Workshop 7 - Doubts About Actions

*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: Mon, 22 Nov 2010 18:43:58 +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/22/t1290451333vpxaf9q2dkrhty1.htm/, Retrieved Mon, 22 Nov 2010 19:42:16 +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/22/t1290451333vpxaf9q2dkrhty1.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 «

24 14 11 12 24 26 25 11 7 8 25 23 17 6 17 8 30 25 18 12 10 8 19 23 18 8 12 9 22 19 16 10 12 7 22 29 20 10 11 4 25 25 16 11 11 11 23 21 18 16 12 7 17 22 17 11 13 7 21 25 23 13 14 12 19 24 30 12 16 10 19 18 23 8 11 10 15 22 18 12 10 8 16 15 15 11 11 8 23 22 12 4 15 4 27 28 21 9 9 9 22 20 15 8 11 8 14 12 20 8 17 7 22 24 31 14 17 11 23 20 27 15 11 9 23 21 34 16 18 11 21 20 21 9 14 13 19 21 31 14 10 8 18 23 19 11 11 8 20 28 16 8 15 9 23 24 20 9 15 6 25 24 21 9 13 9 19 24 22 9 16 9 24 23 17 9 13 6 22 23 24 10 9 6 25 29 25 16 18 16 26 24 26 11 18 5 29 18 25 8 12 7 32 25 17 9 17 9 25 21 32 16 9 6 29 26 33 11 9 6 28 22 13 16 12 5 17 22 32 12 18 12 28 22 25 12 12 7 29 23 29 14 18 10 26 30 22 9 14 9 25 23 18 10 15 8 14 17 17 9 16 5 25 23 20 10 10 8 26 23 15 12 11 8 20 25 20 14 14 10 18 24 33 14 9 6 32 24 29 10 12 8 25 23 23 14 17 7 25 21 26 16 5 4 23 24 18 9 12 8 21 24 20 10 12 8 20 28 11 6 6 4 15 16 28 8 24 20 30 20 26 13 12 8 24 29 22 10 12 8 26 27 17 8 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 'RServer@AstonUniversity' @ vre.aston.ac.uk R Framework error message Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Multiple Linear Regression - Estimated Regression Equation D[t] = + 7.47561072472881 + 0.248860445943252CM[t] -0.105949734415458PE[t] + 0.147529539189438PC[t] -0.192213547252973PS[t] + 0.109733980302452`O `[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 CM 0.248860445943252 0.040037 6.2157 0 0 PE -0.105949734415458 0.073943 -1.4329 0.153941 0.07697 PC 0.147529539189438 0.092876 1.5885 0.114246 0.057123 PS -0.192213547252973 0.056762 -3.3863 9e-04 0.00045 `O ` 0.109733980302452 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) 9.63918424183728 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 942.339708086093 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14 12.2931271728625 1.70687282713751 2 11 11.8542529115495 -0.85425291154948 3 6 8.06227222418893 -2.06227222418893 4 12 10.9476618702182 1.05233812978182 5 8 9.86771537760798 -1.86771537760798 6 10 10.1722752103671 -0.172275210367121 7 10 9.81550154801854 0.184498451981456 8 11 9.79825771186774 1.20174228813226 9 16 10.8629259764013 5.13707402359868 10 11 10.0684635479381 0.931536452061921 11 13 12.4680172993328 0.531982700667187 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 -2.78862400572839 24 14 14.3750612147334 -0.375061214733427 25 11 11.4470289360053 -0.447028936005265 26 8 9.40860163673439 -1.40860163673439 27 9 9.57702770843314 -0.577027708433137 28 9 11.6336575242935 -2.63365752429345 29 9 10.493867050423 -1.49386705042302 30 9 9.50925250089076 -0.509252500890764 31 10 11.7568378002112 -1.75683780021115 32 16 11.7865625795444 4.21343742045558 33 11 9.17755357083023 1.82244642916977 34 8 10.0509478301168 -2.05094783011685 35 9 8.73193357843342 0.268066421566578 36 16 12.6496652378379 3.35033476216209 37 11 12.6518033098243 -1.65180330982433 38 16 9.32356466830619 6.67643533169381 39 12 12.3345724892786 -0.334572489278586 40 12 10.4081205112709 1.59187948872914 41 14 12.5552310099955 1.44476899000448 42 9 10.513552972001 -1.51355297200096 43 10 10.720577052591 -0.720577052591046 44 9 8.46723311669603 0.532766883303966 45 10 10.0998879313339 -0.0998879313338746 46 12 10.1223852113249 1.8776147886751 47 14 11.6185904303772 2.38140956962284 48 14 12.1024170814173 1.89758291858266 49 10 12.3199460232452 -2.3199460232452 50 14 9.93003717571406 4.06996282428594 51 16 12.2190557443743 3.78094425562571 52 9 10.4610692871838 -1.46106928718377 53 10 11.5899396475331 -1.58993964753306 54 6 9.04003585641423 -3.04003585641423 55 8 11.2797735574175 -3.27977355741748 56 13 12.4239821144831 