*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: Thu, 19 Nov 2009 07:06:12 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/19/t12586396208saal9qsm2o0u71.htm/, Retrieved Thu, 19 Nov 2009 15:07:14 +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/2009/Nov/19/t12586396208saal9qsm2o0u71.htm/}, year = {2009}, } @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 = {2009}, 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 «

3.22 157 2.88 3.29 3.98 3.88 3.62 157.4 3.22 2.88 3.29 3.98 3.82 157.2 3.62 3.22 2.88 3.29 3.54 157.5 3.82 3.62 3.22 2.88 2.53 158 3.54 3.82 3.62 3.22 2.22 158.5 2.53 3.54 3.82 3.62 2.85 159 2.22 2.53 3.54 3.82 2.78 159.3 2.85 2.22 2.53 3.54 2.28 160 2.78 2.85 2.22 2.53 2.26 160.8 2.28 2.78 2.85 2.22 2.71 161.9 2.26 2.28 2.78 2.85 2.77 162.5 2.71 2.26 2.28 2.78 2.77 162.7 2.77 2.71 2.26 2.28 2.64 162.8 2.77 2.77 2.71 2.26 2.56 162.9 2.64 2.77 2.77 2.71 2.07 163 2.56 2.64 2.77 2.77 2.32 164 2.07 2.56 2.64 2.77 2.16 164.7 2.32 2.07 2.56 2.64 2.23 164.8 2.16 2.32 2.07 2.56 2.4 164.9 2.23 2.16 2.32 2.07 2.84 165 2.4 2.23 2.16 2.32 2.77 165.8 2.84 2.4 2.23 2.16 2.93 166.1 2.77 2.84 2.4 2.23 2.91 167.2 2.93 2.77 2.84 2.4 2.69 167.7 2.91 2.93 2.77 2.84 2.38 168.3 2.69 2.91 2.93 2.77 2.58 168.6 2.38 2.69 2.91 2.93 3.19 168.9 2.58 2.38 2.69 2.91 2.82 169.1 3.19 2.58 2.38 2.69 2.72 169.5 2.82 3.19 2.58 2.38 2.53 169.6 2.72 2.82 3.19 2.58 2.7 169.7 2.53 2.72 2.82 3.19 2.42 169.8 2.7 2.53 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 Y[t] = + 2.97800660075982 -0.0178884775131215X[t] + 1.13770027938383Y1[t] -0.189411036310105Y2[t] + 0.0135050512884166Y3[t] -0.0350137447939528Y4[t] -0.00610584212118887M1[t] -0.0165912030097572M2[t] -0.0290877279644277M3[t] -0.0262203834456709M4[t] -0.0363526671664465M5[t] -0.0528874969185614M6[t] -0.0144954812421030M7[t] -0.0228599371456861M8[t] -0.0554478823797208M9[t] -0.0148607415103697M10[t] -0.0222110183577529M11[t] + 0.00667066163419205t + 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) 2.97800660075982 3.539772 0.8413 0.401175 0.200588 X -0.0178884775131215 0.02285 -0.7829 0.434631 0.217316 Y1 1.13770027938383 0.071406 15.9329 0 0 Y2 -0.189411036310105 0.109253 -1.7337 0.084499 0.042249 Y3 0.0135050512884166 0.108697 0.1242 0.901245 0.450622 Y4 -0.0350137447939528 0.075492 -0.4638 0.643284 0.321642 M1 -0.00610584212118887 0.12356 -0.0494 0.960637 0.480318 M2 -0.0165912030097572 0.123516 -0.1343 0.89328 0.44664 M3 -0.0290877279644277 0.123525 -0.2355 0.814075 0.407037 M4 -0.0262203834456709 0.123576 -0.2122 0.83218 0.41609 M5 -0.0363526671664465 0.125872 -0.2888 0.773025 0.386513 M6 -0.0528874969185614 0.126127 -0.4193 0.675429 0.337715 M7 -0.0144954812421030 0.126396 -0.1147 0.90881 0.454405 M8 -0.0228599371456861 0.126652 -0.1805 0.856945 0.428473 M9 -0.0554478823797208 0.127066 -0.4364 0.663033 0.331516 M10 -0.0148607415103697 0.125978 -0.118 0.906214 0.453107 M11 -0.0222110183577529 0.125466 -0.177 0.859664 0.429832 t 0.00667066163419205 0.00875 0.7624 0.446735 0.223367 Multiple Linear Regression - Regression Statistics Multiple R 0.934225822739988 R-squared 0.872777887874208 Adjusted R-squared 0.862071076457681 F-TEST (value) 81.5161352825347 F-TEST (DF numerator) 17 F-TEST (DF denominator) 202 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.375339855393874 