*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, 21 Dec 2010 16:18:28 +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/21/t1292948345xpmkkbava3uvvng.htm/, Retrieved Tue, 21 Dec 2010 17:19:08 +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/21/t1292948345xpmkkbava3uvvng.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 «

9,1 4,5 1,0 -1,0 3484,7 9,0 4,3 1,0 3,0 3411,1 9,0 4,3 1,3 2,0 3288,2 8,9 4,2 1,1 3,0 3280,4 8,8 4,0 0,8 5,0 3174,0 8,7 3,8 0,7 5,0 3165,3 8,5 4,1 0,7 3,0 3092,7 8,3 4,2 0,9 2,0 3053,1 8,1 4,0 1,3 1,0 3182,0 7,9 4,3 1,4 -4,0 2999,9 7,8 4,7 1,6 1,0 3249,6 7,6 5,0 2,1 1,0 3210,5 7,4 5,1 0,3 6,0 3030,3 7,2 5,4 2,1 3,0 2803,5 7,0 5,4 2,5 2,0 2767,6 7,0 5,4 2,3 2,0 2882,6 6,8 5,5 2,4 2,0 2863,4 6,8 5,8 3,0 -8,0 2897,1 6,7 5,7 1,7 0,0 3012,6 6,8 5,5 3,5 -2,0 3143,0 6,7 5,6 4,0 3,0 3032,9 6,7 5,6 3,7 5,0 3045,8 6,7 5,5 3,7 8,0 3110,5 6,5 5,5 3,0 8,0 3013,2 6,3 5,7 2,7 9,0 2987,1 6,3 5,6 2,5 11,0 2995,6 6,3 5,6 2,2 13,0 2833,2 6,5 5,4 2,9 12,0 2849,0 6,6 5,2 3,1 13,0 2794,8 6,5 5,1 3,0 15,0 2845,3 6,3 5,1 2,8 13,0 2915,0 6,3 5,0 2,5 16,0 2892,6 6,5 5,3 1,9 10,0 2604,4 7,0 5,4 1,9 14,0 2641,7 7,1 5,3 1,8 14,0 2659,8 7,3 5,1 2,0 15,0 2638,5 7,3 5,0 2,6 13,0 2720,3 7,4 5,0 2,5 8,0 2745,9 7,4 4,6 2,5 7,0 2735,7 7,3 4,8 1,6 3,0 2811,7 7,4 5,1 1,4 3,0 2799,4 7,5 5,1 0,8 4,0 2555,3 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 6 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation werkloosheid[t] = + 13.1121249136743 -0.931678442910017rente[t] -0.077702445244027hicp[t] -0.027613673258089consumer[t] -0.000195934660486037bel20[t] -0.00837512881878393t + 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) 13.1121249136743 0.308908 42.4468 0 0 rente -0.931678442910017 0.051936 -17.939 0 0 hicp -0.077702445244027 0.023244 -3.343 0.001071 0.000535 consumer -0.027613673258089 0.0045 -6.1365 0 0 bel20 -0.000195934660486037 4e-05 -4.9469 2e-06 1e-06 t -0.00837512881878393 0.000891 -9.4014 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.907212309133192 R-squared 0.823034173842778 Adjusted R-squared 0.81652807729288 F-TEST (value) 126.50199202096 F-TEST (DF numerator) 5 F-TEST (DF denominator) 136 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.305771902075493 Sum Squared Residuals 12.7155180294456 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 9.1 8.1783345083788 0.921665491621195 2 9 8.26026116612144 0.739738833878564 3 9 8.28026934676127 0.719730653238734 4 8.9 8.35451716837599 0.54548283162401 5 8.8 8.52140856307195 0.278591436928046 6 8.7 8.70884399890581 -0.00884399890580678 7 8.5 8.49041754008148 0.00958245991851884 8 8.3 8.40870676373622 -0.108706763736225 9 8.1 8.55794404092327 -0.457944040923274 10 7.9 8.43604320267203 -0.536043202672034 11 7.8 7.85246295662663 -0.0524629566266297 12 7.6 7.53339411753783 0.0666058824621682 13 7.4 7.46895460539643 -0.0689546053964328 14 7.2 7.16849054303789 0.0315094569621048 15 7 7.16368216369104 -0.163682163691038 16 7 7.14831503796517 -0.148315037965166 17 6.8 7.04276376581231 -0.24276376581231 18 6.8 6.97779737149662 -0.177797371496616 19 6.7 6.92006342643522 -0.220063426435218 20 6.8 6.98783705154799 -0.187837051547989 21 6.7 6.73094689564526 -0.0309468956452573 22 6.7 6.68812759676323 0.0118724032367666 