Personal standards - Multiple regression

*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, 14 Dec 2010 16:32:11 +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/14/t1292344246nruc4h8rloxd4gw.htm/, Retrieved Tue, 14 Dec 2010 17:30:56 +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/14/t1292344246nruc4h8rloxd4gw.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 «

25 11 7 8 23 25 17 6 17 8 25 30 18 8 12 9 19 22 16 10 12 7 29 22 20 10 11 4 25 25 16 11 11 11 21 23 18 16 12 7 22 17 17 11 13 7 25 21 30 12 16 10 18 19 23 8 11 10 22 15 18 12 10 8 15 16 21 9 9 9 20 22 31 14 17 11 20 23 27 15 11 9 21 23 21 9 14 13 21 19 16 8 15 9 24 23 20 9 15 6 24 25 17 9 13 6 23 22 25 16 18 16 24 26 26 11 18 5 18 29 25 8 12 7 25 32 17 9 17 9 21 25 32 12 18 12 22 28 22 9 14 9 23 25 17 9 16 5 23 25 20 14 14 10 24 18 29 10 12 8 23 25 23 14 17 7 21 25 20 10 12 8 28 20 11 6 6 4 16 15 26 13 12 8 29 24 22 10 12 8 27 26 14 15 13 8 16 14 19 12 14 7 28 24 20 11 11 8 25 25 28 8 12 7 22 20 19 9 9 7 23 21 30 9 15 9 26 27 29 15 18 11 23 23 26 9 15 6 25 25 23 10 12 8 21 20 21 12 14 9 24 22 28 11 13 6 22 25 23 14 13 10 27 25 18 6 11 8 26 17 20 8 16 10 24 25 21 10 11 5 24 26 28 12 16 14 22 27 10 5 8 6 24 19 22 10 15 6 20 22 31 10 21 12 26 32 29 13 18 12 21 21 22 10 13 8 19 18 23 10 15 10 21 23 20 9 19 10 16 20 18 8 15 10 22 21 25 14 11 5 15 17 21 8 10 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 11 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation PS[t] = + 7.46043060983696 + 0.328154021465217CM[t] -0.362736672389800D[t] + 0.186560236681879PE[t] + 0.0233844134026162PC[t] + 0.401270321441297O[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) 7.46043060983696 2.248109 3.3185 0.001131 0.000565 CM 0.328154021465217 0.055544 5.908 0 0 D -0.362736672389800 0.107118 -3.3863 9e-04 0.00045 PE 0.186560236681879 0.10114 1.8446 0.067032 0.033516 PC 0.0233844134026162 0.128621 0.1818 0.855973 0.427987 O 0.401270321441297 0.071773 5.5908 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.605858798778077 R-squared 0.367064884056814 Adjusted R-squared 0.346380729941024 F-TEST (value) 17.7461878306445 F-TEST (DF numerator) 5 F-TEST (DF denominator) 153 p-value 7.54951656745106e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.40927289715423 Sum Squared Residuals 1778.34067815237 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 25 22.3963921073236 2.60360789267640 2 30 24.2529863072522 5.74701369274785 3 22 20.5386282852832 1.46137171471678 4 22 23.1227812851809 -1.12278128518093 5 25 22.5736026083869 2.42639739161312 6 23 19.4568594581893 3.54314054181066 7 17 18.7937770436835 -1.79377704368349 8 21 21.6696775851730 -0.669677585173036 9 19 23.3938848919955 -4.39388489199547 10 15 23.2200335336539 -8.22003353365394 11 16 17.0860954231925 -1.08609542319246 12 22 21.0019432886847 0.998056711315265 13 23 24.0090508616482 -1.00905086164818 14 23 21.5688381779423 1.4311618220577 15 19 22.4295524471459 -3.42955244714589 16 23 22.4483525596049 0.551647440395089 17 25 23.3280787328681 1.67192126713187 18 22 21.5692258736674 0.430774126332575 19 26 23.2232169775374 2.77678302246258 20 29 22.7002038848751 6.29979611512492 21 32 25.1965595373823 6.8034404626177 22 25 21.5830794177202 3.4169205822798 23 28 26.0751635208601 1.92483647913991 24 25 23.4667094578832 1.53329054211676 25 25 22.1055221703104 2.89447782968955 26 18 21.4213727878477 -3.42137278784772 27 25 25.0045460489836 -0.00454604898358882 28 25 21.6915513577573 3.30844864224273 29 20 24.0575114630031 -4.05751146300312 30 15 16.5269290283780 -1.52692902837805 31 24 25.3394958960663 -1.33949589606632 32 26 24.3125491844923 1.68745081550775 33 14 15.6462203516491 -1.64622035164913 34 24 23.3536201567194 0.646379843280557 35 25 22.3044035896075 2.69559641039245 36 20 24.9772106374541 -4.97721063745406 37 21 21.5026773832730 -0.502677383272959 