*Unverified author*

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Mon, 24 Nov 2008 03:44:44 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/24/t1227523535u3w3bortlsxmo1i.htm/, Retrieved Mon, 24 Nov 2008 10:45:59 +0000

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Nov/24/t1227523535u3w3bortlsxmo1i.htm/}, year = {2008}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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7.977 0 8.241 0 8.444 0 8.49 0 8.388 0 8.099 0 7.984 0 7.786 0 8.086 0 9.315 0 9.113 0 9.023 0 9.026 1 9.787 1 9.536 1 9.49 1 9.736 1 9.694 1 9.647 1 9.753 1 10.07 1 10.137 1 9.984 1 9.732 1 9.103 1 9.155 1 9.308 1 9.394 1 9.948 1 10.177 1 10.002 1 9.728 1 10.002 1 10.063 1 10.018 1 9.96 1 10.236 1 10.893 1 10.756 1 10.94 1 10.997 1 10.827 1 10.166 1 10.186 1 10.457 1 10.368 1 10.244 1 10.511 1 10.812 1 10.738 1 10.171 1 9.721 1 9.897 1 9.828 1 9.924 1 10.371 1 10.846 1 10.413 1 10.709 1 10.662 1 10.57 1 10.297 1 10.635 1 10.872 1 10.296 1 10.383 1 10.431 1 10.574 1 10.653 1 10.805 1 10.872 1 10.625 1 10.407 1 10.463 1 10.556 1 10.646 1 10.702 1 11.353 1 11.346 1 11.451 1 11.964 1 12.574 1 13.031 1 13.812 1 14.544 1 14.931 1 14.886 1 16.005 1 17.064 1 15.168 1 16.05 1 15.839 1 15.137 1 14.954 1 15.648 1 15.305 1 15.579 1 16.348 1 15.928 1 16.171 1 15.937 1 15.713 1 15.594 1 15.683 1 16.438 1 17.032 1 17.696 1 17.745 1 19.394 1

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation prijs[t] = + 7.94649741949626 -0.914112177187953dummy[t] + 0.244118104209843M1[t] + 0.0747670489266164M2[t] -0.0755096559660449M3[t] + 0.0122136391412938M4[t] + 0.0696036009152987M5[t] -0.201784215088474M6[t] -0.292616475536691M7[t] -0.347337624873797M8[t] -0.17372544087757M9[t] -0.0305577013257876M10[t] + 0.073276704892662M11[t] + 0.0799433715593283t + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 7.94649741949626 0.586923 13.5392 0 0 dummy -0.914112177187953 0.495432 -1.8451 0.068141 0.034071 M1 0.244118104209843 0.624445 0.3909 0.69672 0.34836 M2 0.0747670489266164 0.641928 0.1165 0.907524 0.453762 M3 -0.0755096559660449 0.641565 -0.1177 0.906557 0.453279 M4 0.0122136391412938 0.641241 0.019 0.984844 0.492422 M5 0.0696036009152987 0.640954 0.1086 0.913754 0.456877 M6 -0.201784215088474 0.640705 -0.3149 0.753497 0.376749 M7 -0.292616475536691 0.640495 -0.4569 0.648815 0.324407 M8 -0.347337624873797 0.640322 -0.5424 0.588784 0.294392 M9 -0.17372544087757 0.640188 -0.2714 0.786698 0.393349 M10 -0.0305577013257876 0.640093 -0.0477 0.962024 0.481012 M11 0.073276704892662 0.640035 0.1145 0.909092 0.454546 t 0.0799433715593283 0.004951 16.1468 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.882360686596556 R-squared 0.778560381251146 Adjusted R-squared 0.748258117632882 F-TEST (value) 25.6931426331425 F-TEST (DF numerator) 13 F-TEST (DF denominator) 95 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.35767920231558 Sum Squared Residuals 175.112817558024 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7.977 8.27055889526541 -0.293558895265411 2 8.241 8.18115121154153 0.0598487884584739 3 8.444 8.1108178782082 0.333182121791807 4 8.49 8.27848454487486 0.211515455125140 5 8.388 8.4158178782082 -0.0278178782081937 6 8.099 8.22437343376375 -0.125373433763751 7 7.984 8.21348454487486 -0.229484544874863 8 7.786 8.23870676709709 -0.452706767097086 9 8.086 8.49226232265264 -0.406262322652641 10 9.315 8.71537343376375 0.599626566236247 11 9.113 8.89915121154153 0.213848788458471 12 9.023 8.9058178782082 0.117182121791805 13 9.026 8.31576717678942 0.710232823210583 14 9.787 8.22635949306552 1.56064050693448 15 9.536 8.15602615973219 1.37997384026781 16 9.49 8.32369282639885 1.16630717360115 17 