23 6.7 6.67740231992774 0.0225976800722627 24 6.5 6.74248334524506 -0.242483345245064 25 6.3 6.54858348279808 -0.248583482798081 26 6.3 6.5920238961888 -0.292023896188795 27 6.3 6.58355194328997 -0.283551943289974 28 6.5 6.73163869700478 -0.231638697004783 29 6.6 6.87706475305945 -0.277064753059452 30 6.5 6.90450566618535 -0.404505666185349 31 6.3 6.95324172709567 -0.653241727095673 32 6.3 6.98289309276172 -0.682893092761718 33 6.5 6.96378630691695 -0.463786306916955 34 7 6.74448027793868 0.255519722061316 35 7.1 6.83349682058051 0.266503179419492 36 7.3 6.97247662630518 0.327523373694815 37 7.3 7.0498477659194 0.250152234080593 38 7.4 7.18229532060703 0.217704679392972 39 7.4 7.5762037757473 -0.176203775747297 40 7.3 7.54698881790155 -0.246988817901552 41 7.4 7.27706064158255 0.122939358417454 42 7.5 7.33552095727673 0.164479042723269 43 7.7 7.3528775404044 0.347122459595606 44 7.7 7.1775472021399 0.522452797860101 45 7.7 7.4097983065134 0.290201693486608 46 7.7 7.69434027871 0.00565972129000357 47 7.7 7.97840865251504 -0.278408652515044 48 7.8 7.87382254582722 -0.0738225458272172 49 8 7.87578006180784 0.124219938192162 50 8.1 8.0960447213302 0.00395527866980601 51 8.1 7.8915390528064 0.208460947193608 52 8.2 8.00828494760131 0.191715052398691 53 8.2 8.28333417668643 -0.0833341766864326 54 8.2 8.43262736379936 -0.232627363799363 55 8.1 8.55086424391526 -0.450864243915261 56 8.1 8.37785348214923 -0.277853482149228 57 8.2 8.35541860620444 -0.15541860620444 58 8.3 8.73765697842555 -0.437656978425552 59 8.3 8.62212500920815 -0.322125009208145 60 8.4 8.44814112907637 -0.0481411290763736 61 8.5 8.46057524977218 0.0394247502278168 62 8.5 8.65374862134787 -0.153748621347867 63 8.4 8.52568994373274 -0.125689943732736 64 8 8.1638805409423 -0.163880540942305 65 7.9 8.24499698238222 -0.344996982382217 66 8.1 8.28610757587629 -0.18610757587629 67 8.5 8.54041248618253 -0.0404124861825325 68 8.8 8.47484230274582 0.325157697254184 69 8.8 8.00786294773446 0.792137052265537 70 8.6 8.0907365722399 0.509263427760104 71 8.3 7.84679540610096 0.453204593899038 72 8.3 7.94854221064975 0.351457789350252 73 8.3 8.0240374591549 0.275962540845107 74 8.4 7.91778549925675 0.482214500743249 75 8.4 8.1071062556057 0.292893744394307 76 8.5 8.24802687838124 0.251973121618757 77 8.6 8.40718139520223 0.192818604797768 78 8.6 8.38132528954181 0.218674710458191 79 8.6 8.28445097303808 0.315549026961923 80 8.6 8.1865962485779 0.413403751422107 81 8.6 8.35290705753909 0.247092942460913 82 8.5 8.69989866224299 -0.199898662242989 83 8.4 8.7910740952735 -0.391074095273502 84 8.4 8.59755553348833 -0.197555533488332 85 8.4 8.74165858391956 -0.341658583919564 86 8.5 8.5286485371385 -0.0286485371385016 87 8.5 8.33239196774106 0.167608032258944 88 8.6 8.28701756616886 0.312982433831137 89 8.6 8.63361590838169 -0.0336159083816935 90 8.4 8.50747673112639 -0.107476731126388 91 8.2 8.48110643897809 -0.281106438978094 92 8 8.14189764861251 -0.141897648612512 93 8 8.0676007459413 -0.0676007459412967 94 8 7.87608866979694 0.123911330203065 95 8 7.76683784168424 0.233162158315763 96 7.9 7.71555597202942 0.184444027970583 97 7.9 7.78416481380353 0.115835186196472 98 7.8 7.8772995934389 -0.0772995934389019 99 7.8 7.88712572667015 -0.0871257266701506 