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# WS7 Multiple regression (inclusief tijd)

*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, 22 Nov 2011 19:04:31 -0500

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Nov/22/t13220067082q9usig36kfycz0.htm/, Retrieved Thu, 23 May 2013 21:44:40 +0000

Original text written by user:

IsPrivate?
No (this computation is public)

User-defined keywords:

System-generated keywords (parent):
(pk = 0)
Estimated Impact
23

Dataseries X:
» Textfile « » CSV « » Correlation Matrix « » Notched Boxplots «

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 16 seconds R Server 'AstonUniversity' @ aston.wessa.net

 Multiple Linear Regression - Estimated Regression Equation O[t] = + 28.2103187556998 -1.21064258019504month[t] -0.0662911074151963CM[t] + 0.220046465031066DA[t] -0.137980253016111PE[t] -0.26784726733119PC[t] + 0.415218299040597PS[t] + e[t]

 Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STATH0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 28.2103187556998 14.945205 1.8876 0.060988 0.030494 month -1.21064258019504 1.484765 -0.8154 0.416133 0.208066 CM -0.0662911074151963 0.06322 -1.0486 0.296039 0.148019 DA 0.220046465031066 0.112769 1.9513 0.052859 0.02643 PE -0.137980253016111 0.105245 -1.311 0.191823 0.095912 PC -0.26784726733119 0.131479 -2.0372 0.043366 0.021683 PS 0.415218299040597 0.076262 5.4447 0 0

 Multiple Linear Regression - Regression Statistics Multiple R 0.475140658091823 R-squared 0.225758644971931 Adjusted R-squared 0.195196486220823 F-TEST (value) 7.38686840842831 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 5.99882120311257e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.50319920019948 Sum Squared Residuals 1865.4055047143