9.736 8.46102615973219 1.27497384026781 18 9.694 8.26958171528774 1.42441828471226 19 9.647 8.25869282639885 1.38830717360115 20 9.753 8.28391504862108 1.46908495137893 21 10.07 8.53747060417663 1.53252939582337 22 10.137 8.76058171528774 1.37641828471226 23 9.984 8.94435949306552 1.03964050693448 24 9.732 8.95102615973219 0.780973840267814 25 9.103 9.27508763550136 -0.172087635501357 26 9.155 9.18567995177746 -0.0306799517774588 27 9.308 9.11534661844412 0.192653381555874 28 9.394 9.2830132851108 0.110986714889208 29 9.948 9.42034661844413 0.527653381555875 30 10.177 9.22890217399968 0.94809782600032 31 10.002 9.2180132851108 0.783986714889208 32 9.728 9.24323550733301 0.484764492666986 33 10.002 9.49679106288857 0.50520893711143 34 10.063 9.71990217399968 0.343097826000320 35 10.018 9.90367995177746 0.114320048222541 36 9.96 9.91034661844413 0.0496533815558748 37 10.236 10.2344080942133 0.00159190578670328 38 10.893 10.1450004104894 0.747999589510602 39 10.756 10.0746670771561 0.681332922843934 40 10.94 10.2423337438227 0.697666256177268 41 10.997 10.3796670771561 0.617332922843935 42 10.827 10.1882226327116 0.638777367288379 43 10.166 10.1773337438227 -0.0113337438227315 44 10.186 10.2025559660450 -0.0165559660449545 45 10.457 10.4561115216005 0.0008884783994903 46 10.368 10.6792226327116 -0.311222632711621 47 10.244 10.8630004104894 -0.6190004104894 48 10.511 10.8696670771561 -0.358667077156067 49 10.812 11.1937285529252 -0.381728552925238 50 10.738 11.1043208692013 -0.366320869201339 51 10.171 11.033987535868 -0.862987535868007 52 9.721 11.2016542025347 -1.48065420253467 53 9.897 11.338987535868 -1.44198753586801 54 9.828 11.1475430914236 -1.31954309142356 55 9.924 11.1366542025347 -1.21265420253467 56 10.371 11.1618764247569 -0.790876424756894 57 10.846 11.4154319803124 -0.56943198031245 58 10.413 11.6385430914236 -1.22554309142356 59 10.709 11.8223208692013 -1.11332086920134 60 10.662 11.828987535868 -1.16698753586800 61 10.57 12.1530490116372 -1.58304901163718 62 10.297 12.0636413279133 -1.76664132791328 63 10.635 11.9933079945799 -1.35830799457995 64 10.872 12.1609746612466 -1.28897466124661 65 10.296 12.2983079945799 -2.00230799457995 66 10.383 12.1068635501355 -1.72386355013550 67 10.431 12.0959746612466 -1.66497466124661 68 10.574 12.1211968834688 -1.54719688346883 69 10.653 12.3747524390244 -1.72175243902439 70 10.805 12.5978635501355 -1.7928635501355 71 10.872 12.7816413279133 -1.90964132791328 72 10.625 12.7883079945799 -2.16330799457995 73 10.407 13.1123694703491 -2.70536947034912 74 10.463 13.0229617866252 -2.55996178662522 75 10.556 12.9526284532919 -2.39662845329189 76 10.646 13.1202951199586 -2.47429511995855 77 10.702 13.2576284532919 -2.55562845329189 78 11.353 13.0661840088474 -1.71318400884744 79 11.346 13.0552951199586 -1.70929511995855 80 11.451 13.0805173421808 -1.62951734218077 81 11.964 13.3340728977363 -1.37007289773633 82 12.574 13.5571840088474 -0.983184008847442 83 13.031 13.7409617866252 -0.709961786625219 84 13.812 13.7476284532919 0.0643715467081137 85 14.544 14.0716899290611 0.472310070938944 86 14.931 13.9822822453372 0.94871775466284 87 14.886 13.9119489120038 0.974051087996174 88 16.005 14.0796155786705 1.92538442132951 89 17.064 14.2169489120038 2.84705108799617 90 15.168 14.0255044675594 1.14249553244062 91 16.05 14.0146155786705 2.03538442132951 92 15.839 14.0398378008927 1.79916219910729 93 15.137 14.2933933564483 0.843606643551731 94 14.954 14.5165044675594 0.437495532440620 95 15.648 14.7002822453372 0.947717754662842 96 15.305 14.7069489120038 0.598051087996175 97 15.579 15.031010387773 0.547989612227004 98 16.348 14.9416027040491 1.4063972959509 99 15.928 14.8712693707158 