include seasonal dummies

*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: Fri, 03 Dec 2010 14:40:13 +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/03/t1291387152aynsvh3jhq4tjus.htm/, Retrieved Fri, 03 Dec 2010 15:39:12 +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/03/t1291387152aynsvh3jhq4tjus.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 «

4 4 1 4 5 4 2 1 4 4 4 3 2 5 5 4 2 1 3 4 4 2 2 4 3 5 2 1 3 5 4 1 3 4 4 3 1 1 3 4 4 1 1 2 4 4 2 1 4 4 4 2 2 2 4 4 2 4 2 4 4 2 2 2 4 2 2 1 1 3 3 1 1 4 4 4 3 3 4 5 3 2 2 2 4 2 2 2 2 2 4 2 3 3 4 3 2 3 3 4 3 3 1 3 4 4 4 2 4 4 3 2 2 3 4 3 2 2 2 4 4 2 2 2 5 4 1 3 4 4 4 2 2 4 4 4 2 2 3 4 4 2 2 4 4 4 2 2 2 4 5 4 2 4 5 4 2 3 4 4 4 4 2 5 2 4 3 2 5 5 3 1 2 4 4 4 4 2 4 5 3 3 2 4 4 4 2 1 2 4 4 4 2 4 4 3 2 1 4 4 5 3 2 4 5 4 3 2 3 4 3 2 2 2 4 3 1 2 3 5 3 2 2 4 4 4 1 3 3 4 4 2 2 2 4 4 4 2 4 4 4 2 2 4 4 4 2 4 3 4 4 2 1 4 4 4 2 2 3 4 5 2 2 4 5 3 1 1 2 3 3 2 5 4 4 5 3 2 4 5 5 2 2 4 5 4 2 2 4 4 4 1 1 3 5 3 1 2 1 2 4 2 2 3 4 4 2 2 3 4 5 1 2 4 4 4 2 2 2 4 4 1 1 3 4 5 4 1 5 5 4 4 2 4 4 3 1 2 4 4 4 1 1 3 4 4 3 2 4 4 4 4 2 2 3 4 2 1 3 4 4 4 3 4 5 4 4 3 3 5 4 3 3 4 4 3 4 2 4 4 4 2 2 3 5 3 2 2 3 4 5 2 1 2 5 4 2 4 4 3 5 2 3 3 4 5 2 2 2 4 4 2 2 2 4 4 1 2 3 4 4 3 1 2 5 4 3 2 2 4 4 2 3 4 4 5 4 1 4 5 4 4 2 4 3 3 2 2 2 4 4 2 2 2 4 3 1 1 4 5 4 1 1 2 4 4 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 7 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation neat[t] = + 1.16440603291601 + 0.233139663569593fail[t] -0.187500338062230performance[t] + 0.0368726688412969goals[t] + 0.504275569488782`organized `[t] -0.103650819474029M1[t] -0.226062653000361M2[t] -0.0783105813127394M3[t] -0.0557740260137624M4[t] + 0.00511871995110706M5[t] -0.297902963614086M6[t] + 0.0502897975057321M7[t] -0.0686403005221799M8[t] + 0.408636087855733M9[t] + 0.451578435262287M10[t] + 0.129307371579808M11[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) 1.16440603291601 0.538332 2.163 0.032204 0.016102 fail 0.233139663569593 0.077657 3.0022 0.003165 0.001582 performance -0.187500338062230 0.080182 -2.3384 0.020751 0.010375 goals 0.0368726688412969 0.081926 0.4501 0.653339 0.326669 `organized ` 0.504275569488782 0.093793 5.3765 0 0 M1 -0.103650819474029 0.3483 -0.2976 0.766448 0.383224 M2 -0.226062653000361 0.345762 -0.6538 0.514284 0.257142 M3 -0.0783105813127394 0.353381 -0.2216 0.824938 0.412469 M4 -0.0557740260137624 0.354427 -0.1574 0.87518 0.43759 M5 0.00511871995110706 0.355562 0.0144 0.988534 0.494267 M6 -0.297902963614086 0.353007 -0.8439 0.400134 0.200067 M7 0.0502897975057321 0.356624 0.141 0.888055 0.444028 M8 -0.0686403005221799 0.355554 -0.1931 0.847193 0.423596 M9 0.408636087855733 0.353382 1.1564 0.249462 0.124731 M10 0.451578435262287 0.356492 1.2667 0.207312 0.103656 M11 0.129307371579808 0.353546 0.3657 0.715097 0.357548 Multiple Linear Regression - Regression Statistics Multiple R 0.559418807599365 R-squared 0.312949402295896 Adjusted R-squared 0.240881157781479 F-TEST (value) 4.34240357045596 F-TEST (DF numerator) 15 F-TEST (DF denominator) 143 p-value 1.20466221420479e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.895728514469576 Sum Squared Residuals 114.733128743644 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4 4.47468205246722 -0.474682052467218 2 4 3.38171532231292 0.61828467768708 3 4 4.11625495783798 -0.116254957837984 4 4 3.51513128045822 0.484868719541778 5 4 2.92112078771338 1.07887921228662 6 5 3.77727791234668 1.22272208765332 7 4 3.04992743312496 