ws 7 5

*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: Wed, 24 Nov 2010 13:43:14 +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/24/t1290606118w69c10s0chw6lai.htm/, Retrieved Wed, 24 Nov 2010 14:41:58 +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/24/t1290606118w69c10s0chw6lai.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 «

27 24 14 11 12 24 23 25 11 7 8 25 25 17 6 17 8 30 23 18 12 10 8 19 19 18 8 12 9 22 29 16 10 12 7 22 25 20 10 11 4 25 21 16 11 11 11 23 22 18 16 12 7 17 25 17 11 13 7 21 24 23 13 14 12 19 18 30 12 16 10 19 22 23 8 11 10 15 15 18 12 10 8 16 22 15 11 11 8 23 28 12 4 15 4 27 20 21 9 9 9 22 12 15 8 11 8 14 24 20 8 17 7 22 20 31 14 17 11 23 21 27 15 11 9 23 20 34 16 18 11 21 21 21 9 14 13 19 23 31 14 10 8 18 28 19 11 11 8 20 24 16 8 15 9 23 24 20 9 15 6 25 24 21 9 13 9 19 23 22 9 16 9 24 23 17 9 13 6 22 29 24 10 9 6 25 24 25 16 18 16 26 18 26 11 18 5 29 25 25 8 12 7 32 21 17 9 17 9 25 26 32 16 9 6 29 22 33 11 9 6 28 22 13 16 12 5 17 22 32 12 18 12 28 23 25 12 12 7 29 30 29 14 18 10 26 23 22 9 14 9 25 17 18 10 15 8 14 23 17 9 16 5 25 23 20 10 10 8 26 25 15 12 11 8 20 24 20 14 14 10 18 24 33 14 9 6 32 23 29 10 12 8 25 21 23 14 17 7 25 24 26 16 5 4 23 24 18 9 12 8 21 28 20 10 12 8 20 16 11 6 6 4 15 20 28 8 24 20 30 29 26 13 12 8 24 27 22 10 12 8 26 22 17 8 14 6 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 7 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation O[t] = + 16.1007876215598 -0.0711082166488146CM[t] + 0.220341505387472D[t] -0.152876682627122PE[t] -0.249255555197606PC[t] + 0.423996843472858PS[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) 16.1007876215598 2.00539 8.0288 0 0 CM -0.0711082166488146 0.063041 -1.128 0.261099 0.130549 D 0.220341505387472 0.112834 1.9528 0.05267 0.026335 PE -0.152876682627122 0.104464 -1.4634 0.145398 0.072699 PC -0.249255555197606 0.130658 -1.9077 0.058305 0.029152 PS 0.423996843472858 0.075759 5.5967 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.471298501870746 R-squared 0.222122277865609 Adjusted R-squared 0.196701437272982 F-TEST (value) 8.7378022397116 F-TEST (DF numerator) 5 F-TEST (DF denominator) 153 p-value 2.60674177576803e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.50596517552417 Sum Squared Residuals 1880.64414723419 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 27 22.9821855694918 4.01781443050821 2 23 24.2825786314523 -1.28257863145234 3 25 24.3409542287986 0.659045771201429 4 23 21.998066544663 1.00193345533700 5 19 21.8336821330798 -2.83368213307984 6 29 22.9150926875476 6.08490731245238 7 25 24.8032936995909 0.196706300409119 8 21 22.7152854982447 -1.71528549824465 9 22 21.9749410692105 0.0250589307894630 10 25 22.4874524501863 2.51254754981370 11 24 20.2543380155075 3.74566198449251 12 18 19.7289967387193 -1.72899673871928 13 22 18.4137842729553 3.58621572704472 14 15 20.7260760142444 -5.72607601424443 15 22 23.5341603804863 -1.53416038048629 16 28 24.2865973568938 3.71340264310620 17 20 22.2993290364022 -2.29932903640223 18 12 19.0571642730681 -7.05716427306815 19 24 21.4255933970418 2.57440660295819 20 20 21.3924266689121 -1.39242666891212 21 21 23.3129722470528 -2.31297224705279 22 20 20.6189146601678 -0.61891466016778 23 21 19.2659328720576 1.73406712794237 24 23 21.0903458955305 1.9096541044695 25 28 21.9777369834725 6.02226301652755 26 24 21.9412653619690 2.05873463803104 27 24 23.4729343532997 0.52706564670029 28 24 20.4158317754752 3.58416822452483 29 23 22.0060777283093 0.993922271690717 30 23 22.7200218380818 0.279978161918176 31 29 24.3261030878547 4.67389691214535 32 24 22.1325950513834 1.86740494861663 33 18 24.9735809453894 -6.97358094538944 34 25 26.0744041616619 -1.07440416166193 35 21 22.6327389723991 -1.63273897239909 36 26 26.7752737608804 -0.775273760880398 37 22 25.1784611738214 -3.17846117382137 38 22 