Multiple Regression 5

*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, 29 Dec 2009 04:15:55 -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/Dec/29/t1262085442u332kmk510s44k4.htm/, Retrieved Tue, 29 Dec 2009 12:17:35 +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/Dec/29/t1262085442u332kmk510s44k4.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:

Met seasonal dummies Met lineair trend Met 2lags

Dataseries X:

» Textbox « » Textfile « » CSV «

4.4 11.2 4.5 4.6 4.4 11.1 4.4 4.5 4.3 10.8 4.4 4.4 4.1 10.4 4.3 4.4 3.9 10.1 4.1 4.3 3.7 9.8 3.9 4.1 3.6 9.7 3.7 3.9 3.9 10.3 3.6 3.7 4.2 10.9 3.9 3.6 4.2 10.8 4.2 3.9 4.1 10.6 4.2 4.2 4.1 10.4 4.1 4.2 4.1 10.3 4.1 4.1 4.1 10.2 4.1 4.1 4.1 10 4.1 4.1 4 9.7 4.1 4.1 3.9 9.4 4 4.1 3.8 9.2 3.9 4 3.8 9.1 3.8 3.9 4 9.6 3.8 3.8 4.4 10.2 4 3.8 4.6 10.2 4.4 4 4.6 10 4.6 4.4 4.6 9.9 4.6 4.6 4.7 9.9 4.6 4.6 4.8 9.9 4.7 4.6 4.8 9.7 4.8 4.7 4.7 9.5 4.8 4.8 4.7 9.4 4.7 4.8 4.7 9.3 4.7 4.7 4.6 9.3 4.7 4.7 5 9.9 4.6 4.7 5.4 10.5 5 4.6 5.5 10.6 5.4 5 5.6 10.6 5.5 5.4 5.6 10.5 5.6 5.5 5.8 10.6 5.6 5.6 6 10.8 5.8 5.6 6.1 10.8 6 5.8 6.1 10.7 6.1 6 6 10.6 6.1 6.1 6 10.6 6 6.1 6.1 10.8 6 6 6.5 11.4 6.1 6 7.1 12.2 6.5 6.1 7.4 12.4 7.1 6.5 7.4 12.4 7.4 7.1 7.5 12.3 7.4 7.4 7.6 12.4 7.5 7.4 7.8 12.5 7.6 7.5 7.8 12.5 7.8 7.6 7.7 12.4 7.8 7.8 7.6 12.3 7.7 7.8 7.5 12.2 7.6 7.7 7.3 12.1 7.5 7.6 7.6 12.6 7.3 7.5 8 13.2 7.6 7.3 8 13.4 8 7.6 7.9 13.2 8 8 7.8 12.9 7.9 8 7.7 12.8 7.8 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 8 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = -0.230404073016308 + 0.063966790884237X[t] + 1.41748644722477Y1[t] -0.518663070635735Y2[t] + 0.151072539337104M1[t] + 0.138136528285187M2[t] -0.0168673683779487M3[t] -0.0294935784935763M4[t] + 0.0153822127343551M5[t] -0.0159516121276719M6[t] -0.00533356626561581M7[t] + 0.424661480534343M8[t] + 0.0636908019214387M9[t] -0.0461693671096149M10[t] + 0.00929006307398224M11[t] + 0.00180052061064903t + 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) -0.230404073016308 0.137337 -1.6777 0.094821 0.04741 X 0.063966790884237 0.019156 3.3392 0.000985 0.000493 Y1 1.41748644722477 0.058391 24.2756 0 0 Y2 -0.518663070635735 0.057404 -9.0353 0 0 M1 0.151072539337104 0.059803 2.5262 0.012228 0.006114 M2 0.138136528285187 0.059899 2.3062 0.022024 0.011012 M3 -0.0168673683779487 0.060112 -0.2806 0.779281 0.38964 M4 -0.0294935784935763 0.05995 -0.492 0.623226 0.311613 M5 0.0153822127343551 0.060654 0.2536 0.800036 0.400018 M6 -0.0159516121276719 0.060902 -0.2619 0.793623 0.396811 M7 -0.00533356626561581 0.060819 -0.0877 0.930197 0.465099 M8 0.424661480534343 0.061623 6.8913 0 0 M9 0.0636908019214387 0.065474 0.9728 0.331726 0.165863 M10 -0.0461693671096149 0.06233 -0.7407 0.459647 0.229823 M11 0.00929006307398224 0.060754 0.1529 0.878606 0.439303 t 0.00180052061064903 0.000517 3.485 0.000593 0.000296 Multiple Linear Regression - Regression Statistics Multiple R 0.988826313218369 R-squared 0.977777477713031 Adjusted R-squared 0.976275955936885 F-TEST (value) 651.191007180978 F-TEST (DF numerator) 15 F-TEST (DF denominator) 222 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.186199809715552 Sum Squared Residuals 7.6968219486599 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4.4 4.63173593242199 -0.231735932421992 2 4.4 4.52432142523339 -0.124321425233390 3 4.3 4.4037943189792 -0.103794318979201 4 4.1 4.22563326839806 -0.125633268398057 