Sum Squared Residuals 28.4577614235130 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3.22 2.74139172020531 0.478608279794694 2 3.62 3.1820783899549 0.437921610045099 3 3.82 3.58913299442473 0.230867005575270 4 3.54 3.76402745148004 -0.224027451480041 5 2.53 3.38868065243283 -0.858680652432829 6 2.22 2.26252556588761 -0.0425255658876074 7 2.85 2.12647790118637 0.72352209881363 8 2.78 2.89104990767199 -0.111049907671993 9 2.28 2.68482003372321 -0.404820033723214 10 2.26 2.18153813026388 0.0784618697361195 11 2.71 2.21012868954325 0.499871310456749 12 2.77 2.73972906596762 0.0302709340323820 13 2.77 2.73698001177269 0.0330199882273122 14 2.64 2.72678935056406 -0.0867893505640593 15 2.56 2.5563277210924 0.00367227890760273 16 2.07 2.49558346717600 -0.425583467176004 17 2.32 1.93015745691554 0.389842543084463 18 2.16 2.28847921489648 -0.128479214896478 19 2.23 2.09855186512907 0.131448134870930 20 2.4 2.22554700624599 0.174452993754008 21 2.84 2.36707690544375 0.472923094556254 22 2.77 2.87495972545018 -0.104959725450181 23 2.93 2.70577858803319 0.224221411966807 24 2.91 2.91026364595576 -0.000263645955755940 25 2.69 2.83247305401538 -0.142473054015377 26 2.38 2.57603119785661 -0.19603119785661 27 2.58 2.24794983246863 0.332050167531370 28 3.19 2.53610793611297 0.653892063887032 29 2.82 3.18870003964114 -0.368700039641137 30 2.72 2.64874591614059 0.0712540838594077 31 2.53 2.64956713352343 -0.119567133523431 32 2.7 2.42250728874978 0.277492711250216 33 2.42 2.63580288223772 -0.215802882237722 34 2.5 2.32250705856780 0.177492941432202 35 2.31 2.46588278734546 -0.155882787345463 36 2.41 2.23582630286082 0.174173697139178 37 2.56 2.39703349985651 0.162966500143491 38 2.76 2.53777683179907 0.222223168200931 39 2.71 2.73908248554853 -0.0290824855485330 40 2.44 2.64522226267889 -0.205222262678888 41 2.46 2.33076797900489 0.129232020995106 42 2.12 2.37459886049598 -0.254598860495979 43 1.99 2.02537069773044 -0.0353706977304384 44 1.86 1.94989943160672 -0.0898994316067203 45 1.88 1.79362370632204 0.0863762936779588 46 1.82 1.88588603143684 -0.065886031436839 47 1.74 1.80879691788489 -0.0687969178848873 48 1.71 1.74674949579190 -0.0367494957919047 49 1.38 1.72503676410371 -0.345036764103705 50 1.27 1.36858335408834 -0.0985833540883417 51 1.19 1.29356781130628 -0.103567811306280 52 1.28 1.22415221126734 0.0558477887326618 53 1.19 1.33399469535989 -0.14399469535989 54 1.22 1.21819470316165 0.00180529683835325 55 1.47 1.31845193632120 0.151548063678805 56 1.46 1.58934534140973 -0.129345341409733 57 1.96 1.50646583675732 0.453534163242678 58 1.88 2.09996102352448 -0.219961023524484 59 2.03 1.89214944683498 0.137850553165023 60 2.04 2.09784208496964 -0.0578420849696427 61 1.9 2.06099612757861 -0.160996127578607 62 1.8 1.89904728837286 -0.0990472883728599 63 1.92 1.79906308323989 0.120936916760107 64 1.92 1.96182538192159 -0.0418253819215934 65 1.97 1.93739700686880 0.0326029931312032 66 2.46 1.98775098560276 0.472249014397242 67 2.36 2.57124805536677 -0.211248055366770 68 2.53 2.36007038242884 0.169929617571160 69 2.31 2.55137003784689 -0.241370037846885 70 1.98 2.28152703287358 -0.301527032873581 71 1.46 1.94214090014250 -0.482140900142502 72 1.26 1.42226754243089 -0.162267542430894 73 1.58 1.29345470637525 0.286545293624747 74 1.74 1.68896282189250 