Power 16 1 Review Post Midterm Cumulative 2 Projects 3 Logistics Put power point slide show on a high density floppy disk or e mail as an attachment for a WINTEL machine Email Llad econ ucsb edu the slide show as a PowerPoint attachment 4 Assignments 1 Project choice 2 Data Retrieval 3 Statistical Analysis 4 PowerPoint Presentation 5 Executive Summary 6 Technical Appendix 7 Graphics Power 13 5 PowerPoint 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 6 6 Executive Summary and Technical Appendix 7 I Your report should have an executive summary of one to one and a half pages that summarizes your findings in words for a nontechnical reader It should explain the problem being examined from an economic perspective i e it should motivate interest in the issue on the part of the reader Your report should explain how you are investigating the issue in simple language It should explain why you are approaching the problem in this particular fashion Your executive report should explain the economic importance of your findings The technical details of your findings you can attach as an appendix 8 Technical 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 variables 9 Technical 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 10 Post 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 6 11 Slide Show Challenger disaster 12 Project 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 ei 13 Project 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 test 14 Project 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 model 15 Challenger Disaster Failure of O rings that sealed grooves on the booster rockets Was there any relationship between oring 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 16 Challenger 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 failure 17 Launches Before Challenger Data number of o rings that failed launch temperature 18 o rings 3 1 1 1 0 0 0 0 0 0 1 temperature 53 57 58 63 66 67 67 67 68 69 70 19 o rings 1 0 0 0 0 2 0 0 0 0 0 temperature 70 70 70 72 73 75 75 76 76 78 79 20 o rings temperature 0 80 0 81 21 Exploratory Analysis Launches where there was a problem 22 Orings temperature 1 1 1 1 1 2 3 58 57 70 63 70 75 53 23 3 5 3 0 ORINGS 2 5 2 0 1 5 1 0 0 5 50 55 60 65 TEMP 70 75 80 Exploratory Analysis All Launches Plot 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 analysis 25 Launches 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 24 26 Launches 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 24 27 Launches and O Ring Failures ChiSquare 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 24 28 Number of O ring Failures Vs Temperature 4 ORINGS 3 2 1 0 50 60 70 TEMP 80 90 Logit Extrapolated to 31F Probit extrapolated to 31F Probability Models 1 Probability 0 8 0 6 Bernoulli LPM Fitted Probit Fitted 0 4 0 2 0 30 40 50 60 70 80 90 0 2 Temperature 30 Extrapolating OLS to 31F OLS Tobit Number of Failed O Rings 3 5 Number of Failed O Rings OLS Fitted Tobit Fitted 3 2 5 Number 2 1 5 1 0 5 0 30 40 50 60 70 80 90 0 5 Temperature 31 Conclusions From extrapolating the probability models to 31 F Linear Probability Probit or Logit there was a high probability of one or more o rings failing From extrapolating the Number of O rings failing to 31 F OLS or Tobit 3 or more orings would fail There had been only one launch out of 24 where as many as 3 o rings had failed Decision theory argument expected cost benefit ratio 32 Conclusions Decision theory argument expected cost benefit ratio 33 Ways to Analyze Challenger Difference in mean temperatures for failures and successes Difference in probability of one or more o ring failures for high and low temperature ranges Probabilty models LPM OLS probit logit Number of o ring failure per launch Vs Temp OLS Tobit Contingency table analysis ANOVA 34 Contingency Table Analysis Challenger example 35 Launches 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 24 36 ANOVA and O Rings Probability one or more o rings fail Low temp 53 62 degrees Medium temp 63 71 degrees High temp 72 81 degrees Average number of …
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