Applied Modelling and Data Analysis ECON 1096
Coursework can be submitted any time up to 3.00pm on the 12th August 2013. Please be advised that the re-sit assessment appears on the Moodle site and can be seen by all students. However, you are only required to undertake the assessment if advised by the Progression and Award Board, usually at the end of June. Please check your Banner Student Profile on a regular basis for notification of any resits you will be required to undertake. RESIT – In-Class Test Course Leader – Larry Su Students should answer the test supplied here. A guide of two hours is suggested. Please submit your answers as you would coursework via the turnitin links.
University of Greenwich Business School
ECON1096 Applied Modelling and Data Analysis
In-class Test (Resit) Level: M Duration: 2 hours Date: August 2013 Course Leader: Larry D. Su
Instructions to Candidates: Answer all questions. Answers should be written on single-sided paper. Answers should be justi?ed by showing details where relevant.
ECON1096 In-class Test (Resit)
Larry D. Su
1. A researcher obtained the following ordinary least squares (OLS) estimates for a UK ?rm’s stock price using 120 observations from 1980 month 1 to 1989 month 12:
ln st = 0.87 -0.54 ln pt +0.65 ln yt +0.34 ln rt -0.32 ln mt (1.06) (0.24) (0.30) (0.12) (0.24) R2 = 0.34, DW = 1.65, RSS = 1.24 where (all variables in logarithms): st is the log of the stock price; pt is the log of pro?ts; yt is the log of its output in the UK; rt is the log of expenditure on research and development (R&D); mt is the log of expenditure on marketing; u is an error term. Figures in parentheses are standard errors and RSS is the Residual Sum of Squares. (1) Brie?y evaluate the reasons behind including the above explanatory variables in the regression. [10 marks] (2) Test the null hypothesis that the explanatory variables are jointly signi?cant. [10 marks] (3) If the White’s Test statistic is 18.85, does the model su?er from heterskedasticity? [10 marks] 2. Explain what autocorrelation is and how it may arise and outline the implications of autocorrelation for OLS estimation.
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University of Greenwich Business School
1
ECON1096 In-class Test (Resit)
Larry D. Su
[20 marks] 3. Consider a model of county-wide health care expenditure: Healtht = ß1 + ß2 Incomet + ß3 Income2 t + ß4 P opt + ß5 Seniort + ut where P op is population and Senior is the percentage of population at least 65 years old. The sample size is n = 51. Regression results follow: Variable Estimate Intercept -5.06 Income 0.1045 2 Income -0.002 P op 0.847 Senior 0.385 2 R = 0.97 T SS = 56.88 Standard Error 2.094 0.025 0.005 0.489 0.164
(1) Explain the meaning of R2 in the above context and derive the adjustedR2 . [15 marks] (2) Propose a test that ?Health/?Income is constant, on average, and does not depend on income. State the null and alternative hypotheses, the test statistic, its distribution under the null, compute the test statistic, state 1%, 5% and 10% critical values and comment. [20 marks] (3) Is it preferable to have an econometric model that has as many explanatory variables as possible, or a smaller more parsimonious model? Explain some of these advantages and disadvantages. [15 marks]