38 27 27.4823128306108 -0.482312830610751 39 23 24.3803773473337 -1.38037734733372 40 25 25.6982731831007 -0.698273183100736 41 20 22.2330812773097 -2.23308127730969 42 22 22.4516157406899 -0.451615740689922 43 25 24.0521764435639 0.947823556436078 44 25 23.4230855798854 1.57691442011461 45 17 23.8630492300674 -6.86304923006741 46 25 23.9709132955503 1.02908670444972 47 26 22.5238707218134 3.47612927818658 48 27 24.4361957884407 2.56380421155931 49 19 20.191563551002 -1.19156355100200 50 22 22.0165688176436 -0.0165688176435811 51 32 28.6372448399853 3.36275516001471 52 21 24.3266944626333 -3.32669446263334 53 18 21.2889468496438 -3.28894684964376 54 23 22.8395308141606 0.16046918583944 55 20 20.9576947616757 -0.957694761675739 56 21 22.3255043730554 -1.32550437305537 57 17 18.7741072251434 -1.77410722514342 58 18 20.3006604066273 -2.30066040662729 59 19 20.7496791060040 -1.74967910600404 60 22 22.0682765809344 -0.0682765809344132 61 14 18.8510893511519 -4.8510893511519 62 18 26.6429142940773 -8.64291429407725 63 35 23.5620327119435 11.4379672880565 64 29 19.2163246027188 9.78367539728123 65 21 21.9816944326307 -0.981694432630688 66 25 20.4953208143283 4.50467918567167 67 26 23.2142002181326 2.78579978186737 68 17 16.8872223911238 0.112777608876169 69 25 20.0947136369743 4.90528636302571 70 20 20.7722734892362 -0.772273489236228 71 22 21.0704752877172 0.929524712282784 72 24 22.7056739110488 1.29432608895116 73 21 22.9951676639565 -1.99516766395646 74 26 25.482195851486 0.517804148514024 75 24 20.5950930960205 3.40490690397949 76 16 20.2987397994430 -4.29873979944297 77 18 20.8107987510593 -2.81079875105926 78 19 19.0560620045677 -0.0560620045676748 79 21 16.8666199037581 4.13338009624188 80 22 18.5260173770404 3.47398262295963 81 23 19.7340241912749 3.26597580872509 82 29 24.8124059410788 4.18759405892122 83 21 19.2156508743754 1.78434912562461 84 23 21.8927879622684 1.10721203773160 85 27 22.9960672725990 4.00393272740102 86 25 25.3746950753506 -0.374695075350648 87 21 21.0001409137780 -0.000140913778044122 88 10 17.1119616413152 -7.1119616413152 89 20 22.6490195793518 -2.64901957935177 90 26 22.5749237282455 3.42507627175453 91 24 23.6474832613484 0.352516738651611 92 29 31.6584752151628 -2.65847521516283 93 19 18.9825826818211 0.0174173181788753 94 24 22.0940161795511 1.90598382044894 95 19 20.7666852307848 -1.76668523078483 96 22 21.8244370969672 0.175562903032759 97 17 23.7736200572454 -6.77362005724542 98 24 23.0236176333508 0.976382366649221 99 19 20.2962579947228 -1.29625799472284 100 19 22.8153403514384 -3.81534035143841 101 23 19.4598225179576 3.54017748204243 102 27 24.0748423820553 2.92515761794465 103 14 16.535329320714 -2.53532932071400 104 22 24.0873202920243 -2.08732029202431 105 21 24.4545998179461 -3.45459981794611 106 18 23.8367869289911 -5.83678692899107 107 20 23.1800605324662 -3.18006053246622 108 19 23.3532655211774 -4.35326552117744 109 24 23.839829931247 0.160170068753001 110 25 25.1649483334544 -0.164948333454413 111 29 24.4099495065135 4.59005049348653 112 28 24.9467056041625 3.05329439583751 113 17 17.1062381095522 -0.106238109552167 114 29 22.9430722049405 6.05692779505950 115 26 27.5286218564100 -1.52862185640998 116 14 19.5469105942641 -5.54691059426405 117 26 21.6780393824329 4.32196061756713 118 20 20.3008968098917 -0.300896809891660 119 32 24.6610362298757 7.33896377012431 120 23 20.8454749613068 2.15452503869318 121 21 22.1588588066973 -1.15885880669729 122 30 26.7173902089880 3.28260979101198 123 24 21.7172524612978 2.28274753870219 124 22 21.4941504714309 0.505849528569086 125 24 22.255359520076 1.74464047992401 126 24 22.9203756085798 1.07962439142021 127 24 19.9850555838132 4.01494441618681 128 19 18.5129061642547 0.487093835745272 129 31 26.8208676764294 4.17913232357062 130 22 26.6010375214530 -4.60103752145304 131 27 21.4697621005205 