WS7 Tutorial Popularity Month effect

*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: Mon, 22 Nov 2010 10:55:52 +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/Nov/22/t1290423305qig4gczb8mce8s4.htm/, Retrieved Mon, 22 Nov 2010 11:55:27 +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/Nov/22/t1290423305qig4gczb8mce8s4.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 «

9 13 13 14 13 3 1 1 0 9 12 12 8 13 5 1 0 0 9 15 10 12 16 6 0 0 0 9 12 9 7 12 6 2 0 1 9 10 10 10 11 5 0 1 2 9 12 12 7 12 3 0 0 1 9 15 13 16 18 8 1 1 1 9 9 12 11 11 4 1 0 0 9 12 12 14 14 4 4 0 0 9 11 6 6 9 4 0 0 0 9 11 5 16 14 6 0 2 1 9 11 12 11 12 6 2 0 0 9 15 11 16 11 5 0 2 2 9 7 14 12 12 4 1 1 1 9 11 14 7 13 6 0 1 0 9 11 12 13 11 4 0 0 1 9 10 12 11 12 6 1 1 0 9 14 11 15 16 6 2 0 1 9 10 11 7 9 4 1 0 0 9 6 7 9 11 4 1 0 0 9 11 9 7 13 2 0 1 1 9 15 11 14 15 7 1 2 0 9 11 11 15 10 5 1 2 1 9 12 12 7 11 4 2 0 0 9 14 12 15 13 6 1 0 0 9 15 11 17 16 6 1 1 0 9 9 11 15 15 7 1 1 0 9 13 8 14 14 5 2 2 0 9 13 9 14 14 6 0 0 2 9 16 12 8 14 4 1 1 1 9 13 10 8 8 4 0 1 2 9 12 10 14 13 7 1 1 1 9 14 12 14 15 7 1 2 1 9 11 8 8 13 4 0 2 0 9 9 12 11 11 4 1 1 0 9 16 11 16 15 6 2 2 0 9 12 12 10 15 6 1 1 1 9 10 7 8 9 5 1 1 2 9 13 11 14 13 6 1 0 1 9 16 11 16 16 7 1 3 1 9 14 12 13 13 6 0 1 2 9 15 9 5 11 3 1 0 0 9 5 15 8 12 3 1 0 0 9 8 11 10 12 4 1 0 0 9 11 11 8 12 6 0 1 1 9 16 11 13 14 7 2 0 1 9 1 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 10 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Popularity[t] = + 0.291123164546368 -0.0511359771771675month[t] + 0.100278815914936FindingFriends[t] + 0.211899695274710KnowingPeople[t] + 0.384406986575042Liked[t] + 0.591650456104061Celebrity[t] + 0.312334530791981bestfriend[t] -0.0295870251376916secondbestfriend[t] + 0.409233788979355thirdbestfriend[t] + 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) 0.291123164546368 3.563591 0.0817 0.935001 0.467501 month -0.0511359771771675 0.35484 -0.1441 0.885611 0.442805 FindingFriends 0.100278815914936 0.097016 1.0336 0.303007 0.151504 KnowingPeople 0.211899695274710 0.063839 3.3193 0.001138 0.000569 Liked 0.384406986575042 0.098679 3.8955 0.000148 7.4e-05 Celebrity 0.591650456104061 0.156115 3.7898 0.000219 0.00011 bestfriend 0.312334530791981 0.210576 1.4832 0.140152 0.070076 secondbestfriend -0.0295870251376916 0.201438 -0.1469 0.883429 0.441714 thirdbestfriend 0.409233788979355 0.213752 1.9145 0.057496 0.028748 Multiple Linear Regression - Regression Statistics Multiple R 0.718941993490984 R-squared 0.51687759000479 Adjusted R-squared 0.490585213950629 F-TEST (value) 19.6588390847615 F-TEST (DF numerator) 8 F-TEST (DF denominator) 147 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.09596780395353 Sum Squared Residuals 645.782912175841 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 11.1561094101339 1.84389058986607 2 12 10.9973203599166 1.00267964008338 3 15 13.0768983942228 1.92310160577722 4 12 11.4133960061974 0.586603993802554 5 10 10.9282941675151 -0.928294167515113 6 12 9.31461202404611 2.68538797595389 7 15 16.8694298030583 -1.86942980305829 8 9 10.2725550164866 -1.27255501648660 9 12 12.9984786544118 -0.998478654411798 10 11 7.53023514068136 3.46976485931864 11 11 13.0043488613008 -2.00434886130083 12 11 12.1525974460617 -1.15259744606174 13 15 12.2703841299406 2.72961587005938 14 7 11.4490660940079 -4.44906609400788 15 11 11.2357071966462 -0.235707196646161 16 11 10.7932536652234 0.206746334776610 17 10 11.8106758901321 -1.81067589013207 18 14 14.8467791465252 -0.84677914652517 19 10 8.55586344632273 1.44413655367727 20 6 9.34736154636249 -3.34736154636249 21 11 8.77694508163459 2.22305491836541 