Statistics 103 Problem Set #2 Part I - Male Fruitflies This dataset is called 'fruitfly.xls'. Here is a list of the variables in the dataset and their descriptions: ID PARTNERS TYPE LNGEVITY THORAX SLEEP This is just an identification number from 1 - 125 This is the number of sexual companions that the fruitfly had (0, 1, or 8) This is the type of companion (0=newly pregnant female, 1=virgin female, 9=not applicable, i.e. PARTNERS=0) This is lifespan, in days Length of the thorax, in mm Percentage of each day spent sleeping 1. Examine the data. Briefly discuss how the data is set up. 2. Create a dummy variable called 'ACTIVE' that is =1 if the fruitfly has at least one partner and =0 if he has no sexual partners. Create a dummy called 'ACTIVE1' if PARTNERS=1. Create a dummy called 'ACTIVE8' if PARTNERS=8. Why do we not need to create a variable called 'ACTIVE0'? 3. Report the means, standard deviations, and medians of all variables. Discuss the meaning of the mean of the TYPE, PARTNERS, and ACTIVE variables. 4. Report and compare the means, standard deviations, and medians for the LNGEVITY variable if the fruitfly has 0, 1, and 8 partners. Does this suggest a relationship between sexual behavior and lifespan? 5. Suppose you are interested in finding the determinants of lifespan for male fruitflies. In the following questions, you will test LNGEVITY = f(PARTNERS, THORAX, SLEEP). What do you predict for the sign of the coefficients on the independent variables? 6. Run an OLS regression with LNGEVITY as your dependent variable and ACTIVE1, ACTIVE8, THORAX, and SLEEP as your independent variables and report the coefficients and t-stats for these variables as well as the constant in a table. Also report the r-squared. Discuss the results. Were your predictions correct? Interpret the coefficients? What variables are significant at the .05 level? 7. Run another OLS regression with LNGEVITY as your dependent variable and THORAX, SLEEP, and TYPE as your dependent variables for those you are active only. Prepare another table similar to the table needed for question 6 above. Discuss these results. 8. What conclusions can you make about the sexual and sleeping behavior of male fruitflies and their lifespan? Part II - CEOs This dataset is called 'ceo.xls'. Here is a list of the variables in the dataset and their descriptions: salary = 1999 salary + bonuses (in thousands of $) totcomp = 1999 CEO total compensation (in thousands of $) tenure = # of years as CEO (=0 if less than 6 months) age = age of CEO sales = total 1998 sales revenue of firm I (in millions of $) profits = 1998 profits for firm i (in millions of $) assets = total assets of firm i in 1998 (in millions of $) 1. Examine the data. Briefly discuss how the data is set up. Are there any outliers in the data? In other words, are there any observations that are considerably higher or considerably lower than the remainder of the data points? 2. Create size Dummies for each SMALL, MEDIUM, and LARGE companies where SMALL are companies with up to $6 billion in sales, LARGE are companies with over $20 billion in sales, and MEDIUM are all those in between. 3. Report the means, standard deviations, and medians of all variables. 4. Report the correlation coefficients for the variables. Discuss your findings. 