*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: Sat, 20 Nov 2010 15:21:49 +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/20/t129026670624u7d07vzitam40.htm/, Retrieved Sat, 20 Nov 2010 16:25:18 +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/20/t129026670624u7d07vzitam40.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 «

14 24 11 12 24 26 11 25 7 8 25 23 6 17 17 8 30 25 12 18 10 8 19 23 8 18 12 9 22 19 10 16 12 7 22 29 10 20 11 4 25 25 11 16 11 11 23 21 16 18 12 7 17 22 11 17 13 7 21 25 13 23 14 12 19 24 12 30 16 10 19 18 8 23 11 10 15 22 12 18 10 8 16 15 11 15 11 8 23 22 4 12 15 4 27 28 9 21 9 9 22 20 8 15 11 8 14 12 8 20 17 7 22 24 14 31 17 11 23 20 15 27 11 9 23 21 16 34 18 11 21 20 9 21 14 13 19 21 14 31 10 8 18 23 11 19 11 8 20 28 8 16 15 9 23 24 9 20 15 6 25 24 9 21 13 9 19 24 9 22 16 9 24 23 9 17 13 6 22 23 10 24 9 6 25 29 16 25 18 16 26 24 11 26 18 5 29 18 8 25 12 7 32 25 9 17 17 9 25 21 16 32 9 6 29 26 11 33 9 6 28 22 16 13 12 5 17 22 12 32 18 12 28 22 12 25 12 7 29 23 14 29 18 10 26 30 9 22 14 9 25 23 10 18 15 8 14 17 9 17 16 5 25 23 10 20 10 8 26 23 12 15 11 8 20 25 14 20 14 10 18 24 14 33 9 6 32 24 10 29 12 8 25 23 14 23 17 7 25 21 16 26 5 4 23 24 9 18 12 8 21 24 10 20 12 8 20 28 6 11 6 4 15 16 8 28 24 20 30 20 13 26 12 8 24 29 10 22 12 8 26 27 8 17 14 6 24 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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Doubts[t] = + 7.47561072472881 + 0.248860445943252Concern[t] -0.105949734415458Expectations[t] + 0.147529539189439Criticism[t] -0.192213547252973Standards[t] + 0.109733980302453Organization[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) 7.47561072472881 1.582911 4.7227 5e-06 3e-06 Concern 0.248860445943252 0.040037 6.2157 0 0 Expectations -0.105949734415458 0.073943 -1.4329 0.153941 0.07697 Criticism 0.147529539189439 0.092876 1.5885 0.114246 0.057123 Standards -0.192213547252973 0.056762 -3.3863 9e-04 0.00045 Organization 0.109733980302453 0.056645 1.9372 0.05456 0.02728 Multiple Linear Regression - Regression Statistics Multiple R 0.489435601598432 R-squared 0.239547208112019 Adjusted R-squared 0.214695809684307 F-TEST (value) 9.63918424183727 F-TEST (DF numerator) 5 F-TEST (DF denominator) 153 p-value 5.12764863902504e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.48174999937267 Sum Squared Residuals 942.339708086094 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14 12.2931271728623 1.7068728271377 2 11 11.8542529115495 -0.85425291154948 3 6 8.06227222418893 -2.06227222418893 4 12 10.9476618702182 1.05233812978182 5 8 9.86771537760797 -1.86771537760797 6 10 10.1722752103671 -0.172275210367124 7 10 9.81550154801854 0.184498451981458 8 11 9.79825771186774 1.20174228813226 9 16 10.8629259764013 5.13707402359868 10 11 10.0684635479381 0.93153645206192 11 13 12.4680172993328 0.53198270066718 12 12 13.0446779919111 -1.04467799191107 13 8 13.0401936526073 -5.0401936526073 14 12 10.6464306695575 1.35356933044252 15 11 9.21654262865863 1.78345737134137 16 4 7.34559388921211 -3.34559388921211 17 9 11.0418798989866 -2.04187989898656 18 8 9.84912475091086 -1.84912475091086 19 8 10.0892984205506 -2.08929842055058 20 14 12.7857320142213 1.21426798577868 21 15 12.2406635388646 2.75933646113537 22 16 13.8107907121416 2.18920928785844 23 9 11.7886240057284 -2.7886240057284 24 14 14.3750612147334 -0.375061214733429 25 11 11.4470289360053 -0.44702893600527 26 8 9.4086016367344 -1.40860163673439 27 9 9.57702770843313 -0.577027708433134 28 9 11.6336575242935 -2.63365752429346 29 9 10.4938670504230 -1.49386705042302 30 9 9.50925250089076 -0.509252500890762 31 10 11.7568378002112 -1.75683780021115 32 16 11.7865625795444 4.21343742045556 33 11 9.17755357083022 1.82244642916978 34 8 10.0509478301168 -2.05094783011685 35 9 8.73193357843342 0.268066421566578 36 16 12.6496652378379 3.35033476216208 37 11 12.6518033098243 -1.65180330982433 38 16 9.32356466830619 6.67643533169381 39 12 12.3345724892786 -0.334572489278588 40 12 10.4081205112709 1.59187948872914 41 14 12.5552310099955 1.44476899000448 42 9 10.5135529720010 -1.51355297200096 43 10 10.7205770525910 -0.720577052591042 44 9 8.46723311669603 0.53276688330397 45 10 10.0998879313339 -0.0998879313338787 46 12 10.1223852113249 1.87761478867509 47 14 11.6185904303772 2.38140956962284 48 14 12.1024170814173 1.89758291858266 49 10 12.3199460232452 -2.3199460232452 50 14 9.93003717571405 4.06996282428595 51 16 12.2190557443743 3.7809442556257 52 9 10.4610692871838 -1.46106928718378 53 10 11.5899396475331 -1.58993964753306 54 6 9.04003585641422 -3.04003585641422 55 8 11.2797735574175 -3.27977355741749 56 13 12.4239821144831 0.576017885516867 57 10 10.8246452755993 -0.824645275599276 58 8 8.9091416916669 -0.909141691666905 59 7 9.15425950080064 -2.15425950080064 60 15 9.8273007573465 5.1726992426535 61 9 9.8928317189735 -0.892831718973498 62 10 10.2300011704603 -0.230001170460275 63 12 10.2127960045576 1.78720399544244 64 13 10.4557571222761 2.54424287772387 65 10 8.4082399506884 1.59176004931160 66 11 11.8100631875226 -0.810063187522588 67 8 13.6099912716085 -5.60999127160853 68 9 9.12149677428637 -0.121496774286373 69 13 8.63232673895495 4.36767326104505 70 11 10.4056197047763 0.594380295223702 71 8 12.7748897940749 -4.77488979407492 72 9 10.7705154168815 -1.77051541688151 73 9 12.3432616515329 -3.34326165153293 74 15 12.5112633288267 2.48873667117329 75 9 11.1799243643951 -2.17992436439510 76 10 11.5683831232456 -1.56838312324565 77 14 8.92549222497563 5.07450777502436 78 12 10.9510671481191 1.04893285188092 79 12 11.0860720089643 0.913927991035738 80 11 11.5603427842052 -0.560342784205158 81 14 11.4548286127589 2.54517138724108 82 6 11.5553411712160 -5.55534117121603 83 12 11.2666600244991 0.733339975500887 84 8 10.0611961307754 -2.06119613077543 85 14 12.4002108724069 1.59978912759315 86 11 10.8285356954152 0.171464304584769 87 10 9.90994400559581 0.0900559944041932 88 14 10.1965799596067 3.80342004039329 89 12 12.0383027999684 -0.0383027999683501 90 10 11.0020524420421 -1.00205244204212 91 14 13.0089075749108 0.991092425089237 92 5 8.98335267342666 -3.98335267342666 93 11 10.4977291896848 0.502270810315231 94 10 10.2124533208687 -0.212453320868745 95 9 11.4401404868287 -2.44014048682872 96 10 11.4379445722869 -1.43794457228688 97 16 13.7416191351070 2.25838086489298 98 13 12.8237520019172 0.176247998082808 99 9 10.8098388947891 -1.80983889478915 100 10 11.3785320767880 -1.37853207678798 101 10 10.9689523566192 -0.968952356619233 102 7 9.47465402457373 -2.47465402457373 103 9 9.8265428213743 -0.8265428213743 104 8 10.2188112017114 -2.21881120171137 105 14 12.8472637784596 1.15273622154039 106 14 11.6477018919235 2.35229810807650 107 8 11.0805233342968 -3.08052333429676 108 9 11.5401625785906 -2.54016257859058 109 14 11.8064163349481 2.19358366505185 110 14 10.7412291054721 3.25877089452788 111 8 