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: Fri, 03 Dec 2010 14:34:34 +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/03/t1291386781g65yxvvkskwuc7n.htm/, Retrieved Fri, 03 Dec 2010 15:33:11 +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/03/t1291386781g65yxvvkskwuc7n.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 «

5 6 5 7 11 2 6 2 3 11 6 6 6 5 15 6 4 4 5 9 6 2 6 3 11 5 7 3 4 17 5 6 5 4 16 6 5 3 5 9 6 6 5 5 14 5 7 4 5 12 5 7 1 6 6 5 4 6 5 4 6 1 6 2 13 5 6 6 5 12 5 4 4 4 10 6 5 6 6 14 6 5 5 5 12 4 6 3 6 9 5 4 5 5 16 5 6 4 2 13 5 3 5 3 12 6 3 6 5 11 5 5 3 6 12 7 5 4 5 12 6 5 5 4 11 6 5 4 5 16 6 5 5 5 9 6 2 6 5 8 4 6 7 5 11 5 7 2 6 9 6 2 4 6 16 4 3 6 6 14 5 6 5 6 10 5 5 5 4 14 5 7 5 4 13 7 5 6 3 12 7 6 6 5 16 6 5 1 6 16 7 3 4 4 15 6 7 2 6 5 5 5 3 3 12 6 5 4 2 11 4 6 5 5 15 6 2 4 5 15 5 3 3 6 10 6 6 4 4 12 6 7 6 3 5 5 5 4 3 16 6 4 5 4 16 5 6 4 5 12 5 7 5 4 6 5 2 6 3 7 6 2 6 4 14 6 2 4 4 8 5 5 4 4 12 7 2 6 3 10 6 5 4 6 11 5 6 2 5 17 5 2 6 5 13 6 4 5 6 15 5 6 6 6 10 5 4 6 4 9 6 3 5 5 16 6 3 5 4 11 3 3 5 6 8 5 6 5 5 14 5 6 3 5 11 6 5 4 5 12 5 3 1 5 14 5 3 5 2 15 4 2 2 5 14 5 3 6 5 11 5 3 5 5 11 2 5 2 2 15 6 3 6 6 7 6 5 5 4 12 6 2 6 4 10 6 5 3 6 13 5 6 4 6 15 5 6 4 4 13 6 5 4 2 15 5 2 4 4 8 5 6 5 5 14 6 7 2 7 11 3 5 3 7 12 6 5 5 5 16 3 2 6 5 8 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 populariteit[t] = + 12.9387027347946 + 0.195517891544743handgebruik[t] + 0.0494195249964288ontmoeting[t] -0.163771214544565extravert[t] -0.316901171073527blozen[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) 12.9387027347946 1.753819 7.3774 0 0 handgebruik 0.195517891544743 0.225475 0.8671 0.387243 0.193621 ontmoeting 0.0494195249964288 0.156231 0.3163 0.752194 0.376097 extravert -0.163771214544565 0.179181 -0.914 0.362175 0.181087 blozen -0.316901171073527 0.200636 -1.5795 0.116318 0.058159 Multiple Linear Regression - Regression Statistics Multiple R 0.152437878229750 R-squared 0.023237306719188 Adjusted R-squared -0.00263720171209170 F-TEST (value) 0.898077224574297 F-TEST (DF numerator) 4 F-TEST (DF denominator) 151 p-value 0.466771085548897 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.96929238748901 Sum Squared Residuals 1331.32128964243 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 11 11.1756450722595 -0.175645072259478 2 11 12.3480097255529 -1.34800972555294 3 15 11.8411940914066 3.15880590859341 4 9 12.0698974705029 -3.06989747050287 5 11 12.2773183335679 -1.27731833356793 6 17 12.5033105395655 4.4966894604345 7 16 12.1263485854799 3.87365141452006 8 9 12.2830882100439 -3.28308821004386 9 14 12.0049653059512 1.99503469404884 10 12 12.0226381539474 -0.0226381539474106 11 6 12.1970506265076 -6.19705062650758 12 4 11.546837149869 -7.546837149869 13 13 12.5447999796450 0.455200020354968 14 12 11.6456761998619 0.354323800138148 15 10 12.1912807500317 -2.19128075003165 16 14 11.4748733953366 2.52512660466336 17 12 11.9555457809547 0.0444542190452687 18 9 11.6245707808773 -2.62457078087728 19 16 11.7106083644136 4.28939163558644 20 13 12.9239221421716 0.0760778578284378 21 12 12.2949911815642 -0.294991181564185 22 11 11.6929355164173 -0.69293551641731 23 12 11.7706691474256 0.229330852574408 24 12 12.3148348870440 -0.314834887044039 25 11 12.2724469520283 -1.27244695202826 26 16 12.1193169954993 3.8806830045007 27 9 11.9555457809547 -2.95554578095473 28 8 11.6435159914209 -3.64351599142088 29 11 11.2863870937725 -0.286387093772544 30 9 12.0332794119630 -3.03327941196301 31 16 11.6541572494365 4.34584275056352 32 14 10.9849985622543 3.01500143774570 33 10 11.4925462433329 -1.49254624333289 34 14 12.0769290604835 1.92307093951648 35 13 12.1757681104764 0.824231889523628 36 12 12.6210948001020 -0.621094800101963 37 16 12.0367119829513 3.96328801704866 38 16 12.2937294680595 3.70627053194053 39 15 12.5328970081247 2.46710299187529 40 5 12.2287973035078 -7.22879730350776 41 12 12.7213726606462 -0.721372660646172 42 11 13.0700205087199 -2.07002050871988 43 15 11.6139295228617 3.38607047713833 44 15 11.97105842051 3.02894157948999 45 10 11.6718300974327 -1.67183009743273 46 12 12.4856376915693 -0.485637691569252 47 5 12.5244159585501 -7.52441595855008 48 16 12.5576014461016 3.44239855389839 49 16 12.2230274270318 3.77697257296817 50 12 11.9732186289510 0.0267813710490179 51 6 12.1757681104764 -6.17576811047637 52 7 12.0818004420232 -5.08180044202319 53 14 11.9604171624944 2.03958283750559 54 8 12.2879595915835 -4.28795959158354 55 12 12.2407002750281 -0.240700275028080 56 10 12.4728362251127 -2.47283622511268 57 11 11.8024158244258 -0.80241582442577 58 17 12.3007610580401 4.69923894195989 59 13 11.4479980998761 1.55200190012386 60 15 11.5892250848848 3.41077491511522 61 10 11.3287750287883 -1.32877502878833 62 9 11.8637383209425 -2.86373832094252 63 16 11.8567067309619 4.14329326903813 64 11 12.1736079020354 -1.1736079020354 65 8 10.9532518852541 -2.95325188525412 66 14 11.8094474144064 2.19055258559358 67 11 12.1369898434955 -1.13698984349555 68 12 12.1193169954993 -0.119316995499296 69 14 12.3162736975954 1.68372630240461 70 15 12.6118923526377 2.38810764736229 71 14 11.9075650665097 2.09243493349034 72 11 11.4974176248726 -0.497417624872566 73 11 11.6611888394171 -0.661188839417131 74 15 12.6154913716300 2.38450862836996 75 7 11.3760343453438 -4.37603434534378 76 12 12.2724469520283 -0.272446952028258 77 10 11.9604171624944 -1.96041716249441 78 13 11.9661870389703 1.03381296102967 79 15 11.6563174578775 3.34368254212254 80 13 12.2901198000245 0.709880199975491 81 15 13.0700205087199 1.92997949128012 82 8 12.0924417000388 -4.09244170003879 83 14 11.8094474144064 2.19055258559358 84 11 11.9118961324342 -0.91189613243423 85 12 11.0627321932626 0.937267806737421 86 16 11.9555457809547 4.04445421904527 87 8 11.0569623167867 -3.05696231678665 88 12 11.7600278894100 0.239972110590012 89 16 11.9625773709354 4.03742262906462 90 11 11.9661870389703 -0.966187038970335 91 13 11.9237991039546 1.07620089604545 92 6 12.3867986415764 -6.3867986415764 93 4 11.9661870389703 -7.96618703897033 94 11 12.3867986415764 -1.38679864157639 95 7 12.1418612250352 -5.14186122503522 96 12 11.8603057499542 0.139694250045802 97 12 12.2031837215520 -0.203183721551975 98 16 12.3303475265993 3.66965247340068 99 15 11.9061262559583 3.09387374404170 100 13 11.8567067309619 1.14329326903813 101 12 11.4431267183365 0.556873281663538 102 9 11.5645099978652 -2.56450999786525 103 16 12.2879595915835 3.71204040841646 104 11 12.4468594245884 -1.44685942458843 105 14 11.8072872059654 2.19271279403455 106 10 12.1369898434955 -2.13698984349555 107 10 11.6435159914209 -1.64351599142088 108 11 11.9109976374980 -0.910997637497979 109 16 13.1455832822446 2.85441671775544 110 8 11.4797447768763 -3.47974477687631 111 16 12.2949911815642 3.70500881843581 112 12 11.5962566748654 0.403743325134577 113 11 11.1558013667795 -0.155801366779509 