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*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 12:15:29 +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/t129129212393u5f81ywogofjd.htm/, Retrieved Thu, 02 Dec 2010 13:15:57 +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/t129129212393u5f81ywogofjd.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 «

15 11 12 13 6 12 12 7 11 4 15 12 13 14 6 12 11 11 12 5 14 11 16 12 5 8 10 10 6 4 11 11 15 10 5 15 9 5 11 3 4 10 4 10 2 13 12 7 12 5 19 12 15 15 6 10 12 5 13 6 15 13 16 18 8 6 9 15 11 6 7 12 13 12 3 14 12 13 13 6 16 12 15 14 6 14 13 10 16 8 15 11 17 16 6 12 12 9 13 4 9 15 6 8 4 12 11 11 14 2 14 12 13 15 6 12 10 12 13 6 14 11 10 16 6 10 13 4 13 6 14 6 13 12 6 16 12 15 15 7 10 12 8 11 4 8 10 10 14 3 12 12 8 13 5 11 12 7 13 6 8 11 9 12 4 13 9 14 14 6 11 10 5 13 3 12 12 7 12 3 16 12 16 14 6 13 12 16 16 6 5 14 4 5 2 14 10 12 15 6 13 10 8 8 4 16 11 17 16 7 15 10 12 16 6 11 10 12 14 5 15 12 13 13 6 16 11 14 14 6 13 8 14 14 5 11 12 15 12 6 12 10 14 13 7 12 7 11 15 5 10 11 13 15 6 8 7 4 13 6 9 11 8 10 4 12 8 13 13 5 14 11 15 14 6 12 12 15 13 6 11 8 8 13 4 14 14 17 18 6 7 14 12 12 4 16 11 13 14 7 16 12 14 16 8 11 14 7 13 6 16 9 16 16 6 13 13 11 15 6 11 8 10 14 5 13 11 14 13 6 14 9 19 12 6 15 12 14 16 4 10 7 8 9 5 15 11 15 15 8 11 12 8 16 6 11 11 8 12 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 FindingFriends[t] = + 10.1709445126328 + 0.100818898434514Popularity[t] -0.0457479600331225KnowingPeople[t] + 0.0459202753566864Liked[t] -0.0882532612200294Celebrity[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) 10.1709445126328 0.92659 10.9768 0 0 Popularity 0.100818898434514 0.073729 1.3674 0.173667 0.086834 KnowingPeople -0.0457479600331225 0.056098 -0.8155 0.41616 0.20808 Liked 0.0459202753566864 0.087762 0.5232 0.60163 0.300815 Celebrity -0.0882532612200294 0.145183 -0.6079 0.544248 0.272124 Multiple Linear Regression - Regression Statistics Multiple R 0.142043863917955 R-squared 0.0201764592767424 Adjusted R-squared -0.00761995322604503 F-TEST (value) 0.725865586960875 F-TEST (DF numerator) 4 F-TEST (DF denominator) 141 p-value 0.57567568711713 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.80338023245963 Sum Squared Residuals 458.557417058485 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 11 11.2016964810699 -0.201696481069856 2 12 11.2126455576586 0.787354442341446 3 12 11.2018687963934 0.79813120360664 4 11 10.9873207316627 0.0126792683372818 5 11 10.9602187283661 0.0397812716338672 6 10 10.4425247070377 -0.442524707037697 7 11 10.6116694423823 0.388330557617659 8 9 11.6948514342484 -2.69485143424837 9 10 10.6739244973652 -0.673924497365182 10 12 11.2711314702297 0.728868529770278 11 12 11.5595687454219 0.440431254578146 12 12 11.0178377091291 0.982162290870917 13 13 11.0717994952807 1.92820050471932 14 9 10.0652419643464 -1.06524196434643 15 12 10.5682368418640 1.43176315813604 16 12 11.0551296226022 0.944870377397843 17 12 11.2111917747616 0.788808225238374 18 13 11.1536278063315 1.84637219366847 19 11 11.1107175069742 -0.110717506974240 20 12 11.2129901883057 0.78700981169432 21 15 10.8181759963181 4.18182400368193 22 11 11.3439210660362 -0.343921066036179 23 12 11.1469701733155 