22 15 14.0613805507328 0.93861944926724 23 11 11.5771781899035 -0.577178189903492 24 12 9.73729076617974 2.26270923382026 25 14 13.0722686829436 0.927731317056356 26 15 14.5194231921656 0.480576807834437 27 9 14.3028672711452 -5.30286727114516 28 13 12.5051707349968 0.494829265003233 29 13 13.4500725736659 -0.450072573665895 30 16 11.1697236542293 4.83027634577075 31 13 8.7596233611365 4.2403766388635 32 12 13.6311085757848 -1.63110857578479 33 14 14.5708931556271 -0.570893155627051 34 11 9.63304605908544 1.36695394091456 35 9 10.2429679913489 -1.24296799134890 36 16 14.2058640159701 1.7941359840299 37 12 13.1612309435618 -1.16123094356184 38 10 9.74717888686278 0.252821113137221 39 13 13.1693239607334 -0.169323960733352 40 16 15.2492336916989 0.750766308301114 41 14 13.1250153144233 0.87498468557674 42 15 8.10866994098946 6.89133005901054 43 5 9.73044890887825 -4.73044890887825 44 8 10.3447834918720 -2.34478349187199 45 11 11.1715972465804 -0.171597246580375 46 16 14.2458162389297 1.75418376107027 47 17 14.2833334528663 2.71666654713366 48 9 8.04833749734074 0.951662502659255 49 9 11.4323057943085 -2.43230579430853 50 13 14.8466231269228 -1.84662312692284 51 10 10.9236847050589 -0.92368470505885 52 6 12.0403434699607 -6.04034346996074 53 12 11.8874045716608 0.112595428339179 54 8 10.4729821368622 -2.47298213686223 55 14 11.8447631214131 2.15523687858688 56 12 12.9277332433333 -0.927733243333263 57 11 11.0230223205811 -0.0230223205810992 58 16 14.0935550957958 1.90644490420420 59 8 10.2043935119364 -2.20439351193644 60 15 14.5606342444178 0.439365755582235 61 7 9.0661419531643 -2.06614195316430 62 16 13.8705998681328 2.12940013186717 63 14 12.8415664966158 1.15843350338421 64 16 13.5746674259143 2.42533257408571 65 9 10.1872012965741 -1.18720129657414 66 14 12.3180173899050 1.68198261009502 67 11 13.2318077556377 -2.23180775563770 68 13 10.3498777008897 2.65012229911031 69 15 12.9473930539210 2.05260694607897 70 5 5.76127050334993 -0.761270503349934 71 15 12.8765972661561 2.12340273384390 72 13 11.9169217836999 1.08307821630008 73 11 12.9968137479744 -1.99681374797437 74 11 14.0952478000063 -3.09524780000629 75 12 12.1930141708868 -0.193014170886771 76 12 13.4007794696081 -1.40077946960814 77 12 12.7519219616863 -0.751921961686308 78 12 12.0811136174823 -0.0811136174822852 79 14 11.0512754440024 2.94872455599760 80 6 7.97861965072775 -1.97861965072775 81 7 9.41630568885595 -2.41630568885595 82 14 12.6155692585780 1.38443074142198 83 14 14.0003351977312 -0.00033519773121668 84 10 10.9673318250210 -0.967331825020967 85 13 9.36744645971611 3.63255354028389 86 12 12.4136399800742 -0.41363998007422 87 9 9.07144712585763 -0.0714471258576263 88 12 12.3554364093057 -0.355436409305704 89 16 15.0703028689144 0.929697131085609 90 10 10.8033161391914 -0.803316139191449 91 14 12.9849893480654 1.01501065193458 92 10 13.6455152362939 -3.64551523629387 93 16 14.9860419996447 1.01395800035533 94 15 13.3152222748656 1.68477772513440 95 12 11.4768444299153 0.523155570084742 96 10 9.27338542269331 0.726614577306685 97 8 10.2857412363574 -2.28574123635735 98 8 8.46845460630873 -0.468454606308727 99 11 12.5556942387404 -1.55569423874035 100 13 12.9920015026263 0.0079984973736558 101 16 15.8784052490512 0.121594750948834 102 16 15.1704776878416 0.82952231215836 103 14 15.6644239192084 -1.66442391920835 104 11 8.993938985927 2.00606101407300 105 4 7.37908943075277 -3.37908943075277 106 14 14.6811824228954 -0.681182422895399 107 9 10.5776716883672 -1.57767168836724 108 14 15.2526155390514 -1.25261553905141 109 8 10.0286106598962 -2.02861065989624 110 8 10.4919319595558 -2.49193195955582 111 11 