Verbetering

*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 14:39:39 +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/t1291127946x2pbt8k2ssqot2f.htm/, Retrieved Tue, 30 Nov 2010 15:39:17 +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/t1291127946x2pbt8k2ssqot2f.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 «

26 1 24 14 11 12 24 23 1 25 11 7 8 25 25 1 17 6 17 8 30 23 1 18 12 10 8 19 19 1 18 8 12 9 22 29 1 16 10 12 7 22 25 1 20 10 11 4 25 21 1 16 11 11 11 23 22 1 18 16 12 7 17 25 2 17 11 13 7 21 24 2 23 13 14 12 19 18 2 30 12 16 10 19 22 2 23 8 11 10 15 15 2 18 12 10 8 16 22 2 15 11 11 8 23 28 2 12 4 15 4 27 20 2 21 9 9 9 22 12 2 15 8 11 8 14 24 2 20 8 17 7 22 20 3 31 14 17 11 23 21 3 27 15 11 9 23 20 3 34 16 18 11 21 21 3 21 9 14 13 19 23 3 31 14 10 8 18 28 3 19 11 11 8 20 24 3 16 8 15 9 23 24 3 20 9 15 6 25 24 3 21 9 13 9 19 23 3 22 9 16 9 24 23 3 17 9 13 6 22 29 3 24 10 9 6 25 24 3 25 16 18 16 26 18 3 26 11 18 5 29 25 3 25 8 12 7 32 21 3 17 9 17 9 25 26 3 32 16 9 6 29 22 3 33 11 9 6 28 22 3 13 16 12 5 17 22 3 32 12 18 12 28 23 3 25 12 12 7 29 30 3 29 14 18 10 26 23 3 22 9 14 9 25 17 3 18 10 15 8 14 23 3 17 9 16 5 25 23 3 20 10 10 8 26 25 3 15 12 11 8 20 24 3 20 14 14 10 18 24 3 33 14 9 6 32 23 3 29 10 12 8 25 21 3 23 14 17 7 25 24 3 26 16 5 4 23 24 3 18 9 12 8 2 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 11 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Organisation[t] = + 16.7236576391504 + 0.366018263287189Week[t] -0.0633161091808469Concern[t] + 0.218004431283425Doubts[t] -0.137045430156790Pexpect[t] -0.246992813773941Pcriticism[t] + 0.398548887973243Pstandards[t] -0.0204592057986341t + 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) 16.7236576391504 2.450451 6.8247 0 0 Week 0.366018263287189 0.662012 0.5529 0.581158 0.290579 Concern -0.0633161091808469 0.062625 -1.011 0.313616 0.156808 Doubts 0.218004431283425 0.111077 1.9626 0.051525 0.025762 Pexpect -0.137045430156790 0.103252 -1.3273 0.186417 0.093208 Pcriticism -0.246992813773941 0.129078 -1.9135 0.057575 0.028787 Pstandards 0.398548887973243 0.075496 5.2791 0 0 t -0.0204592057986341 0.011777 -1.7372 0.084393 0.042197 Multiple Linear Regression - Regression Statistics Multiple R 0.50375119888588 R-squared 0.253765270378961 Adjusted R-squared 0.219171607416397 F-TEST (value) 7.33559989451166 F-TEST (DF numerator) 7 F-TEST (DF denominator) 151 p-value 1.42350557119642e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.4506244838084 Sum Squared Residuals 1797.92820856696 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 26 23.6954519286124 2.30454807138757 2 23 24.8923651834789 -1.89236518347886 3 25 24.9107028330082 0.0892971669918024 4 23 22.7102343491211 0.289765650878871 5 19 22.492320408021 -3.492320408021 6 29 23.5284879106988 5.47151208930121 7 25 25.3284348035751 -0.328434803575101 8 21 23.2531969934192 -2.25319699341922 9 22 22.6557602227755 -0.655760222775531 10 25 23.431763354764 1.56823664523601 11 24 21.2983090814741 2.70169091852586 12 18 20.8365274473605 -2.83652744736046 13 22 19.4782948795850 2.52170512041497 14 15 21.6760138905022 -6.67601389050225 15 22 24.2802953666186 -2.28029536661864 16 28 24.9577385557401 3.04226144425986 17 20 23.0520205959358 -3.05202059593584 18 12 19.9779644636133 -7.97796446361327 19 24 22.2540360485295 1.74596395147045 20 20 22.6217221256068 -2.62172212560682 21 21 24.3887899963036 -3.38878999630362 22 20 21.8927210429306 -1.89272104293058 23 21 20.4264385546318 0.573561445368221 24 23 