*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Wed, 29 Dec 2010 10:42:05 +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/29/t12936192095ghd0cgpll8uzjz.htm/, Retrieved Wed, 29 Dec 2010 11:40:21 +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/29/t12936192095ghd0cgpll8uzjz.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 13 26 14 28 13 26 3 6 2 12 12 12 8 8 13 13 5 5 1 15 10 0 12 0 16 0 6 0 0 12 9 27 7 21 12 36 6 18 3 10 10 30 10 30 11 33 5 15 3 12 12 12 7 7 12 12 3 3 1 15 13 39 16 48 18 54 8 24 3 9 12 12 11 11 11 11 4 4 1 12 12 48 14 56 14 56 4 16 4 11 6 0 6 0 9 0 4 0 0 11 5 15 16 48 14 42 6 18 3 11 12 24 11 22 12 24 6 12 2 15 11 44 16 64 11 44 5 20 4 7 14 42 12 36 12 36 4 12 3 11 14 14 7 7 13 13 6 6 1 11 12 12 13 13 11 11 4 4 1 10 12 24 11 22 12 24 6 12 2 14 11 33 15 45 16 48 6 18 3 10 11 11 7 7 9 9 4 4 1 6 7 7 9 9 11 11 4 4 1 11 9 18 7 14 13 26 2 4 2 15 11 33 14 42 15 45 7 21 3 11 11 44 15 60 10 40 5 20 4 12 12 24 7 14 11 22 4 8 2 14 12 12 15 15 13 13 6 6 1 15 11 22 17 34 16 32 6 12 2 9 11 22 15 30 15 30 7 14 2 13 8 32 14 56 14 56 5 20 4 13 9 18 14 28 14 28 6 12 2 16 12 36 8 24 14 42 4 12 3 13 10 30 8 24 8 24 4 12 3 12 10 30 14 42 13 39 7 21 3 14 12 48 14 56 15 60 7 28 4 11 8 16 8 16 13 26 4 8 2 9 12 24 11 22 11 22 4 8 2 16 11 44 16 64 15 60 6 24 4 12 12 36 10 30 15 45 6 18 3 10 7 28 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 17 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Popularity[t] = -0.956521145565202 + 0.122464404572674FindingFriends[t] -0.00611986826304754sum_friends[t] + 0.129901135405866KnowingPeople[t] + 0.0388655008006025sum_know[t] + 0.422882703355402Liked[t] -0.0255765571618549sum_liked[t] + 0.782432477255013Celebrity[t] -0.0824572683867579sum_celeb[t] + 0.579627939212355Sum[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) -0.956521145565202 2.451522 -0.3902 0.696976 0.348488 FindingFriends 0.122464404572674 0.177249 0.6909 0.490714 0.245357 sum_friends -0.00611986826304754 0.066175 -0.0925 0.926443 0.463221 KnowingPeople 0.129901135405866 0.111901 1.1609 0.247593 0.123797 sum_know 0.0388655008006025 0.045231 0.8593 0.391601 0.1958 Liked 0.422882703355402 0.169634 2.4929 0.013787 0.006893 sum_liked -0.0255765571618549 0.063828 -0.4007 0.689219 0.34461 Celebrity 0.782432477255013 0.291171 2.6872 0.008042 0.004021 sum_celeb -0.0824572683867579 0.117131 -0.704 0.48257 0.241285 Sum 0.579627939212355 0.887544 0.6531 0.514738 0.257369 Multiple Linear Regression - Regression Statistics Multiple R 0.716779838383906 R-squared 0.513773336713658 Adjusted R-squared 0.483800460209705 F-TEST (value) 17.1412756011558 F-TEST (DF numerator) 9 F-TEST (DF denominator) 146 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.10987944174862 Sum Squared Residuals 649.932323772166 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 11.2275438144204 1.77245618557957 2 12 11.0342302638718 0.965769736128203 3 15 13.2876546422484 1.71234535775158 4 12 10.8089897497838 1.19101025021617 5 10 10.7713737590258 -0.771373759025812 6 12 9.06820706373528 2.93179293626472 7 15 16.5909272245955 -1.59092722459553 8 9 10.0459426712359 -1.04594267123586 9 12 12.8313779907896 -0.831377990789564 10 11 7.4933463335247 3.5066536664753 11 11 13.3033553546585 -2.30335535465845 12 11 11.9752469677655 -0.97524696776552 13 15 12.7949933160697 2.20500668393034 14 7 11.4918805935504 -4.49188059355038 15 11 11.7981279091528 -0.798127909152836 16 11 10.3834759436488 0.616524056351206 17 10 11.9752469677655 -1.97524696776552 18 14 14.3737925792916 -0.373792579291638 19 10 8.45991929771326 1.54008070228674 20 6 9.12668671727479 -3.12668671727479 21 11 8.7157022427032 2.28429775729680 22 15 14.3162025817089 0.683797418291134 23 11 12.1890537027534 -1.18905370275341 24 12 9.53795294974255 2.46204705025745 25 14 12.9155719261853 1.08442807381466 26 15 14.5977334778881 0.402266522111863 27 9 14.4282575553238 -5.4282575553238 28 13 12.8920416684156 0.107958331584390 29 13 13.0109285527104 -0.0109285527103813 30 16 10.9899865064923 5.0100134935077 31 13 8.70485871570621 4.29514128429379 32 12 13.5197917181857 -1.51979171818566 33 14 14.5097646766215 -0.509764676621488 34 11 10.0481455926267 0.95185440737331 35 9 10.3684814977708 -1.36848149777083 36 16 14.5299026186096 1.47009738139042 37 12 12.8992561581670 -0.899256158166964 38 10 9.47899553170556 0.521004468294444 39 13 12.8596482997718 0.140351700228154 40 16 15.4508141048570 0.549185895142972 41 14 12.9464430078503 1.05355699214969 42 15 7.98433403619991 7.01566596380009 43 5 9.58600730887062 -4.58600730887062 44 8 10.1581376449133 -2.15813764491331 45 11 11.2421258886977 -0.242125888697726 46 16 13.7235519120314 2.27644808796865 47 17 15.0960283922259 1.90397160777410 48 9 8.17264327132336 0.827356728676637 49 9 11.3590384594999 -2.35903845949989 50 13 14.5003260089276 -1.50032600892764 51 10 11.1011837347548 -1.10118373475478 52 6 12.4348178203754 -6.43481782037539 53 12 12.1066029548912 -0.106602954891221 54 8 10.489044264813 -2.48904426481301 55 14 11.7338684040511 2.26613159594890 56 12 13.1770648027584 -1.17706480275844 57 11 10.6171692196699 0.382830780330139 58 16 14.6545092302766 1.34549076972341 59 8 10.6549086700045 -2.65490867000448 60 15 14.9418047041933 0.0581952958066707 61 7 8.97415066458367 -1.97415066458367 62 16 14.3073110754221 1.69268892457792 63 14 12.8442987158888 1.15570128411122 64 16 13.4250730460563 2.57492695394367 65 9 10.0659685416539 -1.06596854165392 66 14 12.1447228903299 1.85527710967014 67 11 13.3807949873978 -2.38079498739784 68 13 10.4681574814718 2.53184251852822 69 15 13.1306451848893 1.86935481511073 70 5 5.67009245966134 -0.670092459661344 71 15 13.1770648027584 1.82293519724156 72 13 12.6780417811813 0.321958218818715 73 11 12.3299070471522 -1.32990704715223 74 11 14.1104046332066 -3.11040463320657 75 12 12.6493121832400 -0.649312183240023 76 12 13.4394382834657 -1.43943828346566 77 12 12.4158317414769 -0.415831741476938 78 12 11.9949631366214 0.00503686337855314 79 14 10.8607738538447 3.13922614615530 80 6 7.802159072467 -1.80215907246700 81 7 9.76818227260353 -2.76818227260353 82 14 12.4686570648375 1.53134293516252 83 14 13.9943896774927 0.00561032250726964 84 10 11.1372796911909 -1.13727969119086 85 13 9.02312685723487 3.97687314276513 86 12 12.2931037728192 -0.293103772819169 87 9 9.26363082967135 -0.263630829671349 88 12 11.9217944541462 0.078205545853794 89 16 14.8381433587982 1.16185664120178 90 10 10.4400732807768 -0.440073280776769 91 14 13.1443085188386 0.855691481161362 92 10 13.5346442718065 -3.53464427180645 93 16 15.4010674285460 0.598932571453977 94 15 13.4777263217063 1.52227367829373 95 12 11.4681292284869 0.531870771513145 96 10 9.33370043848328 0.666299561516719 97 8 10.4774162463660 -2.47741624636605 98 8 8.65893008827594 -0.658930088275938 99 11 12.654915533214 -1.654915533214 100 13 12.4534477322350 0.546552267765038 101 16 15.5884456356338 0.411554364366184 102 16 14.7951278152298 1.20487218477023 103 14 15.4723250021853 -1.47232500218526 104 11 9.02818057721714 1.97181942278286 105 4 7.0878417326335 -3.08784173263349 106 14 14.4196353340098 -0.419635334009809 107 9 10.6400561163837 -1.64005611638368 108 14 15.0977608916113 -1.09776089161128 109 8 10.1364301921225 -2.13643019212252 110 8 10.7159113020490 -2.71591130204898 111 11 11.8739138822720 -0.873913882271969 112 12 13.1501689898151 -1.15016898981508 113 11 11.6144296642982 -0.614429664298243 114 14 13.3726509461595 0.627349053840509 115 15 14.2734651377469 0.726534862253112 116 16 13.4349888777443 2.56501112225571 117 16 12.9466203154947 3.05337968450529 118 11 12.8392689128711 -1.83926891287107 119 14 14.2583045582921 -0.258304558292107 120 14 10.8376185557630 3.16238144423698 121 12 11.6298240258532 0.370175974146841 122 14 12.7006174175252 1.29938258247478 123 8 10.8907755528467 -2.8907755528467 124 13 14.1199328683343 -1.11993286833428 125 16 14.0219479368138 1.9780520631862 126 12 11.1249787549928 0.875021245007234 127 16 15.3015210854570 0.698478914543027 128 12 12.6536387475452 -0.653638747545174 129 11 11.4526573961540 -0.452657396154021 130 4 5.62386162589304 -1.62386162589304 131 16 15.2457914941984 0.754208505801591 132 15 