100 8 7.8983972779324 0.1016027220676 101 7.8 7.68388689176543 0.116113108234571 102 7.4 7.39353404166503 0.00646595833497051 103 7.2 7.58297637253273 -0.382976372532731 104 7 7.55979890212047 -0.559798902120468 105 7 7.42429758187619 -0.424297581876189 106 7.2 6.93662613354741 0.263373866452591 107 7.2 6.87296355998529 0.327036440014714 108 7.2 7.18848559713591 0.0115144028640902 109 7 7.00906719199719 -0.00906719199719133 110 6.9 6.96189240270785 -0.0618924027078518 111 6.8 7.04888106367968 -0.248881063679675 112 6.8 7.0382482631498 -0.238248263149793 113 6.8 6.77690530882244 0.0230946911775602 114 6.9 7.17255733252114 -0.272557332521139 115 7.2 7.30408127851144 -0.104081278511443 116 7.2 7.17301389787976 0.0269861021202409 117 7.2 7.08029634598874 0.119703654011262 118 7.1 6.96898777065125 0.131012229348746 119 7.2 7.03464355742362 0.165356442576378 120 7.3 7.26389177906323 0.0361082209367677 121 7.5 7.53535433595234 -0.0353543359523406 122 7.6 7.47817490835798 0.121825091642023 123 7.7 7.59842015201891 0.10157984798109 124 7.7 6.72298092426563 0.977019075734374 125 7.7 7.73468644328548 -0.0346864432854808 126 7.8 7.94125739786398 -0.141257397863985 127 8 8.22076450780218 -0.220764507802177 128 8.1 8.315348064672 -0.215348064672002 129 8.1 8.24568571730339 -0.145685717303391 130 8 8.15725036438394 -0.157250364383937 131 8.1 8.41241886449848 -0.312418864498481 132 8.2 8.64289524961736 -0.44289524961736 133 8.3 8.54347960680704 -0.243479606807037 134 8.4 8.65678622706646 -0.256786227066459 135 8.4 8.53480219123345 -0.134802191233451 136 8.4 8.44976159356905 -0.0497615935690538 137 8.5 8.36853237171626 0.131467628283734 138 8.5 8.21977938882753 0.280220611172475 139 8.6 8.30126843138334 0.298731568616659 140 8.6 8.30525891545947 0.294741084540533 141 8.5 8.24337665141431 0.256623348585687 142 8.5 8.6060698446669 -0.106069844666894 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.00448301057267887 0.00896602114535775 0.99551698942732 10 0.00163907684601964 0.00327815369203927 0.99836092315398 11 0.000629406672048534 0.00125881334409707 0.999370593327951 12 0.000140861059661697 0.000281722119323395 0.999859138940338 13 5.71577995495649e-05 0.00011431559909913 0.99994284220045 14 4.75046020049755e-05 9.5009204009951e-05 0.999952495397995 15 1.87396493091837e-05 3.74792986183673e-05 0.99998126035069 16 7.46176970286808e-06 1.49235394057362e-05 0.999992538230297 17 1.62235143885263e-06 3.24470287770526e-06 0.999998377648561 18 4.22508362207069e-05 8.45016724414138e-05 0.99995774916378 19 3.55527590601244e-05 7.11055181202488e-05 0.99996444724094 20 5.30666057012168e-05 0.000106133211402434 0.999946933394299 21 3.15284574794616e-05 6.30569149589231e-05 0.99996847154252 22 2.64770848472695e-05 5.2954169694539e-05 0.999973522915153 23 1.32023171639995e-05 2.6404634327999e-05 0.999986797682836 24 6.43078329924307e-06 1.28615665984861e-05 0.9999935692167 25 2.68224619020621e-06 5.36449238041241e-06 0.99999731775381 26 1.31339766647128e-06 2.62679533294256e-06 0.999998686602333 27 3.16250954723244e-06 6.32501909446487e-06 0.999996837490453 28 3.38136104374955e-05 6.7627220874991e-05 0.999966186389562 29 0.000181005414252053 0.000362010828504106 0.999818994585748 30 0.000153209340035181 0.000306418680070362 