22.2474373149654 0.752562685034579 25 28 22.9928104712764 5.00718952872363 26 24 22.9087584286886 1.09124157131137 27 24 24.3911154347183 -0.391115434718338 28 24 21.4491592108912 2.55084078910884 29 23 22.9469920453075 0.0530079546924787 30 23 23.5981303412588 -0.598130341258829 31 29 25.0962911870246 3.90370881297542 32 24 23.0157543385684 0.984245661431628 33 18 25.7545244826048 -7.75452448260484 34 25 26.6673017094494 -1.66730170944937 35 21 23.4023208142364 -2.4023208142364 36 26 27.3896884241782 -1.38968842417815 37 22 25.8173420648083 -3.81734206480831 38 22 23.6050459546416 -1.60504595464164 39 22 23.3423784396206 -1.34237843962055 40 23 26.2209175358715 -3.22091753587153 41 30 23.6243050697341 6.37569493026593 42 23 23.3536621182121 -0.353662118212101 43 17 19.5303813963318 -2.53038139633176 44 23 24.3432046473012 -1.34320464730125 45 23 24.8306445728357 -1.83064457283566 46 25 23.0344360175119 1.96556398248813 47 24 21.4311854344111 2.56881456558889 48 24 27.8404996467666 -3.84049964676658 49 23 23.5063230187267 -0.50632301872668 50 21 24.2995438561368 -3.29954385613682 51 24 26.1135710126193 -2.11357101261931 52 24 22.3292226191437 1.6707773808563 53 28 22.0015867382936 5.99841326170645 54 16 21.4964541861591 -5.49645418615913 55 20 20.3951605432463 -0.395160543246316 56 29 23.8085213115558 5.19147868844419 57 27 24.1844110245768 2.81558897542322 58 22 23.4673204934033 -1.46732049340335 59 28 24.2016432649244 3.79835673507555 60 16 20.7999523512091 -4.79995235120908 61 25 23.1570597262826 1.84294027371737 62 24 23.7052735262091 0.294726473790939 63 28 23.8634171574082 4.13658284259176 64 24 24.4525654454667 -0.452565445466737 65 23 22.8687123440238 0.131287655976217 66 30 26.9199290110650 3.08007098893503 67 24 21.5168149996598 2.48318500034021 68 21 24.1928071148674 -3.19280711486737 69 25 23.3942575402432 1.60574245975678 70 25 24.0015745410232 0.998425458976798 71 22 20.9377761116785 1.06222388832154 72 23 22.5148514982345 0.485148501765518 73 26 22.8729502107974 3.12704978920264 74 23 21.7245162319689 1.27548376803110 75 25 23.0291769012988 1.97082309870118 76 21 21.3410766773824 -0.341076677382429 77 25 23.5812853738903 1.41871462610970 78 24 22.1388134485727 1.86118655142733 79 29 23.4387098835101 5.56129011648993 80 22 23.5103483768244 -1.51034837682439 81 27 23.4725117556845 3.5274882443155 82 26 19.6042830295982 6.39571697040178 83 22 21.2249089995905 0.775091000409499 84 24 21.8819195876602 2.11808041233978 85 27 23.2855910875914 3.71440891240865 86 24 21.5459506254752 2.45404937452482 87 24 24.8779930945644 -0.877993094564404 88 29 24.4469140240566 4.55308597594342 89 22 22.3202571944919 -0.320257194491883 90 21 20.7252766460663 0.274723353933659 91 24 20.6125387270480 3.38746127295204 92 24 21.7564533710272 2.24354662897284 93 23 21.9769737055147 1.02302629448534 94 20 22.2820924584990 -2.28209245849905 95 27 21.3952387265177 5.60476127348232 96 26 23.3525884804222 2.64741151957780 97 25 21.9564145470378 3.0435854529622 98 21 20.1194141038016 0.8805858961984 99 21 20.7216882505685 0.278311749431548 100 19 20.3452469045800 -1.34524690457997 101 21 21.4861395416052 -0.486139541605241 102 21 21.1231079090763 -0.123107909076271 103 16 19.6733366417202 -3.6733366417202 104 22 20.5082358316002 1.49176416839976 105 29 21.6288555002518 7.37114449974816 106 15 21.5210814810415 -6.52108148104148 107 17 20.4874688148478 -3.48746881484784 108 15 19.7414998689711 -4.74149986897114 109 21 21.422309700241 -0.422309700240991 110 21 20.7646375114165 