRatio":3632},"100%","0.24em","0 0 1062 239","none",[2080,3634],{"d":3635},"M529 0h5l519 115c5 1 9 5 9 10 0 1-1 2-1 3l-4 22\nc-1 5-5 9-11 9h-2L532 67 19 159h-2c-5 0-9-4-11-9l-5-22c-1-6 2-12 8-13z",[1831,3637,3639],{"className":3638},[2383],[1831,3640,3642,3671],{"className":3641},[1887,1888],[1831,3643,3645,3668],{"className":3644},[1892],[1831,3646,3649],{"className":3647,"style":3648},[1896],"height:0.3283em;",[1831,3650,3652,3655],{"style":3651},"top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;",[1831,3653],{"className":3654,"style":2192},[1904],[1831,3656,3658],{"className":3657},[2196,2197,2198,2199],[1831,3659,3661,3664],{"className":3660},[1882,2199],[1831,3662,2332],{"className":3663,"style":2379},[1882,1909,2199],[1831,3665,3489],{"className":3666,"style":3667},[1882,1909,2199],"margin-right:0.0715em;",[1831,3669,1929],{"className":3670},[1928],[1831,3672,3674],{"className":3673},[1892],[1831,3675,3677],{"className":3676,"style":2415},[1896],[1831,3678],{},[1831,3680],{"className":3681,"style":2170},[2144],[1831,3683,2347],{"className":3684},[2174],[1831,3686],{"className":3687,"style":2170},[2144],[1831,3689,3691,3695,3698,3732,3735,3771,3774,4027,4030,4033,4065,4068,4103],{"className":3690},[1873],[1831,3692],{"className":3693,"style":3694},[1877],"height:3.0277em;vertical-align:-1.2777em;",[1831,3696,1969],{"className":3697},[2098],[1831,3699,3701,3704],{"className":3700},[1882],[1831,3702,3257],{"className":3703,"style":3347},[1882,1909],[1831,3705,3707],{"className":3706},[2383],[1831,3708,3710],{"className":3709},[1887],[1831,3711,3713],{"className":3712},[1892],[1831,3714,3717],{"className":3715,"style":3716},[1896],"height:0.8019em;",[1831,3718,3720,3723],{"style":3719},"top:-3.113em;margin-right:0.05em;",[1831,3721],{"className":3722,"style":2192},[1904],[1831,3724,3726],{"className":3725},[2196,2197,2198,2199],[1831,3727,3729],{"className":3728},[1882,2199],[1831,3730,3502],{"className":3731},[1882,2199],[1831,3733,3257],{"className":3734,"style":3347},[1882,1909],[1831,3736,3738,3741],{"className":3737},[2166],[1831,3739,1983],{"className":3740},[2166],[1831,3742,3744],{"className":3743},[2383],[1831,3745,3747],{"className":3746},[1887],[1831,3748,3750],{"className":3749},[1892],[1831,3751,3754],{"className":3752,"style":3753},[1896],"height:0.8641em;",[1831,3755,3756,3759],{"style":3719},[1831,3757],{"className":3758,"style":2192},[1904],[1831,3760,3762],{"className":3761},[2196,2197,2198,2199],[1831,3763,3765,3768],{"className":3764},[1882,2199],[1831,3766,1978],{"className":3767},[1882,2199],[1831,3769,3515],{"className":3770},[1882,2199],[1831,3772],{"className":3773,"style":2265},[2144],[1831,3775,3778,3788,3840,3843,3926,3966,4021],{"className":3776},[3777],"minner",[1831,3779,3783],{"className":3780,"style":3782},[2098,3781],"delimcenter","top:0em;",[1831,3784,1969],{"className":3785},[3786,3787],"delimsizing","size4",[1831,3789,3792],{"className":3790},[3277,3791],"op-limits",[1831,3793,3795,3831],{"className":3794},[1887,1888],[1831,3796,3798,3828],{"className":3797},[1892],[1831,3799,3802,3815],{"className":3800,"style":3801},[1896],"height:1.05em;",[1831,3803,3805,3809],{"style":3804},"top:-1.8723em;margin-left:0em;",[1831,3806],{"className":3807,"style":3808},[1904],"height:3.05em;",[1831,3810,3812],{"className":3811},[2196,2197,2198,2199],[1831,3813,3249],{"className":3814},[1882,1909,2199],[1831,3816,3818,3821],{"style":3817},"top:-3.05em;",[1831,3819],{"className":3820,"style":3808},[1904],[1831,3822,3823],{},[1831,3824,3525],{"className":3825},[3277,3826,3827],"op-symbol","large-op",[1831,3829,1929],{"className":3830},[1928],[1831,3832,3834],{"className":3833},[1892],[1831,3835,3838],{"className":3836,"style":3837},[1896],"height:1.2777em;",[1831,3839],{},[1831,3841],{"className":3842,"style":2265},[2144],[1831,3844,3846,3879],{"className":3845},