Pop

*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: Tue, 23 Nov 2010 22:02:36 +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/23/t12905497188g8k2ge7hjdufet.htm/, Retrieved Tue, 23 Nov 2010 23:02:09 +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/23/t12905497188g8k2ge7hjdufet.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 «

1 14 23 23 26 26 9 9 15 15 6 6 11 11 13 13 4 4 1 18 21 21 20 20 9 9 15 15 6 6 12 12 16 16 4 4 1 11 21 21 21 21 9 9 14 14 13 13 15 15 19 19 6 6 0 12 21 0 31 0 14 0 10 0 8 0 10 0 15 0 8 0 1 16 24 24 21 21 8 8 10 10 7 7 12 12 14 14 8 8 1 18 22 22 18 18 8 8 12 12 9 9 11 11 13 13 4 4 1 14 21 21 26 26 11 11 18 18 5 5 5 5 19 19 4 4 1 14 22 22 22 22 10 10 12 12 8 8 16 16 15 15 5 5 1 15 21 21 22 22 9 9 14 14 9 9 11 11 14 14 5 5 1 15 20 20 29 29 15 15 18 18 11 11 15 15 15 15 8 8 0 17 22 0 15 0 14 0 9 0 8 0 12 0 16 0 4 0 1 19 21 21 16 16 11 11 11 11 11 11 9 9 16 16 4 4 0 10 21 0 24 0 14 0 11 0 12 0 11 0 16 0 4 0 1 18 23 23 17 17 6 6 17 17 8 8 15 15 17 17 4 4 0 14 22 0 19 0 20 0 8 0 7 0 12 0 15 0 4 0 0 14 23 0 22 0 9 0 16 0 9 0 16 0 15 0 8 0 1 17 22 22 31 31 10 10 21 21 12 12 14 14 20 20 4 4 0 14 24 0 28 0 8 0 24 0 20 0 11 0 18 0 4 0 1 16 23 23 38 38 11 11 21 21 7 7 10 10 16 16 4 4 0 18 21 0 26 0 14 0 14 0 8 0 7 0 16 0 4 0 1 14 23 23 25 25 11 11 7 7 8 8 11 11 19 19 8 8 1 12 23 23 25 25 16 16 18 18 16 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 11 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Happiness[t] = + 7.80305927515177 + 17.4163705006130Pop[t] + 0.0579165349035982Age[t] -0.156072330488879Age_p[t] -0.0921950616972788Concern_over_mistakes[t] + 0.149224968338923Concern_over_mistakes_p[t] + 0.0116215720252558Doubts_about_actions[t] -0.44594773439194Doubts_about_actions_p[t] + 0.0441574359203689Parental_expectations[t] -0.00935434412190598Parental_expectations_p[t] + 0.0471039134932978Parental_criticism[t] -0.194860597403451Parental_criticism_p[t] + 0.151966046354645Popularity[t] -0.265853714177041Popularity_p[t] + 0.275841334364272Perceived_learning_competence[t] -0.419494182412067Perceived_learning_competence_p[t] -0.059154172572458Amotivation[t] -0.09235574763941Amotivation_p[t] + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 7.80305927515177 3.855283 2.024 0.045086 0.022543 Pop 17.4163705006130 5.139877 3.3885 0.000938 0.000469 Age 0.0579165349035982 0.080771 0.717 0.474672 0.237336 Age_p -0.156072330488879 0.120191 -1.2985 0.196475 0.098238 Concern_over_mistakes -0.0921950616972788 0.057377 -1.6068 0.110594 0.055297 Concern_over_mistakes_p 0.149224968338923 0.07632 1.9552 0.052768 0.026384 Doubts_about_actions 0.0116215720252558 0.116138 0.1001 0.920451 0.460225 Doubts_about_actions_p -0.44594773439194 0.156561 -2.8484 0.005133 0.002567 Parental_expectations 0.0441574359203689 0.113091 0.3905 0.696857 0.348429 Parental_expectations_p -0.00935434412190598 0.144955 -0.0645 0.948648 0.474324 Parental_criticism 0.0471039134932978 0.144518 0.3259 0.745012 0.372506 Parental_criticism_p -0.194860597403451 0.176933 -1.1013 0.272855 0.136427 Popularity 0.151966046354645 0.097226 1.563 0.120557 0.060278 Popularity_p -0.265853714177041 0.128616 -2.067 0.040779 0.02039 Perceived_learning_competence 0.275841334364272 0.136637 2.0188 0.045631 0.022816 Perceived_learning_competence_p -0.419494182412067 0.182803 -2.2948 0.023399 0.011699 Amotivation -0.059154172572458 0.171926 -0.3441 0.731369 0.365684 Amotivation_p -0.09235574763941 0.190163 -0.4857 0.628048 0.314024 Multiple Linear Regression - Regression Statistics Multiple R 0.551151442308679 R-squared 0.303767912358937 Adjusted