70208 Homework 6 Due March 23, 2016 Homeworks must be turned in during lecture. No late assignments will be accepted. You may work in groups, but you must write up the answers on your own and write down who you worked with. Write your recitation section on your homework assignment. Be sure to explain your answers. The data \u001cle wages_experience.xls, posted on Blackboard, gives information on wages, labor market experience, age, and education for a random sample of individuals. 1. [5 points] Use Excel to obtain the line for the least squares regression that estimates how age a\u001bect wages. In this regression, denote X1 as age and y as wages. Then the population regression can be written as yi = 0 + 1 X1i + ei Print your Excel output in your homework solutions. (a) [10 points] Use the formula for the standard deviation of b1 to calculate the standard deviation of age in the data. Con\u001crm your answer by calculating the standard deviation of age using the raw data. 2. [5 points] Now run a regression with labor market experience and age as independent variables, and wage as the dependent variable. Denote X2 as labor market experience, and the population regression is yi = 0 + 1 X1i + 2 X2i Print your Excel output in your homework solutions. (a) [10 points] Compare the estimates for 1 in the 2 regressions. Explain the di\u001berence in estimates and standard errors when we added in the extra independent variable. (b) [10 points] Use the regression results and your answer in 1(a) to calculate the correlation between age and labor market experience. Con\u001crm your answer by calculating the correlation using the raw data. Does this help to explain the di\u001berences in the results in the \u001crst and second regressions? (c) [5 points] Compare the total sum of squares in the regression in question (1) to the regression in question (2). Why did this value not change? (d) [5 points] Compare the error sum of squares in the regression in question (1) to the regression in question (3). Does it increase or decrease? Why? 1 3. [5 points] Denote education as X3 . Run a regression with age and education as your independent variables: yi = 0 + 1 X1i + 3 X3i + ei (a) [10 points] Compare your results to those in questions 1 and 2. Calculate the correlation between age and education using the raw data. Can this explain why the addition of education changed the results di\u001berently than the addition of labor market experience? 4. [15 points] Use a F test to compare the following 2 models, where the \u001crst one is the full model and the second is the reduced model: yi = 0 + 1 X1i + 2 X2i + 3 X3i + ei yi = 0 + 1 X1i + ei In this hypothesis test, the null hypothesis is that 2 = 3 = 0 . Use a level of signi\u001ccance = 0.05. Explain how to interpret the results of your hypothesis test. 5. [10 points] If you wanted to analyze the determinants of wages using this data, which variables do you think is best to include in the regression? Explain your answer. 2 Wage Age Labor market experience Years of education 54.16632 42.25 48535 15.72541 28.25 19700 25.34607 25.33333 10076 11.04186 29.25 17722 10.96729 24 10395 7.952943 38.91667 14147 22.38268 51.83333 45905 10.58067 43.91667 30193 11.13324 49.66667 45630 9.962626 16.25 323 25.26305 26.41667 11830 9.748137 20.58333 992 9.834792 23.33333 6040 12.76194 24.75 9467 25.99778 42.75 46887 8.0493 31.33333 3978 7.440368 45.5 54449 6.919754 21.58333 2780 51.57046 38.83333 48331 24.9527 35.25 27740 14.99217 48.33333 40200 21.93689 40.25 44722 22.61975 42.25 58108 48.44103 32.16667 27231 6.962955 19.33333 1244 9.414357 28.66667 4430 9.530369 33.75 24868 10.52561 34.16667 10333 17.09111 52.16667 51218 32.97127 40.5 30832 11.86244 26.66667 6560 33.72258 42.41667 43882 22.46765 27.75 21647 17.4582 23.33333 7200 20.94688 35.33333 30400 17.48911 30.83333 26213 13.27907 34.75 22149 10.71573 25.83333 14752 40.5385 50.41667 72350 7.672531 40.83333 18669 19.20148 39.83333 34322 10.06091 39.08333 23133 16.34508 32.58333 22090 36.03295 37.5 37188 10.48349 24.16667 3343 15.07403 47.83333 43058 8.985841 42.16667 36536 14.20341 46.66667 34009 26.7626 48.5 49175 9.874177 32.5 12762 9.517737 17.58333 768 14.03414 35.58333 6643 16.53395 22.66667 11140 41.88013 34.58333 34919 23.56183 33.75 30621 13.10985 25.83333 12827 24.39014 35.75 35620 22.29157 41.75 48100 8.178419 