114 16 11.0344180872507 4.96558191274928 115 9 12.3325077350403 -3.33250773504029 116 13 11.7648992709497 1.23510072905034 117 14 11.4099412307849 2.59005876921507 118 10 12.2031837215520 -2.20318372155198 119 12 12.9062492941753 -0.906249294175312 120 11 11.7825721189459 -0.782572118945915 121 10 10.9532518852541 -0.953251885254119 122 12 11.9555457809547 0.0444542190452687 123 13 12.2407002750281 0.75929972497192 124 14 12.2654153620476 1.73458463795239 125 12 11.6929355164173 0.307064483582691 126 14 11.6435159914209 2.35648400857912 127 13 12.2901198000245 0.709880199975491 128 8 12.2349303985522 -4.23493039855215 129 13 11.2335349977878 1.76646500221221 130 10 11.9732186289510 -1.97321862895098 131 9 12.0289483460384 -3.02894834603844 132 8 12.1193169954993 -4.1193169954993 133 15 11.9732186289510 3.02678137104902 134 15 12.0875703184991 2.91242968150088 135 12 12.1525024830508 -0.152502483050827 136 8 10.9554120936951 -2.95541209369509 137 15 12.7107314026306 2.28926859736943 138 9 12.1912807500317 -3.19128075003165 139 14 11.1579722242631 2.84202777573689 140 16 12.4905090731089 3.50949092689107 141 14 13.2175576858195 0.782442314180456 142 14 11.76002788941 2.23997211059001 143 14 12.3938302315570 1.60616976844296 144 14 11.8072872059654 2.19271279403455 145 14 11.5398055598883 2.46019444011165 146 13 12.4410895481125 0.558910451887501 147 12 12.1687365204957 -0.168736520495725 148 13 11.6774228768620 1.32257712313797 149 19 12.6366074396572 6.36339256034276 150 8 12.3267378585644 -4.32673785856436 151 10 12.2336686850474 -2.23366868504743 152 7 11.6880641348776 -4.68806413487763 153 12 11.8390338829656 0.160966117034377 154 16 11.4149790603286 4.58502093967139 155 15 12.2773183335679 2.72268166643207 156 9 11.7755405289653 -2.77554052896527 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.09376211654665 0.1875242330933 0.90623788345335 9 0.03977356961547 0.07954713923094 0.96022643038453 10 0.0751703304566676 0.150340660913335 0.924829669543332 11 0.063408000426655 0.12681600085331 0.936591999573345 12 0.434822009169151 0.869644018338302 0.565177990830849 13 0.378317808560653 0.756635617121306 0.621682191439347 14 0.305315190984752 0.610630381969503 0.694684809015248 15 0.226427402357663 0.452854804715327 0.773572597642337 16 0.308020076126372 0.616040152252744 0.691979923873628 17 0.231211138789852 0.462422277579703 0.768788861210148 18 0.209676868782632 0.419353737565264 0.790323131217368 19 0.555514306366145 0.88897138726771 0.444485693633855 20 0.567581172791994 0.864837654416012 0.432418827208006 21 0.493274695190034 0.986549390380068 0.506725304809966 22 0.419835703297895 0.83967140659579 0.580164296702105 23 0.44455079652676 0.88910159305352 0.55544920347324 24 0.374460763159449 0.748921526318897 0.625539236840551 25 0.343558260547716 0.687116521095433 0.656441739452284 26 0.43612111789369 0.87224223578738 0.56387888210631 27 0.448880845049046 0.897761690098092 0.551119154950954 28 0.415792026986386 0.831584053972773 0.584207973013614 29 0.377900316005879 0.755800632011758 0.622099683994121 30 0.343292142410595 0.68658428482119 0.656707857589405 31 0.623595644420857 0.752808711158286 0.376404355579143 32 0.650942574264299 0.698114851471403 0.349057425735701 33 0.609184617676106 0.781630764647788 0.390815382323894 34 0.572242071954705 0.85551585609059 0.427757928045295 35 0.515123125932045 0.96975374813591 0.484876874067955 36 