12.5958405702591 2.40415942974090 133 10 11.5261734935842 -1.52617349358419 134 13 13.3974531743112 -0.397453174311151 135 15 13.1339704198430 1.86602958015695 136 12 10.5030216912100 1.49697830878999 137 14 13.6814865155520 0.318513484448036 138 7 10.0808068809741 -3.08080688097409 139 19 13.9209642828889 5.07903571711112 140 12 13.0880115314566 -1.08801153145658 141 12 11.5680436083457 0.431956391654331 142 13 13.3416025568501 -0.341602556850117 143 15 12.2275207676955 2.77247923230451 144 8 9.35313962372137 -1.35313962372137 145 12 10.9043085388271 1.09569146117285 146 10 11.1754834642238 -1.17548346422380 147 8 11.4315364100653 -3.43153641006535 148 10 14.6364792060832 -4.63647920608323 149 15 13.9279841533596 1.07201584664036 150 16 14.6745657025484 1.32543429745160 151 13 13.1309012423538 -0.130901242353844 152 16 15.0129580511699 0.987041948830091 153 9 9.76401987267188 -0.764019872671875 154 14 13.0776185357745 0.92238146422549 155 14 13.2522110205335 0.747788979466463 156 12 10.1384097158563 1.86159028414366 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 13 0.185718828596561 0.371437657193122 0.814281171403439 14 0.776012001489516 0.447975997020969 0.223987998510484 15 0.660751206652745 0.67849758669451 0.339248793347255 16 0.614697812332199 0.770604375335603 0.385302187667801 17 0.512267517201389 0.975464965597223 0.487732482798611 18 0.416244566392151 0.832489132784302 0.583755433607849 19 0.346940566361711 0.693881132723422 0.653059433638289 20 0.680613165798703 0.638773668402594 0.319386834201297 21 0.610802512321098 0.778394975357804 0.389197487678902 22 0.557958758299772 0.884082483400456 0.442041241700228 23 0.530009137069662 0.939981725860675 0.469990862930338 24 0.524101023367653 0.951797953264693 0.475898976632347 25 0.584937256266562 0.830125487466877 0.415062743733438 26 0.522448988002731 0.955102023994538 0.477551011997269 27 0.737140268608154 0.525719462783691 0.262859731391846 28 0.683883548694181 0.632232902611638 0.316116451305819 29 0.62838075741948 0.743238485161041 0.371619242580520 30 0.819404555082696 0.361190889834607 0.180595444917304 31 0.884070567546612 0.231858864906776 0.115929432453388 32 0.855216637124942 0.289566725750117 0.144783362875058 33 0.8174043524608 0.365191295078401 0.182595647539201 34 0.784295099489387 0.431409801021226 0.215704900510613 35 0.769302278354946 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0.0206543451908313 0.0103271725954156 70 0.986611484102173 0.0267770317956545 0.0133885158978273 71 0.986237239955473 0.0275255200890535 0.0137627600445268 72 0.981602810480318 0.0367943790393641 0.0183971895196820 73 0.978114455195821 0.0437710896083572 0.0218855448041786 74 0.987611496070663 0.0247770078586741 0.0123885039293370 75 0.983945213904882 0.0321095721902357 0.0160547860951178 76 0.981148251972344 0.0377034960553119 0.0188517480276559 77 0.974897956227122 0.050204087545755 0.0251020437728775 78 0.966983433991152 0.0660331320176957 0.0330165660088478 79 0.977884026845233 0.0442319463095345 0.0221159731547673 80 0.975880533595292 0.0482389328094167 0.0241194664047083 81 0.981293487987666 0.0374130240246682 0.0187065120123341 82 0.98194890255711 0.0361021948857808 0.0180510974428904 83 0.976281273395385 0.04743745320923 0.023718726604615 84 0.971431957932084 0.0571360841358312 0.0285680420679156 85 0.991875221487154 0.0162495570256920 0.00812477851284599 86 0.988886961293848 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0.177508567174915 0.0887542835874575 104 0.94113890702194 0.117722185956122 0.058861092978061 105 0.941820288348424 0.116359423303152 0.0581797116515760 106 0.92431493022409 0.151370139551818 0.0756850697759092 107 0.918215967755964 0.163568064488072 0.0817840322440358 108 0.925044887984505 0.149910224030990 0.0749551120154952 109 0.916566625749596 0.166866748500808 0.0834333742504041 110 0.905209388773641 0.189581222452717 0.0947906112263585 111 0.884554505282001 0.230890989435997 0.115445494717999 112 0.883094717046194 0.233810565907613 0.116905282953806 113 0.852801707333106 0.294396585333788 0.147198292666894 