5 3.9 4.02148856058998 -0.121488560589985 6 3.7 3.79300054375553 -0.093000543755531 7 3.6 3.619257755822 -0.0192577558220039 8 3.9 4.05141736716782 -0.151417367167825 9 4.2 4.20773952492712 -0.00773952492711593 10 4.2 4.362930210395 -0.162930210395000 11 4.1 4.25179788182168 -0.151797881821678 12 4.1 4.08976633645902 0.0102336635409818 13 4.1 4.28810902438192 -0.188109024381922 14 4.1 4.27057685485223 -0.17057685485223 15 4.1 4.1045801206229 -0.00458012062289699 16 4 4.07456439385265 -0.0745643938526464 17 3.9 3.96030202370348 -0.0603020237034797 18 3.8 3.82809302361635 -0.0280930236163505 19 3.8 3.74423257334173 0.055767426658272 20 4 4.25987784325803 -0.259877843258028 21 4.4 4.22258504923127 0.177414950768731 22 4.6 4.57778736557363 0.0222126344263732 23 4.6 4.69828601938168 -0.0982860193816847 24 4.6 4.58066718370278 0.0193328162972189 25 4.7 4.73354024365053 -0.0335402436505339 26 4.8 4.86415339793174 -0.0641533979317437 27 4.8 4.78803900136131 0.0119609986386873 28 4.7 4.71255364661591 -0.0125536466159133 29 4.7 4.61108463464359 0.0889153653564066 30 4.7 4.62702095836736 0.072979041632635 31 4.6 4.63943952484007 -0.0394395248400707 32 5 4.96786652205874 0.0321334779412574 33 5.4 5.26593732454051 0.134062675459488 34 5.5 5.52380370584415 -0.0238037058441463 35 5.6 5.51534707310658 0.0846529268934248 36 5.6 5.59134318921372 0.00865681078627844 37 5.8 5.69874662118632 0.101253378813675 38 6 5.98390177836686 0.0160982216331417 39 6.1 6.01046307763218 0.0895369223678201 40 6.1 6.03125673963411 0.0687432603658929 41 6 6.01967006532069 -0.0196700653206902 42 6 5.84838811634684 0.151611883653164 43 6.1 5.92546634805996 0.174533651940038 44 6.5 6.53739063472359 -0.0373906347235882 45 7.1 6.74452218125506 0.355477818744941 46 7.4 7.29228253109207 0.107717468907931 47 7.4 7.46359057367231 -0.0635905736723066 48 7.5 7.29410543092983 0.205894569070171 49 7.6 7.59512381468848 0.00487618531151684 50 7.8 7.68026734099454 0.119732659005459 51 7.8 7.75869494732344 0.0413050526765637 52 7.7 7.63773996460289 0.0622600353971133 53 7.6 7.53627095263057 0.0637290473694326 54 7.5 7.41045863163186 0.0895413683681394 55 7.3 7.32659818135724 -0.0265981813572393 56 7.6 7.55874616182858 0.0412538381714152 57 8 7.76693462665145 0.233065373348550 58 8 8.08306399410708 -0.0830639941070812 59 7.9 7.92006535847019 -0.0200653584701852 60 7.8 7.7516371340191 0.0483628659808955 61 7.7 7.80823117721953 -0.108231177219529 62 7.8 7.70081667003093 0.0991833299690657 63 7.7 7.73483156667607 -0.0348315666760743 64 7.5 7.5175975672082 -0.0175975672081985 65 7.3 7.31345285940013 -0.0134528594001268 66 7.1 7.09775820074252 0.00224179925748228 67 7 6.92401541280899 0.0759845871910085 68 7.3 7.35617502415481 -0.0561750241548124 69 7.8 7.51889386100253 0.281106138997473 70 7.9 7.97677187318064 -0.0767718731806352 71 7.9 7.91005225429107 -0.0100522542910680 72 7.8 7.8315063674989 -0.0315063674988899 73 7.8 7.83623410363574 -0.0362341036357417 74 7.9 7.88336159934647 0.0166384006535300 75 7.8 7.86551018892804 -0.0655101889280386 76 7.6 7.64187951037174 -0.0418795103717374 77 7.4 7.44413148165209 -0.0441314816520891 78 7.2 7.21564346481763 -0.0156434648176338 79 6.9 7.03550399779568 -0.135503997795684 80 7.1 7.1713729615197 -0.0713729615197032 81 7.5 7.29607576777209 0.203924232227913 82 7.6 7.65127808411444 -0.0512780841144451 83 7.4 7.61723473502318 -0.217234735023178 84 7.3 7.24879487969762 