0.471213249380018 0.942426498760036 0.528786750619982 37 0.479695873849038 0.959391747698077 0.520304126150962 38 0.570427805496755 0.859144389006491 0.429572194503245 39 0.546669052121823 0.906661895756354 0.453330947878177 40 0.75494644770596 0.490107104588082 0.245053552294041 41 0.711570337683543 0.576859324632914 0.288429662316457 42 0.68710434832491 0.62579130335018 0.31289565167509 43 0.699475495727626 0.601049008544748 0.300524504272374 44 0.70321575596919 0.593568488061619 0.296784244030809 45 0.665934387858775 0.668131224282451 0.334065612141225 46 0.618090685589081 0.763818628821839 0.381909314410919 47 0.835274934632127 0.329450130735747 0.164725065367873 48 0.84906290605309 0.301874187893819 0.150937093946909 49 0.860475997911212 0.279048004177576 0.139524002088788 50 0.831069507968871 0.337860984062257 0.168930492031129 51 0.906034002408346 0.187931995183307 0.0939659975916537 52 0.942774102931483 0.114451794137034 0.0572258970685172 53 0.933020164880635 0.133959670238730 0.0669798351193652 54 0.947630234440323 0.104739531119353 0.0523697655596767 55 0.933704923211049 0.132590153577902 0.0662950767889511 56 0.92910161650337 0.141796766993259 0.0708983834966297 57 0.912711680492395 0.174576639015210 0.0872883195076049 58 0.939748280189256 0.120503439621487 0.0602517198107435 59 0.928115074368705 0.143769851262590 0.0718849256312951 60 0.930497781785732 0.139004436428537 0.0695022182142684 61 0.917651162903012 0.164697674193977 0.0823488370969885 62 0.915918381921833 0.168163236156333 0.0840816180781666 63 0.929672869335805 0.140654261328391 0.0703271306641953 64 0.915196900801056 0.169606198397888 0.0848030991989441 65 0.912973932861262 0.174052134277475 0.0870260671387377 66 0.903709969290415 0.192580061419169 0.0962900307095847 67 0.885545839435312 0.228908321129375 0.114454160564688 68 0.861189543111571 0.277620913776858 0.138810456888429 69 0.84420278343371 0.311594433132579 0.155797216566289 70 0.836153716779795 0.327692566440409 0.163846283220205 71 0.823720385197005 0.35255922960599 0.176279614802995 72 0.792707809189381 0.414584381621238 0.207292190810619 73 0.759361949793331 0.481276100413338 0.240638050206669 74 0.748875949620052 0.502248100759895 0.251124050379948 75 0.788580888279644 0.422838223440712 0.211419111720356 76 0.754239153905319 0.491521692189362 0.245760846094681 77 0.732653167934047 0.534693664131906 0.267346832065953 78 0.697202923439753 0.605594153120494 0.302797076560247 79 0.705191468187733 0.589617063624533 0.294808531812267 80 0.665597453929688 0.668805092140624 0.334402546070312 81 0.63756164748923 0.724876705021539 0.362438352510769 82 0.672681598487895 0.65463680302421 0.327318401512105 83 0.650749399377084 0.698501201245831 0.349250600622916 84 0.610594446090634 0.778811107818731 0.389405553909366 85 0.570099745243908 0.859800509512185 0.429900254756092 86 0.604295136512349 0.791409726975302 0.395704863487651 87 0.604812124775497 0.790375750449007 0.395187875224503 88 0.558767950591279 0.882464098817443 0.441232049408721 89 0.593338327049534 0.813323345900932 0.406661672950466 90 0.55075384560776 0.898492308784479 0.449246154392240 91 0.509565521346304 0.980868957307392 0.490434478653696 92 0.66990700668531 0.660185986629379 0.330092993314690 93 0.886570971706198 0.226858056587603 0.113429028293802 94 0.86926430336149 0.261471393277019 0.130735696638509 95 0.91916087181236 0.161678256375280 0.0808391281876398 96 0.899324080647549 