Power 16ReviewProjectsLogisticsAssignmentsPowerPoint Presentations: Member 4Executive Summary and Technical AppendixPowerPoint PresentationTechnical AppendixTechnical Appendix (Cont.)Post-Midterm ReviewSlide ShowProject IProject I (Cont.)Slide 15Challenger DisasterSlide 17Launches Before ChallengerSlide 19Slide 20Slide 21Exploratory AnalysisSlide 23Slide 24Slide 25Launches and O-Ring Failures (Yes/No)Launches and O-Ring Failures (Yes/No) Expected/ObservedLaunches and O-Ring Failures Chi-Square, 2dof=9.08, crit(=0.05)=6Slide 29Slide 30Slide 31ConclusionsSlide 33Ways to Analyze ChallengerContingency Table AnalysisSlide 36Technical – Alternate ApproachANOVA and O-RingsSlide 39Slide 40Slide 41OutlineAnova and Regression: One-WaySlide 44Anova and Regression: One-Way Alternative SpecificationSlide 46ANOVA and Regression: Two-Way Series of Regressions; Compare to Table 11, Lecture 15Slide 48ANOVA and Regression: Two-Way Series of RegressionsSurvival AnalysisChemotherapy Drug TaxolSlide 52Slide 53Multi-Variate RegressionSlide 55Slide 56Technical – RegressionSlide 58Slide 59Slide 602003 FinalNonparametric Statistics3 Nonparametric TechniquesWilcoxon Rank Sum Test for Independent SamplesRating schemeSlide 66Rank the 30 RatingsSlide 68Slide 69Slide 70Rank Sum, TSlide 721Power 162Review•Post-Midterm•Cumulative3Projects4Logistics•Put power point slide show on a high density floppy disk for a WINTEL machine.•Email [email protected] the slide-show as a PowerPoint attachment5Assignments• 1. Project choice• 2. Data Retrieval•3. Statistical Analysis•4. PowerPoint Presentation•5. Executive Summary•6. Technical Appendix•7. GraphicsPower_136PowerPoint Presentations: Member 4•1. Introduction: Members 1 ,2 , 3–What–Why–How•2. Executive Summary: Member 5•3. Exploratory Data Analysis: Member 3•4. Descriptive Statistics: Member 3•5. Statistical Analysis: Member 3•6. Conclusions: Members 3 & 5• 7. Technical Appendix: Table of Contents, Member 67Executive Summary and Technical Appendix8I. Your report should have an executive summary of one to oneand a half pages that summarizes your findings in words for a non-technical reader. It should explain the problem being examinedfrom an economic perspective, i.e. it should motivate interest in theissue on the part of the reader. Your report should explain how youare investigating the issue, in simple language. It should explainwhy you are approaching the problem in this particular fashion.Your executive report should explain the economic importance ofyour findings.The technical details of your findings you can attach as anappendix.9Technical Appendix•Table of Contents•Spreadsheet of data used and sources or if extensive, a subsample of the data•Descriptive Statistics and Histograms for the variables in the study•If time series data, a plot of each variable against time•If relevant, plot of the dependent Vs. each of the explanatory variables10Technical Appendix (Cont.)•Statistical Results, for example regression•Plot of the actual, fitted and error and other diagnostics•Brief summary of the conclusions, meanings drawn from the exploratory, descriptive, and statistical analysis.11Post-Midterm Review•Project I: Power 16•Contingency Table Analysis: Power 14, Lab 8 •ANOVA: Power 15, Lab 9•Survival Analysis: Power 12, Power 11, Lab 7•Multi-variate Regression: Power 11 , Lab 612Slide Show•Challenger disaster13Project I•Number of O-Rings Failing On Launch i: yi(#) = a + b*tempi + ei–Biased because of zeros, even if divide equation by 6•Two Ways to Proceed–Tobit, non-linear estimation: yi(#) = a + b*tempi + ei–Bernoulli variable: probability models•Probability Models: yi(0,1) = a + b*tempi + ei14Project I (Cont.)•Probability Models: yi(0,1) = a + b*tempi + ei –OLS, Linear Probability Model, linear approximation to the sigmoid–Probit, non-linear estimate of the sigmoid–Logit, non-linear estimate of the sigmoid•Significant Dependence on Temperature–t-test (or z-test) on slope, H0 : b=0–F-test –Wald test15Project I (Cont.)•Plots of Number or Probability Vs Temp.–Label the axes•Answer all parts, a-f–The most frequent sins•Did not explicitly address significance•Did not answer b, 660 : all launches at lower temperatures had one or more o-ring failures•Did not execute c, estimate linear probability model16Challenger Disaster•Failure of O-rings that sealed grooves on the booster rockets•Was there any relationship between o-ring failure and temperature?•Engineers knew that the rubber o-rings hardened and were less flexible at low temperatures•But was there launch data that showed a problem?17Challenger Disaster•What: Was there a relationship between launch temperature and o-ring failure prior to the Challenger disaster?•Why: Should the launch have proceeded?•How: Analyze the relationship between launch temperature and o-ring failure18Launches Before Challenger•Data–number of o-rings that failed–launch temperature19o-rings temperature3 531 571 581 630 660 670 670 670 680 691 7020o-rings temperature1 700 700 700 720 732 750 750 760 760 780 7921o-rings temperature0 800 8122Exploratory Analysis•Launches where there was a problem231 581 571 701 631 702 753 53Orings temperature0.51.01.52.02.53.03.550 55 60 65 70 75 80TEMPORINGS.25Exploratory Analysis•All LaunchesPlot of failures per observation versus temperature range shows temperature dependence: Mean temperature for the 7 launches with o-ring failures was lower, 63.7, than for the 17 launches without o-ring failures,72.6. -Contingency table analysis26Launches and O-Ring Failures (Yes/No) Fail: Yes Fail: No Column Totals 53-62 F 3 0 3 63-71 F 3 8 11 72-81 F 1 9 10 Row Totals 7 17 2427Launches and O-Ring Failures (Yes/No) Expected/Observed Fail: Yes Fail: No Column Totals 53-62 F 0.875/3 2.125/0 3 63-71 F 3.208/3 7.792/8 11 72-81 F 2.917/1 7.083/9 10 Row Totals 7 17 2428Launches and O-Ring Failures Chi-Square, 2dof=9.08, crit(=0.05)=6 Fail: Yes Fail: No Column Totals 53-62 F 5.16 2.125 3 63-71 F 0.013 0.005 11 72-81 F 1.26 0.519 10 Row Totals 7 17 240123450 60 70 80 90TEMPORINGSNumber of O-ring Failures Vs. Temperature30Probability Models-0.200.20.40.60.8130 40 50 60 70 80 90TemperatureProbabilityBernoulliLPM FittedProbit Fitted Logit Extrapolated to 31F: Aren Probit extrapolated to 31F: Jeffrey, Nathan, Hamid, many more31Number of
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