1.05673062928424 100 16.171 15.0389360373824 1.13206396261757 101 15.937 15.1762693707158 0.760730629284232 102 15.713 14.9848249262713 0.728175073728679 103 15.594 14.9739360373824 0.620063962617566 104 15.683 14.9991582596047 0.683841740395345 105 16.438 15.2527138151602 1.18528618483979 106 17.032 15.4758249262713 1.55617507372868 107 17.696 15.6596027040491 2.0363972959509 108 17.745 15.6662693707158 2.07873062928424 109 19.394 15.9903308464849 3.40366915351506 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.00308975798117012 0.00617951596234023 0.99691024201883 18 0.00083660452151312 0.00167320904302624 0.999163395478487 19 0.000235314243166976 0.000470628486333951 0.999764685756833 20 0.000172049006638769 0.000344098013277537 0.99982795099336 21 8.57796818985288e-05 0.000171559363797058 0.999914220318102 22 5.2307754641193e-05 0.000104615509282386 0.999947692245359 23 2.22984582001511e-05 4.45969164003022e-05 0.9999777015418 24 1.24886583765197e-05 2.49773167530394e-05 0.999987511341623 25 2.70144217558213e-06 5.40288435116426e-06 0.999997298557824 26 8.15622061060953e-07 1.63124412212191e-06 0.99999918437794 27 1.74903501246179e-07 3.49807002492357e-07 0.999999825096499 28 3.59201695817349e-08 7.18403391634699e-08 0.99999996407983 29 1.76068779404360e-08 3.52137558808721e-08 0.999999982393122 30 2.81523416508890e-08 5.63046833017780e-08 0.999999971847658 31 1.79814872314502e-08 3.59629744629005e-08 0.999999982018513 32 5.67654528559024e-09 1.13530905711805e-08 0.999999994323455 33 1.69698658292390e-09 3.39397316584779e-09 0.999999998303013 34 7.34937688442494e-10 1.46987537688499e-09 0.999999999265062 35 2.19997937369748e-10 4.39995874739497e-10 0.999999999780002 36 5.6732583746992e-11 1.13465167493984e-10 0.999999999943267 37 2.68108285783456e-10 5.36216571566913e-10 0.999999999731892 38 1.57475983300836e-09 3.14951966601671e-09 0.99999999842524 39 2.09883752540657e-09 4.19767505081313e-09 0.999999997901162 40 3.3130965626165e-09 6.626193125233e-09 0.999999996686903 41 3.01876642950537e-09 6.03753285901075e-09 0.999999996981234 42 2.61608661969429e-09 5.23217323938858e-09 0.999999997383913 43 1.55740527261766e-09 3.11481054523532e-09 0.999999998442595 44 8.57730491081364e-10 1.71546098216273e-09 0.99999999914227 45 5.48827043262362e-10 1.09765408652472e-09 0.999999999451173 46 7.94859497946443e-10 1.58971899589289e-09 0.99999999920514 47 7.84113603758395e-10 1.56822720751679e-09 0.999999999215886 48 5.2081128911093e-10 1.04162257822186e-09 0.999999999479189 49 5.46378096495265e-10 1.09275619299053e-09 0.999999999453622 50 4.4897443250122e-10 8.9794886500244e-10 0.999999999551026 51 5.85217236058030e-10 1.17043447211606e-09 0.999999999414783 52 2.01933315701579e-09 4.03866631403159e-09 0.999999997980667 53 4.61542159368343e-09 9.23084318736686e-09 0.999999995384578 54 9.12441260236737e-09 1.82488252047347e-08 0.999999990875587 55 7.42963202793837e-09 1.48592640558767e-08 0.999999992570368 56 6.45581696018302e-09 1.29116339203660e-08 0.999999993544183 57 1.06918385428256e-08 2.13836770856512e-08 0.999999989308161 58 1.36672639926693e-08 2.73345279853385e-08 0.999999986332736 59 1.17616953143120e-08 2.35233906286240e-08 0.999999988238305 60 1.07960391758469e-08 2.15920783516937e-08 0.99999998920396 61 6.11267437615926e-09 1.22253487523185e-08 0.999999993887326 62 4.10763313079887e-09 8.21526626159774e-09 0.999999995892367 63 2.79033321320196e-09 5.58066642640392e-09 0.999999997209667 64 1.876363220293e-09 3.752726440586e-09 0.999999998123637 65 1.06882980322635e-09 2.13765960645270e-09 0.99999999893117 66 6.26339901657983e-10 1.25267980331597e-09 0.99999999937366 67 2.84196990182285e-10 5.68393980364569e-10 0.999999999715803 