*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: Sun, 19 Dec 2010 13:57:14 +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/Dec/19/t129276690367o81fla4hk4pha.htm/, Retrieved Sun, 19 Dec 2010 14:55:15 +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/19/t129276690367o81fla4hk4pha.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 15 11 11 8 23 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 10 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Organization[t] = + 16.5347825860486 -0.0891335605069494ConcernOverMistakes[t] + 0.209717480920555DoubtsAboutActions[t] -0.136972411791539ParentalExpectations[t] -0.287847153125504ParentalCriticism[t] + 0.433155311009048PersonalStandards[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) 16.5347825860486 2.00538 8.2452 0 0 ConcernOverMistakes -0.0891335605069494 0.061483 -1.4497 0.149179 0.074589 DoubtsAboutActions 0.209717480920555 0.112454 1.8649 0.064107 0.032054 ParentalExpectations -0.136972411791539 0.104781 -1.3072 0.193095 0.096548 ParentalCriticism -0.287847153125504 0.131542 -2.1883 0.030168 0.015084 PersonalStandards 0.433155311009048 0.075367 5.7473 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.475311447164505 R-squared 0.225920971805616 Adjusted R-squared 0.200624271537826 F-TEST (value) 8.93084747868384 F-TEST (DF numerator) 5 F-TEST (DF denominator) 153 p-value 1.83604021986028e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.49245950232918 Sum Squared Residuals 1866.18282643764 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 26 22.7664869637737 3.23351303622630 2 23 24.1806345311823 -1.18063453118232 3 25 24.641168047765 0.358831952235021 4 23 22.0044378342226 0.995562165777394 5 19 21.9032418668590 -2.90324186685895 6 29 23.0766382559650 5.92336174403504 7 25 25.0200838181324 -0.0200838181323613 8 21 22.7050948471841 -1.70509484718409 9 22 21.9908994654292 0.00910053457084511 10 25 22.627094453578 2.37290554642202 11 24 20.0692092529402 3.93079074705976 12 18 19.5373063311390 -1.53730633113897 13 22 18.2746121459269 3.72538785407310 14 15 20.7049719011955 -5.70497190119546 15 22 23.6577698670676 -1.65776986706755 16 28 24.7932683915166 3.20673160848343 17 20 22.2564759016333 -2.25647590163327 18 12 19.1302196252245 -7.13021962522446 19 24 21.6158069931384 2.38419300686164 20 20 21.1754094115923 -1.17540941159228 21 21 23.1391899115409 -2.13918991154088 22 20 20.3241606581029 -0.324160658102906 23 21 19.1207592971464 1.87924070285358 24 23 20.8319811984643 2.16801880153567 25 28 22.0017696920126 5.99823030798739 26 24 22.1037470635073 1.89625293649272 27 24 23.6867823837946 0.313217616205359 28 24 20.4091203214400 3.59087967856003 29 23 22.0748460806036 0.925153919396356 30 23 22.9286619558714 0.0713380441285757 31 29 24.3618000934366 4.63819990656336 32 24 21.8529034920832 2.14709650791683 33 18 25.1809671443811 -7.18096714438113 34 25 26.1865543596518 -1.18655435965179 35 21 22.8166967823559 -1.8166967823559 36 26 26.6396577389406 -0.639657738940561 37 22 25.0687814628218 -3.06878146282179 38 22 23.0122615742149 -1.01226157421491 39 22 22.4077978793724 -0.407797879372415 40 23 25.7259583503069 -2.72595835030686 41 30 22.8040172069673 7.19598279303271 42 23 22.7819462151958 0.21805378480423 43 17 18.7343642583786 -1.73436425837856 44 23 24.1050578066495 -1.10505780664945 45 23 24.4388229284309 -1.43882292843093 46 25 22.5680214149610 2.43197858503904 47 24 20.6888664106236 3.31113358937640 48 24 27.4305551496196 -3.43055514961965 49 23 22.9295207492763 0.070479250723737 50 21 23.906177130168 -2.90617713016798 51 24 25.6991111893451 -1.69911118934514 52 24 21.9676511898960 2.03234881010404 53 28 21.5659462387936 6.43405376120643 54 16 21.3367248878799 -5.3367248878799 55 20 19.6671611239828 0.332838876017181 56 29 23.3929185625497 5.60708143745027 57 27 23.9866109838340 3.01338901616604 58 22 23.6577698670676 -1.65776986706755 59 28 24.3524235735653 3.64757642643469 60 16 20.4134307285922 -4.41343072859221 61 25 23.0684035303045 1.93159646969545 62 24 23.6481558167823 0.351844183217722 63 29 23.0766382559650 5.92336174403504 64 24 24.3660295406460 -0.366029540645974 65 23 23.0246404040221 -0.0246404040220633 66 30 27.0126287910022 2.98737120899776 67 24 21.1693251451857 2.83067485481435 68 21 24.3404770836518 -3.34047708365176 69 25 23.5920516659567 1.40794833404329 70 25 24.0784126865509 0.9215873134491 71 22 20.7212899460224 1.27871005397763 72 23 22.5772820178891 0.422717982110868 73 26 22.7982159413667 3.20178405863327 74 23 21.4264216017352 1.57357839826481 75 25 23.1519810207529 1.84801897924705 76 21 21.2985455572727 -0.298545557272719 77 25 23.9006282914929 1.09937170850705 78 24 22.2007662854372 1.79923371456276 79 29 23.6479255177518 5.35207448224815 80 22 23.6670936851632 -1.66709368516324 81 27 23.5905253179576 3.40947468204237 82 26 19.7428499148896 6.25715008511036 83 22 21.3261199173271 0.67388008267286 84 24 22.1887038785805 1.81129612141947 85 27 23.1156912764886 3.88430872351144 86 24 21.4264876651665 2.57351233483348 87 25 25.0200838181324 -0.0200838181323613 88 29 24.5608671334123 4.43913286658771 89 22 22.0294273277232 -0.0294273277232355 90 21 20.6434610193989 0.356538980601123 91 24 20.2966040428239 3.70339595717613 92 24 22.0991230816684 1.90087691833160 93 23 22.1071907234659 0.892809276534094 94 20 22.4187668106742 -2.41876681067415 95 27 21.4397957349295 5.56020426507046 96 26 23.3992004866998 2.60079951330017 97 25 21.7151452930409 3.28485470695908 98 21 19.8528288647505 1.14717113524952 99 21 20.8668988494874 0.13310115051263 100 19 20.3843960839700 -1.38439608397003 101 21 21.6113999486742 -0.611399948674236 102 21 21.5250005938086 -0.525000593808609 103 18 19.5373063311390 -1.53730633113897 104 22 20.7713221673498 1.22867783265022 105 29 21.6986935864955 7.30130641350453 106 15 21.6601962980819 -6.66019629808195 107 17 20.752859071136 -3.75285907113600 108 15 19.8538724867936 -4.85387248679362 109 21 21.551000287208 -0.551000287208005 110 21 21.0821345952024 -0.0821345952024031 111 19 19.4593614875723 -0.45936148757232 112 24 17.8678539112106 6.1321460887894 113 20 22.3373747364798 -2.33737473647981 114 17 25.3030797285071 -8.30307972850713 115 23 25.2902914675589 -2.29029146755886 116 24 22.6627698775743 1.33723012242572 117 14 22.2971243717058 -8.29712437170584 118 23 22.0044378342226 0.995562165777394 119 24 22.126694593459 1.87330540654099 120 13 20.4428548023190 -7.44285480231896 121 22 25.4086442126656 -3.40864421266558 122 16 21.2988463028542 -5.29884630285418 123 19 23.2548393135475 -4.25483931354754 124 25 22.9897078564874 2.01029214351255 125 25 24.1548360977887 0.845163902211323 126 23 21.5239569717655 1.47604302823453 127 24 23.8838231375904 0.116176862409606 128 26 23.6452573755419 2.35474262445815 129 26 21.6155766941079 4.38442330589207 130 25 23.9819841537313 1.01801584626873 131 18 22.3295039715684 -4.32950397156836 132 21 19.9801417558646 1.01985824413538 133 26 23.9236092435891 2.07639075641095 134 23 22.1990407448388 0.800959255161207 135 23 19.7441914342504 3.25580856574957 136 22 22.5877555839845 -0.5877555839845 137 20 22.5159047978111 -2.51590479781109 138 13 22.1719840677406 -9.17198406774058 139 24 21.5592201163568 2.44077988364315 140 15 21.4439064169319 -6.44390641693191 141 14 22.9360165726826 -8.93601657268255 142 22 24.005831853021 -2.00583185302099 143 10 17.3836024524525 -7.38360245245252 144 24 24.5069589122326 -0.506958912232648 