Workshop 4

*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Thu, 02 Dec 2010 10:27:01 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/02/t1291286474ib52he2zhoacpt8.htm/, Retrieved Thu, 02 Dec 2010 11:41:30 +0100

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/2010/Dec/02/t1291286474ib52he2zhoacpt8.htm/}, year = {2010}, } @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 = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

13 13 14 13 3 12 12 8 13 5 15 10 12 16 6 12 9 7 12 6 10 10 10 11 5 12 12 7 12 3 15 13 16 18 8 9 12 11 11 4 12 12 14 14 4 11 6 6 9 4 11 5 16 14 6 11 12 11 12 6 15 11 16 11 5 7 14 12 12 4 11 14 7 13 6 11 12 13 11 4 10 12 11 12 6 14 11 15 16 6 10 11 7 9 4 6 7 9 11 4 11 9 7 13 2 15 11 14 15 7 11 11 15 10 5 12 12 7 11 4 14 12 15 13 6 15 11 17 16 6 9 11 15 15 7 13 8 14 14 5 13 9 14 14 6 16 12 8 14 4 13 10 8 8 4 12 10 14 13 7 14 12 14 15 7 11 8 8 13 4 9 12 11 11 4 16 11 16 15 6 12 12 10 15 6 10 7 8 9 5 13 11 14 13 6 16 11 16 16 7 14 12 13 13 6 15 9 5 11 3 5 15 8 12 3 8 11 10 12 4 11 11 8 12 6 16 11 13 14 7 17 11 15 14 5 9 15 6 8 4 9 11 12 13 5 13 12 16 16 6 10 12 5 13 6 6 9 15 11 6 12 12 12 14 5 8 12 8 13 4 14 13 13 13 5 12 11 14 13 5 11 9 12 12 4 16 9 16 16 6 8 11 10 15 2 15 11 15 15 8 7 12 8 12 3 16 12 16 14 6 14 9 19 12 6 16 11 14 15 6 9 9 6 12 5 14 12 13 13 5 11 12 15 12 6 13 12 7 12 5 15 12 13 13 6 5 14 4 5 2 15 11 14 13 5 13 12 13 13 5 11 etc...

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 13 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Popularity[t] = + 0.311900251104237 + 0.0962538968572746FindingFriends[t] + 0.243370280084765KnowingPeople[t] + 0.351380635996807Liked[t] + 0.627591839447788Celebrity[t] -0.000729053587325985t + 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) 0.311900251104237 1.430354 0.2181 0.82768 0.41384 FindingFriends 0.0962538968572746 0.096681 0.9956 0.321055 0.160528 KnowingPeople 0.243370280084765 0.061616 3.9498 0.00012 6e-05 Liked 0.351380635996807 0.097657 3.5981 0.000435 0.000217 Celebrity 0.627591839447788 0.156555 4.0088 9.6e-05 4.8e-05 t -0.000729053587325985 0.003824 -0.1907 0.84905 0.424525 Multiple Linear Regression - Regression Statistics Multiple R 0.706626862823286 R-squared 0.499321523263479 Adjusted R-squared 0.482632240705595 F-TEST (value) 29.918693121269 F-TEST (DF numerator) 5 F-TEST (DF denominator) 150 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.11226554360225 Sum Squared Residuals 669.249859003394 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 11.4203795641500 1.57962043585001 2 12 11.1183586120924 0.881641387907585 3 15 13.5803366325678 1.41966336743221 4 12 10.8609797377121 1.13902026228785 5 10 10.7076429457918 -0.707642945791806 6 12 9.26550780276597 2.73449219723403 7 15 16.7976081800186 -1.79760818001857 8 9 10.5137420193814 -1.51374201938136 9 12 12.2972657140387 -0.297265714038744 10 11 8.01514785864563 2.98485214135437 11 11 13.3639545679283 -2.36395456792827 12 11 12.1173901199244 -1.11739011992444 13 15 12.2582860944591 2.74171390554094 14 7 11.2966264076535 -4.29662640765352 15 11 11.6856102685348 -0.685610268534754 16 11 10.9946501508523 0.00534984914772031 17 10 12.1137448519878 -2.11374485198781 18 14 14.3957655658695 -0.395765565869487 19 10 8.73322614073083 1.26677385926917 20 6 9.53698333187755 -3.53698333187755 21 11 8.68959910493328 2.31040089506672 22 15 14.4256902748864 0.5743097251136 23 11 11.6562446425042 -0.656244642504234 24 12 9.52859604164508 2.47140395835491 