5. Suppose you are interested in what determines salary and/or total compensation. Discuss which variables you should include on the right hand side of these regressions. Be careful to discuss the concept of correlation vs. causation here. 6. Run an OLS regression with SALARY as your dependent variable and any appropriate independent variables of your choosing. Report the appropriate coefficients, t-stats, and r-squared in a table. Discuss the results. 7. Repeat question 6 for TOTCOMP. Compare your results to those of question 6. 8. Using the variables you already have in place and/or any new ones you feel are appropriate, develop what you feel are the most appropriate OLS regressions for SALARY and for TOTCOMP. Be sure to discuss your reasons why these are most appropriate and interesting. 9. What conclusions can you make about the determinants of CEO salary and compensation? If you were to extend this study, what additional variables would you want to add and why? salary totcomp 1758 2444 875 1151 2300 2387 906 2627 1866 4311 1073 1090 484 1492 2698 3413 4002 26745 1697 10485 1381 1997 1440 1440 1227 3004 663 1663 1595 1601 2600 3001 633 633 910 4845 1115 1139 1240 1528 1325 1345 600 1184 856 2280 1121 2023 621 701 1225 3973 1075 17811 1990 3286 709 709 1747 8866 1163 1288 1100 1390 1087 1093 1002 1103 1950 4441 1199 8675 1000 1056 900 905 774 777 650 1006 647 673 1325 1352 3300 3514 1920 3328 511 587 1520 2951 1048 1872 1648 1860 2925 3509 tenure 5 7 9 6 10 2 0 18 13 4 8 34 10 5 1 1 2 1 2 10 2 7 1 15 15 4 36 1 3 5 3 3 10 2 10 22 20 9 2 0 2 6 4 10 22 12 4 8 4 age 62 50 57 59 59 51 53 62 55 61 60 58 50 39 46 54 62 65 52 63 53 56 58 61 58 58 68 45 58 64 48 60 52 46 61 59 55 55 51 34 54 55 44 63 60 61 58 62 57 sales 2896.4 2904.7 2910.0 2932.8 2934.0 2936.7 2941.4 2943.3 2972.6 2980.9 2993.8 3005.6 3009.2 3011.9 3020.6 3025.8 3045.3 3050.6 3059.2 3063.4 3064.6 3071.6 3072.5 3074.5 3082.1 3099.6 3100.2 3100.6 3112.1 3116.9 3130.0 3130.0 3142.1 3203.7 3219.9 3221.0 3224.6 3234.6 3242.9 3243.0 3259.1 3261.0 3265.1 3265.8 3266.9 3269.1 3287.0 3289.2 3291.5 profits 16.6 132.0 182.9 193.9 375.0 278.9 60.6 368.6 -68.0 414.3 55.6 92.4 501.8 -233.7 243.0 247.8 -9.4 108.5 58.0 190.9 501.5 153.2 421.7 137.3 20.1 365.9 434.6 -459.6 -28.7 236.6 332.0 399.2 -62.5 54.7 607.1 182.0 23.9 -299.8 227.9 153.0 -120.5 139.3 -286.6 127.9 63.4 106.3 101.7 136.5 1417.3 assets 2854.8 5008.7 2738.7 4986.5 35800.2 3465.1 2750.4 38133.8 5381.2 5935.6 1373.5 1807.6 34427.2 4688.3 1483.4 54812.3 1147.0 1129.5 1167.0 5036.5 37210.0 6087.7 36831.9 1501.6 717.8 4257.1 38468.7 2964.7 1105.7 3846.0 2357.0 8347.4 3098.5 908.9 36600.8 1211.8 1740.0 3597.8 2748.1 7063.0 2554.6 1555.9 7061.1 1550.0 1025.1 1607.2 1984.7 2106.5 4218.3 1437 748 1338 670 407 1210 817 750 8450 1322 6945 1410 1458 1451 1800 1145 746 2500 796 690 772 969 5617 1245 700 900 1147 525 1238 1604 2344 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1948 1049 886 36549 1653 730 2166 2683 20833 3272 1515 880 10799 1613 6435 4771 1861 15 22 12 3 7 2 32 0 3 3 1 18 15 9 1 7 2 2 17 1 11 3 11 4 8 5 1 14 7 5 3 1 7 10 5 3 13 2 5 12 6 23 1 5 4 2 0 4 3 7 46 60 80 56 64 46 65 45 73 52 45 68 63 53 49 59 75 58 52 57 59 50 54 56 61 56 58 76 58 60 57 48 64 61 65 56 55 52 54 56 63 54 51 65 50 47 50 64 56 63 4006.1 4041.7 4050.0 4064.0 4069.3 