46.33333 18820 10.056 28.41667 18160 29.25042 40.33333 39320 13.83951 25.58333 10351 31.65826 30.91667 21203 19.19657 27.75 11131 17.37605 28 12270 19.86583 46.66667 57708 34.36552 43.25 50946 21.24002 26.25 18442 10.69315 37.58333 25460 17.70846 31.83333 33722 14.17448 37.58333 7184 13.18851 35.41667 29182 33.93876 34.83333 23352 27.0859 22.66667 15070 18.19857 45.41667 26993 5.911245 47.83333 34471 10.14196 40.16667 34488 3.675014 16.08333 18 23.50001 48.58333 62291 34.406 48.25 43715 19 12 16 12 10 17 20 12 11 13 12 20 11 20 16 18 13 20 19 20 7 12 13 18 12 12 12 13 12 13 12 15 12 16 16 12 9 16 16 12 12 12 20 16 12 12 12 12 18 11 16 12 12 16 16 18 14 14 14 12 12 12 17 17 17 18 15 16 12 13 12 12 12 10 12 13 12 12 12 14 28.04866 32.11187 26.87564 40.83767 26.76723 14.76018 14.98269 44.28621 42.34636 26.24398 22.15615 14.88528 7.341178 8.479063 26.1346 10.61606 13.07206 13.70983 11.564 12.15636 24.13594 19.95309 11.80196 48.29158 28.37347 11.42128 8.564032 17.41738 8.0493 8.870591 10.54521 26.64944 32.93743 14.43568 12.06865 14.85006 42.01523 10.11021 10.84499 22.49942 31.82349 8.504204 116.9217 6.803364 8.922411 26.47745 20.86001 16.84097 14.82804 8.522236 20.89766 7.608497 4.698355 12.31877 13.18851 18.78581 20.2566 8.803578 8.75843 11.01177 25.61716 15.90542 22.45984 12.75631 10.76881 11.18328 17.8948 24.03001 15.25774 6.463196 9.517737 9.949685 10.39186 16.33653 28.84002 18.02122 9.354625 37.26732 14.17448 28.91308 15.91911 42.91667 31.58333 27.25 39.25 41 40.91667 23.75 49.66667 44 26.25 23.66667 25.5 39.08333 38.58333 43.66667 21.5 33.66667 38.41667 48.75 31.75 34.5 31.58333 44.75 47.41667 30.75 17.16667 44.91667 30 26.58333 39.41667 32 42.41667 42.16667 31.91667 42.33333 37.08333 36.75 21.33333 23.16667 44.58333 51 29.75 37 29.08333 40.08333 50.58333 45.5 31.33333 21.58333 30.75 27.25 40.08333 38.41667 43.91667 35.08333 33.83333 50.83333 23.58333 25.58333 37.75 43.5 29.58333 40.08333 30.58333 27.08333 27.08333 51.25 50.33333 26.75 29.33333 18.16667 24.91667 34.75 30.41667 45.83333 35 29 45.83333 37.25 29.16667 27.25 47335 21617 12161 34638 49414 23705 11916 60566 43456 15686 5906 13310 7444 10703 46722 7440 20114 36628 48398 14151 36385 19097 39992 59095 15061 825 40121 22846 6874 20885 28049 43235 49208 28331 64107 40796 48806 3350 11285 45507 41854 12021 23197 21604 47286 54650 57599 21821 2055 12468 7964 32776 11090 51336 6787 21740 61601 2002 5772 29293 35531 15437 41828 27008 2128 14730 74780 54501 14560 17299 1480 5510 26796 18439 52645 19690 16623 47018 33755 16275 25478 12 18 13 13 12 15 12 16 18 14 15 7 13 16 14 12 13 12 12 12 12 16 12 12 14 12 12 14 14 12 12 18 12 12 13 10 16 12 12 16 16 12 20 13 13 18 12 15 12 12 20 12 12 12 16 13 12 17 12 12 12 17 12 12 12 12 13 14 12 12 12 12 12 18 12 17 12 12 14 13 12 14.43263 6.226848 15.91634 16.05756 5.627781 9.912415 26.33137 7.653784 10.23027 11.77554 9.93026 9.339963 11.19007 14.51845 9.360135 14.54692 15.12722 11.63198 8.215625 14.75177 12.85097 40.88605 13.1658 10.88118 21.18246 22.81612 32.49137 8.839261 25.6956 17.53763 12.83205 20.10618 25.95055 20.67001 33.27227 16.00441 9.281289 21.83567 12.96862 25.98099 9.748137 12.2993 12.17891 24.7134 24.82937 18.76595 11.00973 7.297754 14.8361 22.90809 13.38706 48.57986 10.26953 42.01602 10.31088 9.409459 8.767112 17.25965 15.6029 8.272255 61.87524 9.292667 63.35701 25.33333 26.33333 37.75 44.91667 42.91667 42.41667 51 29.83333 31.83333 42.75 30.83333 21.33333 32.75 36.33333 40.33333 37.33333 36.5 21.33333 20.33333 46.91667 22.33333 32 39.83333 28.33333 28.75 40.08333 45.41667 26.16667 52.08333 23.66667 48.08333 23.41667 36.16667 45.5 42.75 28 40.83333 41.33333 32.58333 27 22.33333 49 22.08333 29 29.83333 34.5 25.16667 32.08333 30.16667 37.66667 27.16667 35.16667 22.58333 37.75 20.33333 35.83333 23.66667 29.5 25.25 23.66667 39.91667 25.08333 52.16667 5231 11732 9080 31547 27798 43544 56898 22877 30114 18679 7877 3890 8432 23413 42768 34501 27400 4688 9571 20855 9945 11667 43177 7450 16114 53077 58531 22590 70397 12569 54619 7394 21448 47956 30095 17598 29316 40556 17298 8192 2316 44023 2360 7395 21533 7960 12803 19462 24128 32384 6087 27848 2303 34247 2120 23051 2704 17602 12495 5600 39043 10624 86509 14 12 12 12 12 12 15 12 12 8 16 14 14 15 9 12 13 12 12 9 8 15 12 12 14 12 19 12 16 12 12 17 17 20 14 20 12 15 12 16 12 15 10 16 12 16 14 16 12 16 14 16 17 12 11 16 20 14 15 12 16 12 16