68 1.48298446920032e-10 2.96596893840064e-10 0.999999999851702 69 7.92253944168254e-11 1.58450788833651e-10 0.999999999920775 70 3.8658762269625e-11 7.731752453925e-11 0.999999999961341 71 1.35830959175107e-11 2.71661918350215e-11 0.999999999986417 72 5.07989296129859e-12 1.01597859225972e-11 0.99999999999492 73 3.78354919587199e-12 7.56709839174398e-12 0.999999999996216 74 5.45677662563326e-12 1.09135532512665e-11 0.999999999994543 75 5.07396418709371e-12 1.01479283741874e-11 0.999999999994926 76 1.88283824572766e-11 3.76567649145533e-11 0.999999999981172 77 4.87353461680585e-10 9.7470692336117e-10 0.999999999512647 78 6.9973467301035e-10 1.3994693460207e-09 0.999999999300265 79 3.47907663609378e-09 6.95815327218756e-09 0.999999996520923 80 2.01982315957572e-08 4.03964631915144e-08 0.999999979801768 81 9.0033602812624e-08 1.80067205625248e-07 0.999999909966397 82 6.21296890907446e-07 1.24259378181489e-06 0.99999937870311 83 1.84092920237351e-05 3.68185840474701e-05 0.999981590707976 84 0.000405832211528032 0.000811664423056063 0.999594167788472 85 0.0109006759650955 0.0218013519301911 0.989099324034904 86 0.0352264572250451 0.0704529144500903 0.964773542774955 87 0.0561072717793549 0.112214543558710 0.943892728220645 88 0.118073966815602 0.236147933631205 0.881926033184398 89 0.382929171250435 0.76585834250087 0.617070828749565 90 0.349452892210771 0.698905784421542 0.650547107789229 91 0.520062178108841 0.95987564378232 0.47993782189116 92 0.752761283439856 0.494477433120288 0.247238716560144 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 68 0.894736842105263 NOK 5% type I error level 69 0.907894736842105 NOK 10% type I error level 70 0.921052631578947 NOK

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227523535u3w3bortlsxmo1i/10taw51227523479.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227523535u3w3bortlsxmo1i/10taw51227523479.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227523535u3w3bortlsxmo1i/153rg1227523478.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227523535u3w3bortlsxmo1i/153rg1227523478.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227523535u3w3bortlsxmo1i/2qbks1227523478.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227523535u3w3bortlsxmo1i/2qbks1227523478.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227523535u3w3bortlsxmo1i/3vqrw1227523478.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227523535u3w3bortlsxmo1i/3vqrw1227523478.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227523535u3w3bortlsxmo1i/4m7hk1227523478.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227523535u3w3bortlsxmo1i/4m7hk1227523478.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227523535u3w3bortlsxmo1i/5ec501227523478.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227523535u3w3bortlsxmo1i/5ec501227523478.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227523535u3w3bortlsxmo1i/6d74l1227523478.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227523535u3w3bortlsxmo1i/6d74l1227523478.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227523535u3w3bortlsxmo1i/7xoy61227523478.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227523535u3w3bortlsxmo1i/7xoy61227523478.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227523535u3w3bortlsxmo1i/8wwfw1227523478.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227523535u3w3bortlsxmo1i/8wwfw1227523478.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227523535u3w3bortlsxmo1i/9r7901227523479.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227523535u3w3bortlsxmo1i/9r7901227523479.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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