Paper 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: Sat, 18 Dec 2010 14:35:02 +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/18/t129268279267pija2gejfqtkp.htm/, Retrieved Sat, 18 Dec 2010 15:33:12 +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/18/t129268279267pija2gejfqtkp.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 «

41 25 15 9 3 38 25 15 9 4 37 19 14 9 4 42 18 10 8 4 40 23 18 15 3 43 25 14 9 4 40 23 11 11 4 45 30 17 6 5 45 32 21 10 4 44 25 7 11 4 42 26 18 16 4 32 25 13 11 5 32 25 13 11 5 41 35 18 7 4 38 20 12 10 4 38 21 9 9 4 24 23 11 15 3 46 17 11 6 5 42 27 16 12 4 46 25 12 10 4 43 18 14 14 5 38 22 13 9 4 39 23 17 14 4 40 25 13 14 3 37 19 13 9 2 41 20 12 8 4 46 26 12 10 4 26 16 12 9 3 37 22 9 9 3 39 25 17 9 4 44 29 18 11 5 38 22 12 10 2 38 32 12 8 0 38 23 9 14 4 33 18 13 10 3 43 26 11 14 4 41 14 13 15 2 49 20 6 8 4 45 25 11 10 5 31 21 18 13 3 30 21 18 13 3 38 23 15 10 4 39 24 11 11 4 40 21 14 10 4 36 17 12 16 2 49 29 8 6 5 41 25 11 11 4 18 16 10 12 2 42 25 17 14 3 41 25 16 9 5 43 21 13 11 4 46 23 15 8 3 41 25 16 8 5 39 25 7 11 4 42 24 16 16 4 35 21 13 12 5 36 22 15 14 3 48 14 12 8 4 41 20 12 10 4 47 21 24 14 3 41 22 15 10 3 31 19 8 5 5 36 28 18 12 4 46 25 17 9 4 44 21 15 8 4 43 27 11 16 2 40 19 12 13 5 40 20 14 8 3 46 17 11 14 3 39 22 10 8 4 44 26 11 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 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation StudyForCareer[t] = + 32.5202067294365 + 0.174192543560943PersonalStandards[t] + 0.0466789923587195ParentalExpectations[t] -0.217373134461697Doubts[t] + 1.39806533965884LeaderPreference[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) 32.5202067294365 3.250358 10.0051 0 0 PersonalStandards 0.174192543560943 0.10383 1.6777 0.095627 0.047814 ParentalExpectations 0.0466789923587195 0.127944 0.3648 0.715779 0.357889 Doubts -0.217373134461697 0.154972 -1.4027 0.162915 0.081457 LeaderPreference 1.39806533965884 0.482225 2.8992 0.00434 0.00217 Multiple Linear Regression - Regression Statistics Multiple R 0.367916033517428 R-squared 0.135362207719197 Adjusted R-squared 0.110833476023288 F-TEST (value) 5.51851638304525 F-TEST (DF numerator) 4 F-TEST (DF denominator) 141 p-value 0.000371345161075842 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.98212870492208 Sum Squared Residuals 3499.84650696961 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 41 39.8130430126621 1.18695698733793 2 38 41.2111083523209 -3.21110835232092 3 37 40.1192740985965 -3.11927409859654 4 42 39.9757387200624 2.02426127993759 5 40 38.3004560958462 1.69954390415383 6 43 41.1644293599622 1.8355706400378 7 40 40.2412610268408 -0.241261026840763 8 45 44.225613797887 0.774386202112998 9 45 42.4931569769381 2.50684302306185 10 44 40.4029301445278 3.59706985547223 11 42 40.0037259317261 1.99627406827385 12 32 42.0810694383389 -10.0810694383389 13 32 42.0810694383389 -10.0810694383389 14 41 43.5278170339299 -2.52781703392991 15 38 39.9827355229783 -1.98273552297835 16 38 40.2342642239248 -2.23426422392483 17 24 37.9737031493351 -13.9737031493351 18 46 41.6810367774424 4.31896322255758 19 42 40.9540530284164 1.04594697158356 20 46 40.8536982407831 5.14630175921693 21 43 40.2562812223860 2.74371877761405 22 38 40.5951727369207 -2.59517273692065 23 39 39.869215577608 -0.86921557760799 24 40 38.6328193556362 1.36718064436384 25 37 37.2764644269201 -0.276464426920151 26 41 40.4174817919017 0.582518208098259 27 46 41.027890784344 4.97210921565599 28 26 38.1052731435374 -12.1052731435374 29 37 39.0103914278269 -2.01039142782694 30 39 41.3044663370384 -2.30446633703836 31 44 