R-squared 0.209831837042285 F-TEST (value) 3.2337726622595 F-TEST (DF numerator) 17 F-TEST (DF denominator) 126 p-value 7.93946563379944e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.11904678725665 Sum Squared Residuals 565.785270109425 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14 16.4449038106865 -2.44490381068653 2 18 15.7541897500416 2.24581024995843 3 11 13.6664783894794 -2.66647838947938 4 12 12.3264143694462 -0.326414369446192 5 16 15.3105723046397 0.689427695360279 6 18 15.9734671883796 2.02653281162036 7 14 15.846137955077 -1.84613795507701 8 14 14.4724372187036 -0.472437218703563 9 15 15.6398598635021 -0.639859863502078 10 15 12.3212337507793 2.67876624922068 11 17 14.6316845729493 2.36831542705073 12 19 14.1210850154642 4.87891498453579 13 10 13.8687769622295 -3.86877696222945 14 18 15.9785438903078 2.02145610969221 15 14 13.9655310745338 0.0344689254662466 16 14 14.437739941546 -0.437739941545996 17 17 14.3689284846416 2.63107151535841 18 14 15.1065775316393 -1.10657753163932 19 16 16.0046013562127 -0.00460135621266727 20 18 13.0205793072042 4.97942069279577 21 14 13.4773267079694 0.522673292030594 22 12 11.8088722476630 0.19112775233703 23 17 13.8985372125633 3.10146278743668 24 9 14.7711227710924 -5.77112277109235 25 16 15.5682321704595 0.431767829540484 26 14 12.9607127455222 1.03928725447783 27 11 13.5753866236095 -2.57538662360950 28 16 16.531157979698 -0.531157979697993 29 13 12.2186271904323 0.781372809567731 30 17 15.0524052292497 1.94759477075034 31 15 15.6822476121662 -0.682247612166205 32 14 14.2757627709241 -0.275762770924058 33 16 11.4510107137883 4.54898928621168 34 9 11.6206886344894 -2.62068863448942 35 15 13.0738996467414 1.92610035325862 36 17 16.3944950210218 0.605504978978197 37 13 13.9194452468857 -0.919445246885724 38 15 14.2756763490710 0.724323650929016 39 16 15.2974497841682 0.702550215831777 40 16 16.0659978482457 -0.065997848245705 41 12 13.3956435702274 -1.39564357022737 42 11 13.3647940920151 -2.36479409201511 43 15 15.1253136743861 -0.125313674386131 44 17 15.0808544660365 1.91914553396351 45 13 14.1074912214962 -1.10749122149620 46 16 12.1624104318225 3.83758956817754 47 14 12.8878826608025 1.11211733919750 48 11 12.1390467713564 -1.13904677135642 49 12 12.6918401028865 -0.691840102886545 50 12 12.0617611816134 -0.0617611816133956 51 15 14.3958818811173 0.604118118882706 52 16 16.1805457428282 -0.180545742828208 53 15 15.338190943667 -0.338190943666999 54 12 14.3182556186467 -2.31825561864671 55 12 14.5678023348977 -2.56780233489766 56 8 12.0913631046910 -4.09136310469096 57 13 13.9499996294482 -0.949999629448203 58 11 14.1719838671055 -3.17198386710553 59 14 16.2529809586942 -2.25298095869415 60 15 13.1905701431104 1.80942985688959 61 10 12.4709057739645 -2.47090577396451 62 11 12.4483158070715 -1.44831580707154 63 12 14.2276371013400 -2.22763710133998 64 15 14.4638333817266 0.536166618273435 65 15 14.5445039769890 0.455496023011029 66 14 13.7141505316615 0.285849468338474 67 16 12.6906172282805 3.30938277171949 68 15 15.0593256490364 -0.0593256490363937 69 15 14.3420406650057 0.657959334994292 70 13 14.6631598442056 -1.66315984420558 71 17 14.7709482012146 2.22905179878537 72 13 12.7178968246213 0.282103175378710 73 15 11.7465401624124 3.25345983758762 74 13 14.3599790923522 -1.35997909235220 75 15 14.8487223470941 0.151277652905856 76 16 14.6729377356415 1.32706226435852 77 15 14.4067536482802 0.59324635171983 78 16 13.3596310079674 2.64036899203256 79 15 13.9583341481188 1.04166585188117 80 14 14.3193755762845 -0.319375576284458 81 15 12.4495158826618 2.55048411733815 82 7 