0.95007256687504 8 3 3.26912534238021 -0.269125342380211 9 4 3.70952906191683 0.290470938083173 10 4 4.05935641057557 -0.0593564105755689 11 4 3.47583967114827 0.524160328851734 12 4 2.971531623444 1.02846837655600 13 4 3.24288148009443 0.757118519905572 14 2 2.76682174630025 -0.766821746300248 15 3 3.29632773043095 -0.296327730430949 16 4 3.91441850623344 0.0855814937665648 17 3 3.35165101951957 -0.351651019519565 18 2 2.04007819697681 -0.0400781969768069 19 4 3.24619442785326 0.753805572146743 20 3 3.12726432982535 -0.127264329825345 21 3 4.21268105789731 -1.21268105789731 22 4 4.33813539965253 -0.338135399652526 23 3 3.51271233998956 -0.512712339989562 24 3 3.34653229956846 -0.346532299568458 25 4 3.74715704958321 0.252842950416789 26 4 2.77357498261887 1.22642501738113 27 4 3.34196705593831 0.658032944061688 28 4 3.32763094239599 0.672369057604008 29 4 3.42539635720216 0.574603642797842 30 4 3.04862933595437 0.951370664045629 31 5 4.44112233138475 0.558877668615247 32 4 3.16413699866664 0.835863001333358 33 4 3.32351458210970 0.676485417890296 34 4 4.64614397441301 -0.646143974413012 35 3 3.31644534526127 -0.316445345261266 36 4 4.39083253387902 -0.390832533879021 37 3 3.54976648134662 -0.549766481346616 38 4 3.30796998463033 0.692030015369673 39 4 3.8082463830775 0.191753616922501 40 3 3.55200394929952 -0.552003949299519 41 5 4.16281159026053 0.837188409739466 42 4 3.31864166836526 0.681358331634738 43 3 3.39682209707419 -0.39682209707419 44 3 3.58590057380676 -0.585900573806764 45 3 3.82891372510678 -0.828913725106785 46 4 3.41434340204022 0.585656597959781 47 4 3.47583967114827 0.524160328851735 48 4 3.88655696439024 0.113443035609762 49 4 3.31662681777702 0.683373182222978 50 4 2.78234163928493 1.21765836071507 51 4 3.52946739400054 0.470532605999458 52 4 3.32763094239599 0.672369057604008 53 5 3.92967192669094 1.07032807330906 54 3 2.49871444095823 0.501285559041775 55 3 2.90806642057009 0.0919335794299056 56 5 4.08905256978725 0.910947430212752 57 5 4.33318929459557 0.666810705404434 58 4 3.87185607251334 0.128143927486661 59 4 3.97134858397098 0.0286514160290192 60 3 2.06796882818000 0.932031171819997 61 4 3.27975414893573 0.720245851064275 62 4 3.15734231540939 0.842657684590606 63 5 3.10882739236872 1.89117260763128 64 4 3.29075827355470 0.709241726445305 65 4 3.3428843628535 0.657115637146501 66 5 4.31730257716846 0.682697422831539 67 4 3.93684676189597 0.0631532381040295 68 3 3.11849767315928 -0.118497673159278 69 4 3.74640173075812 0.253598269241876 70 4 4.10499573608293 -0.104995736082932 71 4 3.43784342879867 0.56215657120133 72 4 3.57090530647198 0.429094693528015 73 4 4.09968137634276 -0.0996813763427617 74 4 3.94039687397513 0.059603126024867 75 4 3.38760638144568 0.612393618554324 76 3 3.83078293837648 -0.830782938376476 77 4 3.89279925784964 0.107200742150356 78 3 3.08550200479567 -0.0855020047956682 79 5 4.0885980046252 0.911401995374799 80 4 2.47236109111563 1.52763890888437 81 5 3.60454071820326 1.39545928179674 82 5 3.79811073483075 1.20188926516925 83 4 3.47583967114827 0.524160328851735 84 4 3.15026530484016 0.849734695159838 85 4 4.16779705121503 -0.167797051215034 86 4 3.35360931013769 0.64639068986231 87 4 3.15446671787608 0.845533282123917 88 5 4.52255884592749 0.477441154072512 89 4 3.38740011485256 0.612599885147437 90 3 3.04862933595437 -0.0486293359543713 91 4 3.39682209707419 0.60317790292581 92 3 3.81027358071029 -0.81027358071029 93 4 3.70952906191683 0.290470938083173 94 4 