0.999846790659965 31 0.000142764393388261 0.000285528786776523 0.999857235606612 32 0.000160897523237901 0.000321795046475803 0.999839102476762 33 0.0212782711238891 0.0425565422477782 0.97872172887611 34 0.469645192633648 0.939290385267295 0.530354807366352 35 0.800699275859329 0.398601448281343 0.199300724140671 36 0.935516411214222 0.128967177571556 0.0644835887857782 37 0.97038734345411 0.0592253130917784 0.0296126565458892 38 0.978986862284433 0.0420262754311337 0.0210131377155669 39 0.974240389293177 0.0515192214136465 0.0257596107068233 40 0.971926334483967 0.0561473310320655 0.0280736655160327 41 0.964874725094295 0.070250549811411 0.0351252749057055 42 0.958429177402982 0.083141645194036 0.041570822597018 43 0.969107490014385 0.0617850199712306 0.0308925099856153 44 0.981127543530374 0.0377449129392514 0.0188724564696257 45 0.976804844287882 0.0463903114242364 0.0231951557121182 46 0.970007350455236 0.059985299089529 0.0299926495447645 47 0.975521176812762 0.0489576463744765 0.0244788231872382 48 0.96922854690796 0.0615429061840806 0.0307714530920403 49 0.961187951070581 0.0776240978588377 0.0388120489294189 50 0.95075429278374 0.0984914144325213 0.0492457072162606 51 0.945116830448495 0.10976633910301 0.0548831695515051 52 0.933922738701733 0.132154522596535 0.0660772612982673 53 0.9205121762495 0.158975647500999 0.0794878237504994 54 0.911213930970974 0.177572138058051 0.0887860690290256 55 0.929468679948053 0.141062640103894 0.0705313200519472 56 0.92580905727207 0.14838188545586 0.0741909427279301 57 0.914110977337005 0.17177804532599 0.0858890226629949 58 0.929926520963204 0.140146958073593 0.0700734790367963 59 0.934474404646853 0.131051190706294 0.065525595353147 60 0.926686453871774 0.146627092256452 0.0733135461282258 61 0.91425443494226 0.171491130115478 0.0857455650577392 62 0.904214884868676 0.191570230262648 0.095785115131324 63 0.894401421240177 0.211197157519647 0.105598578759823 64 0.898383743748333 0.203232512503334 0.101616256251667 65 0.935367959592805 0.12926408081439 0.0646320404071949 66 0.952081098182648 0.0958378036347038 0.0479189018173519 67 0.959671065279172 0.0806578694416553 0.0403289347208276 68 0.966336197546455 0.0673276049070895 0.0336638024535447 69 0.990306513838153 0.0193869723236931 0.00969348616184653 70 0.992137480057232 0.0157250398855355 0.00786251994276774 71 0.99111519748985 0.0177696050203008 0.00888480251015039 72 0.988002561354445 0.0239948772911106 0.0119974386455553 73 0.98362432375786 0.0327513524842805 0.0163756762421402 74 0.983210614711438 0.0335787705771246 0.0167893852885623 75 0.97866143424809 0.0426771315038219 0.0213385657519109 76 0.972851953620021 0.0542960927599571 0.0271480463799786 77 0.965372841126532 0.0692543177469353 0.0346271588734677 78 0.957776311621352 0.0844473767572963 0.0422236883786482 79 0.954554981776676 0.0908900364466484 0.0454450182233242 80 0.96242526915298 0.0751494616940395 0.0375747308470197 81 0.962604583661174 0.0747908326776517 0.0373954163388258 82 0.966647034732618 0.0667059305347647 0.0333529652673823 83 0.978543400368036 0.0429131992639282 0.0214565996319641 84 0.976654356692667 0.0466912866146655 0.0233456433073328 85 0.980483845586327 0.0390323088273458 0.0195161544136729 86 0.974934222237443 