WS7 - Multiple regression model (incl. day) (incl. trend)

*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, 23 Nov 2010 20:52:04 +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/23/t1290545502az8zgx85nnzv49c.htm/, Retrieved Tue, 23 Nov 2010 21:51:53 +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/23/t1290545502az8zgx85nnzv49c.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

13 13 14 13 3 2 1 12 12 8 13 5 1 1 15 10 12 16 6 0 1 12 9 7 12 6 3 1 10 10 10 11 5 3 1 12 12 7 12 3 1 1 15 13 16 18 8 3 1 9 12 11 11 4 1 1 12 12 14 14 4 4 1 11 6 6 9 4 0 1 11 5 16 14 6 3 1 11 12 11 12 6 2 1 15 11 16 11 5 4 1 7 14 12 12 4 3 1 11 14 7 13 6 1 1 11 12 13 11 4 1 1 10 12 11 12 6 2 1 14 11 15 16 6 3 1 10 11 7 9 4 1 2 6 7 9 11 4 1 2 11 9 7 13 2 2 2 15 11 14 15 7 3 2 11 11 15 10 5 4 2 12 12 7 11 4 2 2 14 12 15 13 6 1 2 15 11 17 16 6 2 2 9 11 15 15 7 2 2 13 8 14 14 5 4 2 13 9 14 14 6 2 2 16 12 8 14 4 3 2 13 10 8 8 4 3 2 12 10 14 13 7 3 2 14 12 14 15 7 4 2 11 8 8 13 4 2 3 9 12 11 11 4 2 3 16 11 16 15 6 4 3 12 12 10 15 6 3 3 10 7 8 9 5 4 3 13 11 14 13 6 2 3 16 11 16 16 7 5 3 14 12 13 13 6 3 3 15 9 5 11 3 1 3 5 15 8 12 3 1 3 8 11 10 12 4 1 3 11 11 8 12 6 2 3 16 11 13 14 7 3 3 17 11 15 14 5 9 3 9 15 6 8 4 0 3 9 11 12 13 5 0 3 13 12 16 16 6 2 3 10 12 5 13 6 2 3 6 9 15 11 6 3 4 12 12 12 14 5 1 4 8 12 8 13 4 2 4 14 13 13 13 5 0 4 12 11 14 13 5 5 4 11 9 1 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 10 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Popularity[t] = -0.0931214533089994 + 0.114501138766228FindingFriends[t] + 0.209268449968476KnowingPeople[t] + 0.358378633517791Liked[t] + 0.6165874587436Celebrity[t] + 0.213464699493470Sum_friends[t] + 0.104200617441747Day[t] -0.00667926178074984t + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) -0.0931214533089994 1.454348 -0.064 0.949033 0.474516 FindingFriends 0.114501138766228 0.097256 1.1773 0.240957 0.120479 KnowingPeople 0.209268449968476 0.064112 3.2641 0.001364 0.000682 Liked 0.358378633517791 0.097379 3.6803 0.000326 0.000163 Celebrity 0.6165874587436 0.157441 3.9163 0.000137 6.8e-05 Sum_friends 0.213464699493470 0.120726 1.7682 0.079093 0.039547 Day 0.104200617441747 0.195341 0.5334 0.594537 0.297269 t -0.00667926178074984 0.011864 -0.563 0.5743 0.28715 Multiple Linear Regression - Regression Statistics Multiple R 0.714498470884513 R-squared 0.510508064896307 Adjusted R-squared 0.487356419317078 F-TEST (value) 22.050616797379 F-TEST (DF numerator) 7 F-TEST (DF denominator) 148 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.10259968841939 Sum Squared Residuals 654.296966561714 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 11.3582870168206 1.64171298317940 2 12 11.0012061344565 0.998793865543455 3 15 13.0808570548207 1.91914294517927 4 12 11.1202139688406 0.879786031159374 5 10 10.8808751034701 -0.880875103470149 6 12 9.17366708636009 2.82633291363991 7 15 16.8250435068735 -1.82504350687353 8 9 10.2555911878983 -1.25559118789830 9 12 12.5922472750568 -0.592247275056757 10 11 7.578661615368 3.421338384632 11 11 13.2156278980623 -2.21562789806234 12 11 12.0338923912738 -1.03389239127376 13 15 12.4110175472947 2.58898245270529 14 7 11.4390943772195 -4.43909437721946 15 11 11.5506970176144 -0.550697017614382 16 11 10.6206939935892 0.37930600641075 17 10 12.00049608237 -2.00049608237001 18 14 14.3633687152616 -0.363368715261566 19 10 8.61798772007608 1.38201227992392 20 6 9.28859807020295 -3.28859807020295 21 11 8.78943123505956 2.21056876494044 22 15 14.4897926608376 0.510207339162353 23 11 11.8807784634427 -0.880778463442691 24 12 9.62931451646761 2.37068548353239 25 14 13.0332503394640 0.96674966053602 26 15 14.6192074389008 0.380792561099205 27 9 14.4522001024089 -5.4522001024089 28 13 12.7281248223429 0.271875177657057 29 13 13.0256047590851 -0.0256047590850806 30 16 11.0871079957984 4.91289200420157 31 13 8.70115465537848 4.29884534462152 32 12 13.5917416372283 -1.59174163722834 33 14 14.7442866195091 -0.744286619509097 34 11 10.134743678041 0.865256321958994 35 9 10.4971170541950 -1.49711705419502 36 16 14.5158977540357 1.48410224596428 37 12 13.1546442317169 -1.15464423171687 38 10 9.60352781581116 0.396472184188844 39 13 12.933636402734 0.0663635972660046 40 16 15.6776114986676 0.322388501332421 41 14 13.0389752674637 0.961024732536281 42 15 8.02119594738316 6.97880405261684 43 5 9.687707501623 -4.6877075016230 44 8 10.2581480434579 -2.25814804345788 45 11 11.2795714987209 -0.279571498720851 46 16 13.8660439120551 2.13395608794487 47 17 14.3255148296850 2.67448517031504 48 9 8.20538251796126 0.794617482038739 49 9 11.404790027259 -2.40479002725901 50 13 14.4683384624023 -1.4683384624023 51 10 11.0845703504149 -1.08457035041494 52 6 12.4279802219199 -6.4279802219199 53 12 12.1686180693552 -0.168618069355242 54 8 10.5633636149327 -2.56336361493267 55 14 11.9071858015172 2.09281419848281 56 12 12.9480962096398 -0.948096209639807 57 11 10.6785175796478 0.321482420352153 58 16 14.6025309682863 1.39746903171370 59 8 10.5310501162415 -2.53105011624149 60 15 14.6298437582843 0.370156241715689 61 7 9.11471329121909 -2.11471329121909 62 16 14.2025600704264 1.79743992957359 63 14 13.1230313767364 0.876968623263592 64 16 13.3741480431991 2.62585195680089 65 9 10.4129896433215 -1.41298964332153 66 14 12.1461421821496 1.85385781785035 67 11 13.2431380445186 -2.2431380445186 68 13 10.3053296257660 2.69467037423397 69 15 13.2738218719797 1.72617812802031 70 5 5.85242053591145 -0.852420535911449 71 15 12.9521079003703 2.04789209962970 72 13 12.6371966278938 0.362803372106162 73 11 12.4558579609277 -1.45585796092770 74 11 14.1962017145182 -3.19620171451821 75 12 12.7954755737943 -0.795475573794256 76 12 13.4321392399579 -1.43213923995792 77 12 12.3557265747135 -0.355726574713532 78 12 11.9256518026510 0.0743481973490444 79 14 10.8589613213735 3.14103867862654 80 6 7.91196964212172 -1.91196964212172 81 7 9.70611238131443 -2.70611238131443 82 14 12.3550707022083 1.64492929779175 83 14 14.1409469688363 -0.140946968836333 84 10 11.1241982765507 -1.1241982765507 85 13 9.07120037449782 3.92879962550218 86 12 12.2801990780000 -0.280199077999961 87 9 9.36171217173182 -0.361712171731819 88 12 11.9333143311241 0.0666856688758652 89 16 14.8622073505445 1.13779264945548 90 10 10.4811648028871 -0.481164802887096 91 14 13.1369787431397 0.863021256860287 92 10 13.6131908972401 -3.61319089724007 93 16 15.5372489158858 0.462751084114163 94 15 13.3963793177822 1.60362068221781 95 12 11.4828928526639 0.517107147336102 96 10 9.34754918900215 0.652450810997852 97 8 10.0946873175326 -2.09468731753260 98 8 8.69138666096395 -0.691386660963952 99 11 12.6021489402075 -1.60214894020754 100 13 12.5389637747878 0.461036225212233 101 16 15.5785821328421 0.421417867157914 102 16 14.9094884763728 1.09051152362718 103 14 15.3685027353908 -1.36850273539084 104 11 8.96440667459719 2.03559332540281 105 4 7.05673560355099 -3.05673560355099 106 14 14.7124317109416 -0.712431710941592 107 9 10.517644906001 -1.51764490600101 108 14 15.2622351436140 -1.26223514361397 109 8 10.2264671670019 -2.22646716700188 110 8 10.6419821312154 -2.64198213121536 111 11 11.8648204608645 -0.864820460864535 112 12 13.1317405554262 -1.13174055542617 113 11 11.0788660907255 -0.078866090725452 114 14 13.2580194952846 0.741980504715392 115 15 14.4439672747837 0.556032725216287 116 16 13.4079790483945 2.59202095160549 117 16 12.8754068268996 3.12459317310043 118 11 12.7568035313305 -1.75680353133049 119 14 14.1386402507739 -0.138640250773902 120 14 10.7993282173183 3.20067178268169 121 12 11.4789934273150 0.521006572684956 122 14 12.4530956518678 