0.235362488583492 111 19 19.0438744528935 -0.0438744528935296 112 24 17.8847233717783 6.1152766282217 113 20 21.9050810829565 -1.90508108295652 114 17 24.5639819054456 -7.56398190544563 115 23 24.3177369889856 -1.31773698898557 116 24 21.8984125095616 2.10158749043839 117 14 21.5570315035976 -7.55703150359757 118 19 22.3508313015137 -3.35083130151374 119 24 21.7117032698025 2.28829673019747 120 13 19.9611534042659 -6.96115340426591 121 22 24.6890301896486 -2.6890301896486 122 16 20.6051670376977 -4.60516703769771 123 19 22.6585212406792 -3.65852124067917 124 25 22.1118312817037 2.88816871829627 125 25 23.5345282525220 1.46547174747796 126 23 20.8054091467532 2.19459085324683 127 24 22.7933553471750 1.20664465282497 128 26 22.7824099800164 3.21759001998363 129 26 20.8168027931320 5.18319720686803 130 25 23.3694932188649 1.63050678113515 131 18 21.5793308426234 -3.57933084262337 132 21 19.1923921970356 1.80760780296436 133 26 22.7764829693475 3.22351703065253 134 23 21.1296746756676 1.87032532433243 135 23 19.0324384650189 3.96756153498107 136 22 21.7445518180966 0.255448181903442 137 20 21.5251139662821 -1.52511396628209 138 13 21.2057242336679 -8.2057242336679 139 24 20.5136088420732 3.4863911579268 140 15 20.6771688796649 -5.67716887966494 141 14 22.1658416652423 -8.16584166524233 142 22 23.0314015300016 -1.03140153000162 143 10 16.9351197289185 -6.93511972891846 144 24 23.3572778012203 0.642722198779667 145 22 20.8454963245898 1.15450367541021 146 24 24.6239537408981 -0.623953740898068 147 19 20.5904824995447 -1.59048249954472 148 20 20.9885631513311 -0.988563151331053 149 13 16.2062995568455 -3.20629955684547 150 20 19.0523444703232 0.94765552967677 151 22 21.9899354836866 0.0100645163133675 152 24 22.1896551730356 1.81034482696445 153 29 22.0005228218675 6.99947717813247 154 12 19.7779344455346 -7.77793444553464 155 20 19.7616384831724 0.238361516827564 156 21 20.1906420099984 0.809357990001604 157 24 22.3365774322595 1.66342256774052 158 22 20.6387453261410 1.36125467385902 159 20 16.6795713884280 3.32042861157202 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.675872966961438 0.648254066077125 0.324127033038562 12 0.532331063172114 0.935337873655771 0.467668936827886 13 0.551748585502325 0.89650282899535 0.448251414497675 14 0.778516223810817 0.442967552378367 0.221483776189183 15 0.69493612190174 0.610127756196521 0.305063878098261 16 0.69261174004319 0.61477651991362 0.30738825995681 17 0.607519260305348 0.784961479389303 0.392480739694652 18 0.715567632432861 0.568864735134278 0.284432367567139 19 0.683360114008498 0.633279771983005 0.316639885991502 20 0.641103173183158 0.717793653633683 0.358896826816842 21 0.569117105799804 0.861765788400392 0.430882894200196 22 0.49184802682644 0.98369605365288 0.508151973173561 23 0.472082422538343 0.944164845076687 0.527917577461656 24 0.529006283288849 0.941987433422302 0.470993716711151 25 0.682543931862953 0.634912136274094 0.317456068137047 26 0.618662684261662 0.762674631476676 0.381337315738338 27 0.552151851701747 0.895696296596507 0.447848148298253 28 0.54755656655915 0.9048868668817 0.45244343344085 29 0.479314906710119 0.958629813420239 0.520685093289881 30 0.414260511304764 0.828521022609529 0.585739488695236 31 0.430449432376937 0.860898864753874 0.569550567623063 32 0.368547300067856 0.737094600135712 0.631452699932144 33 0.594739930196525 0.810520139606949 0.405260069803475 34 0.541590102859068 0.916819794281865 0.458409897140932 35 0.496111961715472 0.992223923430944 