9.86606244753663 -1.86606244753663 112 8 13.6926336074711 -5.69263360747113 113 8 10.9525118828595 -2.95251188285949 114 7 8.55085509620331 -1.55085509620331 115 6 7.44027047059843 -1.44027047059843 116 8 9.4148100433135 -1.41481004331350 117 6 8.31398706901332 -2.31398706901332 118 11 9.87854261184873 1.12145738815127 119 14 11.8405591974766 2.15944080252337 120 11 11.1231055546712 -0.123105554671159 121 11 11.9576290110093 -0.957629011009308 122 11 9.2090803108136 1.7909196891864 123 14 10.3696761291700 3.63032387082997 124 8 10.3570748050233 -2.35707480502332 125 20 11.4803602064078 8.51963979359218 126 11 10.3193075266905 0.680692473309466 127 8 9.14405571417421 -1.14405571417421 128 11 10.7075672323317 0.292432767668276 129 10 10.6161673181472 -0.616167318147203 130 14 13.4485919547856 0.551408045214404 131 11 10.558105430536 0.441894569463994 132 9 10.5952141906548 -1.59521419065478 133 9 9.71061082418663 -0.710610824186625 134 8 10.1579861032424 -2.15798610324236 135 10 12.0589843809759 -2.05898438097594 136 13 10.7188783609152 2.28112163908477 137 13 10.1115013821010 2.88849861789897 138 12 9.29557530863078 2.70442469136922 139 8 10.3597383804300 -2.35973838042996 140 13 11.0143393969289 1.98566060307107 141 14 12.4310064834081 1.56899351659186 142 12 11.6674281750066 0.332571824993391 143 14 10.9169138958967 3.08308610410328 144 15 11.2948106795225 3.70518932047750 145 13 10.5165955153937 2.48340448460630 146 16 11.8561435650783 4.14385643492171 147 9 11.9965118610340 -2.99651186103404 148 9 10.4782744530865 -1.47827445308649 149 9 11.0181531709424 -2.01815317094243 150 8 11.2929483065479 -3.29294830654791 151 7 10.0317337558054 -3.03173375580541 152 16 11.9492341671955 4.05076583280446 153 11 13.3481625806087 -2.34816258060872 154 9 10.0171718546235 -1.0171718546235 155 11 9.83326343672508 1.16673656327492 156 9 9.86642518204478 -0.866425182044775 157 14 12.4789828392728 1.52101716072717 158 13 11.0220394382314 1.97796056176859 159 16 14.4647615248554 1.53523847514457 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.476091055083597 0.952182110167194 0.523908944916403 10 0.320155027094972 0.640310054189944 0.679844972905028 11 0.324803577006545 0.64960715401309 0.675196422993455 12 0.233266213547837 0.466532427095675 0.766733786452163 13 0.793564934243949 0.412870131512102 0.206435065756051 14 0.718291593016648 0.563416813966704 0.281708406983352 15 0.641167940924177 0.717664118151647 0.358832059075823 16 0.687698101596045 0.624603796807909 0.312301898403955 17 0.667142450692695 0.66571509861461 0.332857549307305 18 0.645049844354672 0.709900311290656 0.354950155645328 19 0.57631975918551 0.84736048162898 0.42368024081449 20 0.575099313020188 0.849801373959624 0.424900686979812 21 0.585405060746221 0.829189878507558 0.414594939253779 22 0.555126722745432 0.889746554509136 0.444873277254568 23 0.558017709223827 0.883964581552347 0.441982290776173 24 0.510035987515598 0.979928024968803 0.489964012484402 25 0.43954334372347 0.87908668744694 0.56045665627653 26 0.377278219139064 0.754556438278127 0.622721780860936 27 0.314096897330082 0.628193794660164 0.685903102669918 28 0.306692912841130 0.613385825682259 0.69330708715887 29 0.260229892083154 0.520459784166308 0.739770107916846 30 0.210038175247729 0.420076350495459 0.78996182475227 31 0.192881445825193 0.385762891650385 0.807118554174807 32 0.262884027930576 0.525768055861151 0.737115972069424 33 0.235396766876013 