Workshop 7: Model 2: Run sequence plot of Yt

*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, 24 Nov 2010 02:03:27 +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/24/t1290564159wayws8i6bv5zr8d.htm/, Retrieved Wed, 24 Nov 2010 03:02:50 +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/24/t1290564159wayws8i6bv5zr8d.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:

Effect maand?

Dataseries X:

» Textbox « » Textfile « » CSV «

9 4 2 5 4 3 9 4 2 4 3 2 9 5 4 4 2 2 9 3 2 4 2 2 9 4 3 2 2 2 9 3 4 5 2 2 10 4 3 5 3 2 10 3 3 4 2 1 10 2 3 3 1 2 10 4 2 4 2 2 10 2 4 4 2 2 10 2 3 3 2 2 10 1 3 3 2 2 10 4 4 4 2 2 10 4 4 5 1 1 10 2 3 4 2 2 10 2 3 2 2 1 10 3 3 4 3 2 10 3 4 4 4 2 10 3 2 4 4 2 10 4 5 4 4 4 10 3 4 4 4 2 10 2 2 4 4 4 10 2 3 5 2 2 10 4 4 4 2 2 10 4 4 4 4 2 10 3 3 4 2 2 10 4 4 4 3 2 10 2 4 4 2 2 10 4 1 4 4 2 10 4 4 4 3 3 10 5 5 2 4 2 10 5 2 4 2 2 10 4 4 4 2 2 10 4 3 5 4 3 10 4 2 5 5 4 10 2 4 4 2 1 10 4 5 3 4 2 10 4 4 4 4 3 10 4 4 5 5 3 10 3 4 4 3 2 10 2 3 4 2 2 10 3 4 5 3 2 10 4 2 4 2 2 10 3 2 5 1 2 10 2 4 4 2 2 10 4 2 4 4 4 10 4 4 4 4 4 10 3 4 3 4 2 10 4 1 4 4 3 10 3 4 4 2 2 10 4 2 4 2 2 10 2 1 2 1 1 10 4 4 3 4 3 10 4 3 5 2 4 10 4 2 4 4 2 10 4 4 4 2 2 10 3 3 5 2 1 10 1 2 3 1 2 10 3 2 5 2 2 10 3 3 4 2 2 10 4 2 5 2 2 10 2 1 4 2 2 10 3 3 4 1 1 10 5 2 5 5 2 10 4 3 4 3 3 10 4 3 4 2 2 10 3 3 5 1 1 10 4 2 4 2 2 10 2 3 3 4 4 10 3 2 4 2 2 10 4 4 5 5 3 10 3 4 5 4 4 10 4 4 5 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 15 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation YT[t] = + 8.3338907536128 -0.707921514339912T1[t] + 0.0765528746818019X1[t] + 0.247513466468538X2[t] + 0.365683209924910X3[t] -0.115580997002373X4[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) 8.3338907536128 3.587474 2.3231 0.021511 0.010756 T1 -0.707921514339912 0.35828 -1.9759 0.04999 0.024995 X1 0.0765528746818019 0.073027 1.0483 0.296186 0.148093 X2 0.247513466468538 0.081868 3.0233 0.002938 0.001469 X3 0.365683209924910 0.071768 5.0953 1e-06 1e-06 X4 -0.115580997002373 0.088948 -1.2994 0.195782 0.097891 Multiple Linear Regression - Regression Statistics Multiple R 0.478227147881943 R-squared 0.228701204971298 Adjusted R-squared 0.203161509771672 F-TEST (value) 8.95473509702057 F-TEST (DF numerator) 5 F-TEST (DF denominator) 151 p-value 1.80539287519821e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.858434433593512 Sum Squared Residuals 111.273361193631 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4 4.46926005495247 -0.469260054952466 2 4 3.97164437556134 0.0283556244386557 3 5 3.75906691500002 1.24093308499998 4 3 3.60596116563642 -0.605961165636421 5 4 3.18748710738115 0.812512892618853 6 3 4.00658038146856 -1.00658038146856 7 4 3.58778920237175 0.412210797628249 8 3 3.09017352298068 -0.090173522980676 9 2 2.36139584958486 -0.361395849584856 10 4 2.8980396512965 1.10196034870350 11 2 3.05114540066011 -1.05114540066010 12 2 2.72707905950977 -0.727079059509766 13 1 2.72707905950977 -1.72707905950977 14 4 3.05114540066011 0.948854599339895 15 4 3.04855665420611 0.951443345793894 16 2 2.9745925259783 -0.974592525978303 17 2 2.5951465900436 -0.5951465900436 18 3 3.34027573590321 -0.340275735903213 19 3 3.78251182050992 -0.782511820509924 20 3 3.62940607114632 -0.629406071146321 21 4 3.62790270118698 0.372097298813020 22 3 3.78251182050992 -0.782511820509924 23 2 3.39824407714158 -1.39824407714158 24 2 3.22210599244684 -1.22210599244684 25 4 3.05114540066011 0.948854599339895 26 4 3.78251182050992 0.217488179490076 27 3 2.97459252597830 0.0254074740216966 28 4 3.41682861058501 0.583171389414985 29 2 3.05114540066011 -1.05114540066010 30 4 3.55285319646452 0.44714680353548 31 4 3.30124761358264 0.698752386417358 32 5 3.36403776225465 1.63596223774535 33 5 2.8980396512965 2.1019603487035 34 4 