1.54690434813222 123 8 10.7918791805510 -2.79187918055104 124 13 14.0062803811429 -1.00628038114291 125 16 13.8850999805959 2.11490001940407 126 12 10.5245584123814 1.47544158761858 127 16 15.3989404920953 0.601059507904733 128 12 12.652824763762 -0.652824763762011 129 11 11.3105192708351 -0.310519270835101 130 4 5.839463016272 -1.83946301627200 131 16 16.0126175434527 -0.0126175434526787 132 15 12.5241953264478 2.47580467355223 133 10 11.2099749876386 -1.20997498763857 134 13 13.8877219959662 -0.88772199596624 135 15 12.9728410638645 2.02715893613546 136 12 10.3240697517114 1.67593024828857 137 14 13.4769830009672 0.523016999032764 138 7 10.2770195532042 -3.27701955320419 139 19 13.8272401676380 5.17275983236197 140 12 12.8342534850819 -0.8342534850819 141 12 11.7452520712625 0.254747928737472 142 13 13.2395552988095 -0.239555298809516 143 15 12.2895289875902 2.71047101240979 144 8 8.70031081069254 -0.700310810692544 145 12 10.7908901625884 1.20910983741163 146 10 10.6628115577567 -0.662811557756726 147 8 11.1204961318578 -3.12049613185784 148 10 14.5375596268969 -4.53755962689691 149 15 13.7103009270085 1.28969907299154 150 16 14.0364090740864 1.96359092591364 151 13 13.3264786636824 -0.326478663682361 152 16 15.1372417911266 0.862758208873362 153 9 10.2535821517534 -1.25358215175342 154 14 13.4954473181394 0.504552681860618 155 14 13.5870642929889 0.412935707011149 156 12 10.5625930148834 1.43740698511655 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.231958474729755 0.463916949459511 0.768041525270245 12 0.144926878499410 0.289853756998819 0.85507312150059 13 0.676847826321099 0.646304347357802 0.323152173678901 14 0.807318199336137 0.385363601327726 0.192681800663863 15 0.742782021802478 0.514435956395044 0.257217978197522 16 0.656414369221807 0.687171261556385 0.343585630778193 17 0.569129259577527 0.861741480844947 0.430870740422473 18 0.543539522704408 0.912920954591184 0.456460477295592 19 0.45360871693986 0.90721743387972 0.54639128306014 20 0.591434890093033 0.817130219813935 0.408565109906967 21 0.610337566660822 0.779324866678355 0.389662433339178 22 0.636347047142489 0.727305905715023 0.363652952857511 23 0.564409575479091 0.871180849041818 0.435590424520909 24 0.567444251354572 0.865111497290856 0.432555748645428 25 0.521891571512487 0.956216856975026 0.478108428487513 26 0.456473442728911 0.912946885457823 0.543526557271089 27 0.693893229748837 0.612213540502326 0.306106770251163 28 0.650496333610283 0.699007332779433 0.349503666389717 29 0.596651717343825 0.80669656531235 0.403348282656175 30 0.758772132731623 0.482455734536755 0.241227867268377 31 0.836673446029359 0.326653107941282 0.163326553970641 32 0.803113508539584 0.393772982920832 0.196886491460416 33 0.759039376895389 0.481921246209222 0.240960623104611 34 0.728691071849608 0.542617856300783 0.271308928150392 35 0.721376945152427 0.557246109695146 0.278623054847573 36 0.719832316494101 0.560335367011798 0.280167683505899 37 0.693547896178377 0.612904207643246 0.306452103821623 38 0.645252439732475 0.70949512053505 0.354747560267525 39 0.596896456871879 0.806207086256243 0.403103543128121 40 0.553662719314778 0.892674561370444 0.446337280685222 41 0.513807182353511 0.972385635292978 0.486192817646489 42 0.790809631040228 0.418380737919543 0.209190368959772 43 0.957548178963805 0.0849036420723907 0.0424518210361953 44 0.961005488888202 0.0779890222235958 0.0389945111117979 45 0.94878108874027 0.102437822519459 0.0512189112597295 46 0.95566065786787 0.0886786842642597 0.0443393421321299 47 0.955224515339178 0.089550969321645 0.0447754846608225 48 0.945251632253793 0.109496735492414 0.0547483677462069 49 0.942739739691695 0.11452052061661 0.057260260308305 50 0.931630423448571 0.136739153102858 0.068369576551429 51 0.923581468992257 0.152837062015486 