[1882],[1831,3847,3849],{"className":3848},[1882,1883],[1831,3850,3852],{"className":3851},[1887],[1831,3853,3855],{"className":3854},[1892],[1831,3856,3859,3867],{"className":3857,"style":3858},[1896],"height:0.6944em;",[1831,3860,3861,3864],{"style":1900},[1831,3862],{"className":3863,"style":1905},[1904],[1831,3865,3246],{"className":3866},[1882,1909],[1831,3868,3869,3872],{"style":1900},[1831,3870],{"className":3871,"style":1905},[1904],[1831,3873,3876],{"className":3874,"style":3875},[1920],"left:-0.2222em;",[1831,3877,1860],{"className":3878},[1882],[1831,3880,3882],{"className":3881},[2383],[1831,3883,3885,3917],{"className":3884},[1887,1888],[1831,3886,3888,3914],{"className":3887},[1892],[1831,3889,3891,3903],{"className":3890,"style":3753},[1896],[1831,3892,3894,3897],{"style":3893},"top:-2.453em;margin-left:0em;margin-right:0.05em;",[1831,3895],{"className":3896,"style":2192},[1904],[1831,3898,3900],{"className":3899},[2196,2197,2198,2199],[1831,3901,3249],{"className":3902},[1882,1909,2199],[1831,3904,3905,3908],{"style":3719},[1831,3906],{"className":3907,"style":2192},[1904],[1831,3909,3911],{"className":3910},[2196,2197,2198,2199],[1831,3912,3541],{"className":3913},[1882,2199],[1831,3915,1929],{"className":3916},[1928],[1831,3918,3920],{"className":3919},[1892],[1831,3921,3924],{"className":3922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聚类相关",[1798,4114,4115],{},"同一学校、企业、地区、州或个体的观测可能共享冲击。若组内误差相关，样本的有效独立信息量小于观测行数。聚类标准误允许同组内任意相关，而通常要求组间独立或在更高层次上满足适当条件。",[1798,4117,4118],{},"聚类层级应由误差相关和处理分配层级决定，而不是由“哪一种软件选项方便”决定。政策在州层面变化时，只在个人层面使用稳健标准误通常会低估不确定性。",[1793,4120,4122],{"id":4121},"_6-多重检验与经济显著","6. 多重检验与经济显著",[1798,4124,4125],{},"同时检验许多假设，即使所有原假设都正确，也可能偶然出现显著结果。研究者应预先说明主要结果、控制多重检验或报告探索性结果。",[1798,4127,4128],{},"解释结果时同时写：",[4130,4131,4132,4135,4138,4141],"ol",{},[1808,4133,4134],{},"系数单位和数量级；",[1808,4136,4137],{},"置信区间；",[1808,4139,4140],{},"相对于基线均值或政策成本的经济意义；",[1808,4142,4143],{},"识别假设与数据覆盖范围。",[1798,4145,4146],{},"大样本可以让极小且无实际意义的效果显著；小样本可能让重要效果不显著。显著性星号不能替代机制和量级解释。",[1793,4148,4150],{"id":4149},"_7-bootstrap","7. Bootstrap",[1798,4152,4153],{},"Bootstrap 通过重复从样本重抽样近似估计量的抽样分布。它可用于复杂统计量、分位数或有限样本诊断，但需要尊重数据依赖结构：面板要按个体\u002F组重抽，时间序列要使用区块或其他序列方法。",[1798,4155,4156],{},"Bootstrap 不能解决内生性、错误的目标参数或不代表性的样本。它提高的是不确定性近似，不是因果可信度。",[1793,4158,4159],{"id":4159},"研究生扩展",[1805,4161,4162,4165,4168,4171,4174],{},[1808,4163,4164],{},"sandwich 方差与影响函数；",[1808,4166,4167],{},"少量聚类、随机化推断和 wild bootstrap；",[1808,4169,4170],{},"高维同时推断；",[1808,4172,4173],{},"弱识别下的置信区间；",[1808,4175,4176],{},"预先注册、规格曲线和选择后推断。",[1793,4178,4179],{"id":4179},"自测题",[4130,4181,4182,4185,4188,4191,4194],{},[1808,4183,4184],{},"异方差会影响 OLS 点估计还是标准误，取决于什么假设？",[1808,4186,4187],{},"为什么州层面政策需要考虑州内相关？",[1808,4189,4190],{},"95% 置信区间应该如何解释？",[1808,4192,4193],{},"bootstrap 为什么不能修复遗漏变量偏误？",[1808,4195,4196],{},"如何判断一个统计显著结果是否具有经济意义？",[1793,4198,4199],{"id":4199},"下一章",[1798,4201,4202],{},"下一章讨论一个更根本的问题：当解释变量与误差相关时，稳健标准误并不能使 OLS 重新具有因果含义，需要工具变量和更明确的识别设计。",{"title":10,"searchDepth":4204,"depth":4204,"links":4205},2,[4206,4207,4208,4209,4210,4211,4212,4213,4214,4215,4216],{"id":1795,"depth":4204,"text":1796},{"id":1803,"depth":4204,"text":1803},{"id":1825,"depth":4204,"text":1826},{"id":2310,"depth":4204,"text":2311},{"id":3214,"depth":4204,"text":3215},{"id":4111,"depth":4204,"text":4112},{"id":4121,"depth":4204,"text":4122},{"id":4149,"depth":4204,"text":4150},{"id":4159,"depth":4204,"text":4159},{"id":4179,"depth":4204,"text":4179},{"id":4199,"depth":4204,"text":4199},"从抽样分布、t\u002FF 检验到异方差、聚类和 bootstrap 推断。","md",{},true,{"title":1338,"description":4217},"4hwmnUB2kKIN2xS3AXkQvJ4Shmxkt5B13mbCDNcvA60",[4224,4226],{"title":1334,"path":1335,"stem":1336,"description":4225,"children":-1},"推导普通最小二乘、解释 FWL 定理并分析函数形式与遗漏变量偏误。",{"title":1342,"path":1343,"stem":1344,"description":4227,"children":-1},"解释内生性来源、IV 识别、2SLS、弱工具和 LATE。",1785754747547]