3.05114540066011 0.948854599339895 35 4 3.83789141529429 0.162108584705712 36 4 4.01144075353502 -0.0114407535350236 37 2 3.16672639766248 -1.16672639766248 38 4 3.61155122872319 0.388448771276812 39 4 3.66693082350755 0.333069176492448 40 4 4.280127499901 -0.280127499900999 41 3 3.41682861058501 -0.416828610585014 42 2 2.9745925259783 -0.974592525978303 43 3 3.66434207705355 -0.664342077053552 44 4 2.8980396512965 1.10196034870350 45 3 2.77986990784013 0.22013009215987 46 2 3.05114540066011 -1.05114540066010 47 4 3.39824407714158 0.601755922858424 48 4 3.55134982650518 0.448650173494821 49 3 3.53499835404139 -0.534998354041386 50 4 3.43727219946215 0.562727800537853 51 3 3.05114540066010 -0.0511454006601048 52 4 2.8980396512965 1.10196034870350 53 2 2.07635763075509 -0.0763576307550877 54 4 3.41941735703901 0.580582642960986 55 4 2.99094399844210 1.00905600155790 56 4 3.62940607114632 0.370593928853679 57 4 3.05114540066011 0.948854599339895 58 3 3.33768698944921 -0.337686989449214 59 1 2.28484297490305 -1.28484297490305 60 3 3.14555311776504 -0.145553117765040 61 3 2.97459252597830 0.0254074740216966 62 4 3.14555311776504 0.85444688223496 63 2 2.8214867766147 -0.8214867766147 64 3 2.72449031305577 0.275509686944234 65 5 4.24260274753977 0.757397252460232 66 4 3.22469473890084 0.77530526109916 67 4 2.97459252597830 1.02540747402170 68 3 2.97200377952430 0.027996220475696 69 4 2.8980396512965 1.10196034870350 70 2 3.22728348535484 -1.22728348535484 71 3 2.8980396512965 0.101960348703498 72 4 4.280127499901 -0.280127499900999 73 3 3.79886329297372 -0.798863292973717 74 4 3.66434207705355 0.335657922946448 75 4 2.66687765729176 1.33312234270824 76 3 3.09017352298068 -0.090173522980676 77 3 3.29865886712864 -0.298658867128643 78 2 3.22210599244684 -1.22210599244684 79 4 3.55134982650518 0.448650173494821 80 3 3.02997212076267 -0.0299721207626672 81 2 2.72707905950977 -0.727079059509766 82 2 3.70595894582812 -1.70595894582812 83 3 3.78251182050992 -0.782511820509924 84 2 2.78245865429413 -0.78245865429413 85 2 3.05114540066011 -1.05114540066010 86 4 3.26372286122141 0.736277138778588 87 4 3.26113411476741 0.738865885232588 88 4 3.78251182050992 0.217488179490076 89 2 2.9745925259783 -0.974592525978303 90 2 3.55134982650518 -1.55134982650518 91 4 2.8954509048425 1.10454909515750 92 2 2.65052618482796 -0.650526184827964 93 3 3.09276226943468 -0.0927622694346752 94 3 3.22210599244684 -0.222105992446841 95 5 3.87541616765552 1.12458383234448 96 3 2.66687765729176 0.333122342708243 97 4 3.22469473890084 0.77530526109916 98 3 3.05114540066010 -0.0511454006601048 99 2 2.85901152897593 -0.85901152897593 100 4 3.05114540066011 0.948854599339895 101 3 3.09017352298068 -0.090173522980676 102 3 2.97459252597830 0.0254074740216966 103 3 2.8980396512965 0.101960348703498 104 4 3.58778920237175 0.412210797628249 105 1 2.17185072435468 -1.17185072435468 106 3 2.97459252597830 0.0254074740216966 107 2 3.01879814120687 -1.01879814120687 108 3 3.30124761358264 -0.301247613582642 109 2 3.14555311776504 -1.14555311776504 110 2 2.55352972126903 -0.55352972126903 111 2 2.81998340665536 -0.81998340665536 112 4 2.57397331014616 1.42602668985384 113 5 4.22474790511663 0.775252094883365 114 5 2.64793743837396 2.35206256162604 115 3 2.97459252597830 0.0254074740216966 116 4 2.55611846772303 1.44388153227697 117 4 2.07894637720909 1.92105362279091 118 3 3.01211727833953 -0.0121172783395337 119 2 2.84266005651214 -0.842660056512138 120 4 3.95606115875066 0.0439388412493403 121 2 2.72707905950977 -0.727079059509766 122 3 2.61149806250739 0.388501937492607 123 2 3.26113411476741 -1.26113411476741 124 2 2.8980396512965 -0.898039651296502 125 2 2.68805093718919 -0.688050937189195 126 4 3.16672639766248 0.833273602337522 127 4 3.34027573590321 0.659724264096787 