0.0510371781074968 75 1.89 1.81111936993282 0.0788806300671848 76 1.85 1.97054216980349 -0.120542169803493 77 1.62 1.88232844321581 -0.262328443215810 78 1.3 1.61300436306693 -0.313004363066929 79 1.42 1.32819753005282 0.0918024699471758 80 1.15 1.51656714567021 -0.366567145670212 81 0.42 1.16268415941853 -0.742684159418527 82 0.74 0.418342873745907 0.321657126254093 83 1.02 0.899627456959586 0.120372543040414 84 1.51 1.16816022970047 0.341839770299528 85 1.86 1.69946705055398 0.160532949446024 86 1.59 1.99182420956737 -0.401824209567368 87 1.03 1.60755018694242 -0.577550186942424 88 0.44 1.01332050619213 -0.573320506192129 89 0.82 0.426995877325678 0.393004122674322 90 0.86 0.961312361418113 -0.101312361418114 91 0.58 0.991546572930725 -0.411546572930725 92 0.59 0.687721440148176 -0.0977214401481764 93 0.95 0.713451228538836 0.236548771461164 94 0.98 1.14889427509444 -0.168894275094444 95 1.23 1.11336350773845 0.116636492261552 96 1.17 1.39151150022801 -0.221511500228007 97 0.84 1.25352866080541 -0.413528660805411 98 0.74 0.879019143254701 -0.139019143254701 99 0.65 0.803420915945821 -0.153420915945821 100 0.91 0.719995767342446 0.190004232657554 101 1.19 1.03422069856280 0.155779301437205 102 1.3 1.28342972483597 0.0165702751640306 103 1.53 1.40726689307846 0.122733106921544 104 1.94 1.64108678978756 0.298913210212437 105 1.79 2.02974378948319 -0.239743789483185 106 1.95 1.81720958855314 0.132790411446861 107 2.26 2.01551334445696 0.244486655543043 108 2.04 2.34681725668687 -0.306817256686865 109 2.16 2.04578346340453 0.114216536595467 110 2.75 2.21874759239682 0.531252407603184 111 2.79 2.84761019738601 -0.0576101973860074 112 2.88 2.78591655129013 0.0940834487098701 113 3.36 2.86851590952139 0.491484090478607 114 2.97 3.36221643160897 -0.392216431608967 115 3.1 2.86889591185265 0.231104088147351 116 2.49 3.08693810239714 -0.596938102397144 117 2.2 2.31853779839796 -0.11853779839796 118 2.25 2.15071463940468 0.0992853605953172 119 2.09 2.24011513182490 -0.150115131824905 120 2.79 2.07168111398354 0.718318886016456 121 3.14 2.8936715036677 0.246328496332297 122 2.93 3.13903074707556 -0.209030747075564 123 2.65 2.83231661093700 -0.182316610936996 124 2.67 2.54329200308277 0.126707996917227 125 2.26 2.59158436654568 -0.331584366545684 126 2.35 2.11325748744885 0.236742512551150 127 2.13 2.34486796885664 -0.214867968856639 128 2.18 2.06601807842814 0.113981921571859 129 2.9 2.14886078351326 0.751139216486745 130 2.63 2.99430334378881 -0.364303343788807 131 2.67 2.54771389690992 0.122286103090076 132 1.81 2.66690673555841 -0.856906735558415 133 1.33 1.64546122224415 -0.315461222244153 134 0.88 1.26486009775551 -0.384860097755509 135 1.28 0.812449577982176 0.467550422017824 136 1.26 1.38235436262994 -0.122354362629939 137 1.26 1.28215940609639 -0.0221594060963866 138 1.29 1.295452816626 -0.00545281662599885 139 1.1 1.35321551236957 -0.253215512369566 140 1.37 1.12858776107251 0.241412238927489 141 1.21 1.43550971483600 -0.225509714836002 142 1.74 1.24418927299447 0.495810727005526 143 1.76 1.88530669927174 -0.125306699271741 144 1.48 1.82315116855518 -0.343151168555181 145 1.04 1.49982078345391 -0.459820783453905 146 1.62 1.01943278121457 0.600567218785426 147 1.49 1.74696570340259 -0.256965703402591 148 1.79 1.49723935489725 0.292760645102752 