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University of Greenwich Business School
2
ECON1096 In-class Test (Resit)
Larry D. Su
Appendix: Statistical Tables
Table A.1 Area under the Normal Curve from 0 to Z Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0 0 0.00399 0.00798 0.01197 0.01595 0.01994 0.02392 0.1 0.03983 0.0438 0.04776 0.05172 0.05567 0.05962 0.06356 0.2 0.07926 0.08317 0.08706 0.09095 0.09483 0.09871 0.10257 0.3 0.11791 0.12172 0.12552 0.1293 0.13307 0.13683 0.14058 0.4 0.15542 0.1591 0.16276 0.1664 0.17003 0.17364 0.17724 0.5 0.19146 0.19497 0.19847 0.20194 0.2054 0.20884 0.21226 0.6 0.22575 0.22907 0.23237 0.23565 0.23891 0.24215 0.24537 0.7 0.25804 0.26115 0.26424 0.2673 0.27035 0.27337 0.27637 0.8 0.28814 0.29103 0.29389 0.29673 0.29955 0.30234 0.30511 0.9 0.31594 0.31859 0.32121 0.32381 0.32639 0.32894 0.33147 1 0.34134 0.34375 0.34614 0.34849 0.35083 0.35314 0.35543 1.1 0.36433 0.3665 0.36864 0.37076 0.37286 0.37493 0.37698 1.2 0.38493 0.38686 0.38877 0.39065 0.39251 0.39435 0.39617 1.3 0.4032 0.4049 0.40658 0.40824 0.40988 0.41149 0.41308 1.4 0.41924 0.42073 0.4222 0.42364 0.42507 0.42647 0.42785 1.5 0.43319 0.43448 0.43574 0.43699 0.43822 0.43943 0.44062 1.6 0.4452 0.4463 0.44738 0.44845 0.4495 0.45053 0.45154 1.7 0.45543 0.45637 0.45728 0.45818 0.45907 0.45994 0.4608 1.8 0.46407 0.46485 0.46562 0.46638 0.46712 0.46784 0.46856 1.9 0.47128 0.47193 0.47257 0.4732 0.47381 0.47441 0.475 2 0.47725 0.47778 0.47831 0.47882 0.47932 0.47982 0.4803 2.1 0.48214 0.48257 0.483 0.48341 0.48382 0.48422 0.48461 2.2 0.4861 0.48645 0.48679 0.48713 0.48745 0.48778 0.48809 2.3 0.48928 0.48956 0.48983 0.4901 0.49036 0.49061 0.49086 2.4 0.4918 0.49202 0.49224 0.49245 0.49266 0.49286 0.49305 2.5 0.49379 0.49396 0.49413 0.4943 0.49446 0.49461 0.49477 2.6 0.49534 0.49547 0.4956 0.49573 0.49585 0.49598 0.49609 2.7 0.49653 0.49664 0.49674 0.49683 0.49693 0.49702 0.49711 2.8 0.49744 0.49752 0.4976 0.49767 0.49774 0.49781 0.49788 2.9 0.49813 0.49819 0.49825 0.49831 0.49836 0.49841 0.49846 3 0.49865 0.49869 0.49874 0.49878 0.49882 0.49886 0.49889 3.1 0.49903 0.49906 0.4991 0.49913 0.49916 0.49918 0.49921 3.2 0.49931 0.49934 0.49936 0.49938 0.4994 0.49942 0.49944 3.3 0.49952 0.49953 0.49955 0.49957 0.49958 0.4996 0.49961 3.4 0.49966 0.49968 0.49969 0.4997 0.49971 0.49972 0.49973 3.5 0.49977 0.49978 0.49978 0.49979 0.4998 0.49981 0.49981 3.6 0.49984 0.49985 0.49985 0.49986 0.49986 0.49987 0.49987 3.7 0.49989 0.4999 0.4999 0.4999 0.49991 0.49991 0.49992 3.8 0.49993 0.49993 0.49993 0.49994 0.49994 0.49994 0.49994 3.9 0.49995 0.49995 0.49996 0.49996 0.49996 0.49996 0.49996 4 0.49997 0.49997 0.49997 0.49997 0.49997 0.49997 0.49998 Examples: If z ~ N (0, 1), then Pr(Z = 1.53) = 0.5 + 0.43699 = 0.93699.