128 4 2.97459252597830 1.02540747402170 129 4 3.59037794882575 0.40962205117425 130 3 3.53499835404139 -0.534998354041386 131 2 2.9745925259783 -0.974592525978303 132 4 3.78251182050992 0.217488179490076 133 3 3.78251182050992 -0.782511820509924 134 2 2.8980396512965 -0.898039651296502 135 4 3.78251182050992 0.217488179490076 136 3 2.9006283977505 0.0993716022494987 137 3 3.05114540066010 -0.0511454006601048 138 3 2.97459252597830 0.0254074740216966 139 3 2.72966780596377 0.270332194036235 140 3 3.13437913820925 -0.134379138209246 141 4 3.62940607114632 0.370593928853679 142 5 3.84530196918193 1.15469803081807 143 2 3.01362064829887 -1.01362064829887 144 4 3.10911374189847 0.890886258101532 145 3 3.70854769228212 -0.708547692282122 146 3 2.36398459603886 0.636015403961145 147 1 2.47956559304123 -1.47956559304123 148 2 3.05114540066011 -1.05114540066010 149 4 2.80363193419157 1.19636806580843 150 4 2.81998340665536 1.18001659334464 151 5 4.03261403343246 0.96738596656754 152 2 2.80622068064557 -0.806220680645567 153 4 3.37521174181044 0.624788258189556 154 3 2.97459252597830 0.0254074740216966 155 2 3.34027573590321 -1.34027573590321 156 4 3.30124761358264 0.698752386417358 157 2 2.45688894318445 -0.456888943184449 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.478516808529533 0.957033617059066 0.521483191470467 10 0.69957205180478 0.600855896390439 0.300427948195220 11 0.780560893564702 0.438878212870595 0.219439106435298 12 0.768244334651571 0.463511330696857 0.231755665348429 13 0.875271962661018 0.249456074677965 0.124728037338982 14 0.90977637174767 0.180447256504659 0.0902236282523297 15 0.88834616526325 0.223307669473501 0.111653834736751 16 0.870492803375496 0.259014393249007 0.129507196624504 17 0.839516689581751 0.320966620836497 0.160483310418249 18 0.783254306418867 0.433491387162266 0.216745693581133 19 0.726656408485754 0.546687183028493 0.273343591514246 20 0.660211848210979 0.679576303578042 0.339788151789021 21 0.660847588270225 0.67830482345955 0.339152411729775 22 0.606481242314824 0.787037515370351 0.393518757685176 23 0.590115278290766 0.819769443418467 0.409884721709234 24 0.61994931817988 0.760101363640239 0.380050681820120 25 0.642192163329237 0.715615673341527 0.357807836670763 26 0.594939606764987 0.810120786470026 0.405060393235013 27 0.535235464913179 0.929529070173643 0.464764535086821 28 0.506216372845768 0.987567254308464 0.493783627154232 29 0.537069153889377 0.925861692221246 0.462930846110623 30 0.573510510680005 0.852978978639989 0.426489489319995 31 0.580690575485695 0.838618849028609 0.419309424514304 32 0.6579805656958 0.6840388686084 0.3420194343042 33 0.908650861958865 0.182698276082271 0.0913491380411354 34 0.908266076530464 0.183467846939073 0.0917339234695363 35 0.8867807279168 0.226438544166402 0.113219272083201 36 0.862641423852393 0.274717152295214 0.137358576147607 37 0.886842904853329 0.226314190293342 0.113157095146671 38 0.860436524869457 0.279126950261087 0.139563475130544 39 0.830740036478443 0.338519927043115 0.169259963521558 40 0.797717614157092 0.404564771685817 0.202282385842908 41 0.767001447984224 0.465997104031552 0.232998552015776 42 0.766880912704317 0.466238174591366 0.233119087295683 43 0.74326116351356 0.51347767297288 0.25673883648644 44 0.78116407744393 0.43767184511214 0.21883592255607 45 0.747904851060332 0.504190297879335 0.252095148939668 46 0.762661150139035 0.47467769972193 0.237338849860965 47 0.739085139073838 0.521829721852325 0.260914860926162 48 0.70263236295738 0.59473527408524 0.29736763704262 49 0.674812173905653 0.650375652188694 0.325187826094347 50 0.646777248494004 0.706445503011993 0.353222751505997 51 0.598483745067875 0.803032509864249 0.401516254932125 52 0.625391459057926 0.749217081884147 0.374608540942074 53 0.579830328944868 