43.0112345743763 0.988765425623704 32 38 37.5349899307826 0.465010069217436 33 38 36.9155309559977 1.08446904400228 34 38 39.4957836387382 -1.49578363873823 35 33 38.2829640885563 -5.28296408855634 36 43 40.1117192541385 2.88828074586150 37 41 35.1012629023453 5.89873709765475 38 49 40.1374078377494 8.86259216225058 39 45 42.2050845880832 2.79491541191682 40 31 38.3868172776477 -7.38681727764769 41 30 38.3868172776477 -8.38681727764768 42 38 40.6453501307373 -2.64535013073734 43 39 40.4154535704017 -1.41545357040171 44 40 40.2502860512567 -0.250286051256730 45 36 35.3597884062077 0.640211593792333 46 49 43.6313103230976 5.36868967690242 47 41 40.5896461139627 0.41035388603735 48 18 35.9617304157761 -17.9617304157761 49 42 38.8195353250710 3.18046467492896 50 41 42.6558526843385 -1.65585268433848 51 43 39.9862339244363 3.01376607556369 52 46 39.6820310600019 6.31796893999811 53 41 42.8732258188002 -1.87322581880017 54 39 40.4029301445278 -1.40293014452777 55 42 39.5619828598868 2.43801714011318 56 35 41.1669261296335 -6.16692612963345 57 36 38.2035997096708 -2.20359970967077 58 48 39.3723265305361 8.62767346946392 59 41 39.9827355229783 1.01726447702165 60 47 38.4495180973383 8.5504819026617 61 41 39.0730922475176 1.92690775248244 62 31 42.1067580219498 -11.1067580219498 63 36 41.2216035566948 -5.22160355669482 64 46 41.3044663370384 4.69553366296164 65 44 40.7317113125388 3.26828868746116 66 43 37.0550348494584 5.94496515054162 67 40 40.5544889156912 -0.55448891569115 68 40 39.1127744369603 0.887225563039656 69 46 37.1459210224312 8.85407897756882 70 39 40.6725088943062 -1.67250889430619 71 44 41.6333311953704 2.36666880462962 72 38 36.4466540785161 1.55334592148385 73 39 39.7011913888681 -0.7011913888681 74 41 42.9575587791016 -1.95755877910164 75 39 38.6794983479949 0.320501652005117 76 40 39.5605126799289 0.439487320071111 77 44 40.2558126742147 3.74418732578527 78 42 39.4998400817383 2.50015991826170 79 46 42.6538244628384 3.34617553716156 80 44 40.027386293837 3.97261370616297 81 37 40.5088115551191 -3.50881155511914 82 39 37.1936016465766 1.80639835342339 83 40 38.2809358670563 1.71906413294369 84 42 38.8195353250710 3.18046467492896 85 37 38.9295568689834 -1.92955686898343 86 33 37.8422226485037 -4.84222264850373 87 35 39.9290597277037 -4.9290597277037 88 42 35.6620525425129 6.33794745748706 89 36 35.8753692339746 0.124630766025435 90 44 39.4957836387382 4.50421636126177 91 45 39.7633341670166 5.23666583298338 92 47 41.0635165307867 5.93648346921328 93 40 41.0835948011187 -1.08359480111870 94 49 38.6840233391662 10.3159766608338 95 48 44.1176204754746 3.88237952452535 96 29 40.7136612637069 -11.7136612637069 97 45 41.6393263664996 3.3606736335004 98 29 36.4536508814321 -7.45365088143208 99 41 40.374301201001 0.625698798999012 100 34 37.0445396450845 -3.04453964508448 101 38 36.0781907210623 1.92180927893771 102 37 37.8823733861177 -0.882373386117737 103 48 44.0444244514101 3.95557554858987 104 39 40.9345327996266 -1.93453279962657 105 34 40.4384722006495 -6.43847220064954 106 35 36.4898346694169 -1.48983466941690 107 41 40.0680701150665 0.931929884933467 108 43 39.3256475381774 3.67435246182264 109 41 38.4536582306593 2.54634176934068 110 39 36.0405367531195 2.95946324688046 111 36 40.9992618408172 -4.99926184081723 112 32 41.5414433906109 -9.54144339061087 113 46 39.9772089000203 6.02279109997965 114 42 40.8968788316838 1.10312116831618 115 42 36.2669349119972 5.7330650880028 116 45 39.3517797120329 5.64822028796711 117 39 40.7261846895808 -1.72618468958084 118 45 41.018865759928 3.98113424007196 119 48 42.3722803287282 5.62771967127181 