0.07 0.0279 0.06749 0.10642 0.14431 0.18082 0.21566 0.24857 0.27935 0.30785 0.33398 0.35769 0.379 0.39796 0.41466 0.42922 0.44179 0.45254 0.46164 0.46926 0.47558 0.48077 0.485 0.4884 0.49111 0.49324 0.49492 0.49621 0.4972 0.49795 0.49851 0.49893 0.49924 0.49946 0.49962 0.49974 0.49982 0.49988 0.49992 0.49995 0.49996 0.49998
0.08 0.03188 0.07142 0.11026 0.14803 0.18439 0.21904 0.25175 0.2823 0.31057 0.33646 0.35993 0.381 0.39973 0.41621 0.43056 0.44295 0.45352 0.46246 0.46995 0.47615 0.48124 0.48537 0.4887 0.49134 0.49343 0.49506 0.49632 0.49728 0.49801 0.49856 0.49896 0.49926 0.49948 0.49964 0.49975 0.49983 0.49988 0.49992 0.49995 0.49997 0.49998
0.09 0.03586 0.07535 0.11409 0.15173 0.18793 0.2224 0.2549 0.28524 0.31327 0.33891 0.36214 0.38298 0.40147 0.41774 0.43189 0.44408 0.45449 0.46327 0.47062 0.4767 0.48169 0.48574 0.48899 0.49158 0.49361 0.4952 0.49643 0.49736 0.49807 0.49861 0.499 0.49929 0.4995 0.49965 0.49976 0.49983 0.49989 0.49992 0.49995 0.49997 0.49998
c
University of Greenwich Business School
3
ECON1096 In-class Test (Resit)
Larry D. Su
Table A.2 Critical values of t-distributions with ? degrees of freedom ? a = 0.2 a = 0.15 a = 0.1 a = 0.05 a = 0.025 a = 0.01 a = 0.005 a = 0.001 1 1.37638 1.96261 3.07768 6.31375 12.7062 31.8205 63.6567 318.309 2 1.06066 1.38621 1.88562 2.91999 4.3027 6.9646 9.9248 22.327 3 0.97847 1.24978 1.63774 2.35336 3.1824 4.5407 5.8409 10.215 4 0.94096 1.18957 1.53321 2.13185 2.7764 3.7469 4.6041 7.173 5 0.91954 1.15577 1.47588 2.01505 2.5706 3.3649 4.0321 5.893 6 0.90570 1.13416 1.43976 1.94318 2.4469 3.1427 3.7074 5.208 7 0.89603 1.11916 1.41492 1.89458 2.3646 2.9980 3.4995 4.785 8 0.88889 1.10815 1.39682 1.85955 2.3060 2.8965 3.3554 4.501 9 0.88340 1.09972 1.38303 1.83311 2.2622 2.8214 3.2498 4.297 10 0.87906 1.09306 1.37218 1.81246 2.2281 2.7638 3.1693 4.144 11 0.87553 1.08767 1.36343 1.79588 2.2010 2.7181 3.1058 4.025 12 0.87261 1.08321 1.35622 1.78229 2.1788 2.6810 3.0545 3.930 13 0.87015 1.07947 1.35017 1.77093 2.1604 2.6503 3.0123 3.852 14 0.86805 1.07628 1.34503 1.76131 2.1448 2.6245 2.9768 3.787 15 0.86624 1.07353 1.34061 1.75305 2.1314 2.6025 2.9467 3.733 16 0.86467 1.07114 1.33676 1.74588 2.1199 2.5835 2.9208 3.686 17 0.86328 1.06903 1.33338 1.73961 2.1098 2.5669 2.8982 3.646 18 0.86205 1.06717 1.33039 1.73406 2.1009 2.5524 2.8784 3.610 19 0.86095 1.06551 1.32773 1.72913 2.0930 2.5395 2.8609 3.579 20 0.85996 1.06402 1.32534 1.72472 2.0860 2.5280 2.8453 3.552 21 0.85907 1.06267 1.32319 1.72074 2.0796 2.5176 2.8314 3.527 22 0.85827 1.06145 1.32124 1.71714 2.0739 2.5083 2.8188 3.505 23 0.85753 1.06034 1.31946 1.71387 2.0687 2.4999 2.8073 3.485 24 0.85686 1.05932 1.31784 1.71088 2.0639 2.4922 2.7969 3.467 25 0.85624 1.05838 1.31635 1.70814 2.0595 2.4851 2.7874 3.450 26 0.85567 1.05752 1.31497 1.70562 2.0555 2.4786 2.7787 3.435 27 0.85514 1.05673 1.31370 1.70329 2.0518 2.4727 2.7707 3.421 28 0.85465 1.05599 1.31253 1.70113 2.0484 2.4671 2.7633 3.408 29 0.85419 1.05530 1.31143 1.69913 2.0452 2.4620 2.7564 3.396 30 0.85377 1.05466 1.31042 1.69726 2.0423 2.4573 2.7500 3.385 40 0.85070 1.05005 1.30308 1.68385 2.0211 2.4233 2.7045 3.307 50 0.84887 1.04729 1.29871 1.67591 2.0086 2.4033 2.6778 3.261 60 0.84765 1.04547 1.29582 1.67065 2.0003 2.3901 2.6603 3.232 70 0.84679 1.04417 1.29376 1.66691 1.9944 2.3808 2.6479 3.211 80 0.84614 1.04320 1.29222 1.66412 1.9901 2.3739 2.6387 3.195 90 0.84563 1.04244 1.29103 1.66196 1.9867 2.3685 2.6316 3.183 100 0.84523 1.04184 1.29007 1.66023 1.9840 2.3642 2.6259 3.174 200 0.84342 1.03913 1.28580 1.65251 1.9719 2.3451 2.6006 3.131 8 0.84162 1.03644 1.28156 1.64487 1.9600 2.3264 2.5759 3.090 Examples: The 1% critical value for a one-tailed test with 25 degree of freedom is 2.485. The 5% critical value for a two-tailed test with 25 degree of freedom is 2.0595.
