WS7 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: Thu, 02 Dec 2010 22:26:08 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328665xhqel1s5bui5mf8.htm/, Retrieved Thu, 02 Dec 2010 23:24:35 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328665xhqel1s5bui5mf8.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:

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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 22 12 7 7 4 22 28 14 15 13 8 14 16 17 9 12 9 24 25 21 10 13 6 24 24 19 12 14 7 24 28 18 13 8 9 24 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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Org[t] = + 16.2504142572588 -0.0582729173029758concern[t] + 0.200529531559346doubts[t] -0.149647777746776Par_Crit[t] -0.260030170005169Par_Stan[t] + 0.414285431761517Pers_Stand[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) 16.2504142572588 2.023595 8.0305 0 0 concern -0.0582729173029758 0.063966 -0.911 0.363786 0.181893 doubts 0.200529531559346 0.114083 1.7577 0.080873 0.040436 Par_Crit -0.149647777746776 0.108521 -1.379 0.169998 0.084999 Par_Stan -0.260030170005169 0.133749 -1.9442 0.053786 0.026893 Pers_Stand 0.414285431761517 0.077239 5.3637 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.470562869770772 R-squared 0.221429414406904 Adjusted R-squared 0.194947421699656 F-TEST (value) 8.3615087752176 F-TEST (DF numerator) 5 F-TEST (DF denominator) 147 p-value 5.56403168650021e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.51408284048418 Sum Squared Residuals 1815.27039683845 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 25 24.7611407855955 0.238859214404524 2 21 22.5459799328075 -1.54597993280755 3 22 21.8368420677031 0.163157932296894 4 25 22.3999612765086 2.60003872349135 5 24 20.1730133445138 3.82698665548617 6 18 19.7853381763504 -1.78533817635044 7 22 18.4822276329217 3.51777236707831 8 15 20.6597038951926 -5.65970389519259 9 22 23.384343360126 -1.38434336012602 10 28 24.2541266871992 3.74587331280083 11 20 22.2586267469163 -2.25862674691634 12 12 19.0541858795943 -7.05418587959432 13 24 21.4392482506961 2.5607517493039 14 20 21.3755881014603 -1.37558810146028 15 21 23.2271563087225 -2.22715630872253 16 20 20.6236097714002 -0.623609771400234 17 21 19.2274108828772 1.77258911712277 18 23 21.1317858968956 1.86821410310437 19 28 21.9083953956296 6.09160460437044 20 24 21.8658605671527 2.13413943284727 21 24 23.4419598030387 0.558040196961282 22 24 20.4171793406447 3.58282065935532 23 23 21.9813902489090 1.01860975109104 24 23 22.6732178151566 0.326782184843355 25 29 24.3072843318668 4.69271566813318 26 24 21.9193423359088 2.08065766409124 27 18 24.9616099261505 -6.96160992615047 28 25 26.0389768705303 -1.03897687053027 29 21 22.5373924894386 -1.53739248943859 30 26 26.7014199098452 -0.701419909845158 31 22 25.2262139029839 -3.22621390298393 32 22 22.6482669942283 -0.648266994228331 33 22 22.5780053320943 -0.578005332094254 34 23 25.5982387014831 -2.59823870148311 35 30 22.8453726236092 7.15462737639082 36 23 22.6949712361640 0.305028763835966 37 17 18.681835079817 -1.68183507981698 38 23 23.7271609472060 -0.727160947206039 39 23 24.2849533150831 -1.28495331508312 40 25 22.3420165964008 2.65798340359919 41 24 20.6541365362309 3.34586346376907 42 24 27.4849442247080 -3.48494422470804 43 23 23.0469160721013 -0.04691607210127 44 21 23.7104629834278 -2.7104629834278 45 24 25.6839962740913 -1.68399627409135 46 24 21.8302469038286 2.16975309617141 47 28 21.4999451690205 6.50005483097953 48 16 21.0888634862036 -5.08886348620361 49 20 19.8594217120698 0.140578287930204 50 