*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: Tue, 23 Nov 2010 10:29:39 +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/23/t1290508114aay0uj3w8xteqzo.htm/, Retrieved Tue, 23 Nov 2010 11:28:38 +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/23/t1290508114aay0uj3w8xteqzo.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 9 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation Popularity[t] = + 0.291123164546304 -0.051135977177163month[t] + 0.100278815914937FindingFriends[t] + 0.21189969527471KnowingPeople[t] + 0.384406986575043Liked[t] + 0.591650456104063Celebrity[t] + 0.312334530791982bestfriend[t] -0.0295870251376915secondbestfriend[t] + 0.409233788979356thirdbestfriend[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) 0.291123164546304 3.563591 0.0817 0.935001 0.467501 month -0.051135977177163 0.35484 -0.1441 0.885611 0.442805 FindingFriends 0.100278815914937 0.097016 1.0336 0.303007 0.151504 KnowingPeople 0.21189969527471 0.063839 3.3193 0.001138 0.000569 Liked 0.384406986575043 0.098679 3.8955 0.000148 7.4e-05 Celebrity 0.591650456104063 0.156115 3.7898 0.000219 0.00011 bestfriend 0.312334530791982 0.210576 1.4832 0.140152 0.070076 secondbestfriend -0.0295870251376915 0.201438 -0.1469 0.883429 0.441714 thirdbestfriend 0.409233788979356 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 645.78291217584 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 11.156109410134 1.843890589866 2 12 10.9973203599166 1.00267964008339 3 15 13.0768983942228 1.92310160577722 4 12 11.4133960061974 0.586603993802553 5 10 10.9282941675151 -0.92829416751511 6 12 9.3146120240461 2.6853879759539 7 15 16.8694298030583 -1.86942980305829 8 9 10.2725550164866 -1.27255501648659 9 12 12.9984786544118 -0.998478654411791 10 11 7.53023514068135 3.46976485931865 11 11 13.0043488613008 -2.00434886130083 12 11 12.1525974460617 -1.15259744606174 13 15 12.2703841299406 2.72961587005939 14 7 11.4490660940079 -4.44906609400788 15 11 11.2357071966462 -0.235707196646161 16 11 10.7932536652234 0.206746334776617 17 10 11.8106758901321 -1.81067589013207 18 14 14.8467791465252 -0.846779146525167 19 10 8.55586344632273 1.44413655367727 20 6 9.34736154636249 -3.34736154636249 21 11 8.77694508163458 2.22305491836542 22 15 14.0613805507328 0.938619449267243 23 11 11.5771781899035 -0.577178189903485 24 12 9.73729076617973 2.26270923382027 25 14 13.0722686829436 0.927731317056361 26 15 14.5194231921656 0.480576807834443 27 9 14.3028672711452 -5.30286727114516 28 13 12.5051707349968 0.494829265003239 29 13 13.4500725736659 -0.450072573665891 30 16 11.1697236542293 4.83027634577075 31 13 8.7596233611365 4.2403766388635 32 12 13.6311085757848 -1.63110857578478 33 14 14.5708931556271 -0.57089315562705 34 11 9.63304605908543 1.36695394091457 35 9 10.2429679913489 -1.2429679913489 36 16 14.2058640159701 1.7941359840299 37 12 13.1612309435618 -1.16123094356184 38 10 9.74717888686277 0.252821113137227 39 13 13.1693239607333 -0.169323960733348 40 16 15.2492336916989 0.750766308301116 41 14 13.1250153144233 0.874984685576742 42 15 8.10866994098945 6.89133005901054 43 5 9.73044890887825 -4.73044890887825 44 8 10.344783491872 -2.34478349187199 45 11 11.1715972465804 -0.171597246580374 46 16 14.2458162389297 1.75418376107027 47 17 14.2833334528663 2.71666654713366 48 9 8.04833749734074 0.95166250265926 49 9 11.4323057943085 -2.43230579430853 50 13 14.8466231269228 -1.84662312692283 51 10 10.9236847050589 -0.92368470505885 52 6 12.0403434699607 -6.04034346996074 53 12 11.8874045716608 0.112595428339184 54 8 10.4729821368622 -2.47298213686223 55 14 11.8447631214131 2.15523687858689 56 12 12.9277332433333 -0.927733243333258 57 11 11.0230223205811 -0.023022320581098 58 16 14.0935550957958 1.9064449042042 59 8 10.2043935119364 -2.20439351193644 