149 1.8 1.87937253330012 -0.079372533300124 150 1.58 1.79842073293240 -0.218420732932396 151 1.86 1.59095430186868 0.269045698131319 152 1.74 1.93017370213312 -0.190173702133123 153 1.59 1.70600950285506 -0.116009502855064 154 1.26 1.61145948276974 -0.351459482769735 155 1.13 1.24695943285554 -0.116959432855543 156 1.92 1.18367737143538 0.736322628564624 157 2.61 2.10486654567321 0.505133454326791 158 2.26 2.73012956986139 -0.470129569861393 159 2.41 2.20169153228710 0.208308467712897 160 2.26 2.42089183130139 -0.160891831301388 161 2.03 2.18411071674800 -0.154110716748005 162 2.86 1.94990116493553 0.910098835064474 163 2.55 2.96838640206848 -0.418386402068475 164 2.27 2.45536256547284 -0.185362565472843 165 2.26 2.17992474001709 0.0800752599829052 166 2.57 2.2302261125613 0.339773887438698 167 3.07 2.58404514984032 0.485954850159681 168 2.76 3.11305102103304 -0.353051021033036 169 2.51 2.66181570037279 -0.151815700372787 170 2.87 2.42640276953536 0.443597230464644 171 3.14 2.8414975455637 0.2985024544363 172 3.11 3.09392695664004 0.0160730433599578 173 3.16 3.01523090552791 0.144769094472091 174 2.47 3.05360895493659 -0.583608954936594 175 2.57 2.28717363401863 0.282826365981371 176 2.89 2.52809145214721 0.361908547852793 177 2.63 2.83086143843654 -0.200861438436539 178 2.38 2.53648253920985 -0.156482539209849 179 1.69 2.28176764025979 -0.591767640259792 180 1.96 1.55111778388012 0.408882216119881 181 2.19 1.98812721369980 0.201872786300197 182 1.87 2.18712215870421 -0.317122158704212 183 1.6 1.79789581988266 -0.197895819882660 184 1.63 1.54557449416662 0.0844255058333843 185 1.22 1.60964353929644 -0.389643539296437 186 1.21 1.12625372127147 0.0837462787285282 187 1.49 1.24209024005451 0.247909759945489 188 1.64 1.54889260774969 0.091107392250313 189 1.66 1.65302701299191 0.00697298700808624 190 1.77 1.69339217419138 0.0766078258086229 191 1.82 1.80271558263254 0.0172844173674633 192 1.78 1.86087625415493 -0.080876254154925 193 1.28 1.80367009592029 -0.523670095920292 194 1.29 1.23003889580955 0.0599611041904451 195 1.37 1.32263812089280 0.0473618791072038 196 1.12 1.41415721542959 -0.294157215429588 197 1.51 1.12518186799948 0.384818132000524 198 2.24 1.59637074806603 0.643629251933967 199 2.94 2.38832926725769 0.551670732742306 200 3.09 3.04625408399239 0.0437459160076078 201 3.46 3.05102974835133 0.408970251648672 202 3.64 3.45504117571824 0.184958824281755 203 4.39 3.52901586091934 0.860984139080655 204 4.15 4.36072394140915 -0.210723941409154 205 5.21 3.9195586105338 1.29044138946620 206 5.8 5.16741347504149 0.632586524958512 207 5.91 5.59539816615882 0.314601833841176 208 5.39 5.62852741047812 -0.238527410478118 209 5.46 4.97095790563722 0.489042094362779 210 4.72 5.11647624666809 -0.396476246668091 211 3.14 4.27940817633388 -1.13940817633388 212 2.63 2.63588691288794 -0.00588691288793656 213 2.32 2.31120068082936 0.00879931917063523 214 1.93 2.10336551985128 -0.173365519851277 215 0.62 1.75897896654663 -1.13897896654663 216 0.6 0.379647485398268 0.220352514601732 217 -0.37 0.596863265762979 -0.966863265762979 218 -1.1 -0.52329067474488 -0.57670932525512 219 -1.68 -1.13567767539438 -0.544322324605621 220 -0.78 -1.67265733389074 0.892657333890744 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.921516439435697 0.156967121128605 