c
University of Greenwich Business School
4
ECON1096 In-class Test (Resit)
Larry D. Su
Table A.3.a Upper critical values of F0.01 (m, n) n\m 1 2 10 10.044 7.559 11 9.646 7.206 12 9.330 6.927 13 9.074 6.701 14 8.862 6.515 15 8.683 6.359 16 8.531 6.226 17 8.400 6.112 18 8.285 6.013 19 8.185 5.926 20 8.096 5.849 21 8.017 5.780 22 7.945 5.719 23 7.881 5.664 24 7.823 5.614 25 7.770 5.568 26 7.721 5.526 27 7.677 5.488 28 7.636 5.453 29 7.598 5.420 30 7.562 5.390 40 7.314 5.179 50 7.171 5.057 60 7.077 4.977 70 7.011 4.922 80 6.963 4.881 90 6.925 4.849 100 6.895 4.824 8 6.635 4.605
the F -distribution (1% level of signi?cance) 3 6.552 6.217 5.953 5.739 5.564 5.417 5.292 5.185 5.092 5.010 4.938 4.874 4.817 4.765 4.718 4.675 4.637 4.601 4.568 4.538 4.510 4.313 4.199 4.126 4.074 4.036 4.007 3.984 3.782 4 5.994 5.668 5.412 5.205 5.035 4.893 4.773 4.669 4.579 4.500 4.431 4.369 4.313 4.264 4.218 4.177 4.140 4.106 4.074 4.045 4.018 3.828 3.720 3.649 3.600 3.563 3.535 3.513 3.319 5 5.636 5.316 5.064 4.862 4.695 4.556 4.437 4.336 4.248 4.171 4.103 4.042 3.988 3.939 3.895 3.855 3.818 3.785 3.754 3.725 3.699 3.514 3.408 3.339 3.291 3.255 3.228 3.206 3.017 6 5.386 5.069 4.821 4.620 4.456 4.318 4.202 4.102 4.015 3.939 3.871 3.812 3.758 3.710 3.667 3.627 3.591 3.558 3.528 3.499 3.473 3.291 3.186 3.119 3.071 3.036 3.009 2.988 2.802 7 5.200 4.886 4.640 4.441 4.278 4.142 4.026 3.927 3.841 3.765 3.699 3.640 3.587 3.539 3.496 3.457 3.421 3.388 3.358 3.330 3.305 3.124 3.020 2.953 2.906 2.871 2.845 2.823 2.639 8 5.057 4.744 4.499 4.302 4.140 4.004 3.890 3.791 3.705 3.631 3.564 3.506 3.453 3.406 3.363 3.324 3.288 3.256 3.226 3.198 3.173 2.993 2.890 2.823 2.777 2.742 2.715 2.694 2.511 9 4.942 4.632 4.388 4.191 4.030 3.895 3.780 3.682 3.597 3.523 3.457 3.398 3.346 3.299 3.256 3.217 3.182 3.149 3.120 3.092 3.067 2.888 2.785 2.718 2.672 2.637 2.611 2.590 2.407 10 4.849 4.539 4.296 4.100 3.939 3.805 3.691 3.593 3.508 3.434 3.368 3.310 3.258 3.211 3.168 3.129 3.094 3.062 3.032 3.005 2.979 2.801 2.698 2.632 2.585 2.551 2.524 2.503 2.321
c
University of Greenwich Business School
5
ECON1096 In-class Test (Resit)
Larry D. Su
Table A.3.b Upper critical F0.05 (m, n) n\m 1 10 4.965 11 4.844 12 4.747 13 4.667 14 4.600 15 4.543 16 4.494 17 4.451 18 4.414 19 4.381 20 4.351 21 4.325 22 4.301 23 4.279 24 4.260 25 4.242 26 4.225 27 4.210 28 4.196 29 4.183 30 4.171 40 4.085 50 4.034 60 4.001 70 3.978 80 3.960 90 3.947 100 3.936 8 3.842