0.503888038284528 36 0.445743207129956 0.891486414259913 0.554256792870044 37 0.412175467642146 0.824350935284292 0.587824532357854 38 0.361580262253329 0.723160524506658 0.638419737746671 39 0.323041778458255 0.64608355691651 0.676958221541745 40 0.291747663380254 0.583495326760508 0.708252336619746 41 0.520381850285681 0.959236299428638 0.479618149714319 42 0.465993388064798 0.931986776129596 0.534006611935202 43 0.429672038695843 0.859344077391687 0.570327961304157 44 0.381242173673637 0.762484347347273 0.618757826326363 45 0.339058999307164 0.678117998614328 0.660941000692836 46 0.317959174418539 0.635918348837079 0.682040825581461 47 0.300615473832482 0.601230947664964 0.699384526167518 48 0.292434179424033 0.584868358848066 0.707565820575967 49 0.256888005680828 0.513776011361657 0.743111994319172 50 0.251516084758881 0.503032169517761 0.74848391524112 51 0.231507663650269 0.463015327300538 0.768492336349731 52 0.204345892422245 0.408691784844489 0.795654107577755 53 0.278724657768167 0.557449315536334 0.721275342231833 54 0.359405013184409 0.718810026368818 0.640594986815591 55 0.336595681302083 0.673191362604166 0.663404318697917 56 0.403583087684568 0.807166175369136 0.596416912315432 57 0.379995401728031 0.759990803456061 0.620004598271969 58 0.349115187107969 0.698230374215939 0.65088481289203 59 0.348094409551356 0.696188819102712 0.651905590448644 60 0.429021674675724 0.858043349351447 0.570978325324276 61 0.38478168116117 0.76956336232234 0.61521831883883 62 0.342932739069382 0.685865478138763 0.657067260930618 63 0.344237341591627 0.688474683183253 0.655762658408374 64 0.310517716831574 0.621035433663149 0.689482283168426 65 0.27174417971105 0.5434883594221 0.72825582028895 66 0.254076974393460 0.508153948786919 0.74592302560654 67 0.223410805546076 0.446821611092153 0.776589194453924 68 0.250270644583461 0.500541289166922 0.749729355416539 69 0.216334736872633 0.432669473745266 0.783665263127367 70 0.183655427814451 0.367310855628902 0.816344572185549 71 0.154697045236464 0.309394090472928 0.845302954763536 72 0.130257321871118 0.260514643742237 0.869742678128882 73 0.111645172323628 0.223290344647255 0.888354827676372 74 0.09148079237947 0.18296158475894 0.90851920762053 75 0.074170779294559 0.148341558589118 0.925829220705441 76 0.0645746754298448 0.129149350859690 0.935425324570155 77 0.0520574819018544 0.104114963803709 0.947942518098146 78 0.0410241653210272 0.0820483306420545 0.958975834678973 79 0.0427972826628657 0.0855945653257313 0.957202717337134 80 0.0441161292896620 0.0882322585793239 0.955883870710338 81 0.0353889591897694 0.0707779183795388 0.96461104081023 82 0.0408165366066341 0.0816330732132682 0.959183463393366 83 0.0325389781909636 0.0650779563819271 0.967461021809036 84 0.0248802395021145 0.0497604790042289 0.975119760497886 85 0.0230988269966369 0.0461976539932739 0.976901173003363 86 0.0182903102903826 0.0365806205807652 0.981709689709617 87 0.0147302288263008 0.0294604576526016 0.9852697711737 88 0.0152889075416884 0.0305778150833767 0.984711092458312 89 0.0127384581708284 0.0254769163416567 0.987261541829172 90 0.0095625706962758 0.0191251413925516 0.990437429303724 91 0.00814534166179546 0.0162906833235909 0.991854658338205 92 0.00662182267551729 0.0132436453510346 0.993378177324483 93 0.00485119766585654 0.00970239533171308 0.995148802334143 94 0.00459329415770564 0.00918658831541128 0.995406705842294 95 0.00687263501554818 0.0137452700310964 0.993127364984452 96 0.00558276256594835 0.0111655251318967 