3.09756817061367 0.902431829386333 95 4 4.01698790947834 -0.0169879094783445 96 4 3.58642519945667 0.413574800543329 97 4 4.0171693819941 -0.0171693819941009 98 3 3.28549363526542 -0.285493635265418 99 3 3.49259472515925 -0.492594725159245 100 3 3.10325793549247 -0.103257935492466 101 3 3.89167568434135 -0.891675684341345 102 3 3.08550200479567 -0.0855020047956682 103 2 2.28328261438306 -0.283282614383056 104 3 3.12726432982535 -0.127264329825345 105 5 4.33318929459557 0.666810705404434 106 2 3.4064665922133 -1.4064665922133 107 2 3.19593710856301 -1.19593710856301 108 3 2.57112082416049 0.428879175839513 109 3 3.09225381087350 -0.0922538108734954 110 2 3.19421498425069 -1.19421498425069 111 2 3.07195472352742 -1.07195472352742 112 4 2.86022804174851 1.13977195825149 113 3 2.04184454210013 0.958155457899865 114 1 2.01872542112020 -1.01872542112020 115 1 2.7117994258418 -1.71179942584180 116 1 2.15558585968908 -1.15558585968908 117 2 3.61330737486932 -1.61330737486932 118 2 3.45998272754758 -1.45998272754758 119 3 2.35353353179107 0.646466468208935 120 1 2.60911706651008 -1.60911706651008 121 3 2.20421090859419 0.795789091405813 122 1 2.65306674592061 -1.65306674592061 123 2 3.15446671787608 -1.15446671787608 124 1 3.13136394766769 -2.13136394766769 125 2 3.42539635720216 -1.42539635720216 126 2 2.85123876771778 -0.851238767717776 127 3 2.89929976390403 0.100700236095972 128 2 3.01350932944571 -1.01350932944571 129 2 3.49078571782362 -1.49078571782362 130 4 2.52517692625261 1.47482307374739 131 2 3.36208467076863 -1.36208467076863 132 3 3.92455320673983 -0.924553206739833 133 2 2.74535914692427 -0.745359146924266 134 1 2.77357498261887 -1.77357498261887 135 2 3.34196705593831 -1.34196705593831 136 3 2.95150669276323 0.0484933072367657 137 1 1.72506931067358 -0.725069310673583 138 2 2.86112899789214 -0.861128997892141 139 2 2.77879152720577 -0.778791527205772 140 3 2.58611609149527 0.413883908504734 141 3 3.10026514871448 -0.100265148714476 142 3 1.98402868792253 1.01597131207747 143 4 3.57588497882906 0.424115021170941 144 4 3.69141354317024 0.308586456829760 145 2 3.74603347607491 -1.74603347607491 146 3 2.31493873863745 0.685061261362551 147 3 3.38760638144568 -0.387606381445675 148 2 2.67272770368628 -0.672727703686277 149 1 3.5022786887405 -2.5022786887405 150 2 3.04862933595437 -1.04862933595437 151 2 2.86242709506273 -0.86242709506273 152 4 3.48091223009319 0.519087769906806 153 4 2.99415323149261 1.00584676850739 154 2 3.29383516534196 -1.29383516534196 155 3 2.82970308910462 0.170296910895383 156 2 3.23277729918882 -1.23277729918882 157 4 3.31662681777702 0.683373182222978 158 2 2.31493873863745 -0.314938738637449 159 4 3.8082463830775 0.191753616922501 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.389486693830213 0.778973387660425 0.610513306169787 20 0.249194679456689 0.498389358913378 0.750805320543311 21 0.168875740755579 0.337751481511157 0.831124259244421 22 0.127667043866261 0.255334087732523 0.872332956133739 23 0.163141231196963 0.326282462393925 0.836858768803037 24 0.123155430200923 0.246310860401846 0.876844569799077 25 0.0854425794893199 0.170885158978640 0.91455742051068 26 0.0575361222689149 0.115072244537830 0.942463877731085 27 0.057832683132974 0.115665366265948 0.942167316867026 28 0.0371597791906158 0.0743195583812315 0.962840220809384 29 0.0218174447469366 0.0436348894938732 0.978182555253063 30 0.0133897490251056 0.0267794980502112 0.986610250974894 31 0.0130051432752664 