0.0784835605643025 22 0.852444596383978 0.295110807232043 0.147555403616022 23 0.763818888391239 0.472362223217522 0.236181111608761 24 0.664838227312805 0.67032354537439 0.335161772687195 25 0.556016102040632 0.887967795918736 0.443983897959368 26 0.446933271031682 0.893866542063365 0.553066728968318 27 0.383052146915684 0.766104293831367 0.616947853084316 28 0.541072126469344 0.917855747061311 0.458927873530656 29 0.45465050324628 0.90930100649256 0.54534949675372 30 0.535137093346849 0.929725813306302 0.464862906653151 31 0.476434897377874 0.95286979475575 0.523565102622126 32 0.406894383741742 0.813788767483484 0.593105616258258 33 0.389592982598007 0.779185965196014 0.610407017401993 34 0.319333847988801 0.638667695977602 0.680666152011199 35 0.311205021102967 0.622410042205934 0.688794978897033 36 0.252526313418890 0.505052626837781 0.74747368658111 37 0.207138489090554 0.414276978181108 0.792861510909446 38 0.177734941238419 0.355469882476837 0.822265058761581 39 0.136031771090326 0.272063542180652 0.863968228909674 40 0.104542196890638 0.209084393781276 0.895457803109362 41 0.098237499614813 0.196474999229626 0.901762500385187 42 0.0796616012029895 0.159323202405979 0.92033839879701 43 0.0655919433038167 0.131183886607633 0.934408056696183 44 0.050432091540327 0.100864183080654 0.949567908459673 45 0.0364158867599424 0.0728317735198849 0.963584113240058 46 0.0277202760878904 0.0554405521757808 0.97227972391211 47 0.0210657345072521 0.0421314690145043 0.978934265492748 48 0.0144836293257990 0.0289672586515979 0.9855163706742 49 0.0137103337689662 0.0274206675379324 0.986289666231034 50 0.0092948201559945 0.018589640311989 0.990705179844006 51 0.00638454917463178 0.0127690983492636 0.993615450825368 52 0.00450171203056042 0.00900342406112084 0.99549828796944 53 0.00325141245410915 0.00650282490821829 0.99674858754589 54 0.00379061438388502 0.00758122876777004 0.996209385616115 55 0.00382919881435762 0.00765839762871524 0.996170801185642 56 0.00268894844303267 0.00537789688606533 0.997311051556967 57 0.00764480008400511 0.0152896001680102 0.992355199915995 58 0.00521845769388109 0.0104369153877622 0.994781542306119 59 0.00419601412162966 0.00839202824325932 0.99580398587837 60 0.00295033325872795 0.0059006665174559 0.997049666741272 61 0.00195198657589999 0.00390397315179998 0.9980480134241 62 0.00126918754375114 0.00253837508750227 0.99873081245625 63 0.000875421028756689 0.00175084205751338 0.999124578971243 64 0.000560956888348178 0.00112191377669636 0.999439043111652 65 0.000474895540800709 0.000949791081601417 0.9995251044592 66 0.00137091726649296 0.00274183453298591 0.998629082733507 67 0.000951730619679332 0.00190346123935866 0.99904826938032 68 0.000904733595172034 0.00180946719034407 0.999095266404828 69 0.000639861867994456 0.00127972373598891 0.999360138132006 70 0.000544085572099023 0.00108817114419805 0.9994559144279 71 0.000932909054104084 0.00186581810820817 0.999067090945896 72 0.000730313043653242 0.00146062608730648 0.999269686956347 73 0.000582709667160893 0.00116541933432179 0.99941729033284 74 0.000385984184446986 0.000771968368893972 0.999614015815553 75 0.000263020163036627 0.000526040326073254 0.999736979836963 76 0.000172054606189436 0.000344109212378873 0.99982794539381 77 0.000114431062847816 0.000228862125695632 