0.470793533752027 0.764603233123987 34 0.235007038463068 0.470014076926136 0.764992961536932 35 0.19140588032168 0.38281176064336 0.80859411967832 36 0.212302642451889 0.424605284903778 0.787697357548111 37 0.209648116699031 0.419296233398062 0.790351883300969 38 0.606540921417603 0.786918157164794 0.393459078582397 39 0.554135704077907 0.891728591844186 0.445864295922093 40 0.520990964978723 0.958018070042555 0.479009035021278 41 0.481258183394213 0.962516366788426 0.518741816605787 42 0.446585909193591 0.893171818387181 0.553414090806409 43 0.399113225350086 0.798226450700173 0.600886774649914 44 0.350418690892097 0.700837381784193 0.649581309107903 45 0.301831574820829 0.603663149641658 0.69816842517917 46 0.28530085662361 0.57060171324722 0.71469914337639 47 0.276880642043234 0.553761284086469 0.723119357956766 48 0.255998886010795 0.51199777202159 0.744001113989205 49 0.256699729798469 0.513399459596937 0.743300270201531 50 0.320245094302186 0.640490188604372 0.679754905697814 51 0.370824888458201 0.741649776916403 0.629175111541799 52 0.340837659367933 0.681675318735867 0.659162340632067 53 0.3149336797837 0.6298673595674 0.6850663202163 54 0.33176099422921 0.66352198845842 0.66823900577079 55 0.351662726969555 0.703325453939111 0.648337273030445 56 0.307841980911196 0.615683961822393 0.692158019088804 57 0.270238986480131 0.540477972960263 0.729761013519869 58 0.235665698972970 0.471331397945941 0.76433430102703 59 0.223294194809294 0.446588389618588 0.776705805190706 60 0.357926992174277 0.715853984348554 0.642073007825723 61 0.317418096385376 0.634836192770752 0.682581903614624 62 0.276394366413775 0.552788732827549 0.723605633586225 63 0.256535513703847 0.513071027407694 0.743464486296153 64 0.267828266525851 0.535656533051701 0.732171733474149 65 0.244010307289830 0.488020614579659 0.75598969271017 66 0.212324329654130 0.424648659308259 0.78767567034587 67 0.390040519480441 0.780081038960882 0.609959480519559 68 0.345224833395200 0.690449666790401 0.6547751666048 69 0.434822332802387 0.869644665604773 0.565177667197613 70 0.39141042938471 0.78282085876942 0.60858957061529 71 0.518949159678523 0.962101680642954 0.481050840321477 72 0.496464134882847 0.992928269765694 0.503535865117153 73 0.53164136191603 0.93671727616794 0.46835863808397 74 0.531792542649688 0.936414914700624 0.468207457350312 75 0.519911999650482 0.960176000699036 0.480088000349518 76 0.492426975651176 0.984853951302352 0.507573024348824 77 0.644457793217581 0.711084413564838 0.355542206782419 78 0.608445607100602 0.783108785798796 0.391554392899398 79 0.569031770874919 0.861936458250163 0.430968229125081 80 0.526201024255375 0.94759795148925 0.473798975744625 81 0.527674227423092 0.944651545153816 0.472325772576908 82 0.699493157708578 0.601013684582844 0.300506842291422 83 0.661288799796887 0.677422400406225 0.338711200203113 84 0.644279313401498 0.711441373197005 0.355720686598502 85 0.615843118427673 0.768313763144654 0.384156881572327 86 0.57143247127669 0.85713505744662 0.42856752872331 87 0.52519991823769 0.949600163524619 0.474800081762309 88 0.594703454276606 0.810593091446787 0.405296545723394 89 0.550132002192165 0.89973599561567 0.449867997807835 90 0.509575972582258 0.980848054835484 0.490424027417742 91 0.469521789478772 0.939043578957543 0.530478210521228 92 0.528056279019302 0.943887441961396 0.471943720980698 93 0.484267257645203 0.968534515290406 0.515732742354797 94 