0.85302982668447 24 10 10.8992397857663 -0.899239785766253 25 11 11.3301343287716 -0.330134328771585 26 13 11.0635856691622 1.93641433083779 27 6 11.0092093472455 -5.00920934724547 28 12 11.1688587888983 0.831141211101717 29 12 10.9652598007564 1.03474019924360 30 10 10.8981401711112 -0.898140171111218 31 12 11.1704848871188 0.829515112881227 32 12 11.0271606874974 0.972839312502648 33 11 10.7637943192109 0.236205680789062 34 9 10.9544830394912 -1.95448303949121 35 10 11.3834163912237 -1.38341639122369 36 12 11.3468190942353 0.653180905764733 37 12 11.1654438147285 0.834556185271496 38 12 10.9548276701383 1.04517232986166 39 14 10.5451420190163 3.45485798098374 40 10 11.1927181333487 -1.19271813334865 41 10 11.1299556699899 -1.12995566998988 42 11 11.1232831441887 -0.123283144188725 43 10 11.3394573071399 -1.33945730713985 44 10 10.9325944239085 -0.932594423908455 45 12 11.1559485210367 0.844051478963329 46 11 11.2569397347947 -0.256939734794749 47 8 11.0427363007112 -3.04273630071124 48 12 10.6152567318757 1.38474326812432 49 10 10.7194906044800 -0.719490604479978 50 7 11.1250815577328 -4.12508155773278 51 11 10.7436945795775 0.256305420422524 52 7 10.8619478722932 -3.86194787229318 53 11 10.8185206269652 0.181479373034799 54 8 10.9417450869532 -2.94174508695316 55 11 11.0095539778926 -0.0095539778925989 56 12 10.7619959056669 1.23800409433311 57 8 11.1579192499043 -3.15791924990429 58 14 11.1017391592531 2.8982608407469 59 14 10.5257315406771 3.47426845932294 60 11 11.2144344336078 -0.214434433607842 61 12 11.1722737630681 0.827726236931937 62 14 11.0271606874974 2.97283931250265 63 9 11.2572843654419 -2.25728436544188 64 13 11.1376471949473 1.86235280505274 65 8 11.0240903439747 -3.0240903439747 66 11 10.9085627641345 0.0914372358654787 67 9 10.7347215870467 -1.73472158704674 68 12 11.4244679095137 0.575532090486333 69 7 10.785165988823 -3.785165988823 70 11 10.9797866292437 0.0202133707562597 71 12 11.1191735535343 0.880826446465711 72 11 10.9354924521075 0.0645075478924571 73 12 10.8299866495247 1.17001335047535 74 9 11.3801737323775 -2.38017373237747 75 11 10.8927544680738 0.107245531926179 76 13 10.9087350794581 2.09126492054191 77 12 11.0825762565459 0.917423743454129 78 12 10.8131295687374 1.18687043126260 79 11 10.8646132176455 0.135386782354548 80 12 11.1948611775398 0.805138822460166 81 12 11.2569397347947 0.743060265205251 82 11 11.1984538222236 -0.198453822223578 83 11 10.9634613872123 0.0365386127876514 84 8 10.6737426444469 -2.67374264444686 85 9 11.0820593105752 -2.08205931057518 86 12 11.0757463082063 0.924253691793688 87 13 10.8517029497838 2.14829705021616 88 12 11.2178494077776 0.782150592222378 89 6 11.0657340685438 -5.06573406854379 90 12 11.1672422282726 0.832757771727443 91 11 10.6850363516827 0.314963648317259 92 13 11.1433828838222 1.85661711617781 93 11 11.1137878504969 -0.113787850496892 94 12 10.8554625546007 1.14453744539925 95 10 10.9419174022767 -0.941917402276723 96 10 10.7855106194701 -0.785510619470127 97 11 11.1263534877114 -0.126353487711377 98 11 11.0323137076879 -0.0323137076879334 99 9 10.9136038365248 -1.91360383652479 100 7 10.901555145281 -3.901555145281 101 11 10.9783423839416 0.0216576160584226 102 12 11.1690311042218 0.830968895778153 