29 23.4090379869267 5.59096201307328 51 27 23.8691119249836 3.13088807501638 52 22 23.1516113693736 -1.15161136937356 53 28 23.9814703450438 4.01852965495617 54 16 20.2168699623192 -4.21686996231917 55 25 22.8713459464109 2.12865405358905 56 24 23.4692265410271 0.530773458972877 57 28 23.5771534909998 4.42284650900018 58 24 24.2137822663325 -0.213782266332461 59 23 22.598127198051 0.401872801949008 60 30 26.9621920374856 3.03780796251444 61 24 21.4361026568388 2.56389734316115 62 21 24.1080387993479 -3.10803879934794 63 25 23.1476063177736 1.85239368222639 64 25 23.9215496371342 1.07845036286582 65 22 20.8927329374831 1.10726706251687 66 23 22.4809474897711 0.51905251022889 67 26 22.9077109835165 3.09228901648351 68 23 21.5430156898788 1.45698431012120 69 25 23.0923222992209 1.90767770077914 70 21 21.3251264171115 -0.325126417111538 71 25 23.4946717104038 1.50532828959624 72 24 22.1119764528605 1.88802354713950 73 29 23.5014290002202 5.49857099977976 74 22 23.6761310832272 -1.67613108322715 75 27 23.5289635843994 3.47103641560060 76 26 19.7211643598513 6.27883564014874 77 22 21.2787981053279 0.721201894672111 78 24 22.0516618137119 1.94833818628808 79 27 23.09164073259 3.90835926740998 80 24 21.3036408422949 2.6963591577051 81 24 24.8571231300489 -0.85712313004888 82 29 24.2852275102976 4.71477248970239 83 22 22.1760467850279 -0.176046785027854 84 21 20.5753919610441 0.424608038955942 85 24 20.4102739406619 3.58972605933811 86 24 21.7843927034894 2.21560729651058 87 23 21.919743917763 1.080256082237 88 20 22.2830872047076 -2.28308720470756 89 27 21.4015614242620 5.59843857573795 90 26 23.4434175800843 2.55658241991572 91 25 21.9170799743066 3.0829200256934 92 21 20.0533555932319 0.946644406768094 93 21 20.7891478612462 0.210852138753771 94 19 20.4051806931447 -1.40518069314470 95 21 21.5989790391454 -0.598979039145424 96 21 21.2954960691061 -0.295496069106128 97 16 19.7318208532233 -3.73182085322335 98 22 20.6607136990186 1.33928630098142 99 29 21.7568319810854 7.24316801891464 100 15 21.6975807012207 -6.6975807012207 101 17 20.7713680505745 -3.77136805057448 102 15 19.9823304187306 -4.98233041873058 103 21 21.6102357290102 -0.61023572901017 104 21 20.9255152283695 0.07448477163047 105 19 19.2811141064587 -0.281114106458668 106 24 18.1654201129471 5.83457988705285 107 20 22.3666077388697 -2.36660773886969 108 17 25.1432962877541 -8.14329628775415 109 23 24.8858986199411 -1.88589861994107 110 24 22.3767059391439 1.62329406085607 111 14 22.0792882301598 -8.07928823015977 112 19 22.8442971257394 -3.84429712573941 113 24 22.1302960690205 1.86970393097949 114 13 20.4391884692570 -7.43918846925697 115 22 25.4500906041767 -3.45009060417669 116 16 21.0672860791183 -5.06728607911828 117 19 23.1775585539504 -4.17755855395043 118 25 22.8081976989076 2.19180230109235 119 25 24.0078492511477 0.99215074885234 120 23 21.3665212436075 1.63347875639255 121 24 23.5582377914539 0.441762208546083 122 26 23.5072642053727 2.49273579462734 123 26 21.4714507098892 4.52854929011079 124 25 24.1798757386350 0.820124261364955 125 18 22.3113323052576 -4.31133230525765 126 21 19.8753655796270 1.12463442037305 127 26 23.6468289724169 2.35317102758312 128 23 21.9924709248516 1.00752907514835 129 23 19.7845305246714 3.21546947532858 130 22 22.5203662884652 -0.520366288465208 131 20 22.3238545065533 -2.32385450655328 132 13 22.0221575507547 -9.02215755075468 133 24 21.4279601195671 2.57203988043295 134 15 21.5134079425897 -6.51340794258974 135 14 23.1511035807478 -9.1511035807478 136 22 24.0778402717124 -2.07784027171239 137 10 17.5671216847841 -7.56712168478412 