0.0260102865505328 0.986994856724734 32 0.0111193103873773 0.0222386207747545 0.988880689612623 33 0.0118907673808289 0.0237815347616578 0.988109232619171 34 0.011806921422788 0.023613842845576 0.988193078577212 35 0.0127238697438493 0.0254477394876987 0.98727613025615 36 0.00805170318197684 0.0161034063639537 0.991948296818023 37 0.00965307728866883 0.0193061545773377 0.990346922711331 38 0.0088174400998413 0.0176348801996826 0.991182559900159 39 0.00609688600624039 0.0121937720124808 0.99390311399376 40 0.00524589188697837 0.0104917837739567 0.994754108113022 41 0.0038212171065205 0.007642434213041 0.99617878289348 42 0.00240301328533301 0.00480602657066601 0.997596986714667 43 0.00204687648005315 0.0040937529601063 0.997953123519947 44 0.00172603277752368 0.00345206555504736 0.998273967222476 45 0.00261082069046032 0.00522164138092064 0.99738917930954 46 0.00170965383536642 0.00341930767073283 0.998290346164634 47 0.00147762788873598 0.00295525577747197 0.998522372111264 48 0.00092090878753087 0.00184181757506174 0.99907909121247 49 0.00062656264072534 0.00125312528145068 0.999373437359275 50 0.000477037700346319 0.000954075400692638 0.999522962299654 51 0.000353501405094416 0.000707002810188833 0.999646498594906 52 0.000248006158858765 0.00049601231771753 0.999751993841141 53 0.000218208146697895 0.000436416293395791 0.999781791853302 54 0.000136066007673195 0.00027213201534639 0.999863933992327 55 0.000237091447765449 0.000474182895530897 0.999762908552235 56 0.000346606043956244 0.000693212087912489 0.999653393956044 57 0.000278765812574125 0.00055753162514825 0.999721234187426 58 0.000166119212482054 0.000332238424964108 0.999833880787518 59 9.54800918344141e-05 0.000190960183668828 0.999904519908166 60 0.00011664208867968 0.00023328417735936 0.99988335791132 61 8.71007296529408e-05 0.000174201459305882 0.999912899270347 62 6.80191745603982e-05 0.000136038349120796 0.99993198082544 63 0.000320447917812738 0.000640895835625477 0.999679552082187 64 0.000272502577316809 0.000545005154633618 0.999727497422683 65 0.000231199567855927 0.000462399135711853 0.999768800432144 66 0.000168645691274206 0.000337291382548413 0.999831354308726 67 0.000101917422046810 0.000203834844093621 0.999898082577953 68 6.63092256175881e-05 0.000132618451235176 0.999933690774382 69 4.23260735205411e-05 8.46521470410822e-05 0.99995767392648 70 2.43221562476849e-05 4.86443124953698e-05 0.999975677843752 71 2.40579473459002e-05 4.81158946918004e-05 0.999975942052654 72 1.67866214927207e-05 3.35732429854414e-05 0.999983213378507 73 1.07595194635430e-05 2.15190389270859e-05 0.999989240480537 74 7.21226994508636e-06 1.44245398901727e-05 0.999992787730055 75 4.77982837205004e-06 9.55965674410008e-06 0.999995220171628 76 5.92477760722104e-06 1.18495552144421e-05 0.999994075222393 77 4.92431114716134e-06 9.84862229432268e-06 0.999995075688853 78 5.33893024772167e-06 1.06778604954433e-05 0.999994661069752 79 1.03537031425204e-05 2.07074062850407e-05 0.999989646296857 80 2.25553382702842e-05 4.51106765405684e-05 0.99997744466173 81 5.24086790730982e-05 0.000104817358146196 0.999947591320927 82 0.000130259940513657 0.000260519881027315 0.999869740059486 83 0.000107704100628739 0.000215408201257479 0.999892295899371 84 0.000118130556994010 0.000236261113988021 0.999881869443006 85 7.30537924276685e-05 0.000146107584855337 0.999926946207572 86 9.10397751189378e-05 0.000182079550237876 0.999908960224881 87 9.90043636553333e-05 0.000198008727310667 