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Problem Set #5-KeySonoma State University Dr. Cuellar Economics 317- Introduction to Econometrics

(1) Using data set CEOSAL2.dta estimated the regression Salary = β0 + β1ceoten + u.

Source SS df MS Number of obs = 177F( 1, 175) = 3.65

Model 1241694.06 1 1241694.06 Prob > F = 0.0577Residual 59524270.7 175 340138.69 R-squared = 0.0204

Adj R-squared= 0.0148Total 60765964.7 176 345261.163 Root MSE = 583.21

salary Coef. Std. Err. t P>t [95% Conf. Interval]ceoten 11.74613 6.14774 1.91 0.058 -.387127 23.87939_cons 772.4263 65.67567 11.76 0.000 642.8079 902.0446

The estimated regression equation is: Salary =772.4263 + 11.74613ceoten.

(i) What is the expected salary of a CEO who has been with the company for years?Expected Salary =772.4263 + 11.74613(10)=889.8876 or $889,887.6

(ii) Construct a 95% confidence interval on the prediction for the average CEO whohas been with the company for 10 years. What is the margin of error of yourprediction? What is the high and low expected salary?

The lower bound on the prediction is 889.8876 - 90.005737 = 799.8818 The upper bound on the prediction is 889.8876 + 90.005737 = 979.8933

A CEO with 10 years of tenure could expect to make $889,887.6 ± $90.00574 or from $799,881.80 to $ 979,893.30.

(iii) In STATA show graphically the regression line with a 95% confidence on themean prediction.

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(iv) Construct a 95% confidence interval on the prediction for an individual CEO whohas been with the company for 10 years. What is the margin of error of yourprediction? What is the high and low expected salary?

The resulting margin of error is 1154.552 or $1,154,552.The lower bound =-264.6648 or essentially zero.The upper bound = 2044.44 or $2,044,440.A CEO with 10 years of tenure could expect to make $889,887.6 ± $1,154,552 or from between -$264.6648 and $2,044,440

(v) In STATA show graphically the regression line with a 95% confidence on theindividual prediction.

(vi) Construct a 95% confidence interval on the prediction for an individual CEO whohas been with the company for 20 years. What is the margin of error of yourprediction? What is the high and low expected salary? Is the margin of errordifferent for those with ten years? Why? Explain fully.

A CEO with 20 years of tenure could expect to make $1,007,349.00 ± $1,163,501

The margin of error is 1163.501 or $1,163,501.The lower bound =-156.152 or essentially zero.The upper bound = 2170.85 or $2,170,850.

(vii) List the ceo tenure, actual salary, predicted salary, margin of error and confidenceinterval for each value of tenure from lowest to highest.

TenureActualSalary

PredictedSalary

Margin ofError

LowerBound

UpperBound

0 462 772.4263 129.6183 642.8079 902.04461 515 784.1724 120.8552 663.3172 905.02762 577 795.9185 112.7186 683.2 908.63713 1101 807.6647 105.3538 702.3109 913.01844 605 819.4108 98.9332 720.4775 918.3445 1080 831.1569 93.65134 737.5056 924.80836 497 842.9031 89.70955 753.1935 932.61267 1248 854.6492 87.28954 767.3596 941.93878 2199 866.3953 86.5191 779.8762 952.91449 1133 878.1414 87.44186 790.6996 965.583310 600 889.8876 90.00574 799.8818 979.893311 358 901.6337 94.07668 807.557 995.710312 693 913.3798 99.4698 813.91 1012.8513 425 925.126 105.9834 819.1425 1031.10914 1798 936.8721 113.4247 823.4473 1050.29715 1301 948.6182 121.6235 826.9947 1070.24216 559 960.3643 130.4371 829.9272 1090.80117 1276 972.1105 139.7491 832.3614 1111.8618 2220 983.8566 149.4664 834.3901 1133.32319 581 995.6027 159.5151 836.0876 1155.11820 410 1007.349 169.8362 837.5127 1177.18521 1946 1019.095 180.383 838.7119 1199.47822 651 1030.841 191.1182 839.7228 1221.95924 849 1054.333 213.0393 841.2941 1267.37326 300 1077.826 235.421 842.4047 1313.24728 396 1101.318 258.1435 843.1743 1359.46134 853 1171.795 327.6423 844.1523 1499.43737 1200 1207.033 362.8774 844.1556 1569.911

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(2) Using data set Wage2.dta, estimated the regression Wage = β0 + β1IQ + u.Source SS df MS Number of obs = 935

F( 1, 933) = 98.55Model 14589782.6 1 14589782.6 Prob > F = 0.0000Residual 138126386 933 148045.429 R-squared = 0.0955

Adj R-squared= 0.0946Total 152716168 934 163507.675 Root MSE = 384.77

wage Coef. Std. Err. t P>t [95% Conf. Interval]IQ 8.303064 .8363951 9.93 0.000 6.661631 9.944498_cons 116.9916 85.64153 1.37 0.172 -51.08078 285.0639

The estimated regression equation is:Wage = 116.9916 + 8.303064IQ.

(i) What is the expected wage of someone with an IQ of 100?

Expected Wage = 116.9916 + 8.303064(100) = 947.298

(ii) Construct a 95% confidence interval on the prediction for the average person withan IQ of 100. What is the margin of error of your prediction? What is the highand low expected salary?

The margin of error is $24.78423 per monthThe lower bound is $922.5137 per month.The upper bound is $972.0822 per month.

The expected wage of someone with an IQ of 100 is 947.298 ± 24.78423.Or they can expect to make from between $922.5137 and $972.0822.

(iii) In STATA show graphically the regression line with a 95% confidence on themean prediction.