11.0743902824004 -4.07439028240037 83 17 16.3395273344472 0.660472665552797 84 13 14.6977416730483 -1.69774167304829 85 15 13.8447720094466 1.15522799055341 86 14 14.0112754708934 -0.0112754708934258 87 13 13.4775057303095 -0.477505730309453 88 16 16.3508300171744 -0.350830017174373 89 12 13.8147797415958 -1.81477974159582 90 14 15.2288173552706 -1.22881735527064 91 17 12.5093683051598 4.49063169484016 92 15 14.0948319157220 0.905168084277952 93 17 13.1372109262309 3.8627890737691 94 12 14.4642925657112 -2.46429256571117 95 16 15.0734127486121 0.926587251387942 96 11 13.5846150084969 -2.58461500849692 97 15 12.6962856713824 2.30371432861762 98 9 13.1475683942831 -4.14756839428309 99 16 14.3207374251218 1.67926257487817 100 10 11.8142033109291 -1.81420331092914 101 10 12.6928516973584 -2.69285169735840 102 15 15.0703700173387 -0.0703700173386514 103 11 13.4967130072771 -2.49671300727713 104 13 15.4086513356288 -2.40865133562876 105 14 14.2477323247196 -0.247732324719573 106 18 15.3757356593952 2.62426434060484 107 16 14.6997733666157 1.30022663338427 108 14 12.9145808336005 1.08541916639951 109 14 15.3577004055355 -1.35770040553550 110 14 13.8825739553111 0.117426044688885 111 14 15.4281010931093 -1.42810109310932 112 12 13.7535048654012 -1.75350486540121 113 14 13.4811229943765 0.518877005623528 114 15 15.7405108149539 -0.740510814953864 115 15 14.9538852051491 0.0461147948509387 116 13 13.8076319769972 -0.807631976997153 117 17 14.9633509481369 2.03664905186309 118 17 15.7830556443950 1.21694435560503 119 19 15.3272861965998 3.67271380340016 120 15 14.4112736577084 0.588726342291602 121 13 13.3930813795265 -0.393081379526461 122 9 11.0329011410282 -2.03290114102822 123 15 15.4803261391011 -0.480326139101051 124 15 14.2408972415409 0.759102758459076 125 16 14.6698347845364 1.33016521546355 126 11 11.9532693758456 -0.953269375845617 127 14 13.6633150508708 0.33668494912919 128 11 12.9528328761856 -1.95283287618557 129 15 15.5498237842772 -0.54982378427716 130 13 12.0610673678835 0.938932632116483 131 16 13.8102043113500 2.18979568865003 132 14 15.2203160934167 -1.22031609341668 133 15 14.5516631824448 0.448336817555191 134 16 15.1576435446834 0.842356455316636 135 16 14.8470828962593 1.15291710374066 136 11 11.9896549580181 -0.98965495801812 137 13 14.3663242279658 -1.36632422796584 138 16 15.5682321704595 0.431767829540484 139 12 13.1734417187557 -1.17344171875566 140 9 11.4050765582403 -2.40507655824028 141 13 11.6786420211317 1.32135797886827 142 13 14.6977416730483 -1.69774167304829 143 19 15.3272861965998 3.67271380340016 144 13 15.8422351949844 -2.84223519498437 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.943301244428447 0.113397511143106 0.0566987555715528 22 0.98423296160775 0.0315340767844996 0.0157670383922498 23 0.971239997500362 0.0575200049992764 0.0287600024996382 24 0.986953391097773 0.0260932178044547 0.0130466089022273 25 0.975434540797141 0.0491309184057173 0.0245654592028586 26 0.971867029009981 0.0562659419800373 0.0281329709900187 27 0.960228580111234 0.0795428397775322 0.0397714198887661 28 0.94433440623263 0.111331187534740 0.0556655937673699 29 0.924928563767615 0.15014287246477 0.075071436232385 30 0.92788659610135 0.144226807797301 0.0721134038986507 31 0.896118950452477 0.207762099095046 0.103881049547523 32 0.905508051110253 0.188983897779494 0.094491948889747 33 0.96337205040892 0.0732558991821609 0.0366279495910804 34 0.950946861876897 0.0981062762462064 0.0490531381231032 35 0.947560890200473 0.104878219599055 0.0524391097995274 36 0.928868899644877 0.142262200710247 0.0711311003551234 37 0.92781626381196 