103 12 10.9544830394912 1.04551696050879 104 15 10.5953388451605 4.40466115483945 105 11 11.0151173514440 -0.0151173514439601 106 10 11.0187046409373 -1.01870464093730 107 13 10.8500768515634 2.14992314843665 108 13 10.8533195104096 2.14668048959043 109 11 11.1690311042218 -0.169031104221847 110 12 10.7619959056669 1.23800409433311 111 12 10.6974296735737 1.30257032642634 112 12 11.3079010825417 0.692098917458296 113 8 10.1304004027188 -2.13040040271876 114 5 10.6613493225559 -5.66134932255594 115 11 11.2113640900852 -0.21136409008519 116 12 10.7969766420296 1.20302335797042 117 12 10.7271970222225 1.27280297777748 118 11 11.2314638297187 -0.231463829718652 119 12 10.8373388990253 1.16266110097470 120 10 10.7856829347937 -0.78568293479369 121 7 10.5162362469852 -3.51623624698522 122 12 10.9636337025359 1.03636629746409 123 12 10.7982485720082 1.20175142799182 124 9 10.9290071344151 -1.92900713441511 125 12 11.7079340174335 0.292065982566457 126 12 10.7544713408427 1.24552865915733 127 11 10.7180463591778 0.281953640822185 128 11 10.9654321160800 0.0345678839200346 129 12 11.1433828838222 0.856617116177813 130 12 10.7271970222225 1.27280297777748 131 11 10.9118054229807 0.0881945770192629 132 12 11.5391339127360 0.460866087263974 133 12 11.0334133223430 0.966586677657031 134 8 10.8870187791989 -2.88701877919890 135 11 10.8959971269200 0.104002873079963 136 11 11.1928904486722 -0.192890448672217 137 6 10.8906060686922 -4.89060606869224 138 13 11.1733225477946 1.82667745220539 139 12 11.0095539778926 0.9904460221074 140 12 11.0425639853877 0.957436014612327 141 12 11.1722737630681 0.827726236931937 142 12 11.0458066442339 0.95419335576611 143 12 11.0301706634968 0.969829336503247 144 10 10.9072908341559 -0.907290834155922 145 12 11.5062962205645 0.493703779435484 146 12 11.2512040459198 0.748795954080176 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.0919674854131228 0.183934970826246 0.908032514586877 9 0.0751755854506615 0.150351170901323 0.924824414549339 10 0.0364859219372154 0.0729718438744307 0.963514078062785 11 0.0167287242135186 0.0334574484270372 0.983271275786481 12 0.00820259365482063 0.0164051873096413 0.99179740634518 13 0.00366075445231982 0.00732150890463965 0.99633924554768 14 0.0201748429089669 0.0403496858179338 0.979825157091033 15 0.0247359049522437 0.0494718099044875 0.975264095047756 16 0.0140070051540866 0.0280140103081732 0.985992994845913 17 0.00709147700938566 0.0141829540187713 0.992908522990614 18 0.00380368808735597 0.00760737617471195 0.996196311912644 19 0.00316202798387758 0.00632405596775517 0.996837972016122 20 0.00182991562593755 0.00365983125187511 0.998170084374062 21 0.0862433111644597 0.172486622328919 0.91375668883554 22 0.0595048745608822 0.119009749121764 0.940495125439118 23 0.0398471877098824 0.0796943754197648 0.960152812290118 24 0.0412655056307178 0.0825310112614356 0.958734494369282 25 0.0322597921298826 0.0645195842597653 0.967740207870117 26 0.0244795095324369 0.0489590190648738 0.975520490467563 27 0.342067634133476 0.684135268266952 0.657932365866524 28 0.289413157480203 0.578826314960405 0.710586842519797 29 0.246313713366817 0.492627426733635 0.753686286633183 30 0.218391997347098 0.436783994694197 0.781608002652902 31 