4092.0 4092.3 4092.7 4129.7 4151.2 4160.0 4164.0 4174.6 4193.7 4221.0 4234.0 4235.3 4248.8 4258.4 4273.0 4287.2 4334.4 4337.8 4341.3 4378.4 4387.8 4399.9 4424.2 4428.0 4435.6 4468.7 4474.6 4477.8 4481.0 4502.9 4553.0 4559.9 4579.2 4597.0 4630.8 4633.0 4719.0 4719.4 4724.1 4745.7 4781.9 4787.9 4797.2 4798.1 4833.0 46.6 230.9 124.4 297.0 280.6 285.1 84.7 550.9 19.6 263.7 -61.6 433.4 187.1 96.8 443.0 436.0 141.6 360.1 42.6 -27.0 141.3 576.4 48.6 238.5 106.5 60.0 181.4 12.1 734.0 340.9 53.7 -73.3 120.1 249.0 19.3 18.5 -754.8 119.7 -31.5 363.4 319.6 1169.0 -624.5 190.0 338.8 332.3 61.3 263.1 605.3 425.0 6773.0 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8681 5502 3945 2636 1603 3108 2159 21739 9492 4887 2538 1419 2627 1494 14 18 7 8 4 8 8 2 0 8 1 1 4 12 2 28 28 8 2 0 3 14 5 18 4 8 4 5 2 14 12 15 5 4 4 2 6 1 3 0 7 6 2 24 0 6 2 0 2 0 49 43 60 62 61 55 62 51 44 64 46 57 62 63 55 54 53 58 55 51 53 59 51 60 58 51 61 63 53 57 57 34 65 52 60 52 60 52 60 52 51 53 56 62 54 55 62 46 46 60 14258.0 14484.0 14582.0 14704.0 14736.0 14878.8 15021.0 15022.0 15069.3 15128.0 15273.6 15307.0 15327.5 15489.4 15833.0 15872.8 15918.1 16005.1 16108.6 16891.0 17037.0 17134.3 17154.0 17201.4 17353.1 17355.0 17487.3 17561.0 17610.0 17678.0 18048.0 18243.0 18283.6 18425.0 18441.0 18813.0 19132.0 19205.0 19500.0 19530.0 19866.7 19894.0 19942.0 20011.0 20019.0 20482.0 20604.1 20713.0 20857.3 20977.0 108.4 4490.0 168.0 3351.0 740.0 -162.8 1175.0 1015.0 -510.6 1331.0 396.4 511.0 296.8 853.0 662.0 503.0 247.1 567.2 403.6 743.4 -577.0 414.5 3606.0 230.8 -14.7 -166.0 499.5 821.0 1252.0 -2669.0 1700.0 1460.0 3141.2 963.0 1310.0 3533.0 2141.0 1314.0 213.0 864.0 233.7 736.0 719.0 -523.0 395.0 1950.0 848.1 464.8 154.9 1513.0 5260.0 22357.0 31640.0 18302.0 39514.0 10151.2 14153.0 150632.0 3491.0 15560.0 6736.2 4902.0 3780.2 17462.5 13464.0 9686.1 3961.1 6234.0 13833.5 11526.1 28892.0 33231.1 30299.0 4093.0 11112.0 9701.0 13925.8 18559.0 26806.0 80193.0 321421.0 6877.0 16272.5 261067.0 23830.0 19145.0 126933.0 22303.0 27080.0 27939.0 8885.3 154000.0 33234.0 10989.0 30024.0 202475.0 105148.1 70906.4 5607.5 25128.0 4869 3420 2000 5764 2990 2627 1098 533 1875 2418 2523 3195 3071 2605 2344 2244 2460 2550 1195 6163 1800 12962 2900 1062 3343 8888 4417 2060 1523 6229 6000 1990 5236 1185 2130 1911 2493 3500 3300 999 5000 9525 9375 10000 3300 3571 6050 3030 15133 12785 4082 589101 3941 7215 2477 550 1875 2867 4946 9865 12290 3747 2485 116840 4315 2557 3327 10112 2327 18536 3116 1821 11931 48962 18623 6854 4354 11621 31208 14906 20582 4366 2383 4727 6728 3677 7467 2916 24424 12165 42381 68285 13464 7433 14530 8138 11 15 3 15 2 10 2 11 6 4 7 15 5 0 2 1 10 5 9 9 2 2 2 4 5 17 15 4 3 5 32 4 2 0 4 7 5 16 2 3 5 15 6 18 6 11 0 7 55 57 54 57 56 60 50 63 49 56 59 55 57 53 55 59 62 58 59 57 49 52 56 57 56 55 57 52 56 63 74 60 60 56 59 58 61 63 60 57 61 60 57 63 60 63 51 61 21437.0 21543.0 22348.0 22976.0 23123.0 23657.0 23840.5 24269.9 24484.2 24754.0 25473.0 25595.0 25715.0 25879.0 26266.0 26273.0 26801.0 26898.2 28203.3 28777.0 29398.0 30147.0 30219.0 30678.0 30951.0 31131.0 31260.0 31565.9 31707.0 32379.0 33296.0 33674.0 35853.0 37154.0 41322.0 47061.0 47678.0 50777.0 53588.0 56154.0 57813.0 76431.0 81667.0 100469.0 100697.0 139208.0 144416.0 161315.0 1292.0 2891.0 1993.0 1850.0 3527.0 3059.0 613.2 459.8 