25 14 13.4327741796251 0.567225820374939 26 15 14.8766736973404 0.123326302659592 27 9 14.6654152870345 -5.66541528703453 28 13 12.5259899478982 0.47401005210176 29 13 13.2491066306160 -0.249106630615976 30 16 10.8217339081963 5.17826609180369 31 13 8.5202132449136 4.4797867550864 32 12 13.6193845701623 -1.61938457016225 33 14 14.5139245822831 -0.513924582283088 34 11 10.0824214704211 0.917578529578896 35 9 10.4940575725236 -1.49405757252356 36 16 14.2746322453856 1.72536775461442 37 12 12.9099354081469 -0.909935408146939 38 10 9.20532065467509 0.794679345324912 39 13 13.0829432524605 -0.0829432524604587 40 16 15.2506885064809 0.749311493519133 41 14 12.9343687620583 1.06563123794168 42 15 8.11237898688408 6.88762101311592 43 5 9.7706647906915 -4.7706647906915 44 8 10.4992525492924 -2.49925254929239 45 11 11.2669666144311 -0.26696661443111 46 16 13.813442072709 2.18655792729099 47 17 13.0442699003956 3.95573009960437 48 9 8.5023482580459 0.497651741954098 49 9 11.9613203169699 -2.96132031696988 50 13 14.7120600280171 -1.71206002801709 51 10 10.9801159855069 -0.980115985506941 52 6 12.4215667702018 -6.42156677020182 53 12 12.4060386354747 -0.406038635474659 54 8 10.4528559861037 -2.45285598610368 55 14 12.3928240692452 1.60717593075476 56 12 12.4429575020281 -0.44295750202813 57 11 10.7840076191121 0.215992380887868 58 16 14.4174659087467 1.58253409125334 59 8 10.2872749745773 -2.28727497457734 60 15 15.2689483581006 -0.268948358100564 61 7 9.4687801355478 -2.46878013554781 62 16 14.0005501129756 1.99944988702443 63 14 13.7384089370771 0.261591062922897 64 16 13.7674781847709 2.23252181522908 65 9 9.94554534935273 -0.945545349352725 66 14 12.2885505829274 1.71144941707262 67 11 13.0507732929606 -2.05077329296056 68 13 10.4754901592473 2.52450984075266 69 15 12.9139552616132 2.08604473838681 70 5 5.59398903521193 -0.593989035211934 71 15 12.4320216982182 2.56797830178176 72 13 12.2841762614034 0.715823738596576 73 11 12.0518333867861 -1.0518333867861 74 11 13.9816794366049 -2.9816794366049 75 12 12.4737028662899 -0.47370286628992 76 12 13.3955924466714 -1.39559244667144 77 12 12.2687745344120 -0.268774534412027 78 12 11.8947863524504 0.105213647549630 79 14 10.7860102824173 3.21398971758266 80 6 7.98921508177449 -1.98921508177449 81 7 9.8384206231643 -2.83842062316431 82 14 11.9755735478375 2.0244264521625 83 14 13.8616365225238 0.138363477476231 84 10 11.2447986284746 -1.24479862847463 85 13 8.72117200919769 4.27882799080231 86 12 12.4030643314044 -0.403064331404351 87 9 9.27840141287423 -0.278401412874232 88 12 12.0072626315439 -0.00726263154391892 89 16 15.0044355239833 0.995564476016654 90 10 10.2223458041906 -0.22234580419063 91 14 13.1256932535709 0.874306746429133 92 10 13.5036944042410 -3.50369440424103 93 16 15.3083025632099 0.691697436790136 94 15 13.4333319684698 1.56666803153022 95 12 11.3330329358713 0.666967064128683 96 10 9.71947446344238 0.280525536557622 97 8 10.2219397561188 -2.22193975611881 98 8 8.59192749759564 -0.591927497595643 99 11 12.8256077791949 -1.8256077791949 100 13 12.4046140402366 0.595385959763445 101 16 15.4495865177387 0.550413482261253 102 16 14.7069901648424 1.29300983515764 103 14 15.8120595336817 -1.81205953368174 104 11 8.86619283332075 2.13380716667925 105 4 6.94035975221046 -2.94035975221046 106 14 14.5624489223711 -0.562448922371101 107 9 10.3242273530674 -1.32422735306736 108 14 15.2339537859089 -1.23395378590892 109 8 10.4307796018048 -2.43077960180475 110 8 10.8768910530054 -2.87689105300543 111 11 12.1712457336952 -1.17124573369520 112 12 13.6119227695464 -1.61192276954639 113 11 11.4216552232623 -0.421655223262259 114 14 13.5839091221771 0.416090877822868 115 15 14.3187822639496 0.681217736050366 116 16 13.3781867622332 2.62181323776684 117 16 13.4737116055031 2.52628839449689 118 11 12.7155221434008 -1.71552214340081 119 14 13.7156237784132 0.284376221586775 120 14 10.9305850368251 3.06941496317486 121 12 11.3774905160919 0.622509483908102 122 14 12.5301998894373 1.46980011056266 123 8 10.1982870358089 -2.19828703580887 124 13 13.8082324073339 -0.80823240733387 125 16 13.7112494568893 2.28875054311073 126 12 10.8925960430913 1.10740395690872 127 16 15.4243660205190 0.575633979480961 128 12 13.3576816601305 -1.35768166013049 129 11 11.4788744152393 -0.478874415239257 130 4 6.36326604189703 -2.36326604189703 131 16 15.4214498061697 0.578550193830265 132 15 12.5284007086696 2.47159929133039 133 10 11.4494026606953 -1.44940266069535 134 13 13.1788413871184 -0.178841387118357 135 15 13.2172183608465 1.78278163915352 136 12 10.6364438720277 1.36355612797228 137 14 13.6062469169841 0.393753083015917 138 7 10.6294944097475 -3.62949440974753 139 19 14.0524233426635 4.94757665733649 140 12 12.6368437398323 -0.636843739832278 141 12 12.2401366678272 -0.240136667827162 142 13 13.4554852658200 -0.455485265819963 143 15 12.9023338053307 2.09766619466933 144 8 8.22180947772168 -0.221809477721681 145 12 10.8732526698265 1.12674733017345 146 10 10.7637395114835 -0.763739511483482 147 8 11.3640264779270 -3.36402647792696 148 10 14.3346235509494 -4.3346235509494 149 15 13.8408685540209 1.15913144597906 150 16 14.5694765918442 1.43052340815579 151 13 13.1421405299582 -0.142140529958206 152 16 15.0219181214729 0.978081878527133 153 9 10.1764154281891 -1.17641542818909 154 14 13.1188689048848 0.88113109511522 155 14 12.6469924003338 1.35300759966616 156 12 10.1085464206947 1.89145357930532 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.0271288973144725 0.0542577946289451 0.972871102685527 10 0.0237320160187823 0.0474640320375646 0.976267983981218 11 0.0500746483944133 0.100149296788827 0.949925351605587 12 0.0336895022363794 0.0673790044727588 0.96631049776362 13 0.43771699354397 0.87543398708794 0.56228300645603 14 0.631656304602175 0.73668739079565 0.368343695397825 15 0.564406468568958 0.871187062862084 0.435593531431042 16 0.489853896617638 0.979707793235277 0.510146103382362 17 0.407174961263709 0.814349922527417 0.592825038736291 18 0.375228327888680 0.750456655777359 0.62477167211132 19 0.323424298017495 0.64684859603499 0.676575701982505 20 0.450755020313334 0.901510040626668 0.549244979686666 21 0.455250233936695 0.91050046787339 0.544749766063305 22 0.498067015927554 0.996134031855108 0.501932984072446 23 0.436371586039589 0.872743172079178 0.563628413960411 24 0.454569124582036 0.909138249164071 0.545430875417964 25 0.430355914805024 0.860711829610048 0.569644085194976 26 0.37613780328455 0.7522756065691 0.62386219671545 27 0.607141574223036 0.785716851553928 0.392858425776964 28 0.558213708658504 0.883572582682992 0.441786291341496 29 0.501877526164309 0.996244947671382 0.498122473835691 30 0.680614978273516 0.638770043452967 0.319385021726484 31 0.78487482407371 0.430250351852582 0.215125175926291 32 0.747531869458115 0.504936261083771 0.252468130541885 33 0.699162236299025 0.601675527401951 0.300837763700975 34 0.663536604513489 0.672926790973022 0.336463395486511 35 0.669657108768266 