22.8289932628498 -0.828993262849823 39 22 22.5984874210279 -0.598487421027921 40 23 25.6837796527932 -2.68377965279324 41 30 22.9030125051988 7.0969874948012 42 23 22.7358279370364 0.264172062963616 43 17 18.6730159033882 -1.67301590338816 44 23 23.7826378758166 -0.782637875816639 45 23 24.3831450049004 -1.38314500490044 46 25 22.4825113554552 2.51748864454482 47 24 20.7625184377638 3.23748156223624 48 24 27.5354730638752 -3.53547306387521 49 23 23.013420846334 -0.0134208463340025 50 21 23.8063083098388 -2.80630830983878 51 24 25.7679598408398 -1.76795984083984 52 24 21.8792823501921 2.12071764980794 53 28 21.5334105788090 6.46658942119095 54 16 21.0863166062874 -5.08631660628735 55 20 19.9382434156754 0.0617565843245719 56 29 23.46377316897 5.53622683103 57 27 23.9351752063486 3.06482479365144 58 22 23.1947973370129 -1.19479733701295 59 28 24.0506511167089 3.94934888329110 60 16 20.3649096621750 -4.36490966217502 61 25 22.9731255420618 2.02687445793816 62 24 23.5039241638198 0.496075836180247 63 28 23.6846913700676 4.3153086299324 64 24 24.3948900774714 -0.394890077471401 65 23 22.7211392500443 0.278860749955726 66 30 26.9841401260328 3.01585987396719 67 24 21.31140755447 2.68859244553002 68 21 24.1992785117533 -3.19927851175327 69 25 23.356893110285 1.64310688971498 70 25 24.0266129841879 0.973387015812072 71 22 20.7731173900412 1.22688260995881 72 23 22.5160597366222 0.483940263377783 73 26 22.8620792081645 3.13792079183554 74 23 21.6021079249701 1.39789207502990 75 25 23.0462850534068 1.95371494659318 76 21 21.3200859288626 -0.320085928862601 77 25 23.6821653881416 1.31783461185842 78 24 22.1959701394290 1.80402986057096 79 29 23.6229457019056 5.37705429809438 80 22 23.6505049961384 -1.65050499613838 81 27 23.6700483747544 3.32995162524556 82 26 19.6751471427653 6.32485285723467 83 22 21.3261118468352 0.673888153164806 84 24 22.1026939444947 1.89730605550531 85 27 23.1367285030409 3.86327149695906 86 24 21.3203926922368 2.67960730776318 87 24 24.9069267712173 -0.906926771217318 88 29 24.5009382619029 4.49906173809706 89 22 22.2661656990094 -0.266165699009353 90 21 20.5817838202369 0.418216179763108 91 24 20.4103834047932 3.58961659520677 92 24 21.8288062157907 2.17119378420933 93 23 21.9725911338474 1.02740886615261 94 20 22.279068894971 -2.27906889497098 95 27 21.4625397057752 5.53746029422485 96 26 23.4662699529119 2.53373004708814 97 25 21.9422571510179 3.05774284898208 98 21 20.0641756720518 0.935824327948169 99 21 20.7854391583223 0.214560841677722 100 19 20.3903237759386 -1.39032377593858 101 21 21.6349353010046 -0.634935301004597 102 21 21.3024414128131 -0.302441412813057 103 16 19.7444211846365 -3.74442118463651 104 22 20.701799686528 1.29820031347199 105 29 21.8558175226444 7.1441824773556 106 15 21.6878883349162 -6.68788833491623 107 17 20.7286345848914 -3.72863458489142 108 15 19.9532515703311 -4.95325157033112 109 21 21.7008324905864 -0.700832490586391 110 21 21.0066281433363 -0.00662814333629869 111 19 19.2957595789363 -0.295759578936263 112 24 18.0673391965990 5.93266080340104 113 20 22.4284701075653 -2.42847010756527 114 17 25.2117708701399 -8.21177087013988 115 23 25.1139465965675 -2.11394659656751 116 24 22.3960472610679 1.60395273893209 117 14 22.0787535781367 -8.07875357813666 118 19 22.9242178924195 -3.92421789241954 119 24 22.1993436009816 1.80065639901840 120 13 20.3943031311854 -7.39430313118542 121 22 25.4191648291204 -3.41916482912037 122 16 21.1576664088684 -5.15766640886844 123 19 23.3390243535785 -4.33902435357853 124 25 22.8640398574361 2.13596014256388 125 25 24.2446992915658 0.755300708434188 126 23 21.4133655145338 1.58663448546623 127 24 23.5990379242686 0.400962075731441 128 26 23.6026161407151 2.39738385928493 129 26 21.5446149351277 4.45538506487232 130 25 24.1872275273886 0.81277247261139 131 18 22.4068796765704 -4.40687967657038 