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(iv) Construct a 95% confidence interval on the prediction for and individual with anIQ of 100. What is the margin of error of your prediction? What is the high andlow expected salary?

The margin of error is $755.5151 per month.The lower bound is $191.7829 per month.The upper bound is $1,702.813 per month.

The expected wage of someone with an IQ of 100 is 947.298 ± $755.5151,or from between $191.7829 and $1,702.813 per month.

(v) In STATA show graphically the regression line with a 95% confidence on theindividual prediction.

(vi) Construct a 95% confidence interval on the prediction for and individual with anIQ of 125. What is the margin of error of your prediction? What is the high andlow expected monthly wage? Is the margin of error different for those with an IQof 125? Why? Explain fully.

Expected Wage = 116.9916 + 8.303064(125) = 1154.875For a 95% confidence interval on an individual prediction, the margin of error is$756.5146.

The lower bound is $398.36 per month.The upper bound is $1,911.389 per month.

(vii) List the IQ, actual wage, predicted wage, margin of error and confidence intervalfor each value of IQ from lowest to highest.

IQActualSalary

PredictedSalary

Marginof Error

LowerBound

UpperBound

50 750 532.1448 87.72414 444.4207 619.868954 900 565.3571 81.44489 483.9122 646.801955 754 573.6601 79.88229 493.7778 653.542459 480 606.8724 73.66612 533.2062 680.538560 1346 615.1754 72.12177 543.0536 687.297261 462 623.4785 70.58179 552.8967 694.060362 596 631.7816 69.04649 562.735 700.828163 450 640.0846 67.51618 572.5684 707.600864 1874 648.3877 65.99121 582.3965 714.378965 533 656.6907 64.47197 592.2188 721.162766 865 664.9938 62.95885 602.035 727.952767 492 673.2969 61.45233 611.8445 734.749268 400 681.5999 59.95289 621.647 741.552869 1000 689.903 58.46108 631.442 748.364170 753 698.2061 56.9775 641.2286 755.183571 940 706.5092 55.5028 651.0063 762.01272 1000 714.8122 54.03772 660.7745 768.849973 508 723.1152 52.58307 670.5322 775.698374 350 731.4183 51.13972 680.2786 782.55875 260 739.7214 49.70866 690.0127 789.430176 651 748.0245 48.29099 699.7335 796.315577 550 756.3275 46.88793 709.4396 803.215578 1250 764.6306 45.50081 719.1298 810.131379 1200 772.9337 44.13115 728.8025 817.064880 900 781.2367 42.78062 738.4561 824.017381 700 789.5398 41.4511 748.0887 830.990982 442 797.8428 40.14467 757.6982 837.987583 500 806.1459 38.86366 767.2822 845.009584 1200 814.449 37.61066 776.8383 852.059685 575 822.752 36.38857 786.3635 859.140686 951 831.0551 35.20061 795.8545 866.255787 508 839.3582 34.05036 805.3078 873.408588 547 847.6612 32.94176 814.7194 880.60389 610 855.9643 31.87915 824.0851 887.843490 1346 864.2673 30.86729 833.4 895.134691 449 872.5704 29.91133 842.6591 902.481892 692 880.8735 29.0168 851.8567 909.890393 769 889.1766 28.18953 860.9871 917.366194 577 897.4796 27.43563 870.044 924.915295 817 905.7827 26.76128 879.0214 932.543996 1699 914.0858 26.17265 887.9131 940.258497 1832 922.3888 25.67562 896.7132 948.064498 800 930.6919 25.27559 905.4163 955.967599 1200 938.9949 24.97724 914.0177 963.9722100 801 947.298 24.78423 922.5137 972.0822101 980 955.6011 24.69904 930.902 980.3001102 1155 963.9041 24.72277 939.1813 988.6269103 1111 972.2072 24.85511 947.3521 997.0623104 1463 980.5103 25.09436 955.4159 1005.605105 1924 988.8133 25.43748 963.3758 1014.251106 1744 997.1164 25.88035 971.236 1022.997107 3078 1005.419 26.41796 979.0015 1031.837108 1442 1013.723 27.04465 986.6779 1040.767109 1130 1022.026 27.75439 994.2712 1049.78110 1126 1030.329 28.54098 1001.788 1058.87111 654 1038.632 29.39826 1009.233 1068.03

112 1107 1046.935 30.32024 1016.615 1077.255113 722 1055.238 31.30119 1023.937 1086.539114 1384 1063.541 32.33575 1031.205 1095.877115 800 1071.844 33.41893 1038.425 1105.263116 600 1080.147 34.54618 1045.601 1114.693117 1100 1088.45 35.71331 1052.737 1124.163118 1270 1096.753 36.91654 1059.837 1133.67119 1126 1105.056 38.15246 1066.904 1143.209120 962 1113.359 39.41799 1073.941 1152.777121 1161 1121.662 40.71037 1080.952 1162.373122 579 1129.965 42.02713 1087.938 1171.993123 1748 1138.268 43.36604 1094.902 1181.635124 1202 1146.572 44.72511 1101.846 1191.297125 1417 1154.875 46.10256 1108.772 1200.977126 520 1163.178 47.4968 1115.681 1210.674127 1899 1171.481 48.90638 1122.574 1220.387128 635 1179.784 50.33001 1129.454 1230.114129 658 1188.087 51.76655 1136.32 1239.854130 700 1196.39 53.21494 1143.175 1249.605131 417 1204.693 54.67424 1150.019 1259.367132 1122 1212.996 56.14359 1156.853 1269.14134 2771 1229.602 59.10948 1170.493 1288.712137 1001 1254.511 63.61672 1190.895 1318.128145 2137 1320.936 75.88985 1245.046 1396.826