0.144367472376081 0.0721837361880405 38 0.925887321522612 0.148225356954775 0.0741126784773877 39 0.903013349884683 0.193973300230634 0.0969866501153168 40 0.872960851496963 0.254078297006074 0.127039148503037 41 0.858402238539462 0.283195522921076 0.141597761460538 42 0.87805993612833 0.243880127743341 0.121940063871671 43 0.847017201127069 0.305965597745863 0.152982798872931 44 0.833510219295858 0.332979561408284 0.166489780704142 45 0.816219982928694 0.367560034142613 0.183780017071306 46 0.835456266183868 0.329087467632264 0.164543733816132 47 0.80219197447196 0.39561605105608 0.19780802552804 48 0.874519956128545 0.250960087742910 0.125480043871455 49 0.844457599680325 0.311084800639350 0.155542400319675 50 0.81436990242759 0.371260195144820 0.185630097572410 51 0.774315927787588 0.451368144424823 0.225684072212412 52 0.737390849784539 0.525218300430922 0.262609150215461 53 0.69280374617528 0.614392507649441 0.307196253824720 54 0.69615738479118 0.607685230417638 0.303842615208819 55 0.706037015082325 0.58792596983535 0.293962984917675 56 0.8259081196424 0.348183760715201 0.174091880357601 57 0.807540062079463 0.384919875841074 0.192459937920537 58 0.838319492352599 0.323361015294802 0.161680507647401 59 0.855107717105286 0.289784565789428 0.144892282894714 60 0.884899786344764 0.230200427310471 0.115100213655236 61 0.887828255626977 0.224343488746046 0.112171744373023 62 0.895259140353008 0.209481719293984 0.104740859646992 63 0.887664414752807 0.224671170494386 0.112335585247193 64 0.862590277417047 0.274819445165905 0.137409722582953 65 0.837419607093023 0.325160785813953 0.162580392906977 66 0.810012639251043 0.379974721497914 0.189987360748957 67 0.86165200408684 0.27669599182632 0.13834799591316 68 0.831527259690885 0.336945480618230 0.168472740309115 69 0.822268157107777 0.355463685784446 0.177731842892223 70 0.824156142776244 0.351687714447513 0.175843857223756 71 0.84185049113295 0.3162990177341 0.15814950886705 72 0.809586082128986 0.380827835742029 0.190413917871014 73 0.875090117997394 0.249819764005212 0.124909882002606 74 0.881271567115005 0.237456865769991 0.118728432884995 75 0.853324663657492 0.293350672685016 0.146675336342508 76 0.833572038552104 0.332855922895791 0.166427961447896 77 0.799160491523575 0.40167901695285 0.200839508476425 78 0.80998376612644 0.380032467747119 0.190016233873559 79 0.780494427013727 0.439011145972546 0.219505572986273 80 0.737726772899324 0.524546454201352 0.262273227100676 81 0.782147287941674 0.435705424116652 0.217852712058326 82 0.85886701413298 0.28226597173404 0.14113298586702 83 0.827105975177522 0.345788049644957 0.172894024822478 84 0.812641122634996 0.374717754730008 0.187358877365004 85 0.786013941503025 0.42797211699395 0.213986058496975 86 0.742397062793308 0.515205874413384 0.257602937206692 87 0.696579125820716 0.606841748358567 0.303420874179284 88 0.64756414449169 0.704871711016619 0.352435855508309 89 0.628105338025415 0.74378932394917 0.371894661974585 90 0.59238095208388 0.815238095832241 0.407619047916121 91 0.745030899273056 0.509938201453888 0.254969100726944 92 0.702786322336079 0.594427355327842 0.297213677663921 93 0.858458880221833 0.283082239556334 0.141541119778167 94 0.860509924195528 0.278980151608944 0.139490075804472 95 0.85644019206129 0.287119615877422 0.143559807938711 96 0.877399010729529 0.245201978540943 0.122600989270471 97 0.928711753809792 0.142576492380415 0.0712882461902077 98 0.967727634879842 0.0645447302403161 0.0322723651201580 99 0.971657780167688 0.056684439664624 0.028342219832312 100 0.962680579877633 0.0746388402447343 