132 21 19.9015145661254 1.0984854338746 133 26 23.6990276020065 2.30097239799347 134 23 21.9848190163554 1.01518098364457 135 23 19.7663149882688 3.2336850117312 136 22 22.5902422845035 -0.590242284503534 137 20 22.4111657951914 -2.41116579519144 138 13 22.1381746285297 -9.13817462852975 139 24 21.4807935062558 2.51920649374420 140 15 21.6539345726315 -6.65393457263151 141 14 23.1850594569731 -9.18505945697312 142 22 24.121841856075 -2.12184185607499 143 10 17.7287537233398 -7.7287537233398 144 24 24.5001568112989 -0.500156811298874 145 22 21.8831673300128 0.116832669987208 146 24 25.8348513586269 -1.83485135862688 147 19 21.6372239393157 -2.63722393931569 148 20 22.1391981547192 -2.13919815471916 149 13 17.1082779500906 -4.10827795009065 150 20 20.146246659087 -0.146246659087016 151 22 23.3199882509133 -1.31998825091329 152 24 23.3710745213263 0.628925478673697 153 29 23.1631411873271 5.83685881267292 154 12 20.9396135417921 -8.93961354179206 155 20 20.9804482210829 -0.980448221082944 156 21 21.4480313076632 -0.44803130766325 157 24 23.6947749236870 0.305225076313032 158 22 21.9430711903430 0.0569288096570307 159 20 17.7370974776076 2.26290252239236 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.761061813098985 0.477876373802029 0.238938186901014 10 0.642152201009448 0.715695597981103 0.357847798990552 11 0.522654954741613 0.954690090516774 0.477345045258387 12 0.47648579517829 0.95297159035658 0.52351420482171 13 0.503445980373927 0.993108039252147 0.496554019626073 14 0.720444058130955 0.559111883738091 0.279555941869045 15 0.656050779971186 0.687898440057629 0.343949220028814 16 0.613722402769751 0.772555194460498 0.386277597230249 17 0.550621517511789 0.898756964976421 0.449378482488211 18 0.660340470218415 0.67931905956317 0.339659529781585 19 0.587492103389155 0.82501579322169 0.412507896610845 20 0.59991068959596 0.80017862080808 0.40008931040404 21 0.556292606296514 0.887414787406971 0.443707393703486 22 0.488276146720863 0.976552293441725 0.511723853279137 23 0.426196562596475 0.85239312519295 0.573803437403525 24 0.426239175037437 0.852478350074874 0.573760824962563 25 0.565328683301951 0.869342633396098 0.434671316698049 26 0.502899878625906 0.994200242748187 0.497100121374093 27 0.438586258075865 0.87717251615173 0.561413741924135 28 0.43188216563673 0.86376433127346 0.56811783436327 29 0.369886350922535 0.739772701845071 0.630113649077464 30 0.311142966973171 0.622285933946342 0.688857033026829 31 0.334146092723217 0.668292185446434 0.665853907276783 32 0.282309750981762 0.564619501963525 0.717690249018238 33 0.505075092067584 0.98984981586483 0.494924907932415 34 0.459896065495041 0.919792130990082 0.540103934504959 35 0.424767640693018 0.849535281386036 0.575232359306982 36 0.368313310028623 0.736626620057247 0.631686689971377 37 0.345573023770292 0.691146047540583 0.654426976229708 38 0.294953249234692 0.589906498469384 0.705046750765308 39 0.248827099265945 0.497654198531891 0.751172900734055 40 0.225182476861652 0.450364953723305 0.774817523138348 41 0.378502012716058 0.757004025432116 0.621497987283942 42 0.327477852702906 0.654955705405813 0.672522147297094 43 0.293946294426786 0.587892588853572 0.706053705573214 44 0.250590988522888 0.501181977045777 0.749409011477112 45 0.217399012029990 0.434798024059979 0.78260098797001 46 0.195018058397830 0.390036116795661 0.80498194160217 47 0.181608299696624 0.363216599393249 0.818391700303376 48 0.168586637524423 0.337173275048845 0.831413362475577 49 0.138094500713275 0.276189001426549 0.861905499286725 50 0.127940465662458 0.255880931324916 0.872059534337542 51 0.105970270832039 0.211940541664077 0.894029729167961 52 0.08994150823866 0.17988301647732 0.91005849176134 53 0.148354814989209 0.296709629978417 0.851645185010791 54 0.180011100522606 0.360022201045212 0.819988899477394 55 0.173275506608767 