ws4q1

*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, 30 Nov 2010 13:13:58 +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/30/t1291122841cxhfjmqtndlra2i.htm/, Retrieved Tue, 30 Nov 2010 14:14:24 +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/30/t1291122841cxhfjmqtndlra2i.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 «

13 14 13 3 25 55 147 12 8 13 5 158 7 71 10 12 16 6 0 0 0 9 7 12 6 143 10 0 10 10 11 5 67 74 43 12 7 12 3 0 0 0 13 16 18 8 148 138 8 12 11 11 4 28 0 0 12 14 14 4 114 113 34 6 6 9 4 0 0 0 5 16 14 6 123 115 103 12 11 12 6 145 9 0 11 16 11 5 113 114 73 14 12 12 4 152 59 159 14 7 13 6 0 0 0 12 13 11 4 36 114 113 12 11 12 6 0 0 0 11 15 16 6 8 102 44 11 7 9 4 108 0 0 7 9 11 4 112 86 0 9 7 13 2 51 17 41 11 14 15 7 43 45 74 11 15 10 5 120 123 0 12 7 11 4 13 24 0 12 15 13 6 55 5 0 11 17 16 6 103 123 32 11 15 15 7 127 136 126 8 14 14 5 14 4 154 9 14 14 6 135 76 129 12 8 14 4 38 99 98 10 8 8 4 11 98 82 10 14 13 7 43 67 45 12 14 15 7 141 92 8 8 8 13 4 62 13 0 12 11 11 4 62 24 129 11 16 15 6 135 129 31 12 10 15 6 117 117 117 7 8 9 5 82 11 99 11 14 13 6 145 20 55 11 16 16 7 87 91 132 12 13 13 6 76 111 58 9 5 11 3 124 0 0 15 8 12 3 151 58 0 11 10 12 4 131 0 0 11 8 12 6 127 146 101 11 13 14 7 76 129 31 11 15 14 5 25 48 147 15 6 8 4 0 0 0 11 12 13 5 58 111 132 12 16 16 6 115 32 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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Liked[t] = + 6.43355012221171 + 0.193380953793444FindingFriends[t] -0.0464345383611361KnowingPeople[t] -0.0364209175232498Celebrity[t] + 0.00735267314025024firstbestfriend[t] -0.00158359380850347secondbestfriend[t] + 0.0410246866096088thirdbestfriend[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) 6.43355012221171 1.290503 4.9853 2e-06 1e-06 FindingFriends 0.193380953793444 0.08554 2.2607 0.025226 0.012613 KnowingPeople -0.0464345383611361 0.094326 -0.4923 0.623249 0.311625 Celebrity -0.0364209175232498 0.005816 -6.2625 0 0 firstbestfriend 0.00735267314025024 0.004876 1.508 0.133676 0.066838 secondbestfriend -0.00158359380850347 0.004979 -0.3181 0.750891 0.375446 thirdbestfriend 0.0410246866096088 0.006274 6.5386 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.692252665096913 R-squared 0.479213752333779 Adjusted R-squared 0.458242494038495 F-TEST (value) 22.8509775420363 F-TEST (DF numerator) 6 F-TEST (DF denominator) 149 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.98677930956923 Sum Squared Residuals 1329.20674596655 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 14.3155043325520 -1.31550433255197 2 13 12.2639306220099 0.736069377990063 3 16 7.59161969467304 8.40838030532696 4 12 8.666007753656 3.333992246344 5 11 9.86041437169924 1.13958562830077 6 12 8.31981704663535 3.68018295336465 7 18 9.11103973962275 8.88896026037725 8 11 8.30353282359455 2.69646717640544 9 14 10.0124523429385 3.98754765706153 10 9 7.16954494471257 1.83045505528743 11 14 11.3867850013238 2.61321499867616 12 12 9.0767014016808 2.92329859831920 13 11 11.2808079057255 -0.280807905725493 14 12 15.9850847984374 -3.98508479843742 15 13 8.59731620165249 4.40268379834751 16 11 12.7247450247107 -1.72474502471068 17 12 8.02481614062105 3.97518385937895 18 16 9.3480780608605 6.65192193913951 19 9 8.88410387446568 0.115896125534322 20 11 7.91093260759933 3.08906739240067 21 13 9.80617248918043 3.19382751081957 22 15 10.9364406869801 4.0635593130199 23 10 8.36965668929041 1.63034331070959 24 11 8.34097462853127 2.65902537146873 25 13 8.23555704084775 4.76444295915225 26 16 9.42816122316811 6.57183877683189 27 15 13.4968073595258 1.50319264047418 28 14 13.5628144144964 0.437185585503645 29 14 13.4698119812844 0.530188018715643 30 14 12.3800066707803 1.61999332921972 31 8 11.1399111964614 -3.1399111964614 32 13 9.51850475772092 3.48149524227908 33 15 9.06832538328422 5.93167461671578 34 13 7.89871679076215 5.10128320923785 