0.840339342110263 0.420169671055132 54 0.545669462891496 0.908661074217009 0.454330537108504 55 0.542212335675389 0.915575328649223 0.457787664324611 56 0.505987687540508 0.988024624918983 0.494012312459492 57 0.51225637394826 0.97548725210348 0.48774362605174 58 0.466837074967294 0.933674149934588 0.533162925032706 59 0.541974097130315 0.91605180573937 0.458025902869685 60 0.49397201601642 0.98794403203284 0.50602798398358 61 0.445477687859768 0.890955375719535 0.554522312140232 62 0.447618843646287 0.895237687292574 0.552381156353713 63 0.44083103773445 0.8816620754689 0.55916896226555 64 0.400882215253697 0.801764430507395 0.599117784746303 65 0.397559041866029 0.795118083732059 0.602440958133971 66 0.383459154389235 0.766918308778469 0.616540845610765 67 0.399251196884879 0.798502393769758 0.600748803115121 68 0.354464382014966 0.708928764029931 0.645535617985034 69 0.379850194668842 0.759700389337683 0.620149805331158 70 0.437905199823255 0.87581039964651 0.562094800176745 71 0.392299320940246 0.784598641880491 0.607700679059754 72 0.352293967569651 0.704587935139303 0.647706032430349 73 0.347125138708278 0.694250277416555 0.652874861291722 74 0.310781580130208 0.621563160260415 0.689218419869792 75 0.362378445684524 0.724756891369047 0.637621554315476 76 0.319356808447106 0.638713616894213 0.680643191552894 77 0.283300405288823 0.566600810577646 0.716699594711177 78 0.321851423751781 0.643702847503563 0.678148576248219 79 0.291059779450707 0.582119558901413 0.708940220549293 80 0.253275024400287 0.506550048800574 0.746724975599713 81 0.244351734330950 0.488703468661901 0.75564826566905 82 0.351224131811134 0.702448263622269 0.648775868188866 83 0.341637645416440 0.683275290832879 0.65836235458356 84 0.335701150201321 0.671402300402641 0.66429884979868 85 0.358114743350772 0.716229486701543 0.641885256649228 86 0.347211491902517 0.694422983805033 0.652788508097483 87 0.337073240768096 0.674146481536191 0.662926759231904 88 0.298166686522729 0.596333373045458 0.701833313477271 89 0.308525269033448 0.617050538066896 0.691474730966552 90 0.403136734160616 0.806273468321233 0.596863265839384 91 0.436304403286227 0.872608806572453 0.563695596713773 92 0.412238897217148 0.824477794434295 0.587761102782852 93 0.367113806244689 0.734227612489379 0.632886193755311 94 0.325254368996302 0.650508737992603 0.674745631003698 95 0.349558824738263 0.699117649476525 0.650441175261737 96 0.317927959281954 0.635855918563907 0.682072040718046 97 0.31310622021519 0.62621244043038 0.68689377978481 98 0.271719176708364 0.543438353416728 0.728280823291636 99 0.265633691472606 0.531267382945212 0.734366308527394 100 0.270002741131277 0.540005482262555 0.729997258868723 101 0.231443931650197 0.462887863300393 0.768556068349803 102 0.195678467407947 0.391356934815895 0.804321532592053 103 0.164652391764421 0.329304783528842 0.835347608235579 104 0.144129921653128 0.288259843306256 0.855870078346872 105 0.162573636733919 0.325147273467837 0.837426363266081 106 0.133791883418129 0.267583766836258 0.866208116581871 107 0.148599568030555 0.297199136061111 0.851400431969444 108 0.123657803260759 0.247315606521518 0.87634219673924 109 0.134110664532349 0.268221329064698 0.86588933546765 110 0.119995857836530 0.239991715673059 0.88000414216347 111 0.116161724073132 0.232323448146265 0.883838275926868 112 0.164494776612273 0.328989553224547 0.835505223387727 113 0.153006333726774 0.306012667453548 0.846993666273226 114 0.490404398897515 0.98080879779503 0.509595601102485 115 0.439381482237435 0.878762964474871 0.560618517762565 116 0.513323613650870 0.97335277269826 0.48667638634913 117 0.838863886463529 0.322272227072942 0.161136113536471 118 0.812805302051598 0.374389395896803 0.187194697948402 119 0.786819161717193 0.426361676565614 