11.9776325185835 -0.977632518583453 112 12 13.2116678982108 -1.21166789821079 113 11 11.0136006127768 -0.0136006127768117 114 14 13.0242257324375 0.975774267562534 115 15 14.4130525414258 0.586947458574178 116 16 13.3761086868062 2.62389131319384 117 16 12.8813054662748 3.11869453372517 118 11 12.6614687734309 -1.66146877343094 119 14 13.3840908499781 0.615909150021876 120 14 11.0297814360362 2.97021856396378 121 12 11.5817794715759 0.418220528424115 122 14 13.0720629785932 0.92793702140677 123 8 10.8410413471034 -2.84104134710344 124 13 14.2946990610775 -1.29469906107747 125 16 14.5363418010922 1.46365819890779 126 12 10.5944574479731 1.40554255202692 127 16 15.8673232021964 0.132676797803649 128 12 12.7087981749745 -0.708798174974494 129 11 11.3236884710665 -0.323688471066468 130 4 5.75762186245885 -1.75762186245885 131 16 16.1204836827130 -0.120483682712950 132 15 13.1036223819861 1.89637761801388 133 10 11.1658333304308 -1.16583333043083 134 13 14.3080532885827 -1.30805328858271 135 15 12.6102317207247 2.38976827927527 136 12 10.2245120659804 1.77548793401958 137 14 12.9041652702215 1.09583472977847 138 7 10.4379749603298 -3.43797496032983 139 19 13.7603596537789 5.23964034622113 140 12 13.0934132037665 -1.09341320376652 141 12 11.9494526729181 0.0505473270818735 142 13 13.2609522301165 -0.260952230116489 143 15 12.4668185272168 2.53318147278321 144 8 8.98814186294263 -0.988141862942634 145 12 11.1875671061642 0.812432893835844 146 10 10.4485933177299 -0.448593317729926 147 8 11.3305913693145 -3.33059136931448 148 10 14.3439436071780 -4.34394360717797 149 15 14.2387288914726 0.761271108527372 150 16 14.0252139745086 1.97478602549143 151 13 13.2564520239731 -0.256452023973133 152 16 15.0487516272500 0.951248372750046 153 9 9.76941328862813 -0.769413288628131 154 14 13.3629237502419 0.637076249758089 155 14 13.4257622916148 0.574237708385213 156 12 10.0614732457738 1.93852675422620 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 12 0.267851334500296 0.535702669000592 0.732148665499704 13 0.731529606659303 0.536940786681393 0.268470393340697 14 0.914217608110061 0.171564783779878 0.085782391889939 15 0.86647690779497 0.267046184410060 0.133523092205030 16 0.80932561050175 0.381348778996500 0.190674389498250 17 0.739676230751042 0.520647538497917 0.260323769248958 18 0.65373851301835 0.692522973963301 0.346261486981651 19 0.573567683470478 0.852864633059044 0.426432316529522 20 0.798092253147342 0.403815493705316 0.201907746852658 21 0.741599450169642 0.516801099660717 0.258400549830358 22 0.739847510564674 0.520304978870652 0.260152489435326 23 0.673825735686908 0.652348528626185 0.326174264313092 24 0.668104488912187 0.663791022175626 0.331895511087813 25 0.632002133001176 0.735995733997649 0.367997866998824 26 0.571128837906888 0.857742324186224 0.428871162093112 27 0.78204354541431 0.435912909171381 0.217956454585690 28 0.74133963782513 0.517320724349741 0.258660362174870 29 0.683231163606276 0.633537672787448 0.316768836393724 30 0.789418428423551 0.421163143152897 0.210581571576449 31 0.847108877642807 0.305782244714385 0.152891122357193 32 0.812860853051502 0.374278293896997 0.187139146948498 33 0.768612768065328 0.462774463869344 0.231387231934672 34 0.731835603705885 0.53632879258823 0.268164396294115 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0.0198180332763105 0.00990901663815524 53 0.986436003532825 0.0271279929343491 0.0135639964671746 54 0.991022306072572 0.0179553878548560 0.00897769392742801 55 0.993004133562015 0.0139917328759697 0.00699586643798484 56 0.990883733796613 0.0182325324067731 0.00911626620338653 57 0.987474042420853 0.0250519151582930 