0.0512051203023759 85 7.2 7.35725522996162 -0.157255229961622 86 7.3 7.24984072277303 0.0501592772269729 87 7.2 7.27745894032974 -0.0774589403297435 88 7.1 7.06022494086187 0.0397750591381321 89 7 7.0042255568647 -0.004225556864696 90 6.9 6.87201655677757 0.0279834432224327 91 6.8 6.79455278559137 0.00544721440863035 92 7.2 7.17484608987362 0.0251539101263849 93 7.6 7.47931357144381 0.120686428556191 94 7.7 7.73717995274744 -0.0371799527474412 95 7.6 7.71592996183302 -0.115929961833024 96 7.5 7.49563543031837 0.00436456968163192 97 7.5 7.55222947351879 -0.0522294735187948 98 7.6 7.5929602901411 0.00703970985890022 99 7.6 7.57510887972267 0.0248911202773332 100 7.6 7.50602020406569 0.0939797959343088 101 7.5 7.533506478639 -0.0335064786390002 102 7.3 7.3494311714883 -0.0494311714882984 103 7.2 7.1238220764912 0.076177923508802 104 7.4 7.54318832966017 -0.143188329660171 105 8 7.55776184269699 0.442238157303014 106 8.2 8.1964614484843 0.00353855151570254 107 8 8.19403745089994 -0.194037450899937 108 7.7 7.76733460942239 -0.0673346094223852 109 7.7 7.58590099115301 0.114099008846994 110 7.8 7.72396774281404 0.076032257185965 111 7.8 7.7061163323956 0.0938836676043984 112 7.7 7.62423429856178 0.0757657014382217 113 7.5 7.50997192841261 -0.00997192841261137 114 7.3 7.236014283603 0.0639857163969952 115 7.1 7.06227149566948 0.0377285043305208 116 7.1 7.33988910411597 -0.239889104115974 117 7.2 7.11003827659456 0.0899617234054397 118 6.8 7.12453723563136 -0.324537235631363 119 6.6 6.54374626320685 0.0562537367931451 120 6.4 6.43463794319917 -0.034637943199166 121 6.4 6.38855629056384 0.0114437094361579 122 6.5 6.4491700188076 0.050829981192398 123 6.3 6.40573189203547 -0.105731892035474 124 5.9 6.0403525687567 -0.140352568756696 125 5.5 5.63656027400936 -0.136560274009363 126 5.2 5.23470426094552 -0.0347042609455224 127 4.9 5.02294544241667 -0.122945442416667 128 5.4 5.22987075046953 0.17012924953047 129 5.8 5.7670261327125 0.0329738672875002 130 5.7 5.95383616968729 -0.253836169687288 131 5.6 5.65548556841634 -0.0554855684163403 132 5.5 5.53252697194041 -0.0325269719404072 133 5.4 5.56993097787556 -0.169930977875563 134 5.4 5.43053307524485 -0.0305330752448483 135 5.4 5.30360928990224 0.096390710097759 136 5.5 5.27999024222042 0.220009757779585 137 5.8 5.48120855695832 0.31879144304168 138 5.7 5.81865820072238 -0.118658200722376 139 5.4 5.51453916401661 -0.114539164016613 140 5.6 5.59214514158863 0.00785485841136534 141 5.8 5.69126123148732 0.108738768512676 142 6.2 5.78855297473842 0.411447025261579 143 6.8 6.3538516439144 0.446148356085604 144 6.7 6.98938874153163 -0.289388741531631 145 6.7 6.71490203072916 -0.0149020307291611 146 6.4 6.77482288461674 -0.374822884616737 147 6.3 6.1899768953084 0.110023104691604 148 6.3 6.16741476591796 0.132585234082035 149 6.4 6.22118063120115 0.178819368798847 150 6.3 6.32060261349541 -0.0206026134954062 151 6 6.14580290727048 -0.145802907270483 152 6.3 6.29377235481517 0.00622764518483442 153 6.3 6.52824041034791 -0.228240410347909 154 6.6 6.25178848255994 0.348211517440063 155 7.5 6.7023109720795 0.797689027920504 156 7.8 7.79577027366247 0.00422972633753365 157 7.9 7.91988586238234 -0.0198858623823358 158 7.8 7.92048681182652 -0.120486811826520 159 7.6 7.5800651630764 0.0199348369235944 160 7.5 7.31202177483635 0.187978225163649 161 7.6 7.28869866063748 0.311301339362516 162 7.5 7.43359027090688 0.0664097290931154 