0.994417237434052 97 0.00474421605917724 0.00948843211835448 0.995255783940823 98 0.00362587207937500 0.00725174415875001 0.996374127920625 99 0.00272400370363297 0.00544800740726595 0.997275996296367 100 0.00225862115490459 0.00451724230980919 0.997741378845095 101 0.0017718562329708 0.0035437124659416 0.998228143767029 102 0.00129489347324629 0.00258978694649258 0.998705106526754 103 0.00159736749271996 0.00319473498543993 0.99840263250728 104 0.00124203112273985 0.00248406224547969 0.99875796887726 105 0.0054274265720604 0.0108548531441208 0.99457257342794 106 0.0132971588004387 0.0265943176008773 0.986702841199561 107 0.014008233844637 0.028016467689274 0.985991766155363 108 0.0190686692280918 0.0381373384561835 0.980931330771908 109 0.014842544733235 0.02968508946647 0.985157455266765 110 0.0107499912000225 0.0214999824000450 0.989250008799978 111 0.00775658522744646 0.0155131704548929 0.992243414772554 112 0.0223488792291657 0.0446977584583314 0.977651120770834 113 0.0223608521738338 0.0447217043476677 0.977639147826166 114 0.0557637522169602 0.111527504433920 0.94423624778304 115 0.0476051419790593 0.0952102839581186 0.95239485802094 116 0.0398742793427035 0.079748558685407 0.960125720657297 117 0.104297024878992 0.208594049757984 0.895702975121008 118 0.098256332121011 0.196512664242022 0.901743667878989 119 0.0876375347773045 0.175275069554609 0.912362465222696 120 0.152261220761832 0.304522441523663 0.847738779238169 121 0.149211402661699 0.298422805323398 0.850788597338301 122 0.189016196871584 0.378032393743168 0.810983803128416 123 0.187789385134568 0.375578770269136 0.812210614865432 124 0.177968364592408 0.355936729184816 0.822031635407592 125 0.154173227205300 0.308346454410601 0.8458267727947 126 0.123796205211202 0.247592410422404 0.876203794788798 127 0.0969357521267576 0.193871504253515 0.903064247873242 128 0.0945259417295777 0.189051883459155 0.905474058270422 129 0.132653785081492 0.265307570162985 0.867346214918508 130 0.114738929034189 0.229477858068378 0.885261070965811 131 0.0960009486316775 0.192001897263355 0.903999051368322 132 0.0852218820585569 0.170443764117114 0.914778117941443 133 0.0833915883135629 0.166783176627126 0.916608411686437 134 0.07419694155915 0.1483938831183 0.92580305844085 135 0.173388639172696 0.346777278345392 0.826611360827304 136 0.138262026560218 0.276524053120436 0.861737973439782 137 0.115803153986223 0.231606307972445 0.884196846013777 138 0.1628323694767 0.3256647389534 0.8371676305233 139 0.394667675706998 0.789335351413996 0.605332324293002 140 0.339605768262348 0.679211536524696 0.660394231737652 141 0.481929833232171 0.963859666464343 0.518070166767829 142 0.390634950515132 0.781269901030264 0.609365049484868 143 0.552332756550338 0.895334486899323 0.447667243449662 144 0.498813859776171 0.997627719552342 0.501186140223829 145 0.402455715511535 0.80491143102307 0.597544284488465 146 0.298069267224429 0.596138534448858 0.701930732775571 147 0.289509793268831 0.579019586537662 0.710490206731169 148 0.172331530851367 0.344663061702735 0.827668469148633 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 10 0.072463768115942 NOK 5% type I error level 30 0.217391304347826 NOK 10% type I error level 38 0.275362318840580 NOK

Charts produced by software:

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Parameters (Session):

par1 = 6 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = 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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