0.43720021477886 0.87440042955772 0.56279978522114 95 0.433931396934589 0.867862793869179 0.566068603065411 96 0.404100875860118 0.808201751720235 0.595899124139882 97 0.388194529491107 0.776389058982214 0.611805470508893 98 0.343594980740843 0.687189961481687 0.656405019259157 99 0.320168074584798 0.640336149169595 0.679831925415202 100 0.290385090765841 0.580770181531682 0.709614909234159 101 0.256352317706483 0.512704635412967 0.743647682293517 102 0.248521505838521 0.497043011677043 0.751478494161478 103 0.213854846463106 0.427709692926211 0.786145153536894 104 0.204088309924541 0.408176619849081 0.79591169007546 105 0.175105319691062 0.350210639382124 0.824894680308938 106 0.170558236007089 0.341116472014178 0.829441763992911 107 0.184578417463128 0.369156834926255 0.815421582536872 108 0.189248434454485 0.378496868908969 0.810751565545515 109 0.176721115775723 0.353442231551446 0.823278884224277 110 0.202029085947166 0.404058171894332 0.797970914052834 111 0.181318748782535 0.36263749756507 0.818681251217465 112 0.406498565425634 0.812997130851268 0.593501434574366 113 0.465486153700664 0.930972307401328 0.534513846299336 114 0.429649070419864 0.859298140839728 0.570350929580136 115 0.422135996081516 0.844271992163032 0.577864003918484 116 0.379739971174427 0.759479942348854 0.620260028825573 117 0.365472859961179 0.730945719922359 0.634527140038821 118 0.323420729234325 0.64684145846865 0.676579270765675 119 0.302331410044504 0.604662820089008 0.697668589955496 120 0.257541358270712 0.515082716541424 0.742458641729288 121 0.229217140864475 0.45843428172895 0.770782859135525 122 0.215962894307202 0.431925788614404 0.784037105692798 123 0.227881162521209 0.455762325042419 0.77211883747879 124 0.241452989526197 0.482905979052395 0.758547010473803 125 0.790956538438538 0.418086923122924 0.209043461561462 126 0.754537021129095 0.490925957741809 0.245462978870905 127 0.70723225485574 0.585535490288521 0.292767745144261 128 0.650610707546915 0.698778584906169 0.349389292453085 129 0.591211562681126 0.817576874637749 0.408788437318874 130 0.52977551048517 0.94044897902966 0.47022448951483 131 0.473593931496003 0.947187862992005 0.526406068503997 132 0.418388363759168 0.836776727518336 0.581611636240832 133 0.356258908378721 0.712517816757442 0.643741091621279 134 0.316736189482038 0.633472378964076 0.683263810517962 135 0.285367565123947 0.570735130247895 0.714632434876053 136 0.262690626270163 0.525381252540327 0.737309373729837 137 0.298957615224636 0.597915230449273 0.701042384775364 138 0.307974903567051 0.615949807134102 0.692025096432949 139 0.328331373504199 0.656662747008399 0.671668626495801 140 0.265316978126099 0.530633956252197 0.734683021873901 141 0.208208703930898 0.416417407861796 0.791791296069102 142 0.158048550232565 0.31609710046513 0.841951449767435 143 0.184447031478692 0.368894062957383 0.815552968521308 144 0.173591647090988 0.347183294181975 0.826408352909012 145 0.15625503129802 0.31251006259604 0.84374496870198 146 0.273200771077996 0.546401542155991 0.726799228922004 147 0.239791906503731 0.479583813007461 0.76020809349627 148 0.159221051012305 0.318442102024611 0.840778948987695 149 0.112589417860190 0.225178835720380 0.88741058213981 150 0.160999460301461 0.321998920602922 0.839000539698539 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 0 0 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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