Lab FiveLessons to be LearnedLab 5 Data : “Fortune 500” Top 50Exploratory Data AnalysisSlide 5Plot of Assets Vs. RevenueSlide 7Slide 8Slide 9Slide 10Finance Vs. Trade?Slide 12Slide 13Slide 14Ln-ln Regression with Industry DummiesSlide 16Slide 17Slide 18Wald Test: Null HypothesisWald Test Results: reject NullWald Test: drop insurance from GroupWald Test results: Accept NullWald Test: Equivalent to a Likelihood Ratio testLikelihood Ratio TestSlide 25Chi Square Test 2 Degrees of FreedomF-test statisticF2, 23 Test; accept null c(3)=c(6)=c(18)Slide 29Eviews Help11Lab FiveLab Five22Lessons to be LearnedLessons to be Learned““Look before you leap”Look before you leap”Get a feel for the data using graphical techniques, i.e. Get a feel for the data using graphical techniques, i.e. exploratory data analysisexploratory data analysisIn statistics, we do not what the “truth” is, so In statistics, we do not what the “truth” is, so keep an open mindkeep an open mindTry different models, e.g. if linear does not work, try Try different models, e.g. if linear does not work, try log-loglog-logShifting the regression line by shifting the Shifting the regression line by shifting the intercept if the data may fall into different classesintercept if the data may fall into different classes33Lab 5 Data : “Fortune 500” Top 50Lab 5 Data : “Fortune 500” Top 50Rank Company Industry Revenue $M1 General Motors Motor Vehicles and Parts 1890582 Wal-Mart Stores General Merchandisers 1668093 Exxon Mobil Petroleum Refining 1638814 Ford Motor Motor Vehicles and Parts 1625585 General Electric Diversified Financials 1116306 Intl. Business Machines Computers, Office Equipment 875487 Citigroup Diversified Financials 820058 AT&T Telecommunications 623919 Philip Morris Tobacco 6175110 Boeing Aerospace 5799311 Bank of America Corp. Commercial banks 5139212 SBC Communications Telecommunications 4948913 Hewlett-Packard Computers, Office Equipment 4825314 Kroger Food and Drug Stores 45351.6215 State Farm Insurance Cos Insurance; P&C(mutual) 44637.2516 Sears Roebuck General Merchandisers 4107117 American International Group Insurance; P&C(stock) 40656.0818 Enron Pipelines 4011219 TIAA-CREF Insurance: Life, Health(mutual) 39410.220 Compaq Computer Computers, Office Equipment 3852544Exploratory Data AnalysisExploratory Data Analysis55Exploratory Data AnalysisExploratory Data AnalysisSmallest = 25986Q1 = 30133.975Median = 37044.3Q3 = 48562Largest = 189058IQR = 18428.025Outliers: 189058, 166809, 163881, 162558, 111630, 87548, 82005, GMcitigroupAT&TAetna66Plot of Assets Vs. RevenuePlot of Assets Vs. Revenue7788Dependent Variable: ASSETSMethod: Least SquaresSample: 1 50Included observations: 50Variable Coefficient Std. Error t-Statistic Prob. REVENUE 1.067927 0.614944 1.736625 0.0889C 83847.72 39395.83 2.128340 0.0385R-squared 0.059116 Mean dependent var 138113.5Adjusted R-squared 0.039514 S.D. dependent var 173101.5S.E. of regression169647. Akaike info criterion 26.96001Sum squared resid 1.38E+1 Schwarz criterion 27.03649Log likelihood -672.0001 F-statistic 3.015865Durbin-Watson stat 1.952661 Prob(F-statistic) 0.08886899Exploratory data Analysis1010Fortune 500, 1999: Assets Vs. Revenue, In LogsGeneral ElectricCitigroupBank of AmericaFannie MayChase ManhattenMorgan StanleyMerrill LynchPrudential Bank OneAmerican InternationalTIAA-CREFState FarmAllstate100010000100000100000010000 100000 1000000Log RevenueLog AssetsTransformation: Ln Assets = a+b Ln Revenue + e1111Finance Vs. Trade?Finance Vs. Trade?Fortune 500, 1999: Assets Vs. Revenue, In LogsGeneral MotorsExxon MobilWal-MartKrogerIngram MicroCostco WholesaleMcKesson HBOCGeneral ElectricCitigroupBank of AmericaFannie MayChase ManhattenMorgan StanleyMerrill LynchPrudential Bank OneAmerican InternationalTIAA-CREFState FarmAllstate100010000100000100000010000 100000 1000000Log RevenueLog Assets12121313Dependent Variable: LNASSETSMethod: Least SquaresSample: 1 50Included observations: 50Variable Coefficient Std. Error t-Statistic Prob. LNSALES 0.919950 0.319084 2.883096 0.0059C 1.294185 3.406777 0.379885 0.7057R-squared 0.147610 Mean dependent var 11.10485Adjusted R-squared 0.12985 S.D. dependent var 1.243987S.E. of regression1.160413 Akaike info criterion 3.174607Sum squared resid 64.6347 Schwarz criterion 3.251088Log likelihood -77.36517 F-statistic 8.312240Durbin-Watson stat 1.70002 Prob(F-statistic) 0.0058771414Table 1: Industry and Number of FirmsIndustry# of FirmsAerospace 1Chemicals 1Commercial Banks 3Computers, Office Equipment 3Diversified Financials 3Electronics, Electrical Equipment1Entertainment 1Food and Drug Stores 3General Merchandisers 5Health Care 1Insurance 5Mail, Package, Freight Delivery 1Motor Vehicles and Parts 2Network Communications 1Petroleum Refining 3Pharmaceuticals 2Pipelines 1Securities 2Semiconductors 1Soaps, Cosmetics 1Specialty Retailers 2Telecommunications 4Tobacco 1Wholesalers 2Industry # of FirmsAerospace 1Chemicals 1Commercial Banks 3Computers, Office Equipment 3Diversified Financials 3Electronics, Electrical Equipment1Entertainment 1Food and Drug Stores 3General Merchandisers 5Health Care 1Insurance 5Mail, Package, Freight Delivery 1Motor Vehicles and Parts 2Network Communications 1Petroleum Refining 3Pharmaceuticals 2Pipelines 1Securities 2Semiconductors 1Soaps, Cosmetics 1Specialty Retailers 2Telecommunications 4Tobacco 1Wholesalers 2Industry # of FirmsAerospace 1Chemicals 1Commercial Banks 3Computers, Office Equipment 3Diversified Financials 3Electronics, Electrical Equipment1Entertainment 1Food and Drug Stores 3General Merchandisers 5Health Care 1Insurance 5Mail, Package, Freight Delivery 1Motor Vehicles and Parts 2Network Communications 1Petroleum Refining 3Pharmaceuticals 2Pipelines 1Securities 2Semiconductors 1Soaps, Cosmetics 1Specialty Retailers 2Telecommunications 4Tobacco 1Wholesalers 21515Ln-ln Regression with Industry Ln-ln Regression with Industry DummiesDummies1616Log likelihood-0.798333 F-statistic25.09152Durbin-Watson stat2.427065 Prob(F-statistic)0.000000171718181919Wald Test: Null HypothesisWald Test: Null Hypothesis2020Wald Test Results: reject NullWald Test Results: reject NullWald Test:Equation: UntitledNull Hypothesis: C(3)=C(18)C(6)=C(18)C(12)=C(18)F-statistic 3.488804 Probability 0.030516Chi-square 10.46641 Probability 0.0149902121Wald Test: drop insurance from GroupWald Test: drop insurance from Group2222Wald Test
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