0.576017885516871 57 10 10.8246452755993 -0.824645275599272 58 8 8.9091416916669 -0.909141691666907 59 7 9.15425950080064 -2.15425950080064 60 15 9.8273007573465 5.1726992426535 61 9 9.8928317189735 -0.892831718973492 62 10 10.2300011704603 -0.230001170460277 63 12 10.2127960045576 1.78720399544244 64 13 10.4557571222761 2.54424287772388 65 10 8.4082399506884 1.5917600493116 66 11 11.8100631875226 -0.810063187522585 67 8 13.6099912716085 -5.60999127160853 68 9 9.12149677428637 -0.121496774286372 69 13 8.63232673895495 4.36767326104505 70 11 10.4056197047763 0.594380295223705 71 8 12.7748897940749 -4.77488979407492 72 9 10.7705154168815 -1.77051541688151 73 9 12.3432616515329 -3.34326165153292 74 15 12.5112633288267 2.48873667117329 75 9 11.1799243643951 -2.1799243643951 76 10 11.5683831232456 -1.56838312324565 77 14 8.92549222497563 5.07450777502437 78 12 10.9510671481191 1.04893285188092 79 12 11.0860720089643 0.913927991035744 80 11 11.5603427842052 -0.56034278420516 81 14 11.4548286127589 2.54517138724109 82 6 11.555341171216 -5.55534117121603 83 12 11.2666600244991 0.733339975500888 84 8 10.0611961307754 -2.06119613077543 85 14 12.4002108724069 1.59978912759315 86 11 10.8285356954152 0.171464304584766 87 10 9.90994400559581 0.0900559944041918 88 14 10.1965799596067 3.80342004039329 89 12 12.0383027999683 -0.0383027999683422 90 10 11.0020524420421 -1.00205244204212 91 14 13.0089075749108 0.991092425089236 92 5 8.98335267342666 -3.98335267342666 93 11 10.4977291896848 0.50227081031523 94 10 10.2124533208688 -0.21245332086875 95 9 11.4401404868287 -2.44014048682871 96 10 11.4379445722869 -1.43794457228688 97 16 13.741619135107 2.25838086489298 98 13 12.8237520019172 0.17624799808281 99 9 10.8098388947891 -1.80983889478915 100 10 11.378532076788 -1.37853207678798 101 10 10.9689523566192 -0.968952356619231 102 7 9.47465402457373 -2.47465402457373 103 9 9.8265428213743 -0.826542821374303 104 8 10.2188112017114 -2.21881120171137 105 14 12.8472637784596 1.1527362215404 106 14 11.6477018919235 2.3522981080765 107 8 11.0805233342968 -3.08052333429676 108 9 11.5401625785906 -2.54016257859058 109 14 11.8064163349481 2.19358366505185 110 14 10.7412291054721 3.25877089452787 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 7.44027047059842 -1.44027047059841 116 8 9.4148100433135 -1.4148100433135 117 6 8.31398706901332 -2.31398706901332 118 11 9.87854261184873 1.12145738815127 119 14 11.8405591974766 2.15944080252337 120 11 11.1231055546712 -0.123105554671165 121 11 11.9576290110093 -0.95762901100931 122 11 9.2090803108136 1.7909196891864 123 14 10.36967612917 3.63032387082998 124 8 10.3570748050233 -2.35707480502331 125 20 11.4803602064078 8.51963979359219 126 11 10.3193075266905 0.680692473309464 127 8 9.14405571417421 -1.14405571417421 128 11 10.7075672323317 0.29243276766828 129 10 10.6161673181472 -0.616167318147201 130 14 13.4485919547856 0.551408045214407 131 11 10.558105430536 0.441894569463998 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 10.111501382101 2.88849861789897 138 12 9.29557530863078 2.70442469136922 139 8 10.35973838043 -2.35973838042996 140 13 11.0143393969289 1.98566060307108 141 14 12.4310064834081 1.56899351659187 142 12 11.6674281750066 0.332571824993393 143 14 10.9169138958967 3.08308610410329 144 15 11.2948106795225 3.7051893204775 145 13 10.5165955153937 2.4834044846063 146 16 11.8561435650783 4.14385643492171 147 9 11.996511861034 -2.99651186103404 148 9 10.4782744530865 -1.47827445308649 149 9 11.0181531709424 -2.01815317094243 150 8 11.2929483065479 -3.2929483065479 151 7 10.0317337558054 -3.0317337558054 152 16 11.9492341671955 4.05076583280446 153 11 13.3481625806087 -2.34816258060873 154 9 10.0171718546235 -1.01717185462351 155 11 9.83326343672508 1.16673656327492 156 9 9.86642518204478 -0.866425182044778 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 0.952182110167193 0.523908944916403 10 0.320155027094972 0.640310054189944 0.679844972905028 11 0.324803577006544 0.649607154013089 0.675196422993456 12 0.233266213547838 