35 11 13.8077020315985 -2.80770203159851 36 15 9.65935505255663 5.34064494744337 37 15 13.5461212941208 1.45387870587922 38 9 11.8805795442187 -2.88057954421874 39 13 10.9829550644389 2.01704493556111 40 16 13.4736757365950 2.52632426340501 41 13 10.6944031331712 2.30559686682878 42 11 8.74427473136832 2.25572526863168 43 12 9.87193057293912 2.12806942706087 44 12 8.91391174160802 3.08608825839198 45 12 12.8168169422518 -0.816816942251775 46 14 9.32843003484203 4.67156996515797 47 14 13.8205512082169 0.179448791783113 48 8 8.90997352885356 -0.909973528853565 49 13 13.4873563278487 -0.487356327848704 50 16 13.6335623110539 2.36643768894609 51 13 10.6818711502428 2.31812884975725 52 11 12.8825246638535 -1.88252466385354 53 14 14.4653255201928 -0.465325520192839 54 13 8.18391693778226 4.81608306221774 55 13 8.16174893521547 4.83825106478453 56 13 13.2494694760819 -0.249469476081869 57 12 12.9529266975861 -0.952926697586074 58 16 14.4670344139470 1.53296558605302 59 15 9.01541869105406 5.98458130894594 60 8 7.36999273775902 0.630007262240984 61 3 7.91567953154094 -4.91567953154094 62 6 8.35781748343513 -2.35781748343513 63 6 8.28775936850893 -2.28775936850893 64 6 7.45583656471599 -1.45583656471599 65 5 8.08344700919629 -3.08344700919629 66 5 5.511976948737 -0.511976948736998 67 6 8.89147364422693 -2.89147364422693 68 5 4.84504609341077 0.154953906589231 69 6 4.81001909467335 1.18998090532665 70 2 3.83470360018407 -1.83470360018407 71 5 8.38872147939064 -3.38872147939064 72 5 8.14696316584733 -3.14696316584733 73 5 3.75695538040631 1.24304461959369 74 6 8.64614466766673 -2.64614466766673 75 6 7.14385127058835 -1.14385127058835 76 6 5.34055525555205 0.659444744447947 77 5 8.62854438999498 -3.62854438999498 78 5 9.16797337694351 -4.16797337694351 79 4 2.2900183584957 1.7099816415043 80 2 5.42651802844346 -3.42651802844346 81 4 5.09819485093413 -1.09819485093413 82 6 5.1148324058186 0.885167594181396 83 6 5.02832869104215 0.97167130895785 84 5 5.93431490424386 -0.934314904243865 85 3 6.17690695434677 -3.17690695434677 86 6 4.25716151738218 1.74283848261782 87 4 5.32903865947798 -1.32903865947798 88 5 4.46401064067152 0.535989359328476 89 8 7.41258423288402 0.587415767115976 90 4 5.79425528101841 -1.79425528101841 91 6 4.81900788364373 1.18099211635627 92 6 8.42201390247452 -2.42201390247452 93 7 5.29159805129707 1.70840194870293 94 6 3.80433189548142 2.19566810451858 95 5 8.37733346491905 -3.37733346491905 96 4 4.26058255462206 -0.260582554622060 97 6 7.13674586461564 -1.13674586461564 98 3 6.88622964004309 -3.88622964004309 99 5 8.65463320667478 -3.65463320667478 100 6 2.96753006634673 3.03246993365327 101 7 7.7689078576824 -0.768907857682404 102 7 7.01602018530557 -0.0160201853055708 103 6 8.49692186558065 -2.49692186558065 104 3 5.17090585905829 -2.17090585905829 105 2 5.20463452039079 -3.20463452039079 106 8 5.7998801970786 2.20011980292140 107 3 7.71620447360656 -4.71620447360656 108 8 7.8669981010868 0.133001898913202 109 3 7.87981089352825 -4.87981089352825 110 4 7.70313697133771 -3.70313697133771 111 5 5.3616431665055 -0.361643166505503 112 7 7.10401220964308 -0.104012209643079 113 6 4.56746287884706 1.43253712115294 114 6 3.55673450993867 2.44326549006133 115 7 5.12976842138866 1.87023157861134 116 6 6.02203664825643 -0.0220366482564316 117 6 7.56181266301417 -1.56181266301417 118 6 6.43512286675337 -0.435122866753366 119 6 5.95136835655516 0.048631643444842 120 4 8.8168156411907 -4.8168156411907 121 4 9.38340187752423 -5.38340187752423 122 5 9.30798102815149 -4.30798102815149 123 4 6.68280863610045 -2.68280863610045 124 6 7.91640904965717 -1.91640904965717 125 6 5.0075080026229 0.992491997377104 126 5 7.43604854723178 -2.43604854723178 127 8 5.59109100115357 2.40890899884643 128 6 8.819880491615 -2.819880491615 129 5 4.57055686344742 0.429443136552582 130 4 7.90039393084315 -3.90039393084315 131 8 7.87710607089346 