1. 1 Lab Five

2. 2 Lessons to be Learned “Look before you leap” “Look before you leap” Get a feel for the data using graphical techniques, i.e. exploratory data analysis Get a feel for the data using graphical techniques, i.e. exploratory data analysis In statistics, we do not what the “truth” is, so keep an open mind In statistics, we do not what the “truth” is, so keep an open mind Try different models, e.g. if linear does not work, try log-log Try different models, e.g. if linear does not work, try log-log Shifting the regression line by shifting the intercept if the data may fall into different classes Shifting the regression line by shifting the intercept if the data may fall into different classes

3. 3 Lab 5 Data : “Fortune 500” Top 50 RankCompanyIndustryRevenue $M 1General MotorsMotor Vehicles and Parts189058 2 Wal-Mart StoresGeneral Merchandisers166809 3Exxon MobilPetroleum Refining163881 4 Ford MotorMotor Vehicles and Parts162558 5General ElectricDiversified Financials111630 6Intl. Business MachinesComputers, Office Equipment87548 7CitigroupDiversified Financials82005 8 AT&TTelecommunications62391 9Philip MorrisTobacco61751 10 BoeingAerospace57993 11Bank of America Corp.Commercial banks51392 12SBC CommunicationsTelecommunications49489 13 Hewlett-PackardComputers, Office Equipment48253 14KrogerFood and Drug Stores45351.62 15State Farm Insurance CosInsurance; P&C(mutual)44637.25 16Sears RoebuckGeneral Merchandisers41071 17American International GroupInsurance; P&C(stock)40656.08 18EnronPipelines40112 19TIAA-CREFInsurance: Life, Health(mutual)39410.2 20Compaq ComputerComputers, Office Equipment38525

4. 4 Exploratory Data Analysis

5. 5 Smallest = 25986 Q1 = 30133.975 Median = 37044.3 Q3 = 48562 Largest = 189058 IQR = 18428.025 Outliers: 189058, 166809, 163881, 162558, 111630, 87548, 82005, GM citigroup AT&T Aetna

6. 6 Plot of Assets Vs. Revenue

7. 7

8. 8 Dependent Variable: ASSETS Method: Least Squares Sample: 1 50 Included observations: 50 VariableCoefficientStd. Errort-StatisticProb. REVENUE1.0679270.6149441.7366250.0889 C83847.7239395.832.1283400.0385 R-squared0.059116 Mean dependent var138113.5 Adjusted R-squared 0.039514 S.D. dependent var173101.5 S.E. of regression169647. Akaike info criterion26.96001 Sum squared resid 1.38E+1 Schwarz criterion27.03649 Log likelihood-672.0001 F-statistic3.015865 Durbin-Watson stat 1.952661 Prob(F-statistic)0.088868

9. 9 Exploratory data Analysis

10. 10 Transformation: Ln Assets = a+b Ln Revenue + e

11. 11 Finance Vs. Trade?

12. 12

13. 13 Dependent Variable: LNASSETS Method: Least Squares Sample: 1 50 Included observations: 50 VariableCoefficientStd. Errort-StatisticProb. LNSALES0.9199500.3190842.8830960.0059 C1.2941853.4067770.3798850.7057 R-squared0.147610 Mean dependent var11.10485 Adjusted R-squared0.12985 S.D. dependent var1.243987 S.E. of regression1.160413 Akaike info criterion3.174607 Sum squared resid64.6347 Schwarz criterion3.251088 Log likelihood-77.36517 F-statistic8.312240 Durbin-Watson stat1.70002 Prob(F-statistic)0.005877

14. 14 Table 1: Industry and Number of Firms Industry # of Firms Aerospace1 Chemicals1 Commercial Banks3 Computers, Office Equipment3 Diversified Financials3 Electronics, Electrical Equipment 1 Entertainment1 Food and Drug Stores3 General Merchandisers5 Health Care1 Insurance5 Mail, Package, Freight Delivery1 Motor Vehicles and Parts2 Network Communications1 Petroleum Refining3 Pharmaceuticals2 Pipelines1 Securities2 Semiconductors1 Soaps, Cosmetics1 Specialty Retailers2 Telecommunications4 Tobacco1 Wholesalers2 Industry# of Firms Aerospace1 Chemicals1 Commercial Banks3 Computers, Office Equipment3 Diversified Financials3 Electronics, Electrical Equipment 1 Entertainment1 Food and Drug Stores3 General Merchandisers5 Health Care1 Insurance5 Mail, Package, Freight Delivery1 Motor Vehicles and Parts2 Network Communications1 Petroleum Refining3 Pharmaceuticals2 Pipelines1 Securities2 Semiconductors1 Soaps, Cosmetics1 Specialty Retailers2 Telecommunications4 Tobacco1 Wholesalers2 Industry# of Firms Aerospace1 Chemicals1 Commercial Banks3 Computers, Office Equipment3 Diversified Financials3 Electronics, Electrical Equipment 1 Entertainment1 Food and Drug Stores3 General Merchandisers5 Health Care1 Insurance5 Mail, Package, Freight Delivery1 Motor Vehicles and Parts2 Network Communications1 Petroleum Refining3 Pharmaceuticals2 Pipelines1 Securities2 Semiconductors1 Soaps, Cosmetics1 Specialty Retailers2 Telecommunications4 Tobacco1 Wholesalers2