 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals InterpolationForecast ResidualsPrediction Error 1 26 24.0374886522375 1.96251134776248 2 23 25.3495865301589 -2.34958653015894 3 25 25.475972029367 -0.475972029367048 4 23 23.1284201938045 -0.128420193804457 5 19 22.9500814574386 -3.95008145743857 6 29 24.0584511369935 4.94154886300652 7 25 24.7698210792691 0.230178920730872 8 21 22.5496645045615 -1.54966450456146 9 22 21.9594136369515 0.0405863630485437 10 25 22.4483653623576 2.5516346376424 11 24 20.1830584601753 3.8169415398247 12 18 19.758708271868 -1.75870827186802 13 22 18.3715882325683 3.6284117674317 14 15 20.6721227164876 -5.67212271648763 15 22 23.4194974139702 -1.41949741397022 16 28 24.2583867344211 3.74161326557894 17 20 22.1745527790773 -2.17455277907735 18 12 19.0223933275117 -7.02239332751165 19 24 21.452649931995 2.54735006800503 20 20 21.38755577033 -1.38755577033004 21 21 23.2363427177809 -2.23634271778094 22 20 20.6603585270493 -0.660358527049277 23 21 19.1676075475502 1.83239245244976 24 23 21.0808678482334 1.9191321517666 25 28 21.9086780871876 6.09132191281236 26 24 21.8732986320662 2.12670136793381 27 24 23.4621590675112 0.537840932488761 28 24 20.3769768698911 3.62302313010889 29 23 21.9728364986306 1.02716350136943 30 23 22.6913379986673 0.308662001332742 31 29 24.2449226209782 4.75507737902181 32 24 21.9938336523331 2.00616634766692 33 18 25.0192850575274 -7.01928505752744 34 25 25.9632786504055 -0.963278650405516 35 21 22.581530081731 -1.58153008173103 36 26 26.6957457480054 -0.695745748005398 37 22 25.1140040163943 -3.11400401639428 38 22 22.8265637086898 -0.826563708689818 39 22 22.5514357077084 -0.551435707708399 40 23 25.597809613408 -2.59780961340799 41 30 22.8956598965973 7.10434010340269 42 23 22.6640153037034 0.335984696296612 43 17 18.7116919232637 -1.71169192326375 44 23 23.7908994040719 -0.790899404071906 45 23 24.2516305620011 -1.25163056200108 46 25 22.3938889818795 2.6061110181205 47 24 20.7224544830737 3.27754551692626 48 24 27.4350166076499 -3.43501660764986 49 23 22.9638317901915 0.0361682098085087 50 21 23.8197102970576 -2.81971029705757 51 24 25.6897981449798 -1.68979814497982 52 24 21.8121143105652 2.1878856894348 53 28 21.4843602617253 6.51563973827473 54 16 21.0239734605562 -5.02397346055622 55 20 19.7961912185799 0.203808781420071 56 29 23.4076262084897 5.59237379151032 57 27 23.8430878411385 3.15691215886154 58 22 23.1637478787013 -1.16374787870128 59 28 23.9462766584402 4.05372334155984 60 16 20.3530491841121 -4.35304918411208 61 25 22.856213047771 2.14378695222901 62 24 23.4766566321187 0.523343367881267 63 28 23.643504256664 4.35649574333604 64 24 24.2220288125445 -0.222028812544506 65 23 22.6735750918463 0.326424908153682 66 30 26.892670610508 3.10732938949195 67 24 21.2834820011933 2.71651799880671 68 21 24.0991527443775 -3.09915274437747 69 25 23.2701385800396 1.72986141996037 70 25 23.9184784749754 1.08152152502457 71 22 20.7817857396728 1.21821426032724 72 23 22.4276112295295 0.572388770470477 73 26 22.8261427894469 3.1738572105531 74 23 21.6022041971754 1.39779580282461 75 25 23.0644124230201 1.93558757697994 76 21 21.2854869394797 -0.285486939479683 77 25 23.6415164544428 1.35848354555723 78 24 22.14479090909 1.85520909091001 79 29 23.5123597023566 5.48764029764339 80 22 