5.5302378994795 132 19 17.7359069452234 1.26409305477656 133 21 19.2454670687402 1.75453293125985 134 23 23.0320339448358 -0.0320339448358385 135 19 21.4391304477228 -2.43913044772283 136 19 22.3733623294629 -3.37336232946291 137 20 23.1407040596382 -3.14070405963825 138 23 20.8073842775135 2.19261572248651 139 17 20.8970807780462 -3.8970807780462 140 17 23.3435280898338 -6.3435280898338 141 17 19.7459731472925 -2.74597314729248 142 21 23.5510323826098 -2.55103238260975 143 21 24.6834795872242 -3.6834795872242 144 18 21.259817450436 -3.25981745043600 145 19 20.6492902959521 -1.64929029595212 146 20 23.8525057494042 -3.85250574940422 147 15 18.7664416321540 -3.76644163215395 148 24 21.4114487878798 2.58855121212023 149 20 18.4924302963951 1.50756970360488 150 22 23.2253187184531 -1.22531871845307 151 13 16.8359413686559 -3.83594136865588 152 19 18.1285543931859 0.87144560681412 153 21 22.6212243668162 -1.62122436681623 154 23 22.3765319512249 0.623468048775058 155 16 22.3793138772619 -6.37931387726185 156 26 24.0698543662375 1.93014563376249 157 21 22.2168258710245 -1.21682587102449 158 21 19.9639464131369 1.03605358686310 159 24 23.4401554227186 0.559844577281409 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.506439199736594 0.987121600526811 0.493560800263406 10 0.93633645529851 0.12732708940298 0.06366354470149 11 0.908535979716326 0.182928040567347 0.0914640202836736 12 0.854525667551111 0.290948664897778 0.145474332448889 13 0.842415492086984 0.315169015826033 0.157584507913017 14 0.827805382231537 0.344389235536925 0.172194617768463 15 0.784439940084585 0.431120119830830 0.215560059915415 16 0.70966123888635 0.5806775222273 0.29033876111365 17 0.629705021753236 0.740589956493529 0.370294978246764 18 0.553082585143285 0.89383482971343 0.446917414856715 19 0.567971544556787 0.864056910886426 0.432028455443213 20 0.662467149098071 0.675065701803858 0.337532850901929 21 0.784544940097765 0.43091011980447 0.215455059902235 22 0.748674012175588 0.502651975648824 0.251325987824412 23 0.693387675160917 0.613224649678166 0.306612324839083 24 0.630271907570331 0.739456184859338 0.369728092429669 25 0.573643225762806 0.852713548474388 0.426356774237194 26 0.582264339721206 0.835471320557589 0.417735660278794 27 0.520235246852922 0.959529506294156 0.479764753147078 28 0.475042407589305 0.95008481517861 0.524957592410695 29 0.525856787010323 0.948286425979354 0.474143212989677 30 0.475697242773402 0.951394485546804 0.524302757226598 31 0.421899701952758 0.843799403905515 0.578100298047242 32 0.373852662177031 0.747705324354061 0.626147337822969 33 0.326233396471957 0.652466792943915 0.673766603528043 34 0.274583951727089 0.549167903454179 0.725416048272911 35 0.262553984708062 0.525107969416123 0.737446015291938 36 0.363263882729539 0.726527765459078 0.636736117270461 37 0.310063507666197 0.620127015332393 0.689936492333803 38 0.26649688885988 0.53299377771976 0.73350311114012 39 0.236200906383035 0.472401812766071 0.763799093616965 40 0.210261768908630 0.420523537817261 0.78973823109137 41 0.186829621190844 0.373659242381689 0.813170378809156 42 0.152941622538556 0.305883245077112 0.847058377461444 43 0.123826446189900 0.247652892379799 0.8761735538101 44 0.105974823767511 0.211949647535021 0.894025176232489 45 0.205933254620194 0.411866509240387 0.794066745379806 46 0.171241399051658 0.342482798103317 0.828758600948342 47 0.168416911312397 0.336833822624793 0.831583088687603 48 0.166270970497946 0.332541940995892 0.833729029502054 49 0.137252620391451 0.274505240782903 0.862747379608549 50 0.115014333794703 0.230028667589407 0.884985666205297 51 0.104982094994893 0.209964189989785 0.895017905005107 52 0.112973157404932 0.225946314809863 0.887026842595068 53 0.112059255487047 0.224118510974093 0.887940744512953 54 0.089540734525989 0.179081469051978 0.910459265474011 55 