163 7.3 7.25239388559354 0.0476061144064601 164 7.6 7.52931861968385 0.0706813803161488 165 7.5 7.71831704724144 -0.218317047241445 166 7.6 7.31290983290784 0.287090167092157 167 7.9 7.54459469822287 0.355405301777132 168 7.9 7.90408810377497 -0.00408810377496998 169 8.1 7.92055227979727 0.179447720202726 170 8.2 8.2312941533315 -0.0312941533315014 171 8 8.10971012878592 -0.109710128785921 172 7.5 7.7315374473303 -0.231537447330297 173 6.8 7.1092363587994 -0.309236358799402 174 6.5 6.32760403954328 0.172395960456721 175 6.6 6.30982421673569 0.290175783264313 176 7.6 7.16050425273954 0.439495747260458 177 8 8.21173098851745 -0.211730988517451 178 8.1 8.13920949017437 -0.0392094901743731 179 7.7 8.07318274564099 -0.373182745640988 180 7.5 7.39565888451678 0.104341115483216 181 7.6 7.47249988327388 0.127500116726124 182 7.8 7.7260356889475 0.0739643110524969 183 7.8 7.81085997436482 -0.0108599743648217 184 7.8 7.68990499164427 0.110095008355728 185 7.5 7.71099458712916 -0.210994587129158 186 7.5 7.2434219905335 0.256578009466499 187 7.1 7.41783615728535 -0.317836157285351 188 7.5 7.35300061577871 0.146999384221290 189 7.5 7.7810836230975 -0.281083623097506 190 7.6 7.45916206733438 0.140837932665617 191 7.7 7.61979058832056 0.0802094116794367 192 7.7 7.67659666716244 0.0234033328375604 193 7.9 7.78400009913504 0.115999900864957 194 8.1 8.06275857722715 0.0372414227728468 195 8.2 8.08931987649247 0.110680123507526 196 8.2 8.10371685940598 0.0962831405940225 197 8.2 8.08573350600414 0.114266493995863 198 7.9 8.05620020175276 -0.156200201752758 199 7.3 7.64337283405803 -0.343372834058034 200 6.9 7.43144888703189 -0.531448887031887 201 6.6 6.82927535069801 -0.229275350698013 202 6.7 6.49064163818762 0.209358361812378 203 6.9 6.81326575945295 0.0867342405470516 204 7 7.01821716210573 -0.0182171621057252 205 7.1 7.2091062526488 -0.109106252648809 206 7.2 7.29424977895487 -0.0942497789548663 207 7.1 7.23092874056128 -0.130928740561285 208 6.9 7.02648809927025 -0.126488099270254 209 7 6.84793010781588 0.152069892184121 210 6.8 7.03829134606043 -0.23829134606043 211 6.4 6.68336292058249 -0.283362920582488 212 6.7 6.65829320231876 0.0417067976812409 213 6.6 6.91264416947296 -0.312644169472958 214 6.4 6.48165023878566 -0.0816502387856596 215 6.3 6.32007256537537 -0.0200725653753743 216 6.2 6.27456699231671 -0.0745669923167094 217 6.5 6.34395439369398 0.156045606306016 218 6.8 6.8035344653953 -0.00353446539529628 219 6.8 6.90078806505425 -0.100788065054250 220 6.4 6.70238005891643 -0.302380058916432 221 6.1 6.16287175459983 -0.0628717545998337 222 5.8 5.89636770717005 -0.0963677071700458 223 6.1 5.66472597701974 0.435274022980264 224 7.2 6.760523227938 0.439476772061997 225 7.3 7.8369726361344 -0.536972636134396 226 6.9 7.27454553838346 -0.374545538383463 227 6.1 6.68735788687053 -0.587357886870534 228 5.8 5.72775769852798 0.072242301472019 229 6.2 5.88950531808216 0.310494681917837 230 7.1 6.63294672316364 0.467053276836357 231 7.7 7.55441260044758 0.145587399552421 232 7.9 7.91448865752846 -0.0144886575284553 233 7.7 7.90148102098843 -0.201481020988431 234 7.4 7.45273441772283 -0.0527344177228324 235 7.5 7.15003634324368 0.349963656756322 236 8 7.93035290927487 0.0696470907251278 237 8.1 8.25364638417512 -0.153646384175125 238 8 8.0216071660709 -0.0216071660709046 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.00268826961659796 0.00537653923319593 