0.0764185310077431 52 0.988159847541786 0.0236803049164282 0.0118401524582141 53 0.984622234452902 0.0307555310941970 0.0153777655470985 54 0.987601730319476 0.0247965393610485 0.0123982696805243 55 0.992189652957987 0.0156206940840269 0.00781034704201347 56 0.989634898741058 0.0207302025178849 0.0103651012589424 57 0.985936141052105 0.0281277178957903 0.0140638589478951 58 0.984213422086923 0.0315731558261548 0.0157865779130774 59 0.989284773359341 0.0214304532813174 0.0107152266406587 60 0.988459649300983 0.0230807013980337 0.0115403506990168 61 0.988319144616754 0.0233617107664928 0.0116808553832464 62 0.988743927487976 0.0225121450240484 0.0112560725120242 63 0.987352491700388 0.0252950165992242 0.0126475082996121 64 0.98982289512479 0.0203542097504195 0.0101771048752097 65 0.988649527176445 0.0227009456471096 0.0113504728235548 66 0.987951804514628 0.0240963909707438 0.0120481954853719 67 0.988347892798583 0.0233042144028344 0.0116521072014172 68 0.99057491158924 0.0188501768215192 0.00942508841075962 69 0.990078949331199 0.0198421013376025 0.00992105066880124 70 0.986974553168644 0.0260508936627125 0.0130254468313562 71 0.987378870473506 0.0252422590529882 0.0126211295264941 72 0.983188289778963 0.0336234204420748 0.0168117102210374 73 0.9800777006504 0.0398445986991986 0.0199222993495993 74 0.986015334175165 0.0279693316496707 0.0139846658248354 75 0.981551648187315 0.0368967036253707 0.0184483518126854 76 0.978470707782516 0.0430585844349683 0.0215292922174841 77 0.971995017317036 0.0560099653659275 0.0280049826829638 78 0.963342174596101 0.0733156508077985 0.0366578254038992 79 0.976169347397683 0.0476613052046332 0.0238306526023166 80 0.974358599175678 0.0512828016486433 0.0256414008243217 81 0.977408000923024 0.0451839981539525 0.0225919990769763 82 0.977164289683699 0.045671420632603 0.0228357103163015 83 0.969734284664883 0.0605314306702333 0.0302657153351166 84 0.962622815080528 0.0747543698389448 0.0373771849194724 85 0.987965025446746 0.0240699491065081 0.0120349745532540 86 0.98378604879181 0.03242790241638 0.01621395120819 87 0.978264053560481 0.0434718928790378 0.0217359464395189 88 0.971950099547073 0.0560998009058536 0.0280499004529268 89 0.966947842813883 0.0661043143722335 0.0330521571861167 90 0.957445963570876 0.0851080728582472 0.0425540364291236 91 0.950347657270578 0.0993046854588444 0.0496523427294222 92 0.969220584161441 0.0615588316771171 0.0307794158385585 93 0.960649466407138 0.0787010671857232 0.0393505335928616 94 0.956677639974289 0.0866447200514228 0.0433223600257114 95 0.946568848012775 0.106862303974451 0.0534311519872253 96 0.935230355488208 0.129539289023585 0.0647696445117925 97 0.927949909159394 0.144100181681213 0.0720500908406064 98 0.910508466598297 0.178983066803407 0.0894915334017033 99 0.900359997607406 0.199280004785187 0.0996400023925936 100 0.880811326737012 0.238377346525977 0.119188673262988 101 0.854998882791285 0.290002234417429 0.145001117208715 102 0.834783564599055 0.33043287080189 0.165216435400945 103 0.836579419165006 0.326841161669987 0.163420580834994 104 0.888987667832238 0.222024664335523 0.111012332167762 105 0.88619232030717 0.227615359385658 0.113807679692829 106 0.859533103605805 0.280933792788390 0.140466896394195 107 0.832501423297284 0.334997153405431 0.167498576702715 108 0.82471888241522 0.350562235169562 0.175281117584781 109 0.816983430357943 0.366033139284113 0.183016569642057 110 0.837056268206856 0.325887463586287 0.162943731793144 111 0.82614132745682 0.347717345086359 0.173858672543179 112 0.883412890202103 0.233174219595794 0.116587109797897 113 0.854588541673337 0.290822916653326 0.145411458326663 114 0.831082758470782 0.337834483058436 0.168917241529218 115 0.79693925368071 0.40612149263858 0.20306074631929 116 0.785426192137445 0.429147615725109 