138 24 24.3869347400251 -0.386934740025127 139 22 21.7577877429307 0.242212257069307 140 24 25.7483722427375 -1.74837224273750 141 19 21.7215716471969 -2.72157164719692 142 20 22.1233790169746 -2.12337901697458 143 13 17.1296228190527 -4.12962281905268 144 20 20.1629843757919 -0.162984375791931 145 22 23.2736867726531 -1.27368677265314 146 24 23.2954896360117 0.704510363988297 147 29 23.2933312452641 5.70666875473591 148 12 20.9893491556104 -8.98934915561044 149 20 20.8602833556258 -0.860283355625828 150 21 21.4303615198721 -0.430361519872093 151 24 23.6426694616269 0.35733053837311 152 22 21.8445551193649 0.155444880635079 153 20 17.6914881684905 2.30851183150953 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.767979555951333 0.464040888097334 0.232020444048667 10 0.675811848431852 0.648376303136295 0.324188151568148 11 0.542151194213988 0.915697611572025 0.457848805786012 12 0.7238431430688 0.5523137138624 0.2761568569312 13 0.626301165161906 0.747397669676188 0.373698834838094 14 0.638507095284056 0.722985809431887 0.361492904715944 15 0.544115332648313 0.911769334703373 0.455884667351687 16 0.456966628594336 0.913933257188672 0.543033371405664 17 0.372645358615889 0.745290717231779 0.62735464138411 18 0.418609356911593 0.837218713823186 0.581390643088407 19 0.622615456537736 0.754769086924529 0.377384543462264 20 0.54817640833451 0.90364718333098 0.45182359166549 21 0.476671190790816 0.953342381581631 0.523328809209184 22 0.458372670067483 0.916745340134966 0.541627329932517 23 0.388681697425425 0.77736339485085 0.611318302574575 24 0.320254432017438 0.640508864034877 0.679745567982562 25 0.328487748921556 0.656975497843112 0.671512251078444 26 0.275777889699292 0.551555779398584 0.724222110300708 27 0.543245153161149 0.913509693677703 0.456754846838851 28 0.508995679199038 0.982008641601924 0.491004320800962 29 0.465364475428411 0.930728950856822 0.534635524571589 30 0.402141764814656 0.804283529629311 0.597858235185344 31 0.387614561083806 0.775229122167612 0.612385438916194 32 0.330500847041665 0.661001694083329 0.669499152958335 33 0.277948661822004 0.555897323644007 0.722051338177996 34 0.246446588237007 0.492893176474015 0.753553411762993 35 0.424900456135902 0.849800912271804 0.575099543864098 36 0.367960967711573 0.735921935423147 0.632039032288427 37 0.331012742665183 0.662025485330366 0.668987257334817 38 0.281555558260043 0.563111116520085 0.718444441739957 39 0.241175225598946 0.482350451197891 0.758824774401054 40 0.222304127596174 0.444608255192349 0.777695872403826 41 0.211330001414379 0.422660002828758 0.788669998585621 42 0.192994981199642 0.385989962399284 0.807005018800358 43 0.157377555342102 0.314755110684205 0.842622444657898 44 0.142822631369638 0.285645262739276 0.857177368630362 45 0.117781726541127 0.235563453082254 0.882218273458873 46 0.0998002956492169 0.199600591298434 0.900199704350783 47 0.166411125094085 0.332822250188170 0.833588874905915 48 0.202775999911146 0.405551999822293 0.797224000088854 49 0.195549101079359 0.391098202158718 0.80445089892064 50 0.261833255380224 0.523666510760449 0.738166744619776 51 0.252151741303299 0.504303482606598 0.747848258696701 52 0.216982170448912 0.433964340897824 0.783017829551088 53 0.230459308227441 0.460918616454883 0.769540691772559 54 0.253432136897946 0.506864273795891 0.746567863102054 55 0.223965243053121 0.447930486106241 0.77603475694688 56 0.188751320204082 0.377502640408163 0.811248679795918 57 0.208408972367161 0.416817944734321 0.79159102763284 58 0.175570920137438 0.351141840274875 0.824429079862562 59 0.145378224737635 0.29075644947527 