0.997311730383402 20 0.00059594364772589 0.00119188729545178 0.999404056352274 21 0.000203252927516015 0.000406505855032029 0.999796747072484 22 0.00158077693814861 0.00316155387629722 0.998419223061851 23 0.000772630787302363 0.00154526157460473 0.999227369212698 24 0.000334945735941284 0.000669891471882568 0.999665054264059 25 8.71794458079156e-05 0.000174358891615831 0.999912820554192 26 3.19607863468172e-05 6.39215726936344e-05 0.999968039213653 27 1.72979681605025e-05 3.45959363210049e-05 0.99998270203184 28 9.08787875022665e-06 1.81757575004533e-05 0.99999091212125 29 2.37285125293653e-06 4.74570250587306e-06 0.999997627148747 30 5.87692787045742e-07 1.17538557409148e-06 0.999999412307213 31 2.21842628124059e-06 4.43685256248119e-06 0.999997781573719 32 7.10599998690887e-07 1.42119999738177e-06 0.999999289400001 33 2.01153697158545e-07 4.0230739431709e-07 0.999999798846303 34 1.07558271057395e-07 2.1511654211479e-07 0.999999892441729 35 3.79418822330369e-08 7.58837644660739e-08 0.999999962058118 36 1.40454389109792e-08 2.80908778219585e-08 0.99999998595456 37 5.15508940663013e-09 1.03101788132603e-08 0.99999999484491 38 1.79121162491179e-09 3.58242324982358e-09 0.999999998208788 39 4.66933835102045e-10 9.3386767020409e-10 0.999999999533066 40 1.20852544034007e-10 2.41705088068013e-10 0.999999999879147 41 2.00848560160978e-10 4.01697120321956e-10 0.999999999799151 42 6.76003748340286e-11 1.35200749668057e-10 0.9999999999324 43 2.15569125048425e-11 4.31138250096850e-11 0.999999999978443 44 5.72234345148926e-12 1.14446869029785e-11 0.999999999994278 45 7.73611835587272e-12 1.54722367117454e-11 0.999999999992264 46 5.40944105343834e-12 1.08188821068767e-11 0.99999999999459 47 4.42865746314888e-12 8.85731492629776e-12 0.999999999995571 48 1.36256031523922e-12 2.72512063047843e-12 0.999999999998637 49 8.74689250001744e-13 1.74937850000349e-12 0.999999999999125 50 2.48661089926106e-13 4.97322179852212e-13 0.999999999999751 51 3.46095648554570e-13 6.92191297109139e-13 0.999999999999654 52 5.41059622235629e-13 1.08211924447126e-12 0.999999999999459 53 5.49361195189866e-13 1.09872239037973e-12 0.99999999999945 54 6.38756718643511e-13 1.27751343728702e-12 0.99999999999936 55 1.63678382950217e-11 3.27356765900434e-11 0.999999999983632 56 6.27711131690048e-12 1.25542226338010e-11 0.999999999993723 57 3.8028754904658e-12 7.6057509809316e-12 0.999999999996197 58 1.29978723278069e-11 2.59957446556139e-11 0.999999999987002 59 6.75095115175425e-12 1.35019023035085e-11 0.99999999999325 60 5.01851822544748e-12 1.00370364508950e-11 0.999999999994981 61 6.86060300809421e-12 1.37212060161884e-11 0.99999999999314 62 2.9652183624627e-12 5.9304367249254e-12 0.999999999997035 63 2.05853389586361e-12 4.11706779172721e-12 0.999999999997941 64 8.34507228163878e-13 1.66901445632776e-12 0.999999999999166 65 3.2567669834301e-13 6.5135339668602e-13 0.999999999999674 66 1.24777290531126e-13 2.49554581062252e-13 0.999999999999875 67 5.33283942666763e-14 1.06656788533353e-13 0.999999999999947 68 2.14194891764195e-14 4.2838978352839e-14 0.999999999999979 69 3.09726022483851e-14 6.19452044967702e-14 0.99999999999997 70 1.15015555938443e-14 2.30031111876887e-14 0.999999999999988 71 4.8992399401395e-15 9.798479880279e-15 0.999999999999995 72 2.8777040492615e-15 5.755408098523e-15 0.999999999999997 73 9.96238666748623e-16 1.99247733349725e-15 0.999999999999999 74 3.57724707600502e-16 