120 28 38.2422802673268 -10.2422802673268 121 35 37.5314915293246 -2.53149152932460 122 38 38.9460472444866 -0.946047244486552 123 42 38.3592986141552 3.64070138584483 124 36 38.1032449220374 -2.1032449220374 125 37 40.7191878866649 -3.71918788666491 126 38 39.0625970431437 -1.06259704314366 127 43 40.7492033198287 2.25079668017132 128 35 34.6519649860479 0.348035013952111 129 36 39.7186833961579 -3.71868339615793 130 33 36.2814865593712 -3.28148655937117 131 39 38.1559190855253 0.844080914474662 132 32 41.1157221461035 -9.11572214610345 133 45 39.1936089958038 5.80639100419615 134 35 39.7618639870587 -4.76186398705869 135 38 37.7046824410988 0.295317558901173 136 36 37.3542691324769 -1.35426913247690 137 42 38.0620925526367 3.93790744736332 138 41 39.4204757028527 1.57952429714727 139 47 38.7748845542124 8.22511544578764 140 35 38.5540130182927 -3.55401301829269 141 43 37.668498653114 5.33150134688599 142 40 40.1061926311805 -0.106192631180502 143 46 40.6760072957642 5.32399270423585 144 44 41.6393263664996 2.3606736335004 145 35 38.674529766579 -3.67452976657898 146 29 39.6016650493296 -10.6016650493296 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.211144988549241 0.422289977098482 0.788855011450759 9 0.111204897243954 0.222409794487908 0.888795102756046 10 0.0502884049673851 0.100576809934770 0.949711595032615 11 0.0212602482154377 0.0425204964308755 0.978739751784562 12 0.192290413768224 0.384580827536449 0.807709586231776 13 0.231293043209833 0.462586086419666 0.768706956790167 14 0.255249312648083 0.510498625296166 0.744750687351917 15 0.180676729451007 0.361353458902013 0.819323270548993 16 0.128274169695408 0.256548339390816 0.871725830304592 17 0.679868795705663 0.640262408588674 0.320131204294337 18 0.663319813184605 0.67336037363079 0.336680186815395 19 0.618337117238858 0.763325765522284 0.381662882761142 20 0.671881454063035 0.65623709187393 0.328118545936965 21 0.671262670948337 0.657474658103327 0.328737329051663 22 0.621090935446778 0.757818129106445 0.378909064553222 23 0.550426900391233 0.899146199217533 0.449573099608767 24 0.511979370747205 0.97604125850559 0.488020629252795 25 0.454236686571703 0.908473373143405 0.545763313428297 26 0.386715577315803 0.773431154631606 0.613284422684197 27 0.424136510039853 0.848273020079705 0.575863489960147 28 0.69628235846549 0.60743528306902 0.30371764153451 29 0.640231777210623 0.719536445578753 0.359768222789377 30 0.591074062981263 0.817851874037474 0.408925937018737 31 0.530652495859616 0.938695008280767 0.469347504140384 32 0.478851326918952 0.957702653837904 0.521148673081048 33 0.421391285530851 0.842782571061702 0.578608714469149 34 0.365571674487605 0.73114334897521 0.634428325512395 35 0.345391042076974 0.690782084153947 0.654608957923026 36 0.322025043891542 0.644050087783083 0.677974956108458 37 0.395735879350952 0.791471758701904 0.604264120649048 38 0.535998950473374 0.928002099053252 0.464001049526626 39 0.496411765229113 0.992823530458226 0.503588234770887 40 0.524110218303416 0.951779563393168 0.475889781696584 41 0.570177933069157 0.859644133861685 0.429822066930843 42 0.524641418150203 0.950717163699594 0.475358581849797 43 0.474980159035253 0.949960318070505 0.525019840964747 44 0.423320396491331 0.846640792982662 0.576679603508669 45 0.382275731324778 0.764551462649555 0.617724268675222 46 0.366717354501770 0.733434709003539 0.63328264549823 47 0.317838382665456 0.635676765330913 0.682161617334544 48 0.812143776736432 0.375712446527137 0.187856223263568 49 0.80377458342874 0.392450833142519 0.196225416571259 50 0.769503249021533 0.460993501956935 