1 Lab Five

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 Lab 5 Data : “Fortune 500” Top 50 RankCompanyIndustryRevenue $M 1General MotorsMotor Vehicles and Parts Wal-Mart StoresGeneral Merchandisers Exxon MobilPetroleum Refining Ford MotorMotor Vehicles and Parts General ElectricDiversified Financials Intl. Business MachinesComputers, Office Equipment CitigroupDiversified Financials AT&TTelecommunications Philip MorrisTobacco BoeingAerospace Bank of America Corp.Commercial banks SBC CommunicationsTelecommunications Hewlett-PackardComputers, Office Equipment KrogerFood and Drug Stores State Farm Insurance CosInsurance; P&C(mutual) Sears RoebuckGeneral Merchandisers American International GroupInsurance; P&C(stock) EnronPipelines TIAA-CREFInsurance: Life, Health(mutual) Compaq ComputerComputers, Office Equipment38525

4 Exploratory Data Analysis

5 Smallest = Q1 = Median = Q3 = Largest = IQR = Outliers: , , , , , 87548, 82005, GM citigroup AT&T Aetna

6 Plot of Assets Vs. Revenue

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8 Dependent Variable: ASSETS Method: Least Squares Sample: 1 50 Included observations: 50 VariableCoefficientStd. Errort-StatisticProb. REVENUE C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid 1.38E+1 Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic)

9 Exploratory data Analysis

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

11 Finance Vs. Trade?

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13 Dependent Variable: LNASSETS Method: Least Squares Sample: 1 50 Included observations: 50 VariableCoefficientStd. Errort-StatisticProb. LNSALES C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic)

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 Ln-ln Regression with Industry Dummies

16 Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic)

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19 Wald Test: Null Hypothesis

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-statistic Probability Chi-square Probability

21 Wald Test: drop insurance from Group

22 Wald Test results: Accept Null Wald Test: Equation: Untitled Null Hypothesis:C(3)=C(18) C(6)=C(18) F-statistic Probability Chi-square Probability

23 Wald Test: Equivalent to a Likelihood Ratio test Equation with all the dummies Equation with all the dummies R 2 = R 2 = SSR = SSR = Ln Likelihood = Ln Likelihood = 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 = R 2 = SSR = SSR = Ln Likelihood = Ln Likelihood = Estimate 23 regression parameters Estimate 23 regression parameters

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[ – ( )] =2( ) =2[ – ( )] =2( ) -2ln λ = ln λ =

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

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

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

29 Wald Test results: Accept Null Wald Test: Equation: Untitled Null Hypothesis:C(3)=C(18) C(6)=C(18) F-statistic Probability Chi-square Probability

30 Eviews Help