0.122893929106540 132 6 8.31742118095685 -2.31742118095685 133 4 7.07896863176426 -3.07896863176426 134 6 8.35651877783786 -2.35651877783786 135 6 8.86689485117578 -2.86689485117578 136 4 6.32722140752693 -2.32722140752693 137 6 6.37121510410733 -0.371215104107333 138 3 8.88258430050816 -5.88258430050816 139 6 6.22768861828547 -0.227688618285467 140 5 8.04317230387878 -3.04317230387878 141 4 7.2791941882781 -3.2791941882781 142 6 8.68898412379803 -2.68898412379803 143 4 3.5657437202224 0.434256279777599 144 4 7.02504147435917 -3.02504147435917 145 4 6.53786233632064 -2.53786233632064 146 6 3.73585609071569 2.26414390928431 147 5 5.14147386535727 -0.141473865357265 148 6 5.34713791652072 0.65286208347928 149 6 9.7587852777116 -3.75878527771159 150 8 6.38252140459242 1.61747859540758 151 7 7.8928414732326 -0.892841473232592 152 7 8.06172628598513 -1.06172628598513 153 4 8.5878689598422 -4.58786895984219 154 6 4.6570021730758 1.34299782692420 155 6 6.14188311156431 -0.141883111564314 156 2 3.45444477561568 -1.45444477561568 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.263582312525539 0.527164625051078 0.736417687474461 11 0.144714150877034 0.289428301754067 0.855285849122966 12 0.132105238169263 0.264210476338526 0.867894761830737 13 0.185410730265825 0.37082146053165 0.814589269734175 14 0.119004960479286 0.238009920958572 0.880995039520714 15 0.0954400099254571 0.190880019850914 0.904559990074543 16 0.070373186851487 0.140746373702974 0.929626813148513 17 0.0706570519519885 0.141314103903977 0.929342948048012 18 0.0617651661852747 0.123530332370549 0.938234833814725 19 0.0446320291759189 0.0892640583518378 0.955367970824081 20 0.0307449556778491 0.0614899113556981 0.96925504432215 21 0.0858533436159263 0.171706687231853 0.914146656384074 22 0.0625978339317105 0.125195667863421 0.93740216606829 23 0.0905379425599448 0.181075885119890 0.909462057440055 24 0.0687334487765156 0.137466897553031 0.931266551223484 25 0.0607754697382317 0.121550939476463 0.939224530261768 26 0.0747526843179343 0.149505368635869 0.925247315682066 27 0.0521633895477667 0.104326779095533 0.947836610452233 28 0.0355664117091135 0.071132823418227 0.964433588290887 29 0.0235192464755622 0.0470384929511244 0.976480753524438 30 0.0197057833392292 0.0394115666784585 0.98029421666077 31 0.0472526194020465 0.094505238804093 0.952747380597954 32 0.0466421320390200 0.0932842640780401 0.95335786796098 33 0.0551001099310059 0.110200219862012 0.944899890068994 34 0.0846545215692222 0.169309043138444 0.915345478430778 35 0.0756582691248718 0.151316538249744 0.924341730875128 36 0.0967823597075602 0.193564719415120 0.90321764029244 37 0.0863536253255532 0.172707250651106 0.913646374674447 38 0.101534609770583 0.203069219541167 0.898465390229417 39 0.0909214507792902 0.181842901558580 0.90907854922071 40 0.0775539616979505 0.155107923395901 0.92244603830205 41 0.0721346145133822 0.144269229026764 0.927865385486618 42 0.0812335701177074 0.162467140235415 0.918766429882293 43 0.0849699858250933 0.169939971650187 0.915030014174907 44 0.115999406730558 0.231998813461116 0.884000593269442 45 0.0943140528122358 0.188628105624472 0.905685947187764 46 0.141551166652709 0.283102333305418 0.85844883334729 47 0.114484909496062 0.228969818992124 0.885515090503938 48 0.160262354352461 0.320524708704921 0.83973764564754 49 0.130983918836451 0.261967837672902 0.86901608116355 50 0.133684881323056 0.267369762646113 0.866315118676944 51 0.175234577580867 0.350469155161735 0.824765422419133 52 0.216497276358335 0.432994552716670 0.783502723641665 53 0.186984460714258 0.373968921428516 0.813015539285742 54 0.45522876866436 0.91045753732872 0.54477123133564 55 0.779072012016526 0.441855975966949 0.220927987983474 56 0.746155942091714 0.507688115816573 0.253844057908286 57 0.707430703284961 0.585138593430079 0.292569296715039 58 0.697718205309792 0.604563589380415 0.302281794690208 