23.647883644284 -1.64788364428402 81 27 23.5680895071284 3.43191049287156 82 26 19.6290819723257 6.37091802767428 83 22 21.3049635323155 0.695036467684502 84 24 22.0327432801393 1.9672567198607 85 27 23.1059173146214 3.89408268537864 86 24 21.3540418746079 2.64595812539211 87 24 24.8509010035633 -0.85090100356334 88 29 24.3555973150956 4.64440268490436 89 22 22.1416478096984 -0.141647809698429 90 21 20.5728437393499 0.427156260650134 91 24 20.4451840742043 3.55481592579566 92 24 21.7194362584081 2.28056374159187 93 23 21.9413988203372 1.05860117966277 94 20 22.3039684205901 -2.30396842059012 95 27 21.3481089215037 5.65189107849627 96 26 23.4245663221755 2.57543367782448 97 25 21.9468473960217 3.05315260397831 98 21 20.0638274017009 0.936172598299128 99 21 20.7680155733594 0.231984426640602 100 19 20.3833611957976 -1.38336119579757 101 21 21.5815065428908 -0.581506542890761 102 21 21.2761526393298 -0.276152639329839 103 16 19.762757490919 -3.76275749091905 104 22 20.6424325518234 1.35756744817658 105 29 21.7679585179577 7.23204148204232 106 15 21.7289577426614 -6.72895774266144 107 17 20.6913473995302 -3.69134739953016 108 15 19.9102562803143 -4.91025628031433 109 21 21.6460446218128 -0.646044621812844 110 21 21.0230224835545 -0.0230224835545167 111 19 19.2848425566571 -0.284842556657121 112 24 18.0601917928712 5.93980820712883 113 20 22.2492483774651 -2.2492483774651 114 17 25.0896164950748 -8.08961649507482 115 23 24.8187204846044 -1.81872048460442 116 24 22.390211609342 1.60978839065802 117 14 22.0566557391386 -8.05665573913864 118 19 22.8529153427126 -3.85291534271264 119 24 22.1817391564752 1.81826084352478 120 13 20.4211887148614 -7.42118871486136 121 22 25.3603868886685 -3.36038688866847 122 16 21.1243457414569 -5.12434574145691 123 19 23.2285530941963 -4.22855309419634 124 25 22.7392989214982 2.26070107850183 125 25 24.1556659998062 0.844334000193838 126 23 21.4297237607164 1.57027623928362 127 24 23.5535090421773 0.446490957822701 128 26 23.5032601759348 2.49673982406516 129 26 21.4883530022328 4.51164699776715 130 25 24.1320517727117 0.867948227288323 131 18 22.2911756530787 -4.29117565307865 132 21 19.8686050301926 1.1313949698074 133 26 23.6503640710713 2.34963592892873 134 23 21.9643249916158 1.03567500838418 135 23 19.7571959581477 3.24280404185231 136 22 22.5985262477796 -0.598526247779604 137 20 22.3975581072706 -2.39755810727064 138 13 22.0664261853111 -9.0664261853111 139 24 21.3905116856181 2.60948831438186 140 15 21.5031177034133 -6.50311770341332 141 14 23.0933834365365 -9.0933834365365 142 22 24.0488715152901 -2.0488715152901 143 10 17.6446697470617 -7.64466974706173 144 24 24.4269628455801 -0.426962845580127 145 22 21.8304203794509 0.169579620549062 146 24 25.7882219661376 -1.78822196613757 147 19 21.6534545779183 -2.65345457791829 148 20 22.0853596160821 -2.0853596160821 149 13 17.1094479686178 -4.10944796861783 150 20 20.1000300761381 -0.100030076138146 151 22 23.1856636465606 -1.18566364656058 152 24 23.383262376688 0.616737623311961 153 29 23.2741564748344 5.72584352516563 154 12 20.9762473114534 -8.97624731145338 155 20 20.9222015621339 -0.922201562133887 156 21 21.4456831015455 -0.445683101545466 157 24 23.6330707117065 0.366929288293536 158 22 21.8927187463586 0.107281253641443 159 20 17.7211420634604 2.27885793653958