0.346551013217534 0.826724493391233 56 0.229364214704157 0.458728429408314 0.770635785295843 57 0.219507227632970 0.439014455265940 0.78049277236703 58 0.188687384493073 0.377374768986147 0.811312615506927 59 0.199108331090737 0.398216662181475 0.800891668909263 60 0.228444739887971 0.456889479775942 0.77155526011203 61 0.201458022987125 0.40291604597425 0.798541977012875 62 0.169656552392378 0.339313104784756 0.830343447607622 63 0.184537934365762 0.369075868731524 0.815462065634238 64 0.156368228699564 0.312736457399129 0.843631771300436 65 0.129383623539455 0.258767247078910 0.870616376460545 66 0.125237226467586 0.250474452935173 0.874762773532414 67 0.114722617677966 0.229445235355932 0.885277382322034 68 0.115063539810761 0.230127079621523 0.884936460189239 69 0.0978121775846199 0.195624355169240 0.90218782241538 70 0.0800068198145231 0.160013639629046 0.919993180185477 71 0.0653092158990688 0.130618431798138 0.934690784100931 72 0.0517775788897322 0.103555157779464 0.948222421110268 73 0.0486916805098556 0.0973833610197112 0.951308319490144 74 0.039153640813721 0.078307281627442 0.960846359186279 75 0.032751707633737 0.065503415267474 0.967248292366263 76 0.0252495335189614 0.0504990670379228 0.974750466481039 77 0.0198780172378272 0.0397560344756544 0.980121982762173 78 0.0159476420275739 0.0318952840551479 0.984052357972426 79 0.0235903430521322 0.0471806861042644 0.976409656947868 80 0.0188554862754674 0.0377109725509348 0.981144513724533 81 0.0183683866977006 0.0367367733954011 0.9816316133023 82 0.0328146271083913 0.0656292542167827 0.967185372891609 83 0.0254080036471535 0.050816007294307 0.974591996352847 84 0.0212741263055131 0.0425482526110262 0.978725873694487 85 0.0233267531786086 0.0466535063572173 0.976673246821391 86 0.020803841895716 0.041607683791432 0.979196158104284 87 0.0158920113620195 0.0317840227240391 0.98410798863798 88 0.0206090199336926 0.0412180398673852 0.979390980066307 89 0.0163387633629651 0.0326775267259303 0.983661236637035 90 0.0122854760971473 0.0245709521942945 0.987714523902853 91 0.0124096828097223 0.0248193656194445 0.987590317190278 92 0.0108919316167232 0.0217838632334465 0.989108068383277 93 0.00839784404530792 0.0167956880906158 0.991602155954692 94 0.00695437788105185 0.0139087557621037 0.993045622118948 95 0.0126875702620232 0.0253751405240465 0.987312429737977 96 0.0115383761187535 0.0230767522375071 0.988461623881246 97 0.0110072683773790 0.0220145367547581 0.98899273162262 98 0.00847268641733993 0.0169453728346799 0.99152731358266 99 0.00628861922392131 0.0125772384478426 0.993711380776079 100 0.00483996812799857 0.00967993625599714 0.995160031872001 101 0.00360160455222607 0.00720320910445214 0.996398395447774 102 0.00257848653757804 0.00515697307515608 0.997421513462422 103 0.00275881395105147 0.00551762790210295 0.997241186048949 104 0.00217570284525065 0.0043514056905013 0.99782429715475 105 0.00910238974195692 0.0182047794839138 0.990897610258043 106 0.0202674552760714 0.0405349105521428 0.979732544723929 107 0.0201777273770797 0.0403554547541595 0.97982227262292 108 0.025480358276706 0.050960716553412 0.974519641723294 109 0.0198257361005581 0.0396514722011162 0.980174263899442 110 0.0146009519560707 0.0292019039121415 0.98539904804393 111 0.0106594507948939 0.0213189015897877 0.989340549205106 112 0.025966565526597 0.051933131053194 0.974033434473403 113 0.0237896637960436 0.0475793275920872 0.976210336203956 114 0.0654283752798119 0.130856750559624 0.934571624720188 115 0.0563702733298099 0.112740546659620 0.94362972667019 116 0.0461283450715661 0.0922566901431322 0.953871654928434 117 0.132193063996703 0.264386127993406 0.867806936003297 118 0.127570050577709 0.255140101155418 0.87242994942229 119 0.113973407016552 0.227946814033105 0.886026592983448 120 0.195459696719974 0.390919393439949 0.804540303280026 