0.854621775262365 60 0.140003099965024 0.280006199930048 0.859996900034976 61 0.125631810202500 0.251263620405000 0.8743681897975 62 0.125676973115518 0.251353946231037 0.874323026884481 63 0.108271843646489 0.216543687292977 0.891728156353511 64 0.0885262480686746 0.177052496137349 0.911473751931325 65 0.0717043804573877 0.143408760914775 0.928295619542612 66 0.0566901341068237 0.113380268213647 0.943309865893176 67 0.0525936861653169 0.105187372330634 0.947406313834683 68 0.0423119605064039 0.0846239210128078 0.957688039493596 69 0.0350574658614819 0.0701149317229639 0.964942534138518 70 0.0269424960833941 0.0538849921667881 0.973057503916606 71 0.0214298478031956 0.0428596956063911 0.978570152196804 72 0.0171823457898093 0.0343646915796186 0.98281765421019 73 0.0259380918570014 0.0518761837140028 0.974061908142999 74 0.02075385716253 0.04150771432506 0.97924614283747 75 0.0203661946291400 0.0407323892582801 0.97963380537086 76 0.0353989557149713 0.0707979114299427 0.964601044285029 77 0.027328057387103 0.054656114774206 0.972671942612897 78 0.0227194688935897 0.0454389377871793 0.97728053110641 79 0.025131084734482 0.050262169468964 0.974868915265518 80 0.0224249730591749 0.0448499461183498 0.977575026940825 81 0.0170982981137625 0.0341965962275249 0.982901701886238 82 0.0224541849149598 0.0449083698299195 0.97754581508504 83 0.0177699581770900 0.0355399163541800 0.98223004182291 84 0.0133253529188386 0.0266507058376772 0.986674647081161 85 0.0135039329439484 0.0270078658878968 0.986496067056052 86 0.0117321259468524 0.0234642518937049 0.988267874053148 87 0.00900683612513828 0.0180136722502766 0.990993163874862 88 0.00745507708165762 0.0149101541633152 0.992544922918342 89 0.0133513887929268 0.0267027775858536 0.986648611207073 90 0.0120811413076070 0.0241622826152139 0.987918858692393 91 0.0115499613247419 0.0230999226494838 0.988450038675258 92 0.0088468558438529 0.0176937116877058 0.991153144156147 93 0.00654731977080885 0.0130946395416177 0.993452680229191 94 0.00505441190975094 0.0101088238195019 0.99494558809025 95 0.00375649093030542 0.00751298186061084 0.996243509069695 96 0.00268387163816979 0.00536774327633958 0.99731612836183 97 0.00287319771172776 0.00574639542345552 0.997126802288272 98 0.00225014462791089 0.00450028925582178 0.99774985537209 99 0.00937911180684557 0.0187582236136911 0.990620888193154 100 0.0209916711839556 0.0419833423679112 0.979008328816044 101 0.021306242833305 0.04261248566661 0.978693757166695 102 0.0274860402760212 0.0549720805520424 0.972513959723979 103 0.0213505366019137 0.0427010732038274 0.978649463398086 104 0.0157197812768646 0.0314395625537292 0.984280218723135 105 0.0114707337812696 0.0229414675625392 0.98852926621873 106 0.0272197695570097 0.0544395391140195 0.97278023044299 107 0.0253672579831398 0.0507345159662795 0.97463274201686 108 0.0698603259151817 0.139720651830363 0.930139674084818 109 0.0600833163676239 0.120166632735248 0.939916683632376 110 0.0492439476513905 0.098487895302781 0.95075605234861 111 0.138887553787551 0.277775107575103 0.861112446212449 112 0.134100688374156 0.268201376748312 0.865899311625844 113 0.119828211826683 0.239656423653367 0.880171788173317 114 0.205868671985575 0.411737343971151 0.794131328014425 115 0.197797609300692 0.395595218601384 0.802202390699308 116 0.233303725380225 0.46660745076045 0.766696274619775 117 0.226271796073788 0.452543592147577 0.773728203926212 118 0.22535229390359 0.45070458780718 0.77464770609641 119 0.206268070714544 0.412536141429088 0.793731929285456 120 0.170817063245292 0.341634126490584 0.829182936754708 