145 22 21.8570275357412 0.142972464258784 146 24 25.7668029748602 -1.76680297486023 147 19 21.5688269352586 -2.56882693525861 148 20 22.2142036337991 -2.21420363379910 149 13 17.0933627366848 -4.09336273668483 150 20 20.1186050261045 -0.118605026104472 151 22 23.3848509207522 -1.38485092075223 152 24 23.2959142371313 0.704085762868665 153 29 23.1247528766721 5.87524712332788 154 12 21.046555808518 -9.046555808518 155 20 20.9732699037905 -0.973269903790477 156 20 22.2564759016333 -2.25647590163327 157 24 23.5613413342479 0.438658665752077 158 22 21.8965306409338 0.103469359066198 159 18 19.5373063311390 -1.53730633113897 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.726848394659058 0.546303210681883 0.273151605340941 10 0.60031484906407 0.79937030187186 0.39968515093593 11 0.491624704203705 0.98324940840741 0.508375295796295 12 0.447069600014707 0.894139200029413 0.552930399985293 13 0.455862195744912 0.911724391489825 0.544137804255088 14 0.696401281873197 0.607197436253605 0.303598718126803 15 0.62842953584678 0.74314092830644 0.37157046415322 16 0.574747540100246 0.850504919799507 0.425252459899754 17 0.508732217008352 0.982535565983295 0.491267782991648 18 0.639354781640171 0.721290436719658 0.360645218359829 19 0.563862912266736 0.872274175466528 0.436137087733264 20 0.568678757474361 0.862642485051278 0.431321242525639 21 0.520361441671655 0.95927711665669 0.479638558328345 22 0.450948792594101 0.901897585188201 0.549051207405899 23 0.39222998655258 0.78445997310516 0.60777001344742 24 0.393622459881801 0.787244919763603 0.606377540118199 25 0.537474106257213 0.925051787485574 0.462525893742787 26 0.474209113560235 0.94841822712047 0.525790886439765 27 0.41033148218786 0.82066296437572 0.58966851781214 28 0.403799437289586 0.807598874579172 0.596200562710414 29 0.342670495763169 0.685340991526338 0.657329504236831 30 0.285740166316286 0.571480332632572 0.714259833683714 31 0.309685244600535 0.61937048920107 0.690314755399465 32 0.261859714678572 0.523719429357143 0.738140285321428 33 0.490321082678345 0.98064216535669 0.509678917321655 34 0.444322127810005 0.88864425562001 0.555677872189995 35 0.410375044305112 0.820750088610223 0.589624955694888 36 0.354230370276625 0.70846074055325 0.645769629723375 37 0.33078515023099 0.66157030046198 0.66921484976901 38 0.281496922976677 0.562993845953353 0.718503077023323 39 0.236067622012969 0.472135244025937 0.763932377987031 40 0.213040259837531 0.426080519675061 0.78695974016247 41 0.368017641994102 0.736035283988204 0.631982358005898 42 0.317396014518100 0.634792029036201 0.6826039854819 43 0.285392597343302 0.570785194686603 0.714607402656698 44 0.243886148566919 0.487772297133838 0.756113851433081 45 0.210944652792205 0.421889305584409 0.789055347207795 46 0.189144162938978 0.378288325877957 0.810855837061022 47 0.177421419849249 0.354842839698497 0.822578580150751 48 0.16381315280316 0.32762630560632 0.83618684719684 49 0.133870781006078 0.267741562012156 0.866129218993922 50 0.125004559137171 0.250009118274343 0.874995440862829 51 0.103103985494665 0.206207970989329 0.896896014505335 52 0.08721362208337 0.17442724416674 0.91278637791663 53 0.145211351222660 0.290422702445319 0.85478864877734 54 0.180797100967384 0.361594201934768 0.819202899032616 55 0.174192599394419 0.348385198788839 0.825807400605581 56 0.233420934357470 0.466841868714939 0.76657906564253 57 0.223355804107828 0.446711608215655 0.776644195892172 58 0.198710169906778 0.397420339813555 0.801289830093223 59 0.207011236287092 0.414022472574183 0.792988763712908 60 0.235171140920733 0.470342281841467 0.764828859079267 61 0.20723184421747 0.41446368843494 0.79276815578253 62 0.174604664025085 0.349209328050169 0.825395335974915 