7.15449415201004e-16 1 75 1.61405157901376e-16 3.22810315802751e-16 1 76 5.72187595470803e-17 1.14437519094161e-16 1 77 1.96004694346778e-17 3.92009388693555e-17 1 78 7.27070077079389e-18 1.45414015415878e-17 1 79 1.92765870139418e-17 3.85531740278837e-17 1 80 6.8483105510783e-18 1.36966211021566e-17 1 81 4.15645319239058e-18 8.31290638478115e-18 1 82 1.53781021376390e-18 3.07562042752779e-18 1 83 3.79548298232347e-18 7.59096596464693e-18 1 84 1.30012264216112e-18 2.60024528432225e-18 1 85 8.71584117080547e-19 1.74316823416109e-18 1 86 4.11489879170549e-19 8.22979758341097e-19 1 87 1.80526493086474e-19 3.61052986172949e-19 1 88 9.19905386594297e-20 1.83981077318859e-19 1 89 3.32910044286033e-20 6.65820088572065e-20 1 90 1.08696490480745e-20 2.17392980961489e-20 1 91 3.49791330017655e-21 6.9958266003531e-21 1 92 2.89982690434283e-21 5.79965380868566e-21 1 93 1.50434973971522e-21 3.00869947943045e-21 1 94 4.9792872822386e-22 9.9585745644772e-22 1 95 2.12494090154077e-22 4.24988180308154e-22 1 96 7.62536516844007e-23 1.52507303368801e-22 1 97 2.63624774044348e-23 5.27249548088696e-23 1 98 8.14995894318067e-24 1.62999178863613e-23 1 99 2.87042320623896e-24 5.74084641247793e-24 1 100 2.78095750860788e-24 5.56191501721575e-24 1 101 9.63452615927495e-25 1.92690523185499e-24 1 102 7.9857965429004e-25 1.59715930858008e-24 1 103 2.56604254012549e-25 5.13208508025098e-25 1 104 4.00585118685726e-25 8.01170237371453e-25 1 105 1.95517893083641e-23 3.91035786167281e-23 1 106 6.37323758314536e-24 1.27464751662907e-23 1 107 1.84274584796949e-22 3.68549169593898e-22 1 108 2.41079032549471e-21 4.82158065098941e-21 1 109 1.21159880241212e-21 2.42319760482425e-21 1 110 4.71412773754827e-22 9.42825547509654e-22 1 111 1.74926161340500e-22 3.49852322680999e-22 1 112 6.94820094116785e-23 1.38964018823357e-22 1 113 5.09606625671806e-23 1.01921325134361e-22 1 114 2.40317625929207e-23 4.80635251858413e-23 1 115 1.2298785011732e-23 2.4597570023464e-23 1 116 2.77228818867019e-22 5.54457637734039e-22 1 117 8.77634569398608e-22 1.75526913879722e-21 1 118 3.37391465258046e-20 6.74782930516092e-20 1 119 1.25220018231002e-19 2.50440036462004e-19 1 120 4.92349916916862e-20 9.84699833833723e-20 1 121 2.94379187533154e-20 5.88758375066308e-20 1 122 1.17789060203440e-20 2.35578120406880e-20 1 123 1.14134633225625e-20 2.28269266451250e-20 1 124 1.30551229138812e-20 2.61102458277623e-20 1 125 8.03585153742279e-21 1.60717030748456e-20 1 126 3.41632182182146e-21 6.83264364364291e-21 1 127 2.06158148570339e-21 4.12316297140677e-21 1 128 1.75784521581407e-19 3.51569043162814e-19 1 129 1.37530544728563e-19 2.75061089457126e-19 1 130 5.95801155368229e-19 1.19160231073646e-18 1 131 6.21245942564001e-19 1.24249188512800e-18 1 132 2.99731956497135e-19 5.99463912994269e-19 1 133 5.29699144985095e-19 1.05939828997019e-18 1 134 2.76067775231877e-19 5.52135550463754e-19 1 135 2.76489396599679e-19 5.52978793199358e-19 1 136 1.01634926912176e-18 2.03269853824352e-18 1 137 1.49318948398553e-17 2.98637896797105e-17 1 138 5.048034868513e-17 1.0096069737026e-16 1 139 8.66524093694104e-17 1.73304818738821e-16 1 140 6.56970040543e-17 1.313940081086e-16 1 141 5.30390196706113e-17 1.06078039341223e-16 1 142 1.40081376242263e-14 2.80162752484525e-14 0.999999999999986 143 1.27506727698361e-12 2.55013455396722e-12 0.999999999998725 144 3.90991888260276e-11 7.81983776520552e-11 0.9999999999609 145 2.85349340292087e-11 