0.201351838704902 0.100675919352451 97 0.875899953885988 0.248200092228025 0.124100046114012 98 0.883523272877715 0.232953454244571 0.116476727122285 99 0.883295776734285 0.233408446531430 0.116704223265715 100 0.860258567057646 0.279482865884708 0.139741432942354 101 0.831159416737767 0.337681166524466 0.168840583262233 102 0.82606031855984 0.34787936288032 0.17393968144016 103 0.841948537974365 0.316102924051269 0.158051462025635 104 0.82036862964578 0.359262740708439 0.179631370354219 105 0.804365114856324 0.391269770287353 0.195634885143676 106 0.794889157199569 0.410221685600862 0.205110842800431 107 0.76824909906496 0.46350180187008 0.23175090093504 108 0.730384484541648 0.539231030916705 0.269615515458352 109 0.722440808277124 0.555118383445752 0.277559191722876 110 0.752468921701845 0.49506215659631 0.247531078298155 111 0.77543874625408 0.449122507491841 0.224561253745920 112 0.733600679217606 0.532798641564789 0.266399320782394 113 0.688226187727737 0.623547624544527 0.311773812272263 114 0.75672839782945 0.486543204341101 0.243271602170551 115 0.791885774473427 0.416228451053147 0.208114225526573 116 0.76071447170597 0.478571056588062 0.239285528294031 117 0.741435900455488 0.517128199089023 0.258564099544512 118 0.707969349664923 0.584061300670154 0.292030650335077 119 0.665846139151205 0.66830772169759 0.334153860848795 120 0.613882965257863 0.772234069484274 0.386117034742137 121 0.559685787041066 0.880628425917869 0.440314212958934 122 0.502337428266389 0.995325143467223 0.497662571733611 123 0.444432066478855 0.888864132957709 0.555567933521145 124 0.394043899270372 0.788087798540744 0.605956100729628 125 0.337106851703565 0.67421370340713 0.662893148296435 126 0.314506842961347 0.629013685922694 0.685493157038653 127 0.262088561307338 0.524177122614676 0.737911438692662 128 0.323231662476662 0.646463324953324 0.676768337523338 129 0.285788938912870 0.571577877825739 0.71421106108713 130 0.259410550801541 0.518821101603081 0.74058944919846 131 0.278072578392922 0.556145156785845 0.721927421607077 132 0.343491597915263 0.686983195830526 0.656508402084737 133 0.323152490684806 0.646304981369613 0.676847509315194 134 0.303915057147413 0.607830114294826 0.696084942852587 135 0.245723044847635 0.49144608969527 0.754276955152365 136 0.294767266310333 0.589534532620666 0.705232733689667 137 0.240422119670088 0.480844239340177 0.759577880329912 138 0.289653935606737 0.579307871213474 0.710346064393263 139 0.281409869110014 0.562819738220028 0.718590130889986 140 0.255221545279872 0.510443090559744 0.744778454720128 141 0.194914759829761 0.389829519659521 0.80508524017024 142 0.152380528380466 0.304761056760931 0.847619471619534 143 0.103813455595178 0.207626911190357 0.896186544404822 144 0.074622449960949 0.149244899921898 0.925377550039051 145 0.0835010193533834 0.167002038706767 0.916498980646617 146 0.0508543678976538 0.101708735795308 0.949145632102346 147 0.0258564749692831 0.0517129499385663 0.974143525030717 148 0.0257090738064144 0.0514181476128287 0.974290926193586 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 0 0 OK 10% type I error level 3 0.0212765957446809 OK

Charts produced by software:

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Parameters (Session):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 5 ; 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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