 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.527028364314466 0.945943271371068 0.472971635685534 11 0.562072176923445 0.875855646153111 0.437927823076555 12 0.488820121855344 0.977640243710687 0.511179878144656 13 0.540340997121712 0.919318005756577 0.459659002878288 14 0.741634141692737 0.516731716614525 0.258365858307263 15 0.65476777992236 0.690464440155281 0.345232220077641 16 0.623840203621298 0.752319592757404 0.376159796378702 17 0.538160411878577 0.923679176242845 0.461839588121423 18 0.676102822720441 0.647794354559118 0.323897177279559 19 0.601320656317026 0.797358687365949 0.398679343682974 20 0.588507053429423 0.822985893141154 0.411492946570577 21 0.524600811963488 0.950798376073024 0.475399188036512 22 0.455193000843371 0.910386001686743 0.544806999156629 23 0.404513233049431 0.809026466098862 0.595486766950569 24 0.408928632535249 0.817857265070498 0.591071367464751 25 0.571312477989045 0.857375044021909 0.428687522010955 26 0.510036637596389 0.979926724807221 0.489963362403611 27 0.443017030640338 0.886034061280677 0.556982969359662 28 0.437463608820323 0.874927217640646 0.562536391179677 29 0.373317525584631 0.746635051169262 0.626682474415369 30 0.312925469300043 0.625850938600086 0.687074530699957 31 0.34670530259935 0.693410605198699 0.65329469740065 32 0.29568486918651 0.591369738373019 0.70431513081349 33 0.521856236679298 0.956287526641404 0.478143763320702 34 0.470720695493071 0.941441390986142 0.529279304506929 35 0.432758547622968 0.865517095245937 0.567241452377032 36 0.375438918825549 0.750877837651099 0.624561081174451 37 0.348812634024333 0.697625268048665 0.651187365975667 38 0.297200139553495 0.594400279106991 0.702799860446505 39 0.249829277049069 0.499658554098138 0.750170722950931 40 0.222496241741992 0.444992483483984 0.777503758258008 41 0.375109750067578 0.750219500135156 0.624890249932422 42 0.32332935137381 0.64665870274762 0.67667064862619 43 0.291309744409828 0.582619488819656 0.708690255590172 44 0.24774114293544 0.49548228587088 0.75225885706456 45 0.211344650754322 0.422689301508644 0.788655349245678 46 0.19194341644786 0.383886832895721 0.80805658355214 47 0.179511293187928 0.359022586375856 0.820488706812072 48 0.164434998681522 0.328869997363043 0.835565001318478 49 0.134347119861455 0.26869423972291 0.865652880138545 50 0.124730083768585 0.24946016753717 0.875269916231415 51 0.10295397385823 0.205907947716459 0.89704602614177 52 0.0878355009662445 0.175671001932489 0.912164499033756 53 0.147397588452461 0.294795176904922 0.852602411547539 54 0.17678910553817 0.35357821107634 0.82321089446183 55 0.165267186538772 0.330534373077544 0.834732813461228 56 0.222686975466121 0.445373950932242 0.77731302453388 57 0.215131908819759 0.430263817639518 0.784868091180241 58 0.184153643078553 0.368307286157106 0.815846356921447 59 0.197351138089913 0.394702276179827 0.802648861910087 60 0.225091998997231 0.450183997994462 0.774908001002769 61 0.198880236978435 0.39776047395687 0.801119763021565 62 0.167118258423566 0.334236516847133 0.832881741576434 63 0.182344870750505 0.36468974150101 0.817655129249495 64 0.153254812636127 0.306509625272254 0.846745187363873 65 0.12643896851646 0.25287793703292 0.87356103148354 66 0.122883295308344 0.245766590616688 0.877116704691656 67 0.112248217370942 0.224496434741885 0.887751782629058 68 0.111344923410117 0.222689846820233 0.888655076589883 69 0.0947565847496516 0.189513169499303 0.905243415250348 70 0.0773605143249666 0.154721028649933 0.922639485675033 71 0.062868133666416 0.125736267332832 0.937131866333584 72 0.0496562158630924 0.0993124317261848 0.950343784136908 73 0.0466154231049721 0.0932308462099443 0.953384576895028 74 0.0373413642259392 0.0746827284518784 0.96265863577406 75 0.0310314374719754 0.0620628749439507 0.968968562528025 76 0.0238009755904018 0.0476019511808036 0.976199024409598 77 0.018685901416213 0.0373718028324261 0.981314098583787 78 0.0149571406805748 0.0299142813611496 0.985042859319425 79 0.0224781081564358 0.0449562163128716 0.977521891843564 80 0.0179212062081236 0.0358424124162473 0.982078793791876 81 0.0175253641063659 0.0350507282127317 0.982474635893634 82 0.0313505859668952 0.0627011719337903 0.968649414033105 83 0.0241773878607797 0.0483547757215594 0.97582261213922 84 0.0201726522414726 