63 0.235897908701581 0.471795817403162 0.764102091298419 64 0.202177034353868 0.404354068707736 0.797822965646132 65 0.169874776286385 0.339749552572770 0.830125223713615 66 0.164088158024942 0.328176316049885 0.835911841975058 67 0.151735367975228 0.303470735950457 0.848264632024772 68 0.153635378595487 0.307270757190974 0.846364621404513 69 0.131502379899080 0.263004759798159 0.86849762010092 70 0.109079797542854 0.218159595085708 0.890920202457146 71 0.0905340434922723 0.181068086984545 0.909465956507728 72 0.0729858984374738 0.145971796874948 0.927014101562526 73 0.0693464420201827 0.138692884040365 0.930653557979817 74 0.0572543359351602 0.114508671870320 0.94274566406484 75 0.0479723338718258 0.0959446677436516 0.952027666128174 76 0.0377172415087851 0.0754344830175702 0.962282758491215 77 0.0299241392743254 0.0598482785486508 0.970075860725675 78 0.0243149572427410 0.0486299144854821 0.97568504275726 79 0.0349489955663645 0.069897991132729 0.965051004433636 80 0.0284350458939974 0.0568700917879948 0.971564954106003 81 0.0280818396173017 0.0561636792346034 0.971918160382698 82 0.0478199579957265 0.095639915991453 0.952180042004273 83 0.0376660692051609 0.0753321384103218 0.96233393079484 84 0.0316165665839748 0.0632331331679496 0.968383433416025 85 0.0345170433146304 0.0690340866292607 0.96548295668537 86 0.0305260330108494 0.0610520660216987 0.96947396698915 87 0.0232927098627449 0.0465854197254899 0.976707290137255 88 0.029073448322268 0.058146896644536 0.970926551677732 89 0.0234470135472049 0.0468940270944098 0.976552986452795 90 0.0178937725285386 0.0357875450570772 0.982106227471461 91 0.0185545624305983 0.0371091248611966 0.981445437569402 92 0.0157667597743315 0.0315335195486631 0.984233240225668 93 0.0121422316238293 0.0242844632476586 0.98785776837617 94 0.0103406663379013 0.0206813326758025 0.989659333662099 95 0.0186153446388633 0.0372306892777267 0.981384655361137 96 0.0172223052539988 0.0344446105079976 0.982777694746 97 0.0173252381756228 0.0346504763512456 0.982674761824377 98 0.0140178476894008 0.0280356953788016 0.9859821523106 99 0.0105777426172794 0.0211554852345588 0.98942225738272 100 0.00829070757758693 0.0165814151551739 0.991709292422413 101 0.00628767218172449 0.0125753443634490 0.993712327818276 102 0.00456347243595548 0.00912694487191095 0.995436527564045 103 0.00349594676591350 0.006991893531827 0.996504053234087 104 0.00278437943008468 0.00556875886016937 0.997215620569915 105 0.0126479879461980 0.0252959758923960 0.987352012053802 106 0.0271435856712776 0.0542871713425552 0.972856414328722 107 0.0272995666403157 0.0545991332806315 0.972700433359684 108 0.0331569425135388 0.0663138850270776 0.966843057486461 109 0.0263502234146876 0.0527004468293752 0.973649776585312 110 0.0196304087908556 0.0392608175817111 0.980369591209144 111 0.0145314303225422 0.0290628606450845 0.985468569677458 112 0.0447921797936868 0.0895843595873737 0.955207820206313 113 0.041362496856245 0.08272499371249 0.958637503143755 114 0.116028967451295 0.23205793490259 0.883971032548705 115 0.0998330386539684 0.199666077307937 0.900166961346032 116 0.080765518080008 0.161531036160016 0.919234481919992 117 0.254933950839121 0.509867901678242 0.745066049160879 118 0.240747019336932 0.481494038673865 0.759252980663068 119 0.230854502209819 0.461709004419638 0.769145497790181 120 0.333801784638963 0.667603569277925 0.666198215361037 121 0.334179258560565 0.66835851712113 0.665820741439435 122 0.394841585492094 0.789683170984188 0.605158414507906 123 0.386454945392517 0.772909890785034 0.613545054607483 124 0.370584779931572 0.741169559863143 0.629415220068428 125 0.368956562486386 0.737913124972772 0.631043437513614 126 0.31906214450458 