Lab Five 1 Lessons to be Learned Look before you leap 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 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 2 Lab 5 Data Fortune 500 Top 50 Rank Company Industry Revenue M 1 General Motors Motor Vehicles and Parts 189058 2 Wal Mart Stores General Merchandisers 166809 3 Exxon Mobil Petroleum Refining 163881 4 Ford Motor Motor Vehicles and Parts 162558 5 General Electric Diversified Financials 111630 6 Intl Business Machines Computers Office Equipment 87548 7 Citigroup Diversified Financials 82005 8 AT T Telecommunications 62391 9 Philip Morris Tobacco 61751 10 Boeing Aerospace 57993 11 Bank of America Corp Commercial banks 51392 12 SBC Communications Telecommunications 49489 13 Hewlett Packard Computers Office Equipment 48253 14 Kroger Food and Drug Stores 45351 62 15 State Farm Insurance Cos Insurance P C mutual 44637 25 16 Sears Roebuck General Merchandisers 41071 17 American International Group Insurance P C stock 18 Enron Pipelines 19 TIAA CREF Insurance Life Health mutual 20 Compaq Computer Computers Office Equipment 40656 08 40112 39410 2 38525 3 Exploratory Data Analysis 4 Exploratory Data Analysis Smallest 25986 Aetna Q1 30133 975 Median 37044 3 Q3 48562 Largest 189058 AT T citigroup GM IQR 18428 025 Outliers 189058 166809 163881 162558 111630 87548 82005 5 Plot of Assets Vs Revenue 6 7 Dependent Variable ASSETS Method Least Squares Sample 1 50 Included observations 50 Variable Coefficient Std Error t Statistic Prob REVENUE C 1 067927 83847 72 0 614944 39395 83 1 736625 2 128340 0 0889 0 0385 R squared 0 059116 Adjusted R squared 0 039514 S E of regression169647 Sum squared resid 1 38E 1 Log likelihood 672 0001 Durbin Watson stat 1 952661 Mean dependent var S D dependent var Akaike info criterion Schwarz criterion F statistic Prob F statistic 138113 5 173101 5 26 96001 27 03649 3 015865 0 088868 8 Exploratory data Analysis 9 Transformation Ln Assets a b Ln Revenue e Fortune 500 1999 Assets Vs Revenue In Logs 1000000 Citigroup Bank of America Fannie May Chase Manhatten General Electric Morgan Stanley Prudential Merrill Lynch TIAA CREF Bank One American International State Farm 100000 Log Assets Allstate 10000 1000 10000 100000 Log Revenue 1000000 10 Finance Vs Trade Fortune 500 1999 Assets Vs Revenue In Logs 1000000 100000 Citigroup Bank of America Fannie May Chase Manhatten General Electric Morgan Stanley Prudential Merrill Lynch General Motors TIAA CREF Bank One American International Exxon Mobil State Farm Log Assets Allstate Wal Mart Kroger 10000 McKesson HBOC Ingram Micro Costco Wholesale 1000 10000 100000 Log Revenue 1000000 11 12 Dependent Variable LNASSETS Method Least Squares Sample 1 50 Included observations 50 Variable Coefficient Std Error t Statistic Prob LNSALES C 0 919950 1 294185 0 319084 3 406777 2 883096 0 379885 0 0059 0 7057 R squared 0 147610 Adjusted R squared 0 12985 S E of regression1 160413 Sum squared resid 64 6347 Log likelihood 77 36517 Durbin Watson stat 1 70002 Mean dependent var S D dependent var Akaike info criterion Schwarz criterion F statistic Prob F statistic 11 10485 1 243987 3 174607 3 251088 8 312240 0 005877 13 Table 1 Industry and Number of Firms Industry Industry Aerospace Aerospace Chemicals Chemicals Commercial Banks Commercial Banks Computers Office Equipment Computers Office Equipment Diversified Financials Diversified Financials Electronics Electrical Electronics Equipment Electrical Equipment Entertainment Entertainment Food and Drug Stores Food and Drug Stores General Merchandisers General Merchandisers Health Care Health Care Insurance Insurance Mail Package Freight Delivery Mail Package Freight Delivery Motor Vehicles and Parts Motor Vehicles and Parts Network Communications Network Communications Petroleum Refining Petroleum Refining Pharmaceuticals Pharmaceuticals Pipelines Pipelines Securities Securities Semiconductors Semiconductors Soaps Cosmetics Soaps Cosmetics Specialty Retailers Specialty Retailers Telecommunications Telecommunications Tobacco Tobacco Wholesalers Wholesalers of Firms of Firms 1 1 1 1 3 3 3 3 3 3 1 1 1 1 3 3 5 5 1 1 5 5 1 1 2 2 1 1 3 3 2 2 1 1 2 2 1 1 1 1 2 2 4 4 1 1 2 2 14 Ln ln Regression with Industry Dummies 15 L o g l i k e l i h o o d 0 7 16 17 18 Wald Test Null Hypothesis 19 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 3 488804 Probability Chi square 10 46641 Probability 0 030516 0 014990 20 Wald Test drop insurance from Group 21 Wald Test results Accept Null Wald Test Equation Untitled Null Hypothesis C 3 C 18 C 6 C 18 F statistic 0 300921 Probability 0 742780 Chi square 0 740136 0 601842 Probability 22 Wald Test Equivalent to a Likelihood Ratio test Equation with all the dummies R2 0 9601 SSR 3 022 Ln Likelihood 0 798333 Estimate 25 regression parameters Equation with Finance Group Dummy replacing banks divfinanc and securities R2 0 9592 SSR 3 095 Ln Likelihood 1 393045 Estimate 23 regression parameters 23 Likelihood Ratio Test Likelihood ratio Likelihood constrained Likelihood unconstrained Where 2 ln is distributed as Chi square 2 ln 2 ln Lik const ln Lik unconst 2 ln Lik unconst ln Lik const 2 0 798333 1 393045 2 0 594712 2ln 1 189424 24 25 Chi Square Test 2 Degrees of Freedom 0 6 CHIDENSITY 1 19 Our Chi Square statistic 0 4 0 2 5 0 0 0 2 4 6 RCHI 8 5 99 10 26 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 Degrees of freedom 2 Explained mean square 0 073 2 0 0365 Unexplained mean square from regression 1 0 0322 n k 0 0322 25 F2 25 0 0365 0 12088 0 302 27 F2 23 Test accept null c 3 c 6 c 18 1 0 Our F statistic 0 302 DENSITYF 0 8 0 6 F2 23 statistic 0 4 0 2 5 0 0 0 5 10 RANDF 15 28 Wald Test results Accept Null Wald Test Equation Untitled Null Hypothesis C 3 C 18 C 6 C 18 F statistic 0 300921 Probability 0 742780 Chi square 0 740136 0 601842 Probability 29 Eviews Help 30
View Full Document
Unlocking...