15. 15 Ln-ln Regression with Industry Dummies

16. 16 Log likelihood-0.798333 F-statistic25.09152Durbin-Watson stat2.427065 Prob(F-statistic)0.000000Log likelihood-0.798333 F-statistic25.09152Durbin-Watson stat2.427065 Prob(F-statistic)0.000000

17. 17

18. 18

19. 19 Wald Test: Null Hypothesis

20. 20 Wald Test Results: reject Null Wald Test: Equation: Untitled Null Hypothesis:C(3)=C(18) C(6)=C(18) C(12)=C(18) F-statistic3.488804Probability0.030516 Chi-square10.46641Probability0.014990

21. 21 Wald Test: drop insurance from Group

22. 22 Wald Test results: Accept Null Wald Test: Equation: Untitled Null Hypothesis:C(3)=C(18) C(6)=C(18) F-statistic0.300921Probability0.742780 Chi-square0.601842Probability0.740136

23. 23 Wald Test: Equivalent to a Likelihood Ratio test Equation with all the dummies Equation with all the dummies R 2 = 0.9601 R 2 = 0.9601 SSR = 3.022 SSR = 3.022 Ln Likelihood = - 0.798333 Ln Likelihood = - 0.798333 Estimate 25 regression parameters Estimate 25 regression parameters Equation with Finance Group Dummy replacing banks, divfinanc, and securities Equation with Finance Group Dummy replacing banks, divfinanc, and securities R 2 = 0.9592 R 2 = 0.9592 SSR = 3.095 SSR = 3.095 Ln Likelihood = - 1.393045 Ln Likelihood = - 1.393045 Estimate 23 regression parameters Estimate 23 regression parameters

24. 24 Likelihood Ratio Test Likelihood ratio = λ = Likelihood (constrained)/Likelihood(unconstrained) Likelihood ratio = λ = Likelihood (constrained)/Likelihood(unconstrained) Where -2 lnλ is distributed as Chi square Where -2 lnλ is distributed as Chi square -2 ln λ = -2 [ln Lik(const) – ln Lik(unconst) -2 ln λ = -2 [ln Lik(const) – ln Lik(unconst) =2[ln Lik(unconst) –ln Lik(const)] =2[ln Lik(unconst) –ln Lik(const)] =2[-0.798333 – (-1.393045)] =2(0.594712) =2[-0.798333 – (-1.393045)] =2(0.594712) -2ln λ = 1.189424 -2ln λ = 1.189424

25. 25

26. 26 Chi Square Test 2 Degrees of Freedom 5.99 5 % 1.19 Our Chi Square statistic

27. 27 F-test statistic Explained sum of squares from the banks, divfinance and securities dummies equals SSR (regression #2) – SSR(regression #1) = 3.095 – 3.022 = 0.073 Explained sum of squares from the banks, divfinance and securities dummies equals SSR (regression #2) – SSR(regression #1) = 3.095 – 3.022 = 0.073 Degrees of freedom 2 Degrees of freedom 2 Explained mean square = 0.073/2 = 0.0365 Explained mean square = 0.073/2 = 0.0365 Unexplained mean square from regression #1 = 0.0322/(n-k) = 0.0322/25 Unexplained mean square from regression #1 = 0.0322/(n-k) = 0.0322/25 F 2, 25 = 0.0365/0.12088 =0.302 F 2, 25 = 0.0365/0.12088 =0.302

28. 28 F 2, 23 Test; accept null c(3)=c(6)=c(18) F 2,23 statistic 5% Our F statistic = 0.302

29. 29 Wald Test results: Accept Null Wald Test: Equation: Untitled Null Hypothesis:C(3)=C(18) C(6)=C(18) F-statistic0.300921Probability0.742780 Chi-square0.601842Probability0.740136

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