0.230496750978467 51 0.751937998111825 0.49612400377635 0.248062001888175 52 0.790311069146664 0.419377861706672 0.209688930853336 53 0.75704053086572 0.485918938268561 0.242959469134280 54 0.722854274390379 0.554291451219242 0.277145725609621 55 0.696471550591164 0.607056898817673 0.303528449408836 56 0.71290417665301 0.574191646693981 0.287095823346990 57 0.677569477659864 0.644861044680271 0.322430522340136 58 0.784881382096143 0.430237235807714 0.215118617903857 59 0.749640284969128 0.500719430061744 0.250359715030872 60 0.828024937265629 0.343950125468742 0.171975062734371 61 0.800503411148002 0.398993177703996 0.199496588851998 62 0.902822837906015 0.19435432418797 0.097177162093985 63 0.9052599087267 0.189480182546601 0.0947400912733006 64 0.901622446206385 0.196755107587230 0.0983775537936151 65 0.888648330686705 0.22270333862659 0.111351669313295 66 0.902001990407219 0.195996019185562 0.097998009592781 67 0.88124819199468 0.237503616010641 0.118751808005321 68 0.85665259574108 0.286694808517839 0.143347404258920 69 0.909098592902311 0.181802814195377 0.0909014070976885 70 0.890265408306505 0.21946918338699 0.109734591693495 71 0.871481759943171 0.257036480113657 0.128518240056829 72 0.847774282187795 0.304451435624411 0.152225717812205 73 0.820345477268222 0.359309045463556 0.179654522731778 74 0.792545626812585 0.414908746374831 0.207454373187415 75 0.756437044631628 0.487125910736745 0.243562955368372 76 0.717305200987059 0.565389598025882 0.282694799012941 77 0.696931989804292 0.606136020391417 0.303068010195708 78 0.662418490152515 0.675163019694969 0.337581509847485 79 0.637298729453513 0.725402541092973 0.362701270546487 80 0.620042446233309 0.759915107533382 0.379957553766691 81 0.595007313887585 0.80998537222483 0.404992686112415 82 0.556224576252806 0.887550847494388 0.443775423747194 83 0.514042487964941 0.971915024070118 0.485957512035059 84 0.493456865259944 0.986913730519888 0.506543134740056 85 0.451054676532615 0.90210935306523 0.548945323467385 86 0.44087417104331 0.88174834208662 0.55912582895669 87 0.453816629939531 0.907633259879062 0.546183370060469 88 0.476541447790919 0.953082895581837 0.523458552209081 89 0.427437835153116 0.854875670306232 0.572562164846884 90 0.41434874540049 0.82869749080098 0.58565125459951 91 0.41911231815461 0.83822463630922 0.58088768184539 92 0.45403997932663 0.90807995865326 0.54596002067337 93 0.405400525210463 0.810801050420927 0.594599474789537 94 0.576404576700969 0.847190846598063 0.423595423299031 95 0.603263683900706 0.793472632198587 0.396736316099294 96 0.822141942597587 0.355716114804826 0.177858057402413 97 0.802156815743445 0.395686368513110 0.197843184256555 98 0.829999507945019 0.340000984109962 0.170000492054981 99 0.794354573496595 0.41129085300681 0.205645426503405 100 0.775574839772855 0.448850320454289 0.224425160227145 101 0.736071191293159 0.527857617413682 0.263928808706841 102 0.693078195579675 0.613843608840651 0.306921804420326 103 0.682294151739712 0.635411696520577 0.317705848260288 104 0.639926877549822 0.720146244900357 0.360073122450178 105 0.626597576962522 0.746804846074955 0.373402423037478 106 0.586599736022991 0.826800527954019 0.413400263977009 107 0.53365313906841 0.93269372186318 0.46634686093159 108 0.496500502614001 0.993001005228002 0.503499497385999 109 0.449187776508383 0.898375553016767 0.550812223491617 110 0.40144643103838 0.80289286207676 0.59855356896162 111 0.381762670962928 0.763525341925856 0.618237329037072 112 0.567516901573153 0.864966196853694 0.432483098426847 113 0.585356547077123 0.829286905845754 0.414643452922877 114 0.526075409062385 