5.70698680584175e-11 0.999999999971465 146 1.16884642595101e-09 2.33769285190202e-09 0.999999998831154 147 8.36137468808692e-10 1.67227493761738e-09 0.999999999163863 148 6.1429711864961e-10 1.22859423729922e-09 0.999999999385703 149 4.93184943864322e-10 9.86369887728645e-10 0.999999999506815 150 4.20691008288364e-10 8.41382016576728e-10 0.999999999579309 151 1.05317243554020e-09 2.10634487108041e-09 0.999999998946828 152 1.46484465425378e-09 2.92968930850756e-09 0.999999998535155 153 9.54553504484628e-09 1.90910700896926e-08 0.999999990454465 154 3.24187854226299e-08 6.48375708452598e-08 0.999999967581215 155 7.31987528339226e-05 0.000146397505667845 0.999926801247166 156 5.81635580422054e-05 0.000116327116084411 0.999941836441958 157 4.97195554458709e-05 9.94391108917418e-05 0.999950280444554 158 5.12931469380408e-05 0.000102586293876082 0.999948706853062 159 3.37706308361398e-05 6.75412616722796e-05 0.999966229369164 160 2.86921217795681e-05 5.73842435591362e-05 0.99997130787822 161 4.34288315880779e-05 8.68576631761557e-05 0.999956571168412 162 2.81133576469533e-05 5.62267152939066e-05 0.999971886642353 163 1.80781447881686e-05 3.61562895763371e-05 0.999981921855212 164 1.20803365582477e-05 2.41606731164955e-05 0.999987919663442 165 2.53011855637146e-05 5.06023711274293e-05 0.999974698814436 166 3.46271711097364e-05 6.92543422194728e-05 0.99996537282889 167 0.000169830602907389 0.000339661205814778 0.999830169397093 168 0.000113525716930727 0.000227051433861454 0.99988647428307 169 0.000103514590080589 0.000207029180161179 0.99989648540992 170 6.83757515630365e-05 0.000136751503126073 0.999931624248437 171 5.07967942329003e-05 0.000101593588465801 0.999949203205767 172 6.18036302818895e-05 0.000123607260563779 0.999938196369718 173 0.000131567480859519 0.000263134961719038 0.99986843251914 174 0.000117502046829599 0.000235004093659199 0.99988249795317 175 0.000164405108903698 0.000328810217807397 0.999835594891096 176 0.00046121542671093 0.00092243085342186 0.99953878457329 177 0.000532011707957188 0.00106402341591438 0.999467988292043 178 0.000364841909199731 0.000729683818399462 0.9996351580908 179 0.000677452262080665 0.00135490452416133 0.999322547737919 180 0.000585543535307074 0.00117108707061415 0.999414456464693 181 0.000444634756105608 0.000889269512211217 0.999555365243894 182 0.000304562465689810 0.000609124931379621 0.99969543753431 183 0.000199919244626424 0.000399838489252848 0.999800080755374 184 0.000184780200660098 0.000369560401320196 0.99981521979934 185 0.000176711526160899 0.000353423052321797 0.99982328847384 186 0.00045183358517626 0.00090366717035252 0.999548166414824 187 0.00086676135429512 0.00173352270859024 0.999133238645705 188 0.000718505484851446 0.00143701096970289 0.999281494515148 189 0.000753501122772188 0.00150700224554438 0.999246498877228 190 0.000665673800078116 0.00133134760015623 0.999334326199922 191 0.00081430233246593 0.00162860466493186 0.999185697667534 192 0.000624498389253559 0.00124899677850712 0.999375501610746 193 0.000534768926455032 0.00106953785291006 0.999465231073545 194 0.000393847918821215 0.00078769583764243 0.999606152081179 195 0.000699401483836648 0.00139880296767330 0.999300598516163 196 0.0029153093151253 0.0058306186302506 0.997084690684875 197 0.0127076173680779 0.0254152347361558 0.987292382631922 198 0.0304048040728138 0.0608096081456277 0.969595195927186 199 0.0272741664313234 