0.0373194201223672 101 0.955678120749645 0.0886437585007098 0.0443218792503549 102 0.937179251703054 0.125641496593892 0.0628207482969459 103 0.938586674236967 0.122826651526066 0.0614133257630328 104 0.969359527409302 0.0612809451813961 0.0306404725906981 105 0.962588049832229 0.0748239003355426 0.0374119501677713 106 0.952722668936845 0.0945546621263105 0.0472773310631553 107 0.95338292524435 0.0932341495112992 0.0466170747556496 108 0.980981643446963 0.0380367131060748 0.0190183565530374 109 0.972242452666677 0.0555150946666459 0.0277575473333230 110 0.983938746652355 0.0321225066952893 0.0160612533476447 111 0.977943910459217 0.044112179081566 0.022056089540783 112 0.97359331383682 0.0528133723263609 0.0264066861631805 113 0.978940109043986 0.0421197819120272 0.0210598909560136 114 0.96896231457732 0.0620753708453598 0.0310376854226799 115 0.946498386281995 0.107003227436010 0.0535016137180052 116 0.913333563826761 0.173332872346478 0.0866664361732388 117 0.903775875321915 0.192448249356171 0.0962241246780853 118 0.955724996965757 0.0885500060684863 0.0442750030342432 119 0.943789655697362 0.112420688605276 0.0562103443026379 120 0.95674543562426 0.086509128751479 0.0432545643757395 121 0.911405549136428 0.177188901727144 0.0885944508635718 122 0.825738173839069 0.348523652321862 0.174261826160931 123 0.679798054988813 0.640403890022373 0.320201945011187 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 7 0.0679611650485437 NOK 10% type I error level 25 0.242718446601942 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t12905497188g8k2ge7hjdufet/10tet91290549744.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905497188g8k2ge7hjdufet/10tet91290549744.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905497188g8k2ge7hjdufet/1muex1290549744.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905497188g8k2ge7hjdufet/1muex1290549744.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905497188g8k2ge7hjdufet/2fmdi1290549744.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905497188g8k2ge7hjdufet/2fmdi1290549744.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905497188g8k2ge7hjdufet/3fmdi1290549744.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905497188g8k2ge7hjdufet/3fmdi1290549744.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905497188g8k2ge7hjdufet/4fmdi1290549744.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905497188g8k2ge7hjdufet/4fmdi1290549744.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905497188g8k2ge7hjdufet/5fmdi1290549744.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905497188g8k2ge7hjdufet/5fmdi1290549744.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905497188g8k2ge7hjdufet/6qvck1290549744.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905497188g8k2ge7hjdufet/6qvck1290549744.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905497188g8k2ge7hjdufet/7i4u51290549744.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905497188g8k2ge7hjdufet/7i4u51290549744.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905497188g8k2ge7hjdufet/8i4u51290549744.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905497188g8k2ge7hjdufet/8i4u51290549744.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905497188g8k2ge7hjdufet/9tet91290549744.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905497188g8k2ge7hjdufet/9tet91290549744.ps (open in new window)

Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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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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