0.466532427095676 0.766733786452162 13 0.793564934243949 0.412870131512103 0.206435065756051 14 0.718291593016648 0.563416813966704 0.281708406983352 15 0.641167940924177 0.717664118151646 0.358832059075823 16 0.687698101596045 0.624603796807909 0.312301898403955 17 0.667142450692695 0.66571509861461 0.332857549307305 18 0.645049844354671 0.709900311290657 0.354950155645329 19 0.57631975918551 0.847360481628981 0.423680240814491 20 0.575099313020188 0.849801373959624 0.424900686979812 21 0.585405060746221 0.829189878507558 0.414594939253779 22 0.555126722745432 0.889746554509137 0.444873277254568 23 0.558017709223827 0.883964581552346 0.441982290776173 24 0.510035987515598 0.979928024968804 0.489964012484402 25 0.43954334372347 0.87908668744694 0.56045665627653 26 0.377278219139064 0.754556438278128 0.622721780860936 27 0.314096897330081 0.628193794660162 0.685903102669919 28 0.306692912841129 0.613385825682259 0.693307087158871 29 0.260229892083154 0.520459784166307 0.739770107916846 30 0.21003817524773 0.420076350495459 0.78996182475227 31 0.192881445825191 0.385762891650382 0.807118554174809 32 0.262884027930576 0.525768055861152 0.737115972069424 33 0.235396766876013 0.470793533752027 0.764603233123986 34 0.235007038463068 0.470014076926135 0.764992961536932 35 0.191405880321681 0.382811760643362 0.808594119678319 36 0.212302642451889 0.424605284903778 0.787697357548111 37 0.20964811669903 0.41929623339806 0.79035188330097 38 0.606540921417601 0.786918157164797 0.393459078582399 39 0.554135704077906 0.891728591844188 0.445864295922094 40 0.520990964978722 0.958018070042556 0.479009035021278 41 0.481258183394213 0.962516366788426 0.518741816605787 42 0.446585909193592 0.893171818387184 0.553414090806408 43 0.399113225350087 0.798226450700173 0.600886774649913 44 0.350418690892097 0.700837381784194 0.649581309107903 45 0.30183157482083 0.603663149641659 0.69816842517917 46 0.28530085662361 0.570601713247219 0.71469914337639 47 0.276880642043235 0.553761284086469 0.723119357956765 48 0.255998886010793 0.511997772021586 0.744001113989207 49 0.256699729798468 0.513399459596937 0.743300270201532 50 0.320245094302186 0.640490188604372 0.679754905697814 51 0.370824888458202 0.741649776916404 0.629175111541798 52 0.340837659367932 0.681675318735864 0.659162340632068 53 0.314933679783701 0.629867359567403 0.685066320216299 54 0.33176099422921 0.66352198845842 0.66823900577079 55 0.351662726969555 0.70332545393911 0.648337273030445 56 0.307841980911197 0.615683961822394 0.692158019088803 57 0.270238986480131 0.540477972960262 0.729761013519869 58 0.23566569897297 0.47133139794594 0.76433430102703 59 0.223294194809293 0.446588389618586 0.776705805190707 60 0.357926992174276 0.715853984348553 0.642073007825724 61 0.317418096385377 0.634836192770754 0.682581903614623 62 0.276394366413777 0.552788732827554 0.723605633586223 63 0.256535513703846 0.513071027407692 0.743464486296154 64 0.267828266525851 0.535656533051701 0.732171733474149 65 0.24401030728983 0.48802061457966 0.75598969271017 66 0.212324329654128 0.424648659308257 0.787675670345872 67 0.390040519480441 0.780081038960882 0.609959480519559 68 0.345224833395202 0.690449666790404 0.654775166604798 69 0.434822332802387 0.869644665604775 0.565177667197613 70 0.391410429384713 0.782820858769426 0.608589570615287 71 0.518949159678521 0.962101680642958 0.481050840321479 72 0.496464134882848 0.992928269765697 0.503535865117152 73 0.531641361916029 0.936717276167943 0.468358638083971 74 0.53179254264969 0.93641491470062 0.46820745735031 75 0.519911999650483 0.960176000699034 0.480088000349517 76 0.492426975651177 0.984853951302355 0.507573024348823 77 0.644457793217583 0.711084413564833 0.355542206782417 78 0.6084456071006 0.7831087857988 0.3915543928994 79 0.569031770874919 0.861936458250163 0.430968229125081 80 0.526201024255373 0.947597951489254 0.473798975744627 81 0.52767422742309 0.94465154515382 0.47232577257691 82 0.699493157708578 0.601013684582843 0.300506842291422 83 0.661288799796887 0.677422400406225 