values of the F -distribution (5% level of signi?cance) 2 4.103 3.982 3.885 3.806 3.739 3.682 3.634 3.592 3.555 3.522 3.493 3.467 3.443 3.422 3.403 3.385 3.369 3.354 3.340 3.328 3.316 3.232 3.183 3.150 3.128 3.111 3.098 3.087 3.000 3 3.708 3.587 3.490 3.411 3.344 3.287 3.239 3.197 3.160 3.127 3.098 3.072 3.049 3.028 3.009 2.991 2.975 2.960 2.947 2.934 2.922 2.839 2.790 2.758 2.736 2.719 2.706 2.696 2.605 4 3.478 3.357 3.259 3.179 3.112 3.056 3.007 2.965 2.928 2.895 2.866 2.840 2.817 2.796 2.776 2.759 2.743 2.728 2.714 2.701 2.690 2.606 2.557 2.525 2.503 2.486 2.473 2.463 2.372 5 3.326 3.204 3.106 3.025 2.958 2.901 2.852 2.810 2.773 2.740 2.711 2.685 2.661 2.640 2.621 2.603 2.587 2.572 2.558 2.545 2.534 2.449 2.400 2.368 2.346 2.329 2.316 2.305 2.214 6 3.217 3.095 2.996 2.915 2.848 2.790 2.741 2.699 2.661 2.628 2.599 2.573 2.549 2.528 2.508 2.490 2.474 2.459 2.445 2.432 2.421 2.336 2.286 2.254 2.231 2.214 2.201 2.191 2.099 7 3.135 3.012 2.913 2.832 2.764 2.707 2.657 2.614 2.577 2.544 2.514 2.488 2.464 2.442 2.423 2.405 2.388 2.373 2.359 2.346 2.334 2.249 2.199 2.167 2.143 2.126 2.113 2.103 2.010 8 3.072 2.948 2.849 2.767 2.699 2.641 2.591 2.548 2.510 2.477 2.447 2.420 2.397 2.375 2.355 2.337 2.321 2.305 2.291 2.278 2.266 2.180 2.130 2.097 2.074 2.056 2.043 2.032 1.938 9 3.020 2.896 2.796 2.714 2.646 2.588 2.538 2.494 2.456 2.423 2.393 2.366 2.342 2.320 2.300 2.282 2.265 2.250 2.236 2.223 2.211 2.124 2.073 2.040 2.017 1.999 1.986 1.975 1.880 10 2.978 2.854 2.753 2.671 2.602 2.544 2.494 2.450 2.412 2.378 2.348 2.321 2.297 2.275 2.255 2.236 2.220 2.204 2.190 2.177 2.165 2.077 2.026 1.993 1.969 1.951 1.938 1.927 1.831
c
University of Greenwich Business School
6
ECON1096 In-class Test (Resit)
Larry D. Su
Table A.3.c Upper critical F0.1 (m, n) n\m 1 10 3.285 11 3.225 12 3.177 13 3.136 14 3.102 15 3.073 16 3.048 17 3.026 18 3.007 19 2.990 20 2.975 21 2.961 22 2.949 23 2.937 24 2.927 25 2.918 26 2.909 27 2.901 28 2.894 29 2.887 30 2.881 40 2.835 50 2.809 60 2.791 70 2.779 80 2.769 90 2.762 100 2.756 8 2.706