806.7 674.0 2172.0 3108.0 1255.0 3294.0 1001.0 6068.0 1976.0 5248.2 410.8 4023.0 -962.0 970.0 1614.0 594.0 935.0 3276.0 703.0 2965.3 578.0 3782.0 3765.6 568.0 1259.0 3780.0 1048.0 2945.0 1704.0 5165.0 6398.0 1120.0 5372.0 5807.0 6328.0 9296.0 6370.0 4430.0 22071.0 2956.0 114612.0 237363.0 22660.0 41378.0 39410.0 26211.0 11702.8 6259.8 11389.6 21133.0 43615.0 261496.0 18375.0 87691.0 28700.0 31471.0 36535.0 31853.4 6700.1 45066.0 28728.0 26720.0 13465.0 23638.0 15666.0 317590.0 29350.0 55143.9 28570.0 365875.0 194398.0 14166.0 299804.0 30966.0 37675.0 33673.0 42754.0 617679.0 59550.0 36672.0 59920.0 668641.0 86100.0 355935.0 92630.0 49271.0 237545.0 257389.0 11557.8 ID 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 PARTNERS 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 TYPE 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 LNGEVITY THORAX 35 0.639999986 37 0.680000007 49 0.680000007 46 0.720000029 63 0.720000029 39 0.75999999 46 0.75999999 56 0.75999999 63 0.75999999 65 0.75999999 56 0.800000012 65 0.800000012 70 0.800000012 63 0.839999974 65 0.839999974 70 0.839999974 77 0.839999974 81 0.839999974 86 0.839999974 70 0.879999995 70 0.879999995 77 0.920000017 77 0.920000017 81 0.920000017 77 0.939999998 40 0.639999986 37 0.699999988 44 0.720000029 47 0.720000029 47 0.720000029 47 0.75999999 68 0.779999971 47 0.800000012 54 0.839999974 61 0.839999974 71 0.839999974 75 0.839999974 89 0.839999974 58 0.879999995 59 0.879999995 62 0.879999995 79 0.879999995 96 0.879999995 58 0.920000017 62 0.920000017 SLEEP 22 9 49 1 23 83 23 15 9 81 12 15 37 24 26 17 14 14 6 25 18 26 24 29 27 18 6 19 7 16 13 35 2 35 6 15 14 18 50 25 10 33 43 35 17 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 9 9 9 9 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 70 0.920000017 72 0.920000017 75 0.920000017 96 0.920000017 75 0.939999998 46 0.639999986 42 0.680000007 65 0.720000029 46 0.75999999 58 0.75999999 42 0.800000012 48 0.800000012 58 0.800000012 50 0.819999993 80 0.819999993 63 0.839999974 65 0.839999974 70 0.839999974 70 0.839999974 72 0.839999974 97 0.839999974 46 0.879999995 56 0.879999995 70 0.879999995 70 0.879999995 72 0.879999995 76 0.879999995 90 0.879999995 76 0.920000017 92 0.920000017 21 0.680000007 40 0.680000007 44 0.720000029 54 0.75999999 36 0.779999971 40 0.800000012 56 0.800000012 60 0.800000012 48 0.839999974 53 0.839999974 60 0.839999974 60 0.839999974 65 0.839999974 68 0.839999974 60 0.879999995 81 0.879999995 27 22 16 20 37 23 4 20 42 9 32 66 28 10 4 12 17 12 23 40 18 10 38 7 23 36 9 21 62 36 23 62 28 18 10 28 22 29 15 73 10 5 13 27 20 21 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 1 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 81 0.879999995 48 0.899999976 48 0.899999976 56 0.899999976 68 0.899999976 75 0.899999976 81 0.899999976 48 0.920000017 68 0.920000017 16 0.639999986 19 0.639999986 19 0.680000007 32 0.720000029 33 0.720000029 33 0.74000001 30 0.75999999 42 0.75999999 42 0.75999999 33 0.779999971 26 0.800000012 30 0.800000012 40 0.819999993 54 0.819999993 34 0.839999974 34 0.839999974 47 0.839999974 47 0.839999974 42 0.879999995 47 0.879999995 54 0.879999995 54 0.879999995 56 0.879999995 60 0.879999995 44 0.920000017 12 49 17 22 71 17 10 24 18 34 6 4 22 28 31 16 27 8 32 20 35 12 14 17 29 31 6 30 27 40 19 8 8 15