0.999885568937152 78 8.6933330786413e-05 0.000173866661572826 0.999913066669214 79 5.56724362407067e-05 0.000111344872481413 0.99994432756376 80 5.57077159013673e-05 0.000111415431802735 0.999944292284099 81 0.000253455700676030 0.000506911401352059 0.999746544299324 82 0.000233937222648694 0.000467874445297389 0.999766062777351 83 0.000159090449499179 0.000318180898998358 0.9998409095505 84 0.000165472770569834 0.000330945541139667 0.99983452722943 85 0.000150615703601603 0.000301231407203205 0.999849384296398 86 0.000113946611650122 0.000227893223300244 0.99988605338835 87 0.000146252380655934 0.000292504761311868 0.999853747619344 88 0.000210023316517481 0.000420046633034962 0.999789976683483 89 0.000232243303913373 0.000464486607826746 0.999767756696087 90 0.000168583211962029 0.000337166423924059 0.999831416788038 91 0.000197973723807861 0.000395947447615722 0.999802026276192 92 0.000134647750622171 0.000269295501244342 0.999865352249378 93 0.000115918465609442 0.000231836931218885 0.99988408153439 94 7.90556784341398e-05 0.000158111356868280 0.999920944321566 95 6.08835880740868e-05 0.000121767176148174 0.999939116411926 96 4.0065436854982e-05 8.0130873709964e-05 0.999959934563145 97 3.60494659249742e-05 7.20989318499484e-05 0.999963950534075 98 2.3206797962799e-05 4.6413595925598e-05 0.999976793202037 99 1.57026138666035e-05 3.14052277332070e-05 0.999984297386133 100 1.23292948607548e-05 2.46585897215097e-05 0.99998767070514 101 9.99619765774281e-06 1.99923953154856e-05 0.999990003802342 102 6.9739809762315e-06 1.3947961952463e-05 0.999993026019024 103 6.03072971240190e-06 1.20614594248038e-05 0.999993969270288 104 9.40780404759356e-06 1.88156080951871e-05 0.999990592195952 105 6.1599594211869e-06 1.23199188423738e-05 0.999993840040579 106 6.1447604175878e-06 1.22895208351756e-05 0.999993855239582 107 6.35291396091382e-06 1.27058279218276e-05 0.99999364708604 108 4.31425941105944e-06 8.62851882211887e-06 0.99999568574059 109 3.69388416991716e-06 7.38776833983431e-06 0.99999630611583 110 1.05306275721846e-05 2.10612551443693e-05 0.999989469372428 111 6.67654774756987e-06 1.33530954951397e-05 0.999993323452252 112 5.79838336603088e-06 1.15967667320618e-05 0.999994201616634 113 1.16644214710618e-05 2.33288429421235e-05 0.99998833557853 114 1.17507956507553e-05 2.35015913015106e-05 0.99998824920435 115 9.03579320194948e-06 1.80715864038990e-05 0.999990964206798 116 1.99354542363491e-05 3.98709084726982e-05 0.999980064545764 117 1.41085383065957e-05 2.82170766131914e-05 0.999985891461693 118 8.89770255283898e-06 1.77954051056780e-05 0.999991102297447 119 6.79902135635606e-06 1.35980427127121e-05 0.999993200978644 120 2.53573775597269e-05 5.07147551194538e-05 0.99997464262244 121 2.14161226822689e-05 4.28322453645379e-05 0.999978583877318 122 1.47575478458564e-05 2.95150956917128e-05 0.999985242452154 123 9.7257458622417e-06 1.94514917244834e-05 0.999990274254138 124 6.31681012694012e-06 1.26336202538802e-05 0.999993683189873 125 6.35210793996486e-06 1.27042158799297e-05 0.99999364789206 126 4.70360975161386e-06 9.40721950322772e-06 0.999995296390248 127 3.74876761022917e-06 7.49753522045833e-06 0.99999625123239 128 2.37796336719768e-06 4.75592673439535e-06 0.999997622036633 129 1.09213489944080e-05 2.18426979888159e-05 0.999989078651006 