Power 16ReviewProjectsLogisticsAssignmentsPowerPoint Presentations: Member 4Executive Summary and Technical AppendixSlide 8Technical 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 36ANOVA and O-RingsSlide 38Slide 39Slide 40OutlineAnova and Regression: One-WaySlide 43Anova and Regression: One-Way Alternative SpecificationSlide 45ANOVA and Regression: Two-Way Series of Regressions; Compare to Table 11, Lecture 15Slide 47ANOVA and Regression: Two-Way Series of RegressionsSurvival AnalysisChemotherapy Drug TaxolSlide 51Slide 522003 FinalNonparametric Statistics3 Nonparametric TechniquesWilcoxon Rank Sum Test for Independent SamplesRating schemeSlide 58Rank the 30 RatingsSlide 60Slide 61Slide 62Rank Sum, TSlide 641Power 162ReviewPost-MidtermCumulative3Projects4LogisticsPut power point slide show on a high density floppy disk, or e-mail as an attachment, for a WINTEL machine.Email [email protected] the slide-show as a PowerPoint attachment5Assignments 1. Project choice 2. Data Retrieval3. Statistical Analysis4. PowerPoint Presentation5. Executive Summary6. Technical Appendix7. GraphicsPower_136PowerPoint Presentations: Member 41. Introduction: Members 1 ,2 , 3WhatWhyHow2. Executive Summary: Member 53. Exploratory Data Analysis: Member 34. Descriptive Statistics: Member 35. Statistical Analysis: Member 36. 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 AppendixTable of ContentsSpreadsheet of data used and sources or if extensive, a subsample of the dataDescriptive Statistics and Histograms for the variables in the studyIf time series data, a plot of each variable against timeIf relevant, plot of the dependent Vs. each of the explanatory variables10Technical Appendix (Cont.)Statistical Results, for example regressionPlot of the actual, fitted and error and other diagnosticsBrief summary of the conclusions, meanings drawn from the exploratory, descriptive, and statistical analysis.11Post-Midterm ReviewProject I: Power 16Contingency Table Analysis: Power 14, Lab 8 ANOVA: Power 15, Lab 9Survival Analysis: Power 12, Power 11, Lab 7Multi-variate Regression: Power 11 , Lab 612Slide ShowChallenger disaster13Project INumber of O-Rings Failing On Launch i: yi(#) = a + b*tempi + eiBiased because of zeros, even if divide equation by 6Two Ways to ProceedTobit, non-linear estimation: yi(#) = a + b*tempi + eiBernoulli variable: probability modelsProbability 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 sigmoidProbit, non-linear estimate of the sigmoidLogit, non-linear estimate of the sigmoidSignificant Dependence on Temperaturet-test (or z-test) on slope, H0 : b=0F-test Wald test15Project I (Cont.)Plots of Number or Probability Vs Temp.Label the axesAnswer all parts, a-fThe most frequent sinsDid not explicitly address significanceDid not answer b, 660 : all launches at lower temperatures had one or more o-ring failuresDid not execute c, estimate linear probability model16Challenger DisasterFailure of O-rings that sealed grooves on the booster rocketsWas there any relationship between o-ring failure and temperature?Engineers knew that the rubber o-rings hardened and were less flexible at low temperaturesBut was there launch data that showed a problem?17Challenger DisasterWhat: 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 ChallengerDatanumber of o-rings that failedlaunch 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 AnalysisLaunches 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 AnalysisAll 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: Probit extrapolated to 31F:31Number of Failed O-Rings-0.500.511.522.533.530 40 50 60 70 80 90TemperatureNumberNumber of Failed O-RingsOLS FittedTobit FittedExtrapolating OLS to 31F: OLS:
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