121 0.187407649506176 0.374815299012351 0.812592350493824 122 0.222617662729703 0.445235325459407 0.777382337270297 123 0.216569045960918 0.433138091921837 0.783430954039082 124 0.216196809311179 0.432393618622357 0.783803190688821 125 0.198054329838707 0.396108659677415 0.801945670161293 126 0.163498082875726 0.326996165751452 0.836501917124274 127 0.129909069246092 0.259818138492184 0.870090930753908 128 0.134414475144247 0.268828950288493 0.865585524855753 129 0.190208782526723 0.380417565053445 0.809791217473278 130 0.166015944825326 0.332031889650652 0.833984055174674 131 0.147281527543139 0.294563055086279 0.85271847245686 132 0.129353019414475 0.258706038828950 0.870646980585525 133 0.119984371962917 0.239968743925834 0.880015628037083 134 0.0997590288624669 0.199518057724934 0.900240971137533 135 0.134989612742443 0.269979225484887 0.865010387257557 136 0.102704640912813 0.205409281825626 0.897295359087187 137 0.0769844580987031 0.153968916197406 0.923015541901297 138 0.187705786463563 0.375411572927126 0.812294213536437 139 0.261303328802351 0.522606657604702 0.738696671197649 140 0.242129896627062 0.484259793254124 0.757870103372938 141 0.486918383122039 0.973836766244077 0.513081616877961 142 0.438821845983663 0.877643691967326 0.561178154016337 143 0.749669401090875 0.50066119781825 0.250330598909125 144 0.699671203979897 0.600657592040207 0.300328796020103 145 0.600916359880605 0.798167280238791 0.399083640119395 146 0.538074804755642 0.923850390488716 0.461925195244358 147 0.560665949886779 0.878668100226441 0.439334050113221 148 0.433275675098167 0.866551350196333 0.566724324901833 149 0.340056664895419 0.680113329790838 0.659943335104581 150 0.243562691964485 0.48712538392897 0.756437308035515 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 5 0.0352112676056338 NOK 5% type I error level 33 0.232394366197183 NOK 10% type I error level 42 0.295774647887324 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606118w69c10s0chw6lai/10etf71290606183.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606118w69c10s0chw6lai/10etf71290606183.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606118w69c10s0chw6lai/1ijzy1290606183.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606118w69c10s0chw6lai/1ijzy1290606183.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606118w69c10s0chw6lai/2ijzy1290606183.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606118w69c10s0chw6lai/2ijzy1290606183.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606118w69c10s0chw6lai/3ijzy1290606183.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606118w69c10s0chw6lai/3ijzy1290606183.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606118w69c10s0chw6lai/4btg11290606183.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606118w69c10s0chw6lai/4btg11290606183.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606118w69c10s0chw6lai/5btg11290606183.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606118w69c10s0chw6lai/5btg11290606183.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606118w69c10s0chw6lai/6mkym1290606183.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606118w69c10s0chw6lai/6mkym1290606183.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606118w69c10s0chw6lai/7mkym1290606183.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606118w69c10s0chw6lai/7mkym1290606183.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606118w69c10s0chw6lai/8etf71290606183.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606118w69c10s0chw6lai/8etf71290606183.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606118w69c10s0chw6lai/9etf71290606183.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606118w69c10s0chw6lai/9etf71290606183.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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