0.0755826106327876 0.151165221265575 0.924417389367213 56 0.0614806463201382 0.122961292640276 0.938519353679862 57 0.0503290996292948 0.100658199258590 0.949670900370705 58 0.041389857006084 0.082779714012168 0.958610142993916 59 0.032856176721113 0.065712353442226 0.967143823278887 60 0.0246912745305173 0.0493825490610346 0.975308725469483 61 0.0328878970602738 0.0657757941205476 0.967112102939726 62 0.119386310288225 0.238772620576449 0.880613689711775 63 0.557620418422127 0.884759163155745 0.442379581577873 64 0.859899826892168 0.280200346215665 0.140100173107832 65 0.837479466095316 0.325041067809368 0.162520533904684 66 0.852411737455965 0.29517652508807 0.147588262544035 67 0.857544857689829 0.284910284620341 0.142455142310171 68 0.82966002997931 0.34067994004138 0.17033997002069 69 0.86014793920251 0.27970412159498 0.13985206079749 70 0.83427164366201 0.331456712675981 0.165728356337990 71 0.806409644806198 0.387180710387604 0.193590355193802 72 0.77809590518025 0.4438081896395 0.22190409481975 73 0.756328504926041 0.487342990147918 0.243671495073959 74 0.722434339938244 0.555131320123513 0.277565660061756 75 0.721957488183598 0.556085023632804 0.278042511816402 76 0.744552752075792 0.510894495848415 0.255447247924208 77 0.729653789086687 0.540692421826625 0.270346210913313 78 0.68994990422276 0.620100191554479 0.310050095777239 79 0.710364447077719 0.579271105844562 0.289635552922281 80 0.710791816678328 0.578416366643344 0.289208183321672 81 0.712929077592608 0.574141844814783 0.287070922407392 82 0.737599300606628 0.524801398786744 0.262400699393372 83 0.75071709147526 0.498565817049479 0.249282908524740 84 0.725424275345623 0.549151449308754 0.274575724654377 85 0.746909951227742 0.506180097544516 0.253090048772258 86 0.71339330970742 0.573213380585161 0.286606690292581 87 0.672749571506787 0.654500856986427 0.327250428493213 88 0.779384724836279 0.441230550327442 0.220615275163721 89 0.761058780953691 0.477882438092618 0.238941219046309 90 0.762950204542883 0.474099590914235 0.237049795457117 91 0.73235236311215 0.535295273775699 0.267647636887850 92 0.712960786772182 0.574078426455636 0.287039213227818 93 0.679817472573617 0.640365054852766 0.320182527426383 94 0.678536658923611 0.642926682152778 0.321463341076389 95 0.642908456296061 0.714183087407878 0.357091543703939 96 0.604319990649932 0.791360018700137 0.395680009350068 97 0.686134824944723 0.627730350110554 0.313865175055277 98 0.6455874276982 0.708825144603601 0.354412572301801 99 0.60512367410866 0.789752651782681 0.394876325891341 100 0.608250690470183 0.783498619059633 0.391749309529817 101 0.617738740328356 0.764522519343289 0.382261259671644 102 0.6138406618856 0.772318676228801 0.386159338114401 103 0.58141694031023 0.837166119379539 0.418583059689769 104 0.543216005853051 0.913567988293898 0.456783994146949 105 0.526543473817989 0.946913052364022 0.473456526182011 106 0.636613009032417 0.726773981935167 0.363386990967583 107 0.632953778225708 0.734092443548583 0.367046221774292 108 0.66000822532833 0.67998354934334 0.33999177467167 109 0.614947631517613 0.770104736964775 0.385052368482387 110 0.568904113350495 0.86219177329901 0.431095886649505 111 0.592877427557384 0.814245144885232 0.407122572442616 112 0.579490284677843 0.841019430644314 0.420509715322157 113 0.53363254226465 0.9327349154707 0.46636745773535 114 0.666629017622272 0.666741964755456 0.333370982377728 115 0.621539794256840 0.756920411486319 0.378460205743160 116 0.661404604776065 0.67719079044787 0.338595395223935 117 0.6867856425089 0.6264287149822 0.3132143574911 118 0.636726105772641 0.726547788454719 0.363273894227359 119 0.863281110854458 0.273437778291083 0.136718889145542 120 0.875097118177959 0.249805763644082 0.124902881822041 121 0.847021742021776 0.305956515956447 0.152978257978224 122 0.844626004080809 0.310747991838382 0.155373995919191 