59 0.999891111742083 0.000217776515833246 0.000108888257916623 60 0.999982905383057 3.41892338854004e-05 1.70946169427002e-05 61 0.999999994386622 1.12267549963632e-08 5.61337749818159e-09 62 0.999999997168623 5.6627538295087e-09 2.83137691475435e-09 63 0.9999999944618 1.10764001892749e-08 5.53820009463744e-09 64 0.999999995865445 8.26910938794447e-09 4.13455469397223e-09 65 0.999999999833878 3.32244216904573e-10 1.66122108452287e-10 66 0.999999999948454 1.03091502986249e-10 5.15457514931245e-11 67 0.999999999986005 2.79909869098885e-11 1.39954934549443e-11 68 0.99999999997573 4.85393561900936e-11 2.42696780950468e-11 69 0.999999999978627 4.27460368261367e-11 2.13730184130684e-11 70 0.999999999954596 9.08077927007784e-11 4.54038963503892e-11 71 0.999999999982994 3.40116280416127e-11 1.70058140208064e-11 72 0.999999999990698 1.8603695594998e-11 9.301847797499e-12 73 0.999999999987132 2.57358424944906e-11 1.28679212472453e-11 74 0.999999999996222 7.55568715449036e-12 3.77784357724518e-12 75 0.999999999993823 1.23530247009649e-11 6.17651235048244e-12 76 0.9999999999887 2.26018830969202e-11 1.13009415484601e-11 77 0.999999999992453 1.50937844902276e-11 7.5468922451138e-12 78 0.999999999997318 5.36316233354578e-12 2.68158116677289e-12 79 0.999999999996263 7.47324943916945e-12 3.73662471958473e-12 80 0.999999999998744 2.51241692455181e-12 1.25620846227591e-12 81 0.999999999997592 4.81603390464634e-12 2.40801695232317e-12 82 0.999999999995371 9.25809267085742e-12 4.62904633542871e-12 83 0.999999999989295 2.14107906756972e-11 1.07053953378486e-11 84 0.999999999975087 4.98267680180559e-11 2.49133840090280e-11 85 0.999999999984354 3.12927092675092e-11 1.56463546337546e-11 86 0.999999999975904 4.81919179205085e-11 2.40959589602543e-11 87 0.99999999994998 1.00041482533270e-10 5.00207412666352e-11 88 0.9999999998958 2.08398922090946e-10 1.04199461045473e-10 89 0.999999999910811 1.78377242550908e-10 8.9188621275454e-11 90 0.99999999984045 3.19098903952809e-10 1.59549451976405e-10 91 0.999999999632642 7.34715958726463e-10 3.67357979363231e-10 92 0.999999999490386 1.01922790240372e-09 5.09613951201858e-10 93 0.999999999030698 1.93860390428540e-09 9.6930195214270e-10 94 0.999999998576504 2.84699154829328e-09 1.42349577414664e-09 95 0.999999998539825 2.92035062382435e-09 1.46017531191217e-09 96 0.999999996787993 6.42401489702765e-09 3.21200744851383e-09 97 0.999999997623704 4.75259186919359e-09 2.37629593459679e-09 98 0.9999999971297 5.74059842356264e-09 2.87029921178132e-09 99 0.999999997475364 5.04927255294656e-09 2.52463627647328e-09 100 0.999999996588998 6.82200438806172e-09 3.41100219403086e-09 101 0.999999992798295 1.44034103947680e-08 7.20170519738401e-09 102 0.999999985018166 2.99636684108531e-08 1.49818342054265e-08 103 0.99999997968971 4.06205810610318e-08 2.03102905305159e-08 104 0.999999969773612 6.04527753232706e-08 3.02263876616353e-08 105 0.999999974861579 5.02768427219898e-08 2.51384213609949e-08 106 0.999999984845044 3.03099114289308e-08 1.51549557144654e-08 107 0.999999994294316 1.14113674658132e-08 5.70568373290659e-09 108 0.999999994407063 1.11858740718162e-08 5.59293703590808e-09 109 0.99999999642603 7.14793816832067e-09 3.57396908416033e-09 110 0.999999996437489 7.12502233172949e-09 3.56251116586474e-09 111 0.99999999264864 1.47027182844689e-08 7.35135914223446e-09 112 0.99999998952689 2.09462197209658e-08 1.04731098604829e-08 113 0.999999981987253 3.60254932229619e-08 1.80127466114810e-08 114 0.999999961091246 7.78175074080563e-08 3.89087537040281e-08 115 0.999999932697848 1.34604303444207e-07 6.73021517221035e-08 116 0.999999865810882 2.68378236135561e-07 1.34189118067781e-07 117 0.999999715751429 5.68497141843663e-07 2.84248570921831e-07 118 0.999999364295055 1.27140989035312e-06 6.3570494517656e-07 119 0.99999861986197 2.76027606046535e-06 1.38013803023268e-06 120 0.999997965772912 4.06845417683544e-06 