60 15 14.5606342444178 0.439365755582233 61 7 9.0661419531643 -2.0661419531643 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 12.318017389905 1.68198261009502 67 11 13.2318077556377 -2.23180775563771 68 13 10.3498777008897 2.65012229911031 69 15 12.947393053921 2.05260694607897 70 5 5.76127050334993 -0.761270503349932 71 15 12.8765972661561 2.1234027338439 72 13 11.9169217836999 1.08307821630008 73 11 12.9968137479744 -1.99681374797437 74 11 14.0952478000063 -3.09524780000629 75 12 12.1930141708868 -0.193014170886773 76 12 13.4007794696081 -1.40077946960814 77 12 12.7519219616863 -0.75192196168631 78 12 12.0811136174823 -0.0811136174822851 79 14 11.0512754440024 2.94872455599759 80 6 7.97861965072775 -1.97861965072775 81 7 9.41630568885596 -2.41630568885596 82 14 12.615569258578 1.38443074142198 83 14 14.0003351977312 -0.000335197731220629 84 10 10.967331825021 -0.967331825020966 85 13 9.36744645971611 3.63255354028389 86 12 12.4136399800742 -0.413639980074222 87 9 9.07144712585763 -0.0714471258576255 88 12 12.3554364093057 -0.355436409305706 89 16 15.0703028689144 0.929697131085605 90 10 10.8033161391915 -0.80331613919145 91 14 12.9849893480654 1.01501065193457 92 10 13.6455152362939 -3.64551523629387 93 16 14.9860419996447 1.01395800035532 94 15 13.3152222748656 1.6847777251344 95 12 11.4768444299153 0.523155570084741 96 10 9.27338542269332 0.726614577306685 97 8 10.2857412363574 -2.28574123635736 98 8 8.46845460630873 -0.468454606308727 99 11 12.5556942387404 -1.55569423874035 100 13 12.9920015026263 0.00799849737365126 101 16 15.8784052490512 0.121594750948831 102 16 15.1704776878416 0.829522312158356 103 14 15.6644239192084 -1.66442391920836 104 11 8.993938985927 2.006061014073 105 4 7.37908943075277 -3.37908943075277 106 14 14.6811824228954 -0.681182422895407 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 -0.0136006127768161 114 14 13.0242257324375 0.975774267562531 115 15 14.4130525414258 0.586947458574173 116 16 13.3761086868062 2.62389131319384 117 16 12.8813054662748 3.11869453372517 118 11 12.6614687734309 -1.66146877343094 119 14 13.3840908499781 0.615909150021873 120 14 11.0297814360362 2.97021856396378 121 12 11.5817794715759 0.418220528424114 122 14 13.0720629785932 0.92793702140677 123 8 10.8410413471034 -2.84104134710344 124 13 14.2946990610775 -1.29469906107748 125 16 14.5363418010922 1.46365819890779 126 12 10.5944574479731 1.40554255202691 127 16 15.8673232021964 0.132676797803643 128 12 12.7087981749745 -0.708798174974494 129 11 11.3236884710665 -0.323688471066468 130 4 5.75762186245885 -1.75762186245885 131 16 16.120483682713 -0.120483682712955 132 15 13.1036223819861 1.89637761801388 133 10 11.1658333304308 -1.16583333043084 134 13 14.3080532885827 -1.30805328858272 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 0.0505473270818767 142 13 13.2609522301165 -0.260952230116492 143 15 12.4668185272168 2.53318147278321 144 8 8.98814186294263 -0.988141862942632 145 12 11.1875671061642 0.812432893835842 146 10 10.4485933177299 -0.448593317729932 147 8 11.3305913693145 -3.33059136931449 148 10 14.343943607178 -4.34394360717797 149 15 14.2387288914726 0.761271108527371 150 16 14.0252139745086 1.97478602549143 151 13 13.2564520239731 -0.256452023973137 152 16 15.04875162725 0.951248372750044 153 9 9.76941328862813 -0.76941328862813 154 14 13.3629237502419 0.637076249758086 155 14 13.4257622916148 0.574237708385211 156 12 10.0614732457738 1.9385267542262 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 12 0.267851334500298 0.535702669000596 0.732148665499702 13 0.731529606659303 0.536940786681393 0.268470393340697 14 0.914217608110061 0.171564783779878 0.085782391889939 15 0.86647690779497 0.267046184410062 0.133523092205031 16 0.80932561050175 0.3813487789965 0.19067438949825 17 