123 0.843575696648866 0.312848606702269 0.156424303351134 124 0.805300048623895 0.389399902752210 0.194699951376105 125 0.772734832620398 0.454530334759204 0.227265167379602 126 0.75256069329912 0.494878613401762 0.247439306700881 127 0.76893147398216 0.462137052035681 0.231068526017841 128 0.71850912039552 0.562981759208961 0.281490879604480 129 0.891264503505985 0.217470992988031 0.108735496494016 130 0.86722768904831 0.265544621903381 0.132772310951690 131 0.96322862231644 0.0735427553671223 0.0367713776835611 132 0.94632259978747 0.107354800425059 0.0536774002125297 133 0.93214686439889 0.135706271202221 0.0678531356011107 134 0.908165044086528 0.183669911826945 0.0918349559134725 135 0.878403344640567 0.243193310718867 0.121596655359433 136 0.84202875573458 0.315942488530842 0.157971244265421 137 0.795697047350653 0.408605905298695 0.204302952649347 138 0.76622768251373 0.467544634972541 0.233772317486270 139 0.73539740025374 0.52920519949252 0.26460259974626 140 0.801208067771503 0.397583864456993 0.198791932228497 141 0.743723457584673 0.512553084830654 0.256276542415327 142 0.685977098826686 0.628045802346628 0.314022901173314 143 0.658404018384371 0.683191963231259 0.341595981615629 144 0.595459932849199 0.809080134301603 0.404540067150801 145 0.493151227948234 0.986302455896467 0.506848772051766 146 0.576328324530136 0.847343350939727 0.423671675469864 147 0.524400553377452 0.951198893245096 0.475599446622548 148 0.562706038221604 0.874587923556792 0.437293961778396 149 0.62189911068965 0.7562017786207 0.37810088931035 150 0.482294617312521 0.964589234625043 0.517705382687479 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 1 0.00704225352112676 OK 10% type I error level 5 0.0352112676056338 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292344246nruc4h8rloxd4gw/10qdo71292344319.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292344246nruc4h8rloxd4gw/10qdo71292344319.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292344246nruc4h8rloxd4gw/11cre1292344319.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292344246nruc4h8rloxd4gw/11cre1292344319.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292344246nruc4h8rloxd4gw/2b3qg1292344319.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292344246nruc4h8rloxd4gw/2b3qg1292344319.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292344246nruc4h8rloxd4gw/3b3qg1292344319.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292344246nruc4h8rloxd4gw/3b3qg1292344319.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292344246nruc4h8rloxd4gw/4b3qg1292344319.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292344246nruc4h8rloxd4gw/4b3qg1292344319.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292344246nruc4h8rloxd4gw/5mcpj1292344319.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292344246nruc4h8rloxd4gw/5mcpj1292344319.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292344246nruc4h8rloxd4gw/6mcpj1292344319.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292344246nruc4h8rloxd4gw/6mcpj1292344319.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292344246nruc4h8rloxd4gw/7x4o41292344319.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292344246nruc4h8rloxd4gw/7x4o41292344319.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292344246nruc4h8rloxd4gw/8x4o41292344319.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292344246nruc4h8rloxd4gw/8x4o41292344319.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292344246nruc4h8rloxd4gw/9qdo71292344319.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292344246nruc4h8rloxd4gw/9qdo71292344319.ps (open in new window)

Parameters (Session):

par1 = 6 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 6 ; 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') }

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by