121 0.136061235870412 0.272122471740824 0.863938764129588 122 0.140478746435491 0.280957492870983 0.859521253564509 123 0.197686394380411 0.395372788760823 0.802313605619589 124 0.172534223769342 0.345068447538684 0.827465776230658 125 0.153362129099558 0.306724258199116 0.846637870900442 126 0.134647415111445 0.269294830222889 0.865352584888555 127 0.124951439090553 0.249902878181106 0.875048560909447 128 0.103907361155283 0.207814722310566 0.896092638844717 129 0.139537176285867 0.279074352571734 0.860462823714133 130 0.106245566688325 0.212491133376651 0.893754433311675 131 0.0796638677371195 0.159327735474239 0.92033613226288 132 0.192529173994852 0.385058347989704 0.807470826005148 133 0.26641431136164 0.53282862272328 0.73358568863836 134 0.247169719269558 0.494339438539116 0.752830280730442 135 0.493680575961812 0.987361151923624 0.506319424038188 136 0.445101158082741 0.890202316165482 0.554898841917259 137 0.753249111525827 0.493501776948347 0.246750888474173 138 0.703270905853057 0.593458188293885 0.296729094146943 139 0.604749686879308 0.790500626241385 0.395250313120692 140 0.541621502742614 0.916756994514771 0.458378497257386 141 0.56393158369546 0.87213683260908 0.43606841630454 142 0.436390663689313 0.872781327378627 0.563609336310687 143 0.342987203516609 0.685974407033219 0.65701279648339 144 0.245804415732924 0.491608831465847 0.754195584267076 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 4 0.0294117647058824 NOK 5% type I error level 30 0.220588235294118 NOK 10% type I error level 41 0.301470588235294 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328665xhqel1s5bui5mf8/10n7ox1291328757.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328665xhqel1s5bui5mf8/10n7ox1291328757.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328665xhqel1s5bui5mf8/19f8o1291328757.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328665xhqel1s5bui5mf8/19f8o1291328757.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328665xhqel1s5bui5mf8/29f8o1291328757.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328665xhqel1s5bui5mf8/29f8o1291328757.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328665xhqel1s5bui5mf8/39f8o1291328757.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328665xhqel1s5bui5mf8/39f8o1291328757.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328665xhqel1s5bui5mf8/4j6qr1291328757.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328665xhqel1s5bui5mf8/4j6qr1291328757.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328665xhqel1s5bui5mf8/5j6qr1291328757.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328665xhqel1s5bui5mf8/5j6qr1291328757.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328665xhqel1s5bui5mf8/6j6qr1291328757.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328665xhqel1s5bui5mf8/6j6qr1291328757.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328665xhqel1s5bui5mf8/7uf7u1291328757.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328665xhqel1s5bui5mf8/7uf7u1291328757.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328665xhqel1s5bui5mf8/8n7ox1291328757.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328665xhqel1s5bui5mf8/8n7ox1291328757.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328665xhqel1s5bui5mf8/9n7ox1291328757.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328665xhqel1s5bui5mf8/9n7ox1291328757.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') }

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Software written by Ed van Stee & Patrick Wessa

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