values of the F -distribution (10% level of signi?cance) 2 2.924 2.860 2.807 2.763 2.726 2.695 2.668 2.645 2.624 2.606 2.589 2.575 2.561 2.549 2.538 2.528 2.519 2.511 2.503 2.495 2.489 2.440 2.412 2.393 2.380 2.370 2.363 2.356 2.303 3 2.728 2.660 2.606 2.560 2.522 2.490 2.462 2.437 2.416 2.397 2.380 2.365 2.351 2.339 2.327 2.317 2.307 2.299 2.291 2.283 2.276 2.226 2.197 2.177 2.164 2.154 2.146 2.139 2.084 4 2.605 2.536 2.480 2.434 2.395 2.361 2.333 2.308 2.286 2.266 2.249 2.233 2.219 2.207 2.195 2.184 2.174 2.165 2.157 2.149 2.142 2.091 2.061 2.041 2.027 2.016 2.008 2.002 1.945 5 2.522 2.451 2.394 2.347 2.307 2.273 2.244 2.218 2.196 2.176 2.158 2.142 2.128 2.115 2.103 2.092 2.082 2.073 2.064 2.057 2.049 1.997 1.966 1.946 1.931 1.921 1.912 1.906 1.847 6 2.461 2.389 2.331 2.283 2.243 2.208 2.178 2.152 2.130 2.109 2.091 2.075 2.060 2.047 2.035 2.024 2.014 2.005 1.996 1.988 1.980 1.927 1.895 1.875 1.860 1.849 1.841 1.834 1.774 7 2.414 2.342 2.283 2.234 2.193 2.158 2.128 2.102 2.079 2.058 2.040 2.023 2.008 1.995 1.983 1.971 1.961 1.952 1.943 1.935 1.927 1.873 1.840 1.819 1.804 1.793 1.785 1.778 1.717 8 2.377 2.304 2.245 2.195 2.154 2.119 2.088 2.061 2.038 2.017 1.999 1.982 1.967 1.953 1.941 1.929 1.919 1.909 1.900 1.892 1.884 1.829 1.796 1.775 1.760 1.748 1.739 1.732 1.670 9 2.347 2.274 2.214 2.164 2.122 2.086 2.055 2.028 2.005 1.984 1.965 1.948 1.933 1.919 1.906 1.895 1.884 1.874 1.865 1.857 1.849 1.793 1.760 1.738 1.723 1.711 1.702 1.695 1.632 10 2.323 2.248 2.188 2.138 2.095 2.059 2.028 2.001 1.977 1.956 1.937 1.920 1.904 1.890 1.877 1.866 1.855 1.845 1.836 1.827 1.819 1.763 1.729 1.707 1.691 1.680 1.670 1.663 1.599
c
University of Greenwich Business School
7
ECON1096 In-class Test (Resit)
Larry D. Su
Table A.4.a Upper critical values of the ?2 -distribution with ? degrees of freedom ? 0.1 0.05 0.025 0.01 1 2.706 3.841 5.024 6.635 2 4.605 5.991 7.378 9.210 3 6.251 7.815 9.348 11.345 4 7.779 9.488 11.143 13.277 5 9.236 11.070 12.833 15.086 6 10.645 12.592 14.449 16.812 7 12.017 14.067 16.013 18.475 8 13.362 15.507 17.535 20.090 9 14.684 16.919 19.023 21.666 10 15.987 18.307 20.483 23.209 11 17.275 19.675 21.920 24.725 12 18.549 21.026 23.337 26.217 13 19.812 22.362 24.736 27.688 14 21.064 23.685 26.119 29.141 15 22.307 24.996 27.488 30.578 16 23.542 26.296 28.845 32.000 17 24.769 27.587 30.191 33.409 18 25.989 28.869 31.526 34.805 19 27.204 30.144 32.852 36.191 20 28.412 31.410 34.170 37.566 21 29.615 32.671 35.479 38.932 22 30.813 33.924 36.781 40.289 23 32.007 35.172 38.076 41.638 24 33.196 36.415 39.364 42.980 25 34.382 37.652 40.646 44.314 26 35.563 38.885 41.923 45.642 27 36.741 40.113 43.195 46.963 28 37.916 41.337 44.461 48.278 29 39.087 42.557 45.722 49.588 30 40.256 43.773 46.979 50.892 40 51.805 55.758 59.342 63.691 50 63.167 67.505 71.420 76.154 60 74.397 79.082 83.298 88.379 70 85.527 90.531 95.023 100.425 80 96.578 101.879 106.629 112.329 90 107.565 113.145 118.136 124.116 100 118.498 124.342 129.561 135.807