2.03422708841772e-06 121 0.999998216048197 3.56790360613776e-06 1.78395180306888e-06 122 0.999997016891542 5.9662169156031e-06 2.98310845780155e-06 123 0.999994931123753 1.01377524932722e-05 5.06887624663609e-06 124 0.999988683627912 2.26327441755489e-05 1.13163720877745e-05 125 0.999975054947065 4.98901058698661e-05 2.49450529349330e-05 126 0.999949194495917 0.000101611008166418 5.08055040832088e-05 127 0.999977155936508 4.56881269843372e-05 2.28440634921686e-05 128 0.999952841774687 9.43164506252129e-05 4.71582253126064e-05 129 0.999895891999082 0.000208216001835973 0.000104108000917986 130 0.999833256217018 0.000333487565963756 0.000166743782981878 131 0.999759513217193 0.000480973565614339 0.000240486782807170 132 0.999531087116624 0.000937825766752634 0.000468912883376317 133 0.999330679656188 0.00133864068762343 0.000669320343811715 134 0.99866072949167 0.00267854101666116 0.00133927050833058 135 0.997375472514568 0.00524905497086352 0.00262452748543176 136 0.997175267415376 0.00564946516924894 0.00282473258462447 137 0.994814515202772 0.0103709695944558 0.00518548479722792 138 0.993867104294203 0.0122657914115946 0.00613289570579732 139 0.987113954807589 0.0257720903848223 0.0128860451924111 140 0.979495073314488 0.0410098533710238 0.0205049266855119 141 0.971354328538626 0.0572913429227471 0.0286456714613735 142 0.948513989437764 0.102972021124473 0.0514860105622363 143 0.916523126211482 0.166953747577035 0.0834768737885176 144 0.87584862398679 0.248302752026418 0.124151376013209 145 0.812044103941203 0.375911792117594 0.187955896058797 146 0.688334611452606 0.623330777094789 0.311665388547394 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 78 0.569343065693431 NOK 5% type I error level 84 0.613138686131387 NOK 10% type I error level 90 0.656934306569343 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/30/t1291122841cxhfjmqtndlra2i/10agng1291122827.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291122841cxhfjmqtndlra2i/10agng1291122827.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291122841cxhfjmqtndlra2i/1lf841291122827.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291122841cxhfjmqtndlra2i/1lf841291122827.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291122841cxhfjmqtndlra2i/2w6771291122827.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291122841cxhfjmqtndlra2i/2w6771291122827.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291122841cxhfjmqtndlra2i/3w6771291122827.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291122841cxhfjmqtndlra2i/3w6771291122827.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291122841cxhfjmqtndlra2i/4w6771291122827.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291122841cxhfjmqtndlra2i/4w6771291122827.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291122841cxhfjmqtndlra2i/5og7a1291122827.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291122841cxhfjmqtndlra2i/5og7a1291122827.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291122841cxhfjmqtndlra2i/6og7a1291122827.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291122841cxhfjmqtndlra2i/6og7a1291122827.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291122841cxhfjmqtndlra2i/7z7od1291122827.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291122841cxhfjmqtndlra2i/7z7od1291122827.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291122841cxhfjmqtndlra2i/8z7od1291122827.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291122841cxhfjmqtndlra2i/8z7od1291122827.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291122841cxhfjmqtndlra2i/9agng1291122827.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291122841cxhfjmqtndlra2i/9agng1291122827.ps (open in new window)

Parameters (Session):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 3 ; 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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