0.94784918187523 0.473924590937615 115 0.531598695000636 0.936802609998728 0.468401304999364 116 0.506609087303489 0.986781825393021 0.493390912696511 117 0.450507050427387 0.901014100854774 0.549492949572613 118 0.415076569148514 0.830153138297029 0.584923430851486 119 0.430769205591751 0.861538411183503 0.569230794408249 120 0.624033411038418 0.751933177923164 0.375966588961582 121 0.569913020226775 0.86017395954645 0.430086979773225 122 0.500337197811327 0.999325604377346 0.499662802188673 123 0.459886339610148 0.919772679220296 0.540113660389852 124 0.398858539680772 0.797717079361544 0.601141460319228 125 0.357068103512239 0.714136207024479 0.64293189648776 126 0.297704066501127 0.595408133002254 0.702295933498873 127 0.282099493345237 0.564198986690474 0.717900506654763 128 0.219336978578568 0.438673957157135 0.780663021421433 129 0.190835118970411 0.381670237940822 0.809164881029589 130 0.185449569254518 0.370899138509036 0.814550430745482 131 0.145699568027308 0.291399136054615 0.854300431972692 132 0.294841984767451 0.589683969534902 0.705158015232549 133 0.222658914217525 0.445317828435050 0.777341085782475 134 0.216604687971725 0.43320937594345 0.783395312028275 135 0.151416674285676 0.302833348571352 0.848583325714324 136 0.108566874284727 0.217133748569455 0.891433125715273 137 0.0613836461685375 0.122767292337075 0.938616353831462 138 0.0354848615253590 0.0709697230507181 0.964515138474641 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 0.00763358778625954 OK 10% type I error level 2 0.0152671755725191 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/18/t129268279267pija2gejfqtkp/10762m1292682892.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t129268279267pija2gejfqtkp/10762m1292682892.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t129268279267pija2gejfqtkp/10n5t1292682892.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t129268279267pija2gejfqtkp/10n5t1292682892.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t129268279267pija2gejfqtkp/2teme1292682892.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t129268279267pija2gejfqtkp/2teme1292682892.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t129268279267pija2gejfqtkp/3teme1292682892.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t129268279267pija2gejfqtkp/3teme1292682892.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t129268279267pija2gejfqtkp/4teme1292682892.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t129268279267pija2gejfqtkp/4teme1292682892.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t129268279267pija2gejfqtkp/5teme1292682892.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t129268279267pija2gejfqtkp/5teme1292682892.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t129268279267pija2gejfqtkp/6464z1292682892.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t129268279267pija2gejfqtkp/6464z1292682892.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t129268279267pija2gejfqtkp/7ff311292682892.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t129268279267pija2gejfqtkp/7ff311292682892.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t129268279267pija2gejfqtkp/8ff311292682892.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t129268279267pija2gejfqtkp/8ff311292682892.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t129268279267pija2gejfqtkp/9762m1292682892.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t129268279267pija2gejfqtkp/9762m1292682892.ps (open in new window)

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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