0.214573807862555 117 0.786821097777057 0.426357804445885 0.213178902222943 118 0.789854032337384 0.420291935325232 0.210145967662616 119 0.748581867277772 0.502836265444455 0.251418132722228 120 0.793943506863747 0.412112986272507 0.206056493136253 121 0.75433919195016 0.491321616099681 0.245660808049840 122 0.7197070026217 0.560585994756598 0.280292997378299 123 0.717372545258142 0.565254909483716 0.282627454741858 124 0.677315790509525 0.645368418980951 0.322684209490475 125 0.660111497850825 0.679777004298351 0.339888502149175 126 0.641479430541531 0.717041138916937 0.358520569458469 127 0.577534188305695 0.84493162338861 0.422465811694305 128 0.546398743138503 0.907202513722994 0.453601256861497 129 0.548882644834061 0.902234710331877 0.451117355165939 130 0.563778420032804 0.872443159934393 0.436221579967196 131 0.505231785948185 0.98953642810363 0.494768214051815 132 0.460419743735638 0.920839487471276 0.539580256264362 133 0.444859617438533 0.889719234877066 0.555140382561467 134 0.372399455088229 0.744798910176459 0.62760054491177 135 0.319623803936112 0.639247607872224 0.680376196063888 136 0.301683126782112 0.603366253564223 0.698316873217888 137 0.234538290034389 0.469076580068778 0.765461709965611 138 0.321884958067844 0.643769916135687 0.678115041932156 139 0.705327897048977 0.589344205902047 0.294672102951023 140 0.661692581754983 0.676614836490035 0.338307418245017 141 0.594686867285913 0.810626265428175 0.405313132714087 142 0.493156672302713 0.986313344605427 0.506843327697287 143 0.42306968322476 0.84613936644952 0.57693031677524 144 0.297113493667415 0.59422698733483 0.702886506332585 145 0.527634846431587 0.944730307136827 0.472365153568413 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 31 0.229629629629630 NOK 10% type I error level 47 0.348148148148148 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545502az8zgx85nnzv49c/10b71m1290545513.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545502az8zgx85nnzv49c/10b71m1290545513.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545502az8zgx85nnzv49c/1ff3v1290545513.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545502az8zgx85nnzv49c/1ff3v1290545513.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545502az8zgx85nnzv49c/2ff3v1290545513.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545502az8zgx85nnzv49c/2ff3v1290545513.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545502az8zgx85nnzv49c/3ff3v1290545513.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545502az8zgx85nnzv49c/3ff3v1290545513.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545502az8zgx85nnzv49c/47o2g1290545513.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545502az8zgx85nnzv49c/47o2g1290545513.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545502az8zgx85nnzv49c/57o2g1290545513.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545502az8zgx85nnzv49c/57o2g1290545513.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545502az8zgx85nnzv49c/67o2g1290545513.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545502az8zgx85nnzv49c/67o2g1290545513.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545502az8zgx85nnzv49c/7ix111290545513.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545502az8zgx85nnzv49c/7ix111290545513.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545502az8zgx85nnzv49c/8b71m1290545513.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545502az8zgx85nnzv49c/8b71m1290545513.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545502az8zgx85nnzv49c/9b71m1290545513.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545502az8zgx85nnzv49c/9b71m1290545513.ps (open in new window)

Parameters (Session):

par1 = 1 ; 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') }

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by