0.176940145659200 0.353880291318400 0.8230598543408 32 0.142050250490071 0.284100500980141 0.85794974950993 33 0.109800936563802 0.219601873127605 0.890199063436198 34 0.128011056169752 0.256022112339504 0.871988943830248 35 0.120239625694544 0.240479251389087 0.879760374305456 36 0.098539370078695 0.19707874015739 0.901460629921305 37 0.0817738093345542 0.163547618669108 0.918226190665446 38 0.0664524726834492 0.132904945366898 0.93354752731655 39 0.127525760878865 0.255051521757730 0.872474239121135 40 0.116701016343749 0.233402032687498 0.883298983656251 41 0.104473010043853 0.208946020087706 0.895526989956147 42 0.08102397959612 0.16204795919224 0.91897602040388 43 0.073724772073222 0.147449544146444 0.926275227926778 44 0.0624560398690059 0.124912079738012 0.937543960130994 45 0.0502836183328673 0.100567236665735 0.949716381667133 46 0.03760792199064 0.07521584398128 0.96239207800936 47 0.0634974834710746 0.126994966942149 0.936502516528925 48 0.054971388364802 0.109942776729604 0.945028611635198 49 0.0475311131322985 0.095062226264597 0.952468886867702 50 0.140682874019765 0.281365748039530 0.859317125980235 51 0.113580697371040 0.227161394742080 0.88641930262896 52 0.281892768217913 0.563785536435825 0.718107231782087 53 0.240826728374009 0.481653456748018 0.759173271625991 54 0.305921202501871 0.611842405003741 0.69407879749813 55 0.262917461913029 0.525834923826059 0.73708253808697 56 0.241081708049891 0.482163416099782 0.758918291950109 57 0.315299814926633 0.630599629853265 0.684700185073367 58 0.416200775388789 0.832401550777578 0.583799224611211 59 0.546785721455997 0.906428557088006 0.453214278544003 60 0.49832168570349 0.99664337140698 0.50167831429651 61 0.457908812162321 0.915817624324641 0.542091187837679 62 0.533272834780053 0.933454330439893 0.466727165219947 63 0.55697188861851 0.88605622276298 0.44302811138149 64 0.559091203399351 0.881817593201298 0.440908796600649 65 0.641731734484134 0.716536531031731 0.358268265515866 66 0.59540731646458 0.80918536707084 0.40459268353542 67 0.592934380947382 0.814131238105236 0.407065619052618 68 0.56123485154538 0.87753029690924 0.43876514845462 69 0.71433598013998 0.57132803972004 0.28566401986002 70 0.67176213064903 0.65647573870194 0.32823786935097 71 0.637929641527045 0.72414071694591 0.362070358472955 72 0.591984738399252 0.816030523201495 0.408015261600748 73 0.564248161566784 0.871503676866432 0.435751838433216 74 0.609863089088958 0.780273821822084 0.390136910911042 75 0.563873233351463 0.872253533297073 0.436126766648537 76 0.581531952882251 0.836936094235498 0.418468047117749 77 0.547187015146868 0.905625969706263 0.452812984853132 78 0.52806039695727 0.94387920608546 0.47193960304273 79 0.479698976677853 0.959397953355706 0.520301023322147 80 0.441953761666891 0.883907523333782 0.558046238333109 81 0.402195415392598 0.804390830785195 0.597804584607402 82 0.361019260807661 0.722038521615322 0.638980739192339 83 0.316272789512975 0.632545579025951 0.683727210487024 84 0.362160114654175 0.72432022930835 0.637839885345825 85 0.374414746733095 0.74882949346619 0.625585253266905 86 0.338072587251130 0.676145174502259 0.66192741274887 87 0.352014109757006 0.704028219514012 0.647985890242994 88 0.31608268142868 