0.739676230751042 0.520647538497916 0.260323769248958 18 0.65373851301835 0.692522973963301 0.346261486981651 19 0.57356768347048 0.852864633059041 0.426432316529521 20 0.798092253147342 0.403815493705315 0.201907746852658 21 0.741599450169642 0.516801099660716 0.258400549830358 22 0.739847510564675 0.520304978870649 0.260152489435325 23 0.673825735686907 0.652348528626186 0.326174264313093 24 0.668104488912187 0.663791022175625 0.331895511087813 25 0.632002133001176 0.735995733997648 0.367997866998824 26 0.571128837906888 0.857742324186224 0.428871162093112 27 0.78204354541431 0.435912909171382 0.217956454585691 28 0.741339637825131 0.517320724349738 0.258660362174869 29 0.683231163606274 0.633537672787452 0.316768836393726 30 0.78941842842355 0.421163143152902 0.210581571576451 31 0.847108877642808 0.305782244714384 0.152891122357192 32 0.812860853051502 0.374278293896996 0.187139146948498 33 0.768612768065328 0.462774463869344 0.231387231934672 34 0.731835603705884 0.536328792588232 0.268164396294116 35 0.706367759331849 0.587264481336302 0.293632240668151 36 0.735487244046577 0.529025511906846 0.264512755953423 37 0.712434629932256 0.575130740135487 0.287565370067744 38 0.666628997855147 0.666742004289706 0.333371002144853 39 0.617651363890346 0.764697272219309 0.382348636109654 40 0.575214959701756 0.849570080596487 0.424785040298244 41 0.527993850036624 0.944012299926752 0.472006149963376 42 0.861221780511166 0.277556438977669 0.138778219488834 43 0.966583310438297 0.0668333791234067 0.0334166895617033 44 0.96819576598334 0.0636084680333191 0.0318042340166595 45 0.959256047933049 0.0814879041339026 0.0407439520669513 46 0.964720518292833 0.0705589634143338 0.0352794817071669 47 0.971786803183193 0.0564263936336143 0.0282131968168071 48 0.968360992512939 0.0632780149741231 0.0316390074870615 49 0.964612424908323 0.070775150183353 0.0353875750916765 50 0.955528699561904 0.088942600876192 0.044471300438096 51 0.949332844304232 0.101334311391536 0.050667155695768 52 0.990090983361845 0.0198180332763105 0.00990901663815526 53 0.986436003532825 0.0271279929343494 0.0135639964671747 54 0.991022306072572 0.0179553878548561 0.00897769392742805 55 0.993004133562015 0.0139917328759696 0.0069958664379848 56 0.990883733796613 0.0182325324067733 0.00911626620338664 57 0.987474042420853 0.025051915158293 0.0125259575791465 58 0.987149205674605 0.02570158865079 0.012850794325395 59 0.99020016521662 0.0195996695667595 0.00979983478337977 60 0.989018955123747 0.0219620897525051 0.0109810448762525 61 0.988863729907921 0.022272540184158 0.011136270092079 62 0.99042608214018 0.0191478357196388 0.00957391785981941 63 0.988880380817605 0.0222392383647901 0.0111196191823951 64 0.989295536736391 0.0214089265272171 0.0107044632636085 65 0.988765738900037 0.0224685221999259 0.0112342610999629 66 0.98671368239457 0.0265726352108619 0.0132863176054309 67 0.988428403213569 0.0231431935728628 0.0115715967864314 68 0.989826418319203 0.0203471633615933 0.0101735816807967 69 0.989206381890125 0.021587236219751 0.0107936181098755 70 0.986375738127255 0.0272485237454908 0.0136242618727454 71 0.986462443949735 0.0270751121005294 0.0135375560502647 72 0.982921268377207 0.0341574632455864 0.0170787316227932 73 0.984150493637229 0.0316990127255431 0.0158495063627715 74 0.989499613487193 0.0210007730256148 0.0105003865128074 75 0.985993152923994 0.0280136941520124 0.0140068470760062 76 0.983731221588844 0.0325375568223121 0.016268778411156 77 0.979027526019643 0.0419449479607139 0.020972473980357 78 0.972743830040854 0.0545123399182929 0.0272561699591464 79 0.978904693927037 0.0421906121459257 0.0210953060729628 80 0.978666833914724 0.0426663321705513 0.0213331660852756 81 0.980298795133093 0.0394024097338148 0.0197012048669074 82 0.978072652136558 0.0438546957268833 