0.001 10.828 13.816 16.266 18.467 20.515 22.458 24.322 26.125 27.877 29.588 31.264 32.910 34.528 36.123 37.697 39.252 40.790 42.312 43.820 45.315 46.797 48.268 49.728 51.179 52.620 54.052 55.476 56.892 58.301 59.703 73.402 86.661 99.607 112.317 124.839 137.208 149.449
c
University of Greenwich Business School
8
ECON1096 In-class Test (Resit)
Larry D. Su
Table A.4.b Lower critical values of the ?2 -distribution with ? degrees of freedom ? 0.9 0.95 0.975 0.99 0.999 1 0.016 0.004 0.001 0.000 0.000 2 0.211 0.103 0.051 0.020 0.002 3 0.584 0.352 0.216 0.115 0.024 4 1.064 0.711 0.484 0.297 0.091 5 1.610 1.145 0.831 0.554 0.210 6 2.204 1.635 1.237 0.872 0.381 7 2.833 2.167 1.690 1.239 0.598 8 3.490 2.733 2.180 1.646 0.857 9 4.168 3.325 2.700 2.088 1.152 10 4.865 3.940 3.247 2.558 1.479 11 5.578 4.575 3.816 3.053 1.834 12 6.304 5.226 4.404 3.571 2.214 13 7.042 5.892 5.009 4.107 2.617 14 7.790 6.571 5.629 4.660 3.041 15 8.547 7.261 6.262 5.229 3.483 16 9.312 7.962 6.908 5.812 3.942 17 10.085 8.672 7.564 6.408 4.416 18 10.865 9.390 8.231 7.015 4.905 19 11.651 10.117 8.907 7.633 5.407 20 12.443 10.851 9.591 8.260 5.921 21 13.240 11.591 10.283 8.897 6.447 22 14.041 12.338 10.982 9.542 6.983 23 14.848 13.091 11.689 10.196 7.529 24 15.659 13.848 12.401 10.856 8.085 25 16.473 14.611 13.120 11.524 8.649 26 17.292 15.379 13.844 12.198 9.222 27 18.114 16.151 14.573 12.879 9.803 28 18.939 16.928 15.308 13.565 10.391 29 19.768 17.708 16.047 14.256 10.986 30 20.599 18.493 16.791 14.953 11.588 40 29.051 26.509 24.433 22.164 17.916 50 37.689 34.764 32.357 29.707 24.674 60 46.459 43.188 40.482 37.485 31.738 70 55.329 51.739 48.758 45.442 39.036 80 64.278 60.391 57.153 53.540 46.520 90 73.291 69.126 65.647 61.754 54.155 100 82.358 77.929 74.222 70.065 61.918
c
University of Greenwich Business School
9
ECON1096 In-class Test (Resit)
Larry D. Su