0.999900995636345 88 0.000101518672678962 0.000203037345357924 0.999898481327321 89 9.97726549201909e-05 0.000199545309840382 0.99990022734508 90 0.000105357659784301 0.000210715319568602 0.999894642340216 91 0.000188122408086916 0.000376244816173832 0.999811877591913 92 0.000165111444092899 0.000330222888185799 0.999834888555907 93 0.000209758491939863 0.000419516983879726 0.99979024150806 94 0.000367932468270651 0.000735864936541303 0.99963206753173 95 0.00031759928739896 0.00063519857479792 0.999682400712601 96 0.000233567144064923 0.000467134288129846 0.999766432855935 97 0.000171556616743938 0.000343113233487877 0.999828443383256 98 0.000170833944427675 0.000341667888855349 0.999829166055572 99 0.000182212698923837 0.000364425397847674 0.999817787301076 100 0.000184098667333636 0.000368197334667272 0.999815901332666 101 0.000218359243460419 0.000436718486920838 0.99978164075654 102 0.000261396416246797 0.000522792832493595 0.999738603583753 103 0.000245658378166939 0.000491316756333878 0.999754341621833 104 0.000179237051826798 0.000358474103653596 0.999820762948173 105 0.00097211740510289 0.00194423481020578 0.999027882594897 106 0.00111436500001181 0.00222873000002361 0.998885634999988 107 0.00120288597204819 0.00240577194409638 0.998797114027952 108 0.000852016201824213 0.00170403240364843 0.999147983798176 109 0.000646658460009051 0.00129331692001810 0.999353341539991 110 0.00104872719211681 0.00209745438423362 0.998951272807883 111 0.00166381858445355 0.00332763716890711 0.998336181415546 112 0.00656312332872981 0.0131262466574596 0.99343687667127 113 0.00846964660058085 0.0169392932011617 0.99153035339942 114 0.0184663153094279 0.0369326306188557 0.981533684690572 115 0.0687181719146942 0.137436343829388 0.931281828085306 116 0.119903699886556 0.239807399773112 0.880096300113444 117 0.141470223290784 0.282940446581569 0.858529776709216 118 0.191730687838782 0.383461375677564 0.808269312161218 119 0.191103469059285 0.382206938118571 0.808896530940715 120 0.271776454131851 0.543552908263702 0.728223545868149 121 0.242404158039366 0.484808316078732 0.757595841960634 122 0.265328095053003 0.530656190106006 0.734671904946997 123 0.265770009772756 0.531540019545513 0.734229990227244 124 0.30895597716663 0.61791195433326 0.69104402283337 125 0.323235379729501 0.646470759459002 0.676764620270499 126 0.272771471690516 0.545542943381031 0.727228528309484 127 0.261620132092966 0.523240264185932 0.738379867907034 128 0.342105337854558 0.684210675709115 0.657894662145442 129 0.383069323905937 0.766138647811874 0.616930676094063 130 0.412552647129808 0.825105294259617 0.587447352870192 131 0.460224376432994 0.920448752865988 0.539775623567006 132 0.393839313137776 0.787678626275551 0.606160686862224 133 0.366641057271185 0.733282114542371 0.633358942728815 134 0.502130807289713 0.995738385420575 0.497869192710287 135 0.559758693039568 0.880482613920864 0.440241306960432 136 0.513188303751176 0.973623392497648 0.486811696248824 137 0.418932406280501 0.837864812561002 0.581067593719499 138 0.308880514807516 0.617761029615032 0.691119485192484 139 0.202736494743768 0.405472989487537 0.797263505256232 140 0.385020900656009 0.770041801312019 0.61497909934399 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 71 0.581967213114754 NOK 5% type I error level 86 0.704918032786885 NOK 10% type I error level 87 0.71311475409836 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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