0.0219273478634417 83 0.970875888786057 0.0582482224278855 0.0291241112139427 84 0.963612914580625 0.0727741708387503 0.0363870854193751 85 0.984468697908029 0.0310626041839427 0.0155313020919714 86 0.979530176024867 0.0409396479502658 0.0204698239751329 87 0.9729417695303 0.0541164609393983 0.0270582304696992 88 0.96531881830544 0.069362363389119 0.0346811816945595 89 0.956503549604284 0.0869929007914315 0.0434964503957157 90 0.945679005183953 0.108641989632094 0.0543209948160472 91 0.936049539038855 0.12790092192229 0.063950460961145 92 0.963166649795986 0.0736667004080281 0.036833350204014 93 0.953976103877734 0.0920477922445327 0.0460238961222664 94 0.94896035430909 0.102079291381818 0.0510396456909092 95 0.936390937631744 0.127218124736513 0.0636090623682565 96 0.921425005003787 0.157149989992426 0.078574994996213 97 0.91742480930999 0.165150381380019 0.0825751906900093 98 0.89759480693174 0.20481038613652 0.10240519306826 99 0.88813378309076 0.22373243381848 0.11186621690924 100 0.86179285718119 0.276414285637621 0.13820714281881 101 0.832625671896551 0.334748656206898 0.167374328103449 102 0.801849136971912 0.396301726056175 0.198150863028088 103 0.830250346198641 0.339499307602718 0.169749653801359 104 0.872528287551913 0.254943424896173 0.127471712448087 105 0.879408339913798 0.241183320172404 0.120591660086202 106 0.852491560219526 0.295016879560949 0.147508439780474 107 0.82868655651909 0.342626886961821 0.17131344348091 108 0.822586054606013 0.354827890787975 0.177413945393988 109 0.812576971778245 0.374846056443511 0.187423028221755 110 0.834747212330977 0.330505575338046 0.165252787669023 111 0.820540928486847 0.358918143026307 0.179459071513153 112 0.867531975525258 0.264936048949485 0.132468024474742 113 0.834454896623193 0.331090206753614 0.165545103376807 114 0.801076197783576 0.397847604432849 0.198923802216425 115 0.760017224608493 0.479965550783015 0.239982775391507 116 0.772319613638931 0.455360772722138 0.227680386361069 117 0.782083959981742 0.435832080036517 0.217916040018258 118 0.762200018641286 0.475599962717428 0.237799981358714 119 0.716557374778684 0.566885250442632 0.283442625221316 120 0.802196243653025 0.395607512693949 0.197803756346975 121 0.768066552121913 0.463866895756174 0.231933447878087 122 0.718107649450574 0.563784701098853 0.281892350549426 123 0.716778496832857 0.566443006334286 0.283221503167143 124 0.681936715058389 0.636126569883221 0.318063284941611 125 0.655177156610558 0.689645686778885 0.344822843389442 126 0.636624975522514 0.726750048954972 0.363375024477486 127 0.570312300490667 0.859375399018667 0.429687699509333 128 0.55293792483073 0.894124150338539 0.447062075169269 129 0.541560975749484 0.916878048501033 0.458439024250516 130 0.527317168301534 0.945365663396933 0.472682831698466 131 0.458210747592225 0.91642149518445 0.541789252407775 132 0.427590417090005 0.85518083418001 0.572409582909995 133 0.391322998815491 0.782645997630981 0.608677001184509 134 0.346312414681866 0.692624829363731 0.653687585318134 135 0.298773924810123 0.597547849620245 0.701226075189877 136 0.274118017018751 0.548236034037503 0.725881982981249 137 0.241330563724719 0.482661127449438 0.758669436275281 138 0.264217980801054 0.528435961602108 0.735782019198946 139 0.643546302035174 0.712907395929652 0.356453697964826 140 0.633255871622839 0.733488256754322 0.366744128377161 141 0.526023833069467 0.947952333861066 0.473976166930533 142 0.51212567630266 0.97574864739468 0.48787432369734 143 0.378082678354519 0.756165356709038 0.621917321645481 144 0.257890618619672 0.515781237239343 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:

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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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