Table A.5 Critical Values for the Durbin-Watson Statistic with 5% Level of Signi?cance k=l k=2 k=3 k=4 n dL dU dL dU dL dU dL dU 10 0.88 1.32 0.7 1.64 0.53 2.02 0.38 2.41 11 0.93 1.32 0.66 1.6 0.6 1.93 0.44 2.28 12 0.97 1.33 0.81 1.58 0.66 1.86 0.51 2.18 13 1.01 1.34 0.86 1.56 0.72 1.82 0.57 2.09 14 1.05 1.35 0.91 1.55 0.77 1.78 0.63 2.03 15 1.08 1.36 0.95 1.54 0.82 1.75 0.69 1.97 16 1.1 1.37 0.98 1.54 0.86 1.73 0.74 1.93 17 1.13 1.38 1.02 1.54 0.9 1.71 0.78 1.9 18 1.16 1.39 1.05 1.53 0.93 1.69 0.92 1.87 19 1.18 1.4 1.08 1.53 0.97 1.68 0.86 1.85 20 1.2 1.41 1.1 1.54 1 1.68 0.9 1.83 21 1.22 1.42 1.13 1.54 1.03 1.67 0.93 1.81 22 1.24 1.43 1.15 1.54 1.05 1.66 0.96 1.8 23 1.26 1.44 1.17 1.54 1.08 1.66 0.99 1.79 24 1.27 1.45 1.19 1.55 1.1 1.66 1.01 1.78 25 1.29 1.45 1.21 1.55 1.12 1.66 1.04 1.77 26 1.3 1.46 1.22 1.55 1.14 1.65 1.06 1.76 27 1.32 1.47 1.24 1.56 1.16 1.65 1.08 1.76 28 1.33 1.48 1.26 1.56 1.18 1.65 1.1 1.75 29 1.34 1.48 1.27 1.56 1.2 1.65 1.12 1.74 30 1.35 1.49 1.28 1.57 1.21 1.65 1.14 1.74 31 1.36 1.5 1.3 1.57 1.23 1.65 1.16 1.74 32 1.37 1.5 1.31 1.57 1.24 1.65 1.18 1.73 33 1.38 1.51 1.32 1.58 1.26 1.65 1.19 1.73 34 1.39 1.51 1.33 1.58 1.27 1.65 1.21 1.73 35 1.4 1.52 1.34 1.58 1.28 1.65 1.22 1.73 36 1.41 1.52 1.35 1.59 1.29 1.65 1.24 1.73 37 1.42 1.53 1.36 1.59 1.31 1.66 1.25 1.72 38 1.43 1.54 1.37 1.59 1.32 1.66 1.26 1.72 39 1.43 1.54 1.38 1.6 1.33 1.66 1.27 1.72 40 1.44 1.54 1.39 1.6 1.34 1.66 1.29 1.72 45 1.48 1.57 1,43 1.62 1.38 1.67 1.34 1.72 50 1.5 1.59 1.46 1.63 1.42 1.67 1.38 1.72 55 1.53 1.6 1.49 1.64 1.45 1.68 1.41 1.72 60 1.55 1.62 1.51 1.65 1.48 1.69 1.44 1.73 65 1.57 1.63 1.54 1.66 1.5 1.7 1.47 1.73 70 1.58 1.64 1.55 1.67 1.52 1.7 1.49 1.74 75 1.6 1.65 1.57 1.68 1.54 1.71 1.51 1.74 80 1.61 1.66 1.59 1.69 1.56 1.72 1.53 1.74 85 1.62 1.67 1.6 1.7 1.57 1.72 1.55 1.75 90 1.63 1.68 1.61 1.7 1.59 1.73 1.57 1.75 95 1.64 1.69 1.62 1.71 1.6 1.73 1.58 1.75 100 1.65 1.69 1.63 1.72 1.61 1.74 1.59 1.76 150 1.72 1.75 1.71 1.76 1.69 1.77 1.68 1.79 200 1.76 1.78 1.75 1.79 1.74 1.8 1.73 1.81 n = number of observations k = number of independent variables (excluding constant)
k=5 dL dU 0.24 2.82 0.32 2.65 0.38 2.51 0.45 2.39 0.51 2.3 0.56 2.21 0.62 2.15 0.67 2.1 0.71 2.06 0.75 2.02 0.79 1.99 0.83 1.96 0.96 1.94 0.9 1.92 0.93 1.9 0.95 1.89 0.98 1.88 1.01 1.86 1.03 1.85 1.05 1.84 1.07 1.83 1.09 1.83 1.11 1.82 1.13 1.81 1.15 1.81 1.16 1.8 1.18 1.8 1.19 1.8 1.21 1.79 1.22 1.79 1.23 1.79 1.29 1.78 1.34 1.77 1.38 1.77 1.41 1.77 1.44 1.77 1.46 1.77 1.49 1.77 1.51 1.77 1.52 1.77 1.54 1.78 1.56 1.78 1.57 1.78 1.66 1.8 1.72 1.82
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