0.660685782463467 0.330342891231734 36 0.677031010873087 0.645937978253827 0.322968989126913 37 0.644196270547146 0.711607458905707 0.355803729452854 38 0.594445117584089 0.811109764831822 0.405554882415911 39 0.540247519348869 0.919504961302263 0.459752480651131 40 0.510925384464888 0.978149231070224 0.489074615535112 41 0.470276725018734 0.940553450037468 0.529723274981266 42 0.735932527574331 0.528134944851338 0.264067472425669 43 0.949896926661653 0.100206146676694 0.0501030733383468 44 0.961863763625622 0.0762724727487554 0.0381362363743777 45 0.950479420029323 0.099041159941353 0.0495205799706765 46 0.95612156244137 0.087756875117259 0.0438784375586295 47 0.978005041638857 0.0439899167222855 0.0219949583611428 48 0.970977851856593 0.0580442962868146 0.0290221481434073 49 0.97986997120834 0.0402600575833185 0.0201300287916592 50 0.976882069208047 0.0462358615839068 0.0231179307919534 51 0.972188747529155 0.0556225049416906 0.0278112524708453 52 0.99731387743686 0.00537224512628198 0.00268612256314099 53 0.996146192790614 0.00770761441877232 0.00385380720938616 54 0.99690985734227 0.00618028531546141 0.00309014265773070 55 0.996789174791947 0.00642165041610637 0.00321082520805318 56 0.99547462674024 0.0090507465195201 0.00452537325976005 57 0.993655762891814 0.0126884742163714 0.00634423710818572 58 0.992966186786152 0.0140676264276952 0.0070338132138476 59 0.994591443992065 0.0108171120158696 0.0054085560079348 60 0.992928010947237 0.0141439781055268 0.00707198905276341 61 0.993793912215512 0.0124121755689765 0.00620608778448825 62 0.994479896176263 0.0110402076474742 0.00552010382373709 63 0.992674929042306 0.0146501419153876 0.00732507095769381 64 0.993195313062856 0.0136093738742873 0.00680468693714367 65 0.99136242508632 0.0172751498273610 0.00863757491368051 66 0.990606359909093 0.0187872801818146 0.00939364009090729 67 0.99051511443123 0.0189697711375376 0.00948488556876878 68 0.992012311213737 0.0159753775725256 0.00798768878626282 69 0.992159276137787 0.0156814477244258 0.0078407238622129 70 0.989475595730578 0.0210488085388444 0.0105244042694222 71 0.99114658164435 0.0177068367112994 0.0088534183556497 72 0.988363180633268 0.0232736387334636 0.0116368193667318 73 0.985394380199667 0.0292112396006669 0.0146056198003334 74 0.98942340946403 0.0211531810719391 0.0105765905359696 75 0.985733315128355 0.0285333697432905 0.0142666848716452 76 0.983271056609379 0.0334578867812428 0.0167289433906214 77 0.977992489647992 0.0440150207040159 0.0220075103520080 78 0.97099138969605 0.0580172206079015 0.0290086103039507 79 0.981765248884743 0.0364695022305145 0.0182347511152572 80 0.980886214979935 0.0382275700401303 0.0191137850200652 81 0.984064893625104 0.031870212749793 0.0159351063748965 82 0.985001189458743 0.0299976210825148 0.0149988105412574 83 0.979919393845565 0.040161212308869 0.0200806061544345 84 0.97530171908528 0.0493965618294395 0.0246982809147198 85 0.993587234709698 0.0128255305806038 0.00641276529030189 86 0.991135110114601 0.0177297797707974 0.00886488988539868 87 0.98802044905002 0.0239591018999588 0.0119795509499794 88 0.984352853029984 0.0312942939400328 0.0156471469700164 89 0.980594392819938 0.0388112143601248 0.0194056071800624 90 0.974571293674754 0.0508574126504927 0.0254287063252463 91 0.970102708590616 0.0597945828187673 0.0298972914093836 92 0.981754149379339 0.0364917012413225 0.0182458506206612 93 0.976473922759029 0.0470521544819423 0.0235260772409712 94 0.973686917170783 0.0526261656584347 