0.0125259575791465 58 0.987149205674605 0.0257015886507902 0.0128507943253951 59 0.99020016521662 0.0195996695667594 0.0097998347833797 60 0.989018955123747 0.0219620897525050 0.0109810448762525 61 0.98886372990792 0.0222725401841581 0.0111362700920791 62 0.99042608214018 0.0191478357196388 0.00957391785981939 63 0.988880380817605 0.0222392383647899 0.0111196191823949 64 0.989295536736391 0.0214089265272172 0.0107044632636086 65 0.988765738900037 0.0224685221999260 0.0112342610999630 66 0.98671368239457 0.0265726352108617 0.0132863176054308 67 0.988428403213568 0.0231431935728632 0.0115715967864316 68 0.989826418319203 0.0203471633615937 0.0101735816807968 69 0.989206381890125 0.0215872362197506 0.0107936181098753 70 0.986375738127255 0.0272485237454905 0.0136242618727453 71 0.986462443949735 0.0270751121005291 0.0135375560502646 72 0.982921268377207 0.0341574632455866 0.0170787316227933 73 0.984150493637228 0.0316990127255433 0.0158495063627716 74 0.989499613487193 0.0210007730256145 0.0105003865128073 75 0.985993152923994 0.0280136941520126 0.0140068470760063 76 0.983731221588844 0.0325375568223122 0.0162687784111561 77 0.979027526019643 0.0419449479607137 0.0209724739803568 78 0.972743830040854 0.054512339918293 0.0272561699591465 79 0.978904693927037 0.0421906121459253 0.0210953060729627 80 0.978666833914724 0.0426663321705513 0.0213331660852757 81 0.980298795133093 0.0394024097338148 0.0197012048669074 82 0.978072652136558 0.0438546957268834 0.0219273478634417 83 0.970875888786057 0.0582482224278853 0.0291241112139427 84 0.963612914580625 0.0727741708387508 0.0363870854193754 85 0.984468697908029 0.0310626041839428 0.0155313020919714 86 0.979530176024867 0.0409396479502659 0.0204698239751329 87 0.97294176953030 0.0541164609393982 0.0270582304696991 88 0.965318818305441 0.0693623633891184 0.0346811816945592 89 0.956503549604284 0.0869929007914318 0.0434964503957159 90 0.945679005183953 0.108641989632094 0.0543209948160468 91 0.936049539038855 0.127900921922290 0.0639504609611449 92 0.963166649795986 0.0736667004080280 0.0368333502040140 93 0.953976103877733 0.0920477922445334 0.0460238961222667 94 0.94896035430909 0.102079291381819 0.0510396456909093 95 0.936390937631744 0.127218124736513 0.0636090623682564 96 0.921425005003787 0.157149989992426 0.0785749949962131 97 0.91742480930999 0.165150381380018 0.0825751906900092 98 0.89759480693174 0.204810386136522 0.102405193068261 99 0.88813378309076 0.223732433818481 0.111866216909240 100 0.86179285718119 0.276414285637621 0.138207142818810 101 0.83262567189655 0.334748656206899 0.167374328103450 102 0.801849136971911 0.396301726056177 0.198150863028089 103 0.83025034619864 0.339499307602719 0.169749653801360 104 0.872528287551913 0.254943424896174 0.127471712448087 105 0.879408339913797 0.241183320172405 0.120591660086203 106 0.852491560219525 0.295016879560949 0.147508439780475 107 0.828686556519089 0.342626886961823 0.171313443480911 108 0.822586054606012 0.354827890787976 0.177413945393988 109 0.812576971778244 0.374846056443512 0.187423028221756 110 0.834747212330976 0.330505575338048 0.165252787669024 111 0.820540928486847 0.358918143026306 0.179459071513153 112 0.867531975525258 0.264936048949483 0.132468024474742 113 0.834454896623193 0.331090206753614 0.165545103376807 114 0.801076197783575 0.397847604432849 0.198923802216425 115 0.760017224608492 0.479965550783015 0.239982775391508 116 0.772319613638931 0.455360772722138 0.227680386361069 117 0.78208395998174 0.435832080036518 0.217916040018259 118 0.762200018641286 0.475599962717428 0.237799981358714 119 0.716557374778685 0.566885250442629 0.283442625221315 