130 9.45731079337781e-06 1.89146215867556e-05 0.999990542689207 131 6.61200869114593e-06 1.32240173822919e-05 0.999993387991309 132 3.17653797937762e-05 6.35307595875524e-05 0.999968234620206 133 3.18902509196824e-05 6.37805018393649e-05 0.99996810974908 134 3.74970222274626e-05 7.49940444549252e-05 0.999962502977773 135 4.27915914321057e-05 8.55831828642114e-05 0.999957208408568 136 2.95373427798412e-05 5.90746855596825e-05 0.99997046265722 137 1.89417402507514e-05 3.78834805015028e-05 0.99998105825975 138 1.20421868055271e-05 2.40843736110542e-05 0.999987957813194 139 8.81429359582e-06 1.762858719164e-05 0.999991185706404 140 6.82366976053194e-06 1.36473395210639e-05 0.99999317633024 141 4.70914384724795e-06 9.4182876944959e-06 0.999995290856153 142 7.10039255040312e-06 1.42007851008062e-05 0.99999289960745 143 4.37773045012308e-06 8.75546090024615e-06 0.99999562226955 144 3.85816465018212e-06 7.71632930036423e-06 0.99999614183535 145 4.64627205320642e-06 9.29254410641285e-06 0.999995353727947 146 8.56662386570902e-06 1.71332477314180e-05 0.999991433376134 147 6.19387655397951e-06 1.23877531079590e-05 0.999993806123446 148 4.8698349098634e-06 9.7396698197268e-06 0.99999513016509 149 3.13902079812645e-06 6.27804159625291e-06 0.999996860979202 150 2.23619777186206e-06 4.47239554372412e-06 0.999997763802228 151 1.78890118512571e-06 3.57780237025142e-06 0.999998211098815 152 1.16291213823851e-06 2.32582427647702e-06 0.999998837087862 153 7.07457187098803e-07 1.41491437419761e-06 0.999999292542813 154 6.64672149065831e-07 1.32934429813166e-06 0.999999335327851 155 4.10415738636009e-07 8.20831477272017e-07 0.999999589584261 156 1.29063218720680e-06 2.58126437441359e-06 0.999998709367813 157 1.91095198171495e-06 3.8219039634299e-06 0.999998089048018 158 2.20795022584366e-06 4.41590045168731e-06 0.999997792049774 159 1.65417922893378e-06 3.30835845786756e-06 0.999998345820771 160 1.14778542970548e-06 2.29557085941096e-06 0.99999885221457 161 7.40916722146151e-07 1.48183344429230e-06 0.999999259083278 162 6.31644521155898e-06 1.26328904231180e-05 0.999993683554788 163 5.92721258359694e-06 1.18544251671939e-05 0.999994072787416 164 4.16259948584106e-06 8.32519897168211e-06 0.999995837400514 165 2.48203726264974e-06 4.96407452529947e-06 0.999997517962737 166 2.00490227793163e-06 4.00980455586327e-06 0.999997995097722 167 3.51331782180361e-06 7.02663564360722e-06 0.999996486682178 168 3.22295424983807e-06 6.44590849967613e-06 0.99999677704575 169 2.06332843977796e-06 4.12665687955591e-06 0.99999793667156 170 2.08198229800661e-06 4.16396459601322e-06 0.999997918017702 171 1.99498241834682e-06 3.98996483669364e-06 0.999998005017582 172 1.08591247580098e-06 2.17182495160196e-06 0.999998914087524 173 6.2704754067323e-07 1.25409508134646e-06 0.99999937295246 174 1.26936847799313e-06 2.53873695598626e-06 0.999998730631522 175 9.74576598902521e-07 1.94915319780504e-06 0.9999990254234 176 8.84448116827963e-07 1.76889623365593e-06 0.999999115551883 177 5.52677853914556e-07 1.10535570782911e-06 0.999999447322146 178 3.20086505137867e-07 6.40173010275734e-07 0.999999679913495 179 4.47799896486332e-07 8.95599792972664e-07 0.999999552200104 180 4.80371783067018e-07 9.60743566134036e-07 0.999999519628217 181 4.00615889135638e-07 8.01231778271276e-07 0.999999599384111 