0.0545483328626468 0.972725833568677 200 0.088130028403252 0.176260056806504 0.911869971596748 201 0.0737511996973355 0.147502399394671 0.926248800302665 202 0.0757553400283501 0.1515106800567 0.92424465997165 203 0.1464261795239 0.2928523590478 0.8535738204761 204 0.165556424603331 0.331112849206663 0.834443575396669 205 0.135351444389993 0.270702888779986 0.864648555610007 206 0.102290029679832 0.204580059359663 0.897709970320168 207 0.0755421517244488 0.151084303448898 0.924457848275551 208 0.0553630266466488 0.110726053293298 0.944636973353351 209 0.0847085739170762 0.169417147834152 0.915291426082924 210 0.072949329793017 0.145898659586034 0.927050670206983 211 0.133914971762867 0.267829943525734 0.866085028237133 212 0.173203085410665 0.346406170821329 0.826796914589335 213 0.139894481380031 0.279788962760063 0.860105518619969 214 0.138511211317234 0.277022422634468 0.861488788682766 215 0.646833998684655 0.706332002630691 0.353166001315346 216 0.697820904352215 0.604358191295571 0.302179095647785 217 0.721391454147182 0.557217091705637 0.278608545852818 218 0.734224270602757 0.531551458794487 0.265775729397243 219 0.749141009766237 0.501717980467526 0.250858990233763 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 178 0.885572139303483 NOK 5% type I error level 179 0.890547263681592 NOK 10% type I error level 181 0.90049751243781 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/29/t1262085442u332kmk510s44k4/103na41262085345.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t1262085442u332kmk510s44k4/103na41262085345.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t1262085442u332kmk510s44k4/1ng5q1262085345.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t1262085442u332kmk510s44k4/1ng5q1262085345.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t1262085442u332kmk510s44k4/2r7o01262085345.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t1262085442u332kmk510s44k4/2r7o01262085345.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t1262085442u332kmk510s44k4/3ttaq1262085345.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t1262085442u332kmk510s44k4/3ttaq1262085345.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t1262085442u332kmk510s44k4/4mhlf1262085345.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t1262085442u332kmk510s44k4/4mhlf1262085345.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t1262085442u332kmk510s44k4/5lurg1262085345.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t1262085442u332kmk510s44k4/5lurg1262085345.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t1262085442u332kmk510s44k4/6ss8v1262085345.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t1262085442u332kmk510s44k4/6ss8v1262085345.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t1262085442u332kmk510s44k4/7qsbr1262085345.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t1262085442u332kmk510s44k4/7qsbr1262085345.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t1262085442u332kmk510s44k4/8yrk11262085345.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t1262085442u332kmk510s44k4/8yrk11262085345.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t1262085442u332kmk510s44k4/9qat71262085345.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t1262085442u332kmk510s44k4/9qat71262085345.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') }

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