0.213180838282807 120 0.744550375205668 0.510899249588664 0.255449624794332 121 0.711509073442546 0.576981853114909 0.288490926557454 122 0.681053678082919 0.637892643834163 0.318946321917081 123 0.684366803406942 0.631266393186116 0.315633196593058 124 0.65495541313343 0.690089173733139 0.345044586866570 125 0.64431083639607 0.71137832720786 0.35568916360393 126 0.651380011786686 0.697239976426628 0.348619988213314 127 0.638289798638442 0.723420402723115 0.361710201361558 128 0.716684175536018 0.566631648927964 0.283315824463982 129 0.664317821510786 0.671364356978429 0.335682178489214 130 0.642266389266562 0.715467221466876 0.357733610733438 131 0.621088869934561 0.757822260130877 0.378911130065439 132 0.553176344118871 0.893647311762258 0.446823655881129 133 0.597149550747421 0.805700898505159 0.402850449252579 134 0.5445755807565 0.910848838487 0.4554244192435 135 0.47431672118837 0.94863344237674 0.52568327881163 136 0.415346516010255 0.83069303202051 0.584653483989745 137 0.342274581821334 0.684549163642668 0.657725418178666 138 0.277347193606546 0.554694387213091 0.722652806393454 139 0.228488327468747 0.456976654937493 0.771511672531253 140 0.184861908683889 0.369723817367778 0.815138091316111 141 0.176974519404652 0.353949038809303 0.823025480595349 142 0.182597227441930 0.365194454883859 0.81740277255807 143 0.131544370816263 0.263088741632526 0.868455629183737 144 0.109943167222919 0.219886334445838 0.89005683277708 145 0.0741942899200109 0.148388579840022 0.92580571007999 146 0.123552961809528 0.247105923619055 0.876447038190472 147 0.0776491481155252 0.155298296231050 0.922350851884475 148 0.0988286351840012 0.197657270368002 0.901171364815999 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 0 0 OK 10% type I error level 0 0 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290564159wayws8i6bv5zr8d/107fdq1290564190.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290564159wayws8i6bv5zr8d/107fdq1290564190.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290564159wayws8i6bv5zr8d/1ieyf1290564190.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290564159wayws8i6bv5zr8d/1ieyf1290564190.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290564159wayws8i6bv5zr8d/2toyi1290564190.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290564159wayws8i6bv5zr8d/2toyi1290564190.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290564159wayws8i6bv5zr8d/3toyi1290564190.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290564159wayws8i6bv5zr8d/3toyi1290564190.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290564159wayws8i6bv5zr8d/44fxl1290564190.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290564159wayws8i6bv5zr8d/44fxl1290564190.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290564159wayws8i6bv5zr8d/54fxl1290564190.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290564159wayws8i6bv5zr8d/54fxl1290564190.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290564159wayws8i6bv5zr8d/64fxl1290564190.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290564159wayws8i6bv5zr8d/64fxl1290564190.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290564159wayws8i6bv5zr8d/7woe51290564190.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290564159wayws8i6bv5zr8d/7woe51290564190.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290564159wayws8i6bv5zr8d/87fdq1290564190.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290564159wayws8i6bv5zr8d/87fdq1290564190.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290564159wayws8i6bv5zr8d/97fdq1290564190.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290564159wayws8i6bv5zr8d/97fdq1290564190.ps (open in new window)

Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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