182 2.68256079395785e-07 5.3651215879157e-07 0.99999973174392 183 1.45140203042927e-07 2.90280406085853e-07 0.999999854859797 184 6.7136633768207e-08 1.34273267536414e-07 0.999999932863366 185 1.07626588205392e-07 2.15253176410783e-07 0.999999892373412 186 5.19802465906873e-08 1.03960493181375e-07 0.999999948019753 187 3.71027812409579e-08 7.42055624819157e-08 0.999999962897219 188 1.53876251153675e-08 3.07752502307351e-08 0.999999984612375 189 1.64704506729820e-08 3.29409013459641e-08 0.99999998352955 190 1.87805428263500e-08 3.75610856527000e-08 0.999999981219457 191 1.21013772843429e-08 2.42027545686857e-08 0.999999987898623 192 1.60445964719372e-08 3.20891929438745e-08 0.999999983955403 193 2.46749181323483e-07 4.93498362646966e-07 0.999999753250819 194 1.59037006745192e-07 3.18074013490383e-07 0.999999840962993 195 5.77384715309238e-08 1.15476943061848e-07 0.999999942261528 196 2.56294680177683e-07 5.12589360355366e-07 0.99999974370532 197 9.43311907783696e-06 1.88662381556739e-05 0.999990566880922 198 0.000412637536359543 0.000825275072719086 0.99958736246364 199 0.000247276170970042 0.000494552341940084 0.99975272382903 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 146 0.815642458100559 NOK 5% type I error level 153 0.854748603351955 NOK 10% type I error level 155 0.865921787709497 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/19/t12586396208saal9qsm2o0u71/10wruo1258639561.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586396208saal9qsm2o0u71/10wruo1258639561.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586396208saal9qsm2o0u71/1vcr01258639561.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586396208saal9qsm2o0u71/1vcr01258639561.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586396208saal9qsm2o0u71/2t65j1258639561.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586396208saal9qsm2o0u71/2t65j1258639561.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586396208saal9qsm2o0u71/3i7621258639561.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586396208saal9qsm2o0u71/3i7621258639561.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586396208saal9qsm2o0u71/4p4yi1258639561.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586396208saal9qsm2o0u71/4p4yi1258639561.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586396208saal9qsm2o0u71/5zvx01258639561.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586396208saal9qsm2o0u71/5zvx01258639561.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586396208saal9qsm2o0u71/6e46o1258639561.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586396208saal9qsm2o0u71/6e46o1258639561.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586396208saal9qsm2o0u71/7gewl1258639561.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586396208saal9qsm2o0u71/7gewl1258639561.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586396208saal9qsm2o0u71/8i09r1258639561.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586396208saal9qsm2o0u71/8i09r1258639561.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586396208saal9qsm2o0u71/9okyd1258639561.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t12586396208saal9qsm2o0u71/9okyd1258639561.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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