0.0403453044829452 0.979827347758527 85 0.022091303637997 0.044182607275994 0.977908696362003 86 0.0195779068105892 0.0391558136211784 0.98042209318941 87 0.0148833956440961 0.0297667912881921 0.985116604355904 88 0.0194348449283247 0.0388696898566493 0.980565155071675 89 0.015281934022926 0.030563868045852 0.984718065977074 90 0.0114350397674319 0.0228700795348638 0.988564960232568 91 0.0114936015000235 0.0229872030000471 0.988506398499976 92 0.0100487965261463 0.0200975930522927 0.989951203473854 93 0.00770634889142413 0.0154126977828483 0.992293651108576 94 0.00637095445167188 0.0127419089033438 0.993629045548328 95 0.0116764304090459 0.0233528608180919 0.988323569590954 96 0.0105750728633662 0.0211501457267324 0.989424927136634 97 0.0100579317377318 0.0201158634754636 0.989942068262268 98 0.0076964588109711 0.0153929176219422 0.992303541189029 99 0.00567885222764849 0.011357704455297 0.994321147772351 100 0.00434752048485553 0.00869504096971106 0.995652479515144 101 0.00321226565962362 0.00642453131924725 0.996787734340376 102 0.00228563328783021 0.00457126657566042 0.99771436671217 103 0.00244396470857392 0.00488792941714783 0.997556035291426 104 0.00191465160345203 0.00382930320690406 0.998085348396548 105 0.008114129825285 0.01622825965057 0.991885870174715 106 0.0181671846008459 0.0363343692016918 0.981832815399154 107 0.0180295512597239 0.0360591025194478 0.981970448740276 108 0.0227211535015447 0.0454423070030894 0.977278846498455 109 0.0175296500642828 0.0350593001285657 0.982470349935717 110 0.0128035457053405 0.0256070914106811 0.98719645429466 111 0.00926976201671092 0.0185395240334218 0.99073023798329 112 0.0227330945126732 0.0454661890253465 0.977266905487327 113 0.0205964481526727 0.0411928963053455 0.979403551847327 114 0.0571932627149 0.1143865254298 0.9428067372851 115 0.0484501837172541 0.0969003674345082 0.951549816282746 116 0.0392647290608798 0.0785294581217597 0.96073527093912 117 0.115712576239434 0.231425152478868 0.884287423760566 118 0.110870623556605 0.22174124711321 0.889129376443395 119 0.0982975543600395 0.196595108720079 0.90170244563996 120 0.171823904570047 0.343647809140093 0.828176095429954 121 0.163706791636378 0.327413583272757 0.836293208363622 122 0.195062023880454 0.390124047760908 0.804937976119546 123 0.18804298051162 0.37608596102324 0.81195701948838 124 0.187225642039559 0.374451284079118 0.81277435796044 125 0.169993306586363 0.339986613172726 0.830006693413637 126 0.138332383081952 0.276664766163903 0.861667616918048 127 0.108170210302971 0.216340420605942 0.891829789697029 128 0.111622507273308 0.223245014546616 0.888377492726692 129 0.160124830965552 0.320249661931104 0.839875169034448 130 0.137944002820249 0.275888005640497 0.862055997179751 131 0.120411351115569 0.240822702231139 0.87958864888443 132 0.104288622865574 0.208577245731148 0.895711377134426 133 0.0956630435677008 0.191326087135402 0.9043369564323 134 0.0780905262947187 0.156181052589437 0.921909473705281 135 0.106568501534918 0.213137003069835 0.893431498465082 136 0.0790195243729828 0.158039048745966 0.920980475627017 137 0.0576295417966276 0.115259083593255 0.942370458203372 138 0.146858066608714 0.293716133217428 0.853141933391286 139 0.208120044670052 0.416240089340103 0.791879955329948 140 0.188513100213958 0.377026200427916 0.811486899786042 141 0.406025649917164 0.812051299834328 0.593974350082836 142 0.356376040738363 0.712752081476727 0.643623959261637 143 0.66600437326796 0.66799125346408 0.33399562673204 144 0.60479794654466 0.79040410691068 0.39520205345534 145 0.494173129371249 0.988346258742499 0.505826870628751 146 0.423286503602423 0.846573007204846 0.576713496397577 147 0.43358327498895 0.8671665499779 0.56641672501105 148 0.303283812156225 0.60656762431245 0.696716187843775 149 0.211402600164403 0.422805200328805 0.788597399835597

 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 5 0.0357142857142857 NOK 5% type I error level 37 0.264285714285714 NOK 10% type I error level 44 0.314285714285714 NOK

Charts produced by software:
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Parameters (Session):
par1 = 7 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):
par1 = 7 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

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