0.63216536285736 0.68391731857132 89 0.714651113877129 0.570697772245742 0.285348886122871 90 0.676295254778605 0.64740949044279 0.323704745221395 91 0.638636626405152 0.722726747189696 0.361363373594848 92 0.629287822435034 0.741424355129933 0.370712177564966 93 0.580148827434237 0.839702345131526 0.419851172565763 94 0.559020555378522 0.881958889242956 0.440979444621478 95 0.519340034663897 0.961319930672207 0.480659965336103 96 0.480793178984582 0.961586357969163 0.519206821015418 97 0.429583250014853 0.859166500029706 0.570416749985147 98 0.384415059160387 0.768830118320775 0.615584940839613 99 0.39836325547761 0.79672651095522 0.60163674452239 100 0.548230679547204 0.903538640905592 0.451769320452796 101 0.494957118796237 0.989914237592475 0.505042881203763 102 0.455957102869968 0.911914205739935 0.544042897130032 103 0.424342302235027 0.848684604470053 0.575657697764973 104 0.774256402943643 0.451487194112714 0.225743597056357 105 0.749665415689497 0.500669168621006 0.250334584310503 106 0.746705255703438 0.506589488593123 0.253294744296562 107 0.757682279540764 0.484635440918471 0.242317720459236 108 0.767530596129791 0.464938807740419 0.232469403870209 109 0.721224965356999 0.557550069286002 0.278775034643001 110 0.713971097313712 0.572057805372577 0.286028902686288 111 0.718399515086487 0.563200969827025 0.281600484913513 112 0.669455829180564 0.661088341638871 0.330544170819436 113 0.794296668578292 0.411406662843415 0.205703331421708 114 0.977623932438222 0.0447521351235555 0.0223760675617778 115 0.968603783975398 0.0627924320492042 0.0313962160246021 116 0.97778803663627 0.0444239267274582 0.0222119633637291 117 0.972706276336176 0.0545874473276489 0.0272937236638244 118 0.97710977353966 0.0457804529206819 0.0228902264603409 119 0.96625234490422 0.0674953101915601 0.0337476550957800 120 0.955922428452405 0.0881551430951895 0.0440775715475948 121 0.986790256520304 0.0264194869593910 0.0132097434796955 122 0.979268776408945 0.0414624471821097 0.0207312235910549 123 0.967841319982552 0.0643173600348971 0.0321586800174485 124 0.991655186137832 0.0166896277243359 0.00834481386216794 125 0.987871172961734 0.0242576540765327 0.0121288270382663 126 0.995955877443234 0.0080882451135311 0.00404412255676555 127 0.996254233284033 0.00749153343193462 0.00374576671596731 128 0.992674334070865 0.0146513318582708 0.0073256659291354 129 0.991844420347716 0.016311159304568 0.008155579652284 130 0.993321285260185 0.0133574294796295 0.00667871473981474 131 0.987423489524193 0.0251530209516149 0.0125765104758074 132 0.987986354653389 0.0240272906932227 0.0120136453466113 133 0.990955383323317 0.0180892333533657 0.00904461667668284 134 0.986975938818012 0.026048122363976 0.013024061181988 135 0.973935077077702 0.0521298458445953 0.0260649229222977 136 0.945293246826528 0.109413506346944 0.0547067531734722 137 0.996164776465406 0.00767044706918774 0.00383522353459387 138 0.983743295812945 0.0325134083741105 0.0162567041870552 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 7 0.0534351145038168 NOK 5% type I error level 29 0.221374045801527 NOK 10% type I error level 41 0.312977099236641 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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