0.0263130828292174 95 0.96749354240508 0.0650129151898406 0.0325064575949203 96 0.959984093492007 0.0800318130159869 0.0400159065079935 97 0.956231924218429 0.0875361515631423 0.0437680757815712 98 0.944653293551337 0.110693412897327 0.0553467064486635 99 0.939551430804507 0.120897138390987 0.0604485691954934 100 0.927186228815638 0.145627542368725 0.0728137711843623 101 0.90965443157833 0.180691136843340 0.0903455684216701 102 0.897477661405154 0.205044677189692 0.102522338594846 103 0.89906165461446 0.201876690771080 0.100938345385540 104 0.934848375124725 0.130303249750549 0.0651516248752747 105 0.931324635983792 0.137350728032416 0.0686753640162081 106 0.912549356355866 0.174901287288268 0.0874506436441342 107 0.893024651661996 0.213950696676009 0.106975348338004 108 0.884385350042088 0.231229299915824 0.115614649957912 109 0.880434174354857 0.239131651290286 0.119565825645143 110 0.902229301375204 0.195541397249593 0.0977706986247963 111 0.893033452157635 0.213933095684730 0.106966547842365 112 0.927979968102992 0.144040063794017 0.0720200318970083 113 0.90683113463983 0.186337730720340 0.0931688653601698 114 0.883707520886727 0.232584958226546 0.116292479113273 115 0.85636259365643 0.287274812687139 0.143637406343570 116 0.851984345793722 0.296031308412557 0.148015654206278 117 0.856968071949157 0.286063856101685 0.143031928050843 118 0.85091577610826 0.29816844778348 0.14908422389174 119 0.816568062541469 0.366863874917062 0.183431937458531 120 0.863431181346933 0.273137637306134 0.136568818653067 121 0.836895978377214 0.326208043245573 0.163104021622786 122 0.815218552596204 0.369562894807593 0.184781447403796 123 0.802197681751186 0.395604636497628 0.197802318248814 124 0.761517246718793 0.476965506562414 0.238482753281207 125 0.763932977711337 0.472134044577326 0.236067022288663 126 0.754777102760487 0.490445794479025 0.245222897239513 127 0.701166807279828 0.597666385440345 0.298833192720172 128 0.664311142846483 0.671377714307035 0.335688857153517 129 0.679217672931071 0.641564654137859 0.320782327068929 130 0.680976361163367 0.638047277673267 0.319023638836633 131 0.629433684744462 0.741132630511076 0.370566315255538 132 0.601317962540632 0.797364074918736 0.398682037459368 133 0.588562363407912 0.822875273184176 0.411437636592088 134 0.513980516509781 0.972038966980438 0.486019483490219 135 0.471456293692949 0.942912587385897 0.528543706307051 136 0.461456555572394 0.922913111144788 0.538543444427606 137 0.386247460572805 0.77249492114561 0.613752539427195 138 0.458288756373684 0.916577512747368 0.541711243626316 139 0.819063253587959 0.361873492824083 0.180936746412041 140 0.825905389449817 0.348189221100366 0.174094610550183 141 0.789378580520582 0.421242838958836 0.210621419479418 142 0.719747878942648 0.560504242114704 0.280252121057352 143 0.657440650234045 0.685118699531909 0.342559349765955 144 0.542451151397969 0.915097697204062 0.457548848602031 145 0.620754860570403 0.758490278859195 0.379245139429597 146 0.772988593262024 0.454022813475951 0.227011406737976 147 0.630413159579241 0.739173680841518 0.369586840420759 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 5 0.0359712230215827 NOK 5% type I error level 43 0.309352517985612 NOK 10% type I error level 57 0.410071942446043 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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Software written by Ed van Stee & Patrick Wessa

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