0.0501315555251148 0.0250657777625574 87 0.972988692956 0.0540226140880022 0.0270113070440011 88 0.979748109278216 0.0405037814435676 0.0202518907217838 89 0.97619437345534 0.0476112530893187 0.0238056265446594 90 0.971363296358915 0.0572734072821707 0.0286367036410853 91 0.969509148296982 0.0609817034060358 0.0304908517030179 92 0.964061811855872 0.0718763762882562 0.0359381881441281 93 0.956794629340464 0.0864107413190727 0.0432053706595363 94 0.95303145953438 0.0939370809312408 0.0469685404656204 95 0.960496541659623 0.0790069166807533 0.0395034583403766 96 0.97019631252774 0.0596073749445203 0.0298036874722601 97 0.979789632452742 0.0404207350945164 0.0202103675472582 98 0.983613254702312 0.032773490595377 0.0163867452976885 99 0.989560375096166 0.0208792498076672 0.0104396249038336 100 0.999359584193718 0.00128083161256324 0.000640415806281618 101 0.999991716317992 1.65673640165649e-05 8.28368200828243e-06 102 0.999999021099387 1.95780122568335e-06 9.78900612841675e-07 103 0.999999428865883 1.14226823325277e-06 5.71134116626386e-07 104 0.99999926205849 1.47588301946389e-06 7.37941509731943e-07 105 0.99999865903099 2.68193801836737e-06 1.34096900918368e-06 106 0.999999448397343 1.10320531306419e-06 5.51602656532093e-07 107 0.999999971465023 5.70699534934044e-08 2.85349767467022e-08 108 0.999999998856988 2.28602366416737e-09 1.14301183208369e-09 109 0.999999999731071 5.37857653288076e-10 2.68928826644038e-10 110 0.99999999966368 6.72639309272512e-10 3.36319654636256e-10 111 0.99999999882195 2.35609946338462e-09 1.17804973169231e-09 112 0.99999999642647 7.1470585447841e-09 3.57352927239205e-09 113 0.99999999184851 1.63029822046809e-08 8.15149110234045e-09 114 0.999999989559498 2.08810042232522e-08 1.04405021116261e-08 115 0.999999980226067 3.95478669220432e-08 1.97739334610216e-08 116 0.999999961573233 7.68535333439568e-08 3.84267666719784e-08 117 0.999999986219827 2.75603452379062e-08 1.37801726189531e-08 118 0.999999957057996 8.58840076801688e-08 4.29420038400844e-08 119 0.999999874316667 2.51366666761751e-07 1.25683333380876e-07 120 0.999999781950562 4.36098876495333e-07 2.18049438247666e-07 121 0.999999262502403 1.47499519382856e-06 7.37497596914282e-07 122 0.999997259262609 5.48147478277279e-06 2.7407373913864e-06 123 0.99999007777145 1.98444571001379e-05 9.92222855006895e-06 124 0.999983418664422 3.31626711564182e-05 1.65813355782091e-05 125 0.999968078685788 6.38426284241642e-05 3.19213142120821e-05 126 0.999991279300392 1.74413992160579e-05 8.72069960802896e-06 127 0.999980198908864 3.96021822711256e-05 1.98010911355628e-05 128 0.999930055405923 0.00013988918815408 6.994459407704e-05 129 0.999841049902977 0.000317900194046456 0.000158950097023228 130 0.999255030762084 0.00148993847583112 0.000744969237915558 131 0.99885360174087 0.00229279651826161 0.0011463982591308 132 0.999002206611863 0.00199558677627385 0.000997793388136924 133 0.993909626443534 0.0121807471129321 0.00609037355646604 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 57 0.456 NOK 5% type I error level 78 0.624 NOK 10% type I error level 107 0.856 NOK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; 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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