120 0.802196243653025 0.395607512693950 0.197803756346975 121 0.768066552121913 0.463866895756174 0.231933447878087 122 0.718107649450573 0.563784701098853 0.281892350549427 123 0.716778496832857 0.566443006334287 0.283221503167144 124 0.68193671505839 0.636126569883221 0.318063284941610 125 0.655177156610557 0.689645686778885 0.344822843389443 126 0.636624975522513 0.726750048954974 0.363375024477487 127 0.570312300490665 0.85937539901867 0.429687699509335 128 0.552937924830732 0.894124150338536 0.447062075169268 129 0.541560975749484 0.916878048501031 0.458439024250516 130 0.527317168301533 0.945365663396933 0.472682831698467 131 0.458210747592227 0.916421495184453 0.541789252407773 132 0.427590417090005 0.85518083418001 0.572409582909995 133 0.391322998815491 0.782645997630982 0.608677001184509 134 0.346312414681866 0.692624829363733 0.653687585318134 135 0.298773924810124 0.597547849620248 0.701226075189876 136 0.274118017018751 0.548236034037502 0.725881982981249 137 0.241330563724718 0.482661127449436 0.758669436275282 138 0.264217980801055 0.52843596160211 0.735782019198945 139 0.643546302035173 0.712907395929653 0.356453697964826 140 0.633255871622839 0.733488256754322 0.366744128377161 141 0.526023833069466 0.947952333861067 0.473976166930534 142 0.51212567630266 0.97574864739468 0.48787432369734 143 0.378082678354520 0.756165356709039 0.62191732164548 144 0.257890618619672 0.515781237239344 0.742109381380328 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 32 0.240601503759398 NOK 10% type I error level 48 0.360902255639098 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/22/t1290423305qig4gczb8mce8s4/106fpl1290423340.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290423305qig4gczb8mce8s4/106fpl1290423340.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290423305qig4gczb8mce8s4/1zesr1290423340.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290423305qig4gczb8mce8s4/1zesr1290423340.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290423305qig4gczb8mce8s4/2zesr1290423340.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290423305qig4gczb8mce8s4/2zesr1290423340.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290423305qig4gczb8mce8s4/3zesr1290423340.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290423305qig4gczb8mce8s4/3zesr1290423340.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290423305qig4gczb8mce8s4/4an9c1290423340.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290423305qig4gczb8mce8s4/4an9c1290423340.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290423305qig4gczb8mce8s4/5an9c1290423340.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290423305qig4gczb8mce8s4/5an9c1290423340.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290423305qig4gczb8mce8s4/6an9c1290423340.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290423305qig4gczb8mce8s4/6an9c1290423340.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290423305qig4gczb8mce8s4/7kerf1290423340.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290423305qig4gczb8mce8s4/7kerf1290423340.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290423305qig4gczb8mce8s4/8vo8i1290423340.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290423305qig4gczb8mce8s4/8vo8i1290423340.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290423305qig4gczb8mce8s4/9vo8i1290423340.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290423305qig4gczb8mce8s4/9vo8i1290423340.ps (open in new window)

Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No 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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