0.338711200203113 84 0.644279313401495 0.711441373197011 0.355720686598505 85 0.615843118427675 0.76831376314465 0.384156881572325 86 0.57143247127669 0.85713505744662 0.42856752872331 87 0.525199918237691 0.949600163524618 0.474800081762309 88 0.594703454276606 0.810593091446788 0.405296545723394 89 0.550132002192166 0.899735995615669 0.449867997807834 90 0.509575972582257 0.980848054835487 0.490424027417743 91 0.469521789478776 0.939043578957552 0.530478210521224 92 0.528056279019302 0.943887441961397 0.471943720980698 93 0.4842672576452 0.968534515290399 0.5157327423548 94 0.437200214778865 0.87440042955773 0.562799785221135 95 0.433931396934591 0.867862793869182 0.566068603065409 96 0.40410087586012 0.80820175172024 0.59589912413988 97 0.388194529491108 0.776389058982215 0.611805470508892 98 0.343594980740843 0.687189961481686 0.656405019259157 99 0.320168074584797 0.640336149169595 0.679831925415203 100 0.290385090765841 0.580770181531681 0.709614909234159 101 0.256352317706483 0.512704635412967 0.743647682293517 102 0.248521505838521 0.497043011677043 0.751478494161479 103 0.213854846463103 0.427709692926206 0.786145153536897 104 0.204088309924541 0.408176619849082 0.79591169007546 105 0.175105319691062 0.350210639382124 0.824894680308938 106 0.170558236007089 0.341116472014178 0.829441763992911 107 0.184578417463128 0.369156834926256 0.815421582536872 108 0.189248434454485 0.37849686890897 0.810751565545515 109 0.176721115775724 0.353442231551449 0.823278884224276 110 0.202029085947166 0.404058171894331 0.797970914052834 111 0.181318748782535 0.362637497565071 0.818681251217465 112 0.406498565425633 0.812997130851266 0.593501434574367 113 0.465486153700663 0.930972307401327 0.534513846299337 114 0.429649070419864 0.859298140839727 0.570350929580136 115 0.422135996081516 0.844271992163031 0.577864003918484 116 0.379739971174427 0.759479942348855 0.620260028825573 117 0.365472859961179 0.730945719922357 0.634527140038821 118 0.323420729234327 0.646841458468654 0.676579270765673 119 0.302331410044504 0.604662820089008 0.697668589955496 120 0.257541358270712 0.515082716541425 0.742458641729288 121 0.229217140864474 0.458434281728948 0.770782859135526 122 0.215962894307203 0.431925788614407 0.784037105692797 123 0.22788116252121 0.455762325042421 0.77211883747879 124 0.241452989526194 0.482905979052387 0.758547010473806 125 0.790956538438538 0.418086923122925 0.209043461561462 126 0.754537021129096 0.490925957741809 0.245462978870904 127 0.70723225485574 0.58553549028852 0.29276774514426 128 0.650610707546916 0.698778584906168 0.349389292453084 129 0.591211562681127 0.817576874637746 0.408788437318873 130 0.529775510485169 0.940448979029662 0.470224489514831 131 0.473593931496003 0.947187862992005 0.526406068503997 132 0.418388363759167 0.836776727518335 0.581611636240833 133 0.356258908378722 0.712517816757443 0.643741091621278 134 0.316736189482038 0.633472378964076 0.683263810517962 135 0.285367565123948 0.570735130247895 0.714632434876052 136 0.262690626270164 0.525381252540327 0.737309373729836 137 0.298957615224638 0.597915230449275 0.701042384775362 138 0.307974903567051 0.615949807134102 0.69202509643295 139 0.328331373504199 0.656662747008397 0.671668626495801 140 0.265316978126099 0.530633956252198 0.734683021873901 141 0.208208703930898 0.416417407861796 0.791791296069102 142 0.158048550232565 0.31609710046513 0.841951449767435 143 0.184447031478692 0.368894062957384 0.815552968521308 144 0.173591647090987 0.347183294181975 0.826408352909013 145 0.156255031298021 0.312510062596041 0.84374496870198 146 0.273200771077995 0.546401542155991 0.726799228922005 147 0.239791906503731 0.479583813007462 0.760208093496269 148 0.159221051012305 0.318442102024611 0.840778948987695 149 0.11258941786019 0.22517883572038 0.88741058213981 150 0.16099946030146 0.321998920602921 0.83900053969854 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 = 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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