0.63812428900916 0.68093785549542 127 0.279281722510847 0.558563445021694 0.720718277489153 128 0.272127995735700 0.544255991471399 0.7278720042643 129 0.348887070730044 0.697774141460088 0.651112929269956 130 0.337620563321151 0.675241126642301 0.662379436678849 131 0.309570175964184 0.619140351928367 0.690429824035816 132 0.287270402514753 0.574540805029505 0.712729597485247 133 0.243765294864384 0.487530589728767 0.756234705135616 134 0.198214565055592 0.396429130111185 0.801785434944408 135 0.311270449167768 0.622540898335535 0.688729550832232 136 0.255746628170480 0.511493256340961 0.74425337182952 137 0.207496144408538 0.414992288817076 0.792503855591462 138 0.475364929542297 0.950729859084595 0.524635070457703 139 0.519889007226082 0.960221985547837 0.480110992773918 140 0.480982660727056 0.961965321454112 0.519017339272944 141 0.656927213051382 0.686145573897235 0.343072786948618 142 0.61434981010173 0.77130037979654 0.38565018989827 143 0.82260460733949 0.354790785321019 0.177395392660509 144 0.809678718730443 0.380642562539115 0.190321281269557 145 0.728752134281228 0.542495731437545 0.271247865718772 146 0.663373955479337 0.673252089041325 0.336626044520663 147 0.706153050693191 0.587693898613618 0.293846949306809 148 0.629031969263453 0.741936061473094 0.370968030736547 149 0.814551781550186 0.370896436899628 0.185448218449814 150 0.908543770370411 0.182912459259178 0.0914562296295889 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 3 0.0211267605633803 NOK 5% type I error level 21 0.147887323943662 NOK 10% type I error level 39 0.274647887323944 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t129276690367o81fla4hk4pha/109nbx1292767023.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t129276690367o81fla4hk4pha/109nbx1292767023.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t129276690367o81fla4hk4pha/1vvwo1292767023.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t129276690367o81fla4hk4pha/1vvwo1292767023.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t129276690367o81fla4hk4pha/2vvwo1292767023.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t129276690367o81fla4hk4pha/2vvwo1292767023.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t129276690367o81fla4hk4pha/3n4vr1292767023.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t129276690367o81fla4hk4pha/3n4vr1292767023.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t129276690367o81fla4hk4pha/4n4vr1292767023.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t129276690367o81fla4hk4pha/4n4vr1292767023.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t129276690367o81fla4hk4pha/5n4vr1292767023.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t129276690367o81fla4hk4pha/5n4vr1292767023.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t129276690367o81fla4hk4pha/6n4vr1292767023.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t129276690367o81fla4hk4pha/6n4vr1292767023.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t129276690367o81fla4hk4pha/7yecc1292767023.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t129276690367o81fla4hk4pha/7yecc1292767023.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t129276690367o81fla4hk4pha/89nbx1292767023.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t129276690367o81fla4hk4pha/89nbx1292767023.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t129276690367o81fla4hk4pha/99nbx1292767023.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t129276690367o81fla4hk4pha/99nbx1292767023.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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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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