114 0.820202540797502 0.359594918404997 0.179797459202498 115 0.780303992353168 0.439392015293664 0.219696007646832 116 0.773997986364078 0.452004027271843 0.226002013635922 117 0.783854093906539 0.432291812186922 0.216145906093461 118 0.766366044502706 0.467267910994588 0.233633955497294 119 0.71706564605935 0.565868707881301 0.282934353940651 120 0.790497126662921 0.419005746674157 0.209502873337079 121 0.756531998231144 0.486936003537712 0.243468001768856 122 0.715215508640922 0.569568982718157 0.284784491359078 123 0.713747013648639 0.572505972702723 0.286252986351361 124 0.658871174476172 0.682257651047656 0.341128825523828 125 0.658447507623791 0.683104984752417 0.341552492376209 126 0.638085781623484 0.723828436753033 0.361914218376517 127 0.57331141042449 0.85337717915102 0.42668858957551 128 0.607959819907075 0.78408036018585 0.392040180092925 129 0.601789364792552 0.796421270414896 0.398210635207448 130 0.573454118945877 0.853091762108246 0.426545881054123 131 0.496908003271029 0.993816006542058 0.503091996728971 132 0.475930254917933 0.951860509835865 0.524069745082067 133 0.472516560690425 0.94503312138085 0.527483439309575 134 0.39742492926294 0.79484985852588 0.60257507073706 135 0.358982351379126 0.717964702758252 0.641017648620874 136 0.360248443401389 0.720496886802778 0.639751556598611 137 0.276286312732383 0.552572625464766 0.723713687267617 138 0.338802972277989 0.677605944555977 0.661197027722011 139 0.629964957691365 0.74007008461727 0.370035042308635 140 0.791103058847174 0.417793882305652 0.208896941152826 141 0.72370138362754 0.55259723274492 0.27629861637246 142 0.684162606963402 0.631674786073197 0.315837393036598 143 0.73133744636969 0.537325107260621 0.268662553630311 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 35 0.267175572519084 NOK 10% type I error level 49 0.374045801526718 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936192095ghd0cgpll8uzjz/10mb4x1293619307.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t12936192095ghd0cgpll8uzjz/10mb4x1293619307.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t12936192095ghd0cgpll8uzjz/1fs731293619307.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t12936192095ghd0cgpll8uzjz/1fs731293619307.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t12936192095ghd0cgpll8uzjz/2qko61293619307.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t12936192095ghd0cgpll8uzjz/2qko61293619307.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t12936192095ghd0cgpll8uzjz/3qko61293619307.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t12936192095ghd0cgpll8uzjz/3qko61293619307.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t12936192095ghd0cgpll8uzjz/4qko61293619307.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t12936192095ghd0cgpll8uzjz/4qko61293619307.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t12936192095ghd0cgpll8uzjz/51bo91293619307.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t12936192095ghd0cgpll8uzjz/51bo91293619307.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t12936192095ghd0cgpll8uzjz/61bo91293619307.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t12936192095ghd0cgpll8uzjz/61bo91293619307.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t12936192095ghd0cgpll8uzjz/7t2nu1293619307.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t12936192095ghd0cgpll8uzjz/7t2nu1293619307.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t12936192095ghd0cgpll8uzjz/8t2nu1293619307.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t12936192095ghd0cgpll8uzjz/8t2nu1293619307.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t12936192095ghd0cgpll8uzjz/9mb4x1293619307.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t12936192095ghd0cgpll8uzjz/9mb4x1293619307.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

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

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

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Software written by Ed van Stee & Patrick Wessa

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