Nov 1 2005 LAB 5 ECON 240A 1 L Phillips Exploratory Data Analysis Scatterplots and Regression I The Fortune 500 1999 Fifty Firms Ranked by Revenues Source http www fortune com fortune Data for these fifty firms includes in addition to revenues in millions of dollars firm name firm industry profits assets stockholders equity market value all of the preceding quantitative variables in millions of dollars earnings per share total return to investors in 1999 in percent number of employees A Assets Versus Revenue 1 Select these two variables assets as the dependent variable and revenue as the explanatory variable and insert an xy chart Note that the data is fan shaped when the data is linear in scale 2 Take the natural logarithms of these two variables and insert an xy chart Explore the data points at the top of the chart For example the data point with the highest value of assets is Citigroup in the diversified financials industry The point to its left with the second highest value of assets is Bank of America If you select the data points and then double click on the point of interest and go to the format menu there is a format data series box Select the data labels tab and select the show value button From the value you can identify the company and then select the value and type in the company name The points along the top edge tend to be in the financial sector from industries such as 1 commercial banks 2 diversified financials 3 insurance and securities To check this select the company name and industry columns and copy them to two new columns Then select the industry column go to the data menu and choose sort Sort by column x and expand the selection to next sort by column w Under options choose normal and case sensitive Note there are 3 commercial banks 3 diversified financials 5 insurance companies and 2 securities firms I selected and labeled the appropriate data points and the results are displayed in Figure 1 State Farm and Allstate look like they may belong to a different set leaving 11 firms I chose these 11 firms to run the regression Nov 1 2005 LAB 5 ECON 240A 2 L Phillips Exploratory Data Analysis Scatterplots and Regression 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 1000000 Log Revenue Figure 1 Log of Assets Versus Log of Revenue 50 Fortune 500 Firms Looking along the lower edge I identified the firms as shown in Figure 2 Most of these were wholesalers specialty retailers food and drug store or general merchandisers The exceptions were in the upper right hand lower edge General Motors and Exxon Mobil From this graphical analysis I formed the following hypothesis With the variables in log log form the relationship had a constant slope but the intercept varied by industry Ln Assets j a k b ln Revenue j where j indexes firm and k indexes industry Thus the regression shifts up and down depending on the industry There are 24 different industries among the 50 firms counting the different insurance companies together which may not be appropriate The industries and number of firms in each are shown in Table 1 Some grouping may be necessary to implement the regression analysis but we will start with all 24 industries Nov 1 2005 LAB 5 ECON 240A 3 L Phillips Exploratory Data Analysis Scatterplots and Regression 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 Figure 2 Log of Assets Vs Log of Revenu Table 1 Industry and Number of Firms Industry Aerospace Chemicals Commercial Banks Computers Office Equipment Diversified Financials Electronics Electrical Equipment Entertainment Food and Drug Stores General Merchandisers Health Care Insurance Mail Package Freight Delivery Motor Vehicles and Parts Network Communications Petroleum Refining Pharmaceuticals Pipelines Securities Semiconductors Soaps Cosmetics Specialty Retailers Telecommunications Tobacco of Firms 1 1 3 3 3 1 1 3 5 1 5 1 2 1 3 2 1 2 1 1 2 4 1 1000000 Nov 1 2005 LAB 5 ECON 240A 4 L Phillips Exploratory Data Analysis Scatterplots and Regression Wholesalers 2 II Regression with Eviews Open EViews file Fortune 50 wf1 Go to the quick menu choose estimate equation and specify lnassets aero banks chem computers divfinanc electronics entertain fooddrug genmerch health insurance mail netcom petrol pharma pipelines securities semicon soaps specretail telecom tobac vehicles wholesale lnsales and hit OK The goodness of fit R2 0 96 and the elasticity of assets to sales is 0 78 and significant Under View look at actual fitted residual graph The fit looks pretty good over the 50 observations Of course for the industries with only one firm there are no degrees of freedom Note that the group we discovered using graphical exploratory analysis all have a large intercept in the range from 3 71 to 4 77 These intercepts are all significantly different from zero at the 5 level This group includes commercial banks diversified financials health care Aetna which may be similar to the 5 other insurance companies insurance and securities We can test whether the coefficients for food and drug companies general merchandisers and specialty retailers are equal Under View look at representations and notice that the coefficients for these four industries are c 8 c 9 and c 20 Under View go to coefficient tests Wald coefficient restrictions In the box type in c 8 c 9 c 20 This restriction is not significant at the 5 level so we could group these observations into one industry trade To do this go to the workfile window and select the Genr command in the menu bar Enter the equation trade fooddrug genmerch specretail Reestimate the equation substituting trade for its three components III Orientation to Eviews Help Menu About Eviews credits Help Menu Read Me Help Menu Eviews Help Topics contents tab 1 Eviews Basics 2 Statistical Views and Procedures 3 Estimation Methods Ordinary Least Squares Nov 1 2005 LAB 5 ECON 240A 5 L Phillips Exploratory Data Analysis Scatterplots and Regression IV Exercises 1 Search for possible groupings
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