Multiple Regression 2

*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: Mon, 28 Dec 2009 10:27:53 -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/28/t1262021332ghmyfyued1fxe2e.htm/, Retrieved Mon, 28 Dec 2009 18:29:05 +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/28/t1262021332ghmyfyued1fxe2e.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 zonder lineaire trend

Dataseries X:

» Textbox « » Textfile « » CSV «

4.6 11.7 4.5 11.4 4.4 11.2 4.4 11.1 4.3 10.8 4.1 10.4 3.9 10.1 3.7 9.8 3.6 9.7 3.9 10.3 4.2 10.9 4.2 10.8 4.1 10.6 4.1 10.4 4.1 10.3 4.1 10.2 4.1 10 4 9.7 3.9 9.4 3.8 9.2 3.8 9.1 4 9.6 4.4 10.2 4.6 10.2 4.6 10 4.6 9.9 4.7 9.9 4.8 9.9 4.8 9.7 4.7 9.5 4.7 9.4 4.7 9.3 4.6 9.3 5 9.9 5.4 10.5 5.5 10.6 5.6 10.6 5.6 10.5 5.8 10.6 6 10.8 6.1 10.8 6.1 10.7 6 10.6 6 10.6 6.1 10.8 6.5 11.4 7.1 12.2 7.4 12.4 7.4 12.4 7.5 12.3 7.6 12.4 7.8 12.5 7.8 12.5 7.7 12.4 7.6 12.3 7.5 12.2 7.3 12.1 7.6 12.6 8 13.2 8 13.4 7.9 13.2 7.8 12.9 7.7 12.8 7.8 12.7 7.7 12.6 7.5 12.4 7.3 12.1 7.1 12 7 11.9 7.3 12.5 7.8 13.2 7.9 13.4 7.9 13.3 7.8 13 7.8 12.9 7.9 13 7.8 12.9 7.6 12.6 7.4 12.4 7.2 12.1 6.9 11.9 7.1 12.3 7.5 13 7.6 13 7.4 12.6 7.3 12.2 7.2 12.1 7.3 12 7.2 11.8 7.1 11.6 7 11.4 6.9 11.2 6.8 11.2 7.2 11.8 7.6 12.5 7.7 12.6 7.6 12.4 7.5 12.1 7.5 12 7.6 12 7.6 11.9 7.6 11.8 7.5 11.5 7.3 11.3 7.2 11.2 7.4 11.6 8 12.2 8.2 12.2 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 9 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 4.99679000275911 + 0.180172709660390X[t] -0.164189637420380M1[t] -0.177840415167166M2[t] -0.107840415167166M3[t] + 0.00815094934981393M4[t] + 0.0097716745090601M5[t] -0.0651851480758428M6[t] -0.147439380015839M7[t] -0.274603110987156M8[t] -0.42690052034225M9[t] -0.215228325490940M10[t] -0.059008635483022M11[t] + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 4.99679000275911 0.554546 9.0106 0 0 X 0.180172709660390 0.046331 3.8889 0.000132 6.6e-05 M1 -0.164189637420380 0.378872 -0.4334 0.665162 0.332581 M2 -0.177840415167166 0.379199 -0.469 0.639527 0.319764 M3 -0.107840415167166 0.379199 -0.2844 0.776371 0.388185 M4 0.00815094934981393 0.379108 0.0215 0.982865 0.491433 M5 0.0097716745090601 0.37935 0.0258 0.979472 0.489736 M6 -0.0651851480758428 0.380113 -0.1715 0.863992 0.431996 M7 -0.147439380015839 0.381304 -0.3867 0.699362 0.349681 M8 -0.274603110987156 0.382526 -0.7179 0.473577 0.236788 M9 -0.42690052034225 0.382622 -1.1157 0.265721 0.13286 M10 -0.215228325490940 0.37935 -0.5674 0.571029 0.285515 M11 -0.059008635483022 0.378869 -0.1557 0.876369 0.438184 Multiple Linear Regression - Regression Statistics Multiple R 0.288332841742365 R-squared 0.0831358276272278 Adjusted R-squared 0.0346672370172134 F-TEST (value) 1.71525160069438 F-TEST (DF numerator) 12 F-TEST (DF denominator) 227 p-value 0.0646419472974461 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.19806691188221 Sum Squared Residuals 325.827701853762 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4.6 6.94062106836534 -2.34062106836534 2 4.5 6.87291847772039 -2.37291847772039 3 4.4 6.90688393578832 -2.50688393578832 4 4.4 7.00485802933926 -2.60485802933926 5 4.3 6.95242694160039 -2.65242694160039 6 4.1 6.80540103515133 -2.70540103515133 7 3.9 6.66909499031322 -2.76909499031322 8 3.7 6.48787944644377 -2.78787944644377 9 3.6 6.31756476612265 -2.71756476612265 10 3.9 6.6373405867702 -2.73734058677019 11 4.2 6.90166390257435 -2.70166390257435 12 4.2 6.94265526709133 -2.74265526709133 13 4.1 6.74243108773887 -2.64243108773887 14 4.1 6.69274576806 -2.59274576806000 15 4.1 6.74472849709396 -2.64472849709397 16 4.1 6.8427025906449 -2.74270259064491 17 4.1 6.80828877387207 -2.70828877387207 18 4 6.67928013838905 -2.67928013838905 19 3.9 6.54297409355094 -2.64297409355094 20 3.8 6.37977582064755 -2.57977582064755 21 3.8 6.20946114032641 -2.40946114032641 22 4 6.51121969000792 -2.51121969000792 23 4.4 6.77554300581207 -2.37554300581207 24 4.6 6.83455164129509 -2.23455164129509 25 4.6 6.63432746194263 -2.03432746194263 26 4.6 6.60265941322981 -2.00265941322981 27 4.7 6.67265941322981 -1.97265941322981 28 4.8 6.78865077774679 -1.98865077774679 29 4.8 6.75423696097396 -1.95423696097396 30 4.7 6.64324559645698 -1.94324559645698 31 4.7 6.54297409355094 -1.84297409355094 32 4.7 6.39779309161358 -1.69779309161358 33 4.6 6.24549568225849 -1.64549568225849 34 5 6.56527150290604 -1.56527150290604 35 5.4 6.82959481871019 -1.42959481871019 36 5.5 6.90662072515925 -1.40662072515925 37 5.6 6.74243108773887 -1.14243108773887 38 5.6 6.71076303902604 -1.11076303902604 39 5.8 6.79878030999208 -0.99878030999208 40 6 6.95080621644114 -0.95080621644114 41 6.1 6.95242694160039 -0.852426941600385 42 6.1 6.85945284804944 -0.759452848049446 43 6 6.75918134514341 -0.759181345143409 44 6 6.63201761417209 -0.632017614172091 45 6.1 6.51575474674908 -0.415754746749075 46 6.5 6.83553056739662 -0.33553056739662 47 7.1 7.13588842513285 -0.0358884251328513 48 7.4 7.23093160254795 0.169068397452050 49 7.4 7.06674196512757 0.333258034872431 50 7.5 7.03507391641474 0.464926083585255 51 7.6 7.12309118738078 0.476908812619216 52 7.8 7.2570998228638 0.542900177136197 53 7.8 7.25872054802305 0.541279451976951 54 7.7 7.16574645447211 0.534253545527891 55 7.6 7.06547495156607 0.534525048433927 56 7.5 6.92029394962872 0.579706050371284 57 7.3 6.74997926930758 0.550020730692418 58 7.6 7.05173781898909 0.548262181010911 59 8 7.31606113479324 0.683938865206758 60 8 7.41110431220834 0.58889568779166 61 7.9 7.21088013285588 0.689119867144119 62 7.8 7.14317754221098 0.65682245778902 63 7.7 7.19516027124494 0.504839728755061 64 7.8 7.29313436479588 0.50686563520412 65 7.7 7.27673781898909 0.423262181010913 66 7.5 7.16574645447211 0.334253545527891 67 7.3 7.029440409634 0.270559590366005 68 7.1 6.88425940769664 0.215740592303362 69 7 6.7139447273755 0.286055272624496 70 7.3 7.03372054802305 0.26627945197695 71 7.8 7.31606113479324 0.483938865206758 72 7.9 7.41110431220834 0.48889568779166 73 7.9 7.22889740382192 0.67110259617808 74 7.8 7.16119481317702 0.638805186822982 75 7.8 7.21317754221098 0.586822457789022 76 7.9 7.347186177694 0.552813822306002 77 7.8 7.3307896318872 0.469210368112795 78 7.6 7.20178099640419 0.398219003595813 79 7.4 7.08349222253211 0.316507777467889 80 7.2 6.90227667866268 0.297723321337323 81 6.9 6.7139447273755 0.186055272624496 82 7.1 6.99768600609097 0.102313993909028 83 7.5 7.28002659286116 0.219973407138837 84 7.6 7.33903522834418 0.260964771655815 85 7.4 7.10277650705965 0.297223492940353 86 7.3 7.0170566454487 0.282943354551294 87 7.2 7.06903937448267 0.130960625517334 88 7.3 7.16701346803361 0.132986531966392 89 7.2 7.13259965126077 0.0674003487392249 90 7.1 7.0216082867438 0.078391713256203 91 7 6.90331951287172 0.0966804871282786 92 6.9 6.74012123996833 0.159878760031675 93 6.8 6.58782383061323 0.212176169386769 94 7.2 6.90759965126078 0.292400348739224 95 7.6 7.18994023803097 0.410059761969031 96 7.7 7.26696614448003 0.433033855519972 97 7.6 7.06674196512757 0.53325803487243 98 7.5 6.99903937448267 0.500960625517333 99 7.5 7.05102210351663 0.448977896483373 100 7.6 7.16701346803361 0.432986531966392 101 7.6 7.15061692222681 0.449383077773185 102 7.6 7.05764282867588 0.542357171324125 103 7.5 6.92133678383776 0.57866321616224 104 7.3 6.75813851093436 0.541861489065635 105 7.2 6.58782383061323 0.612176169386769 106 7.4 6.8715651093287 0.528434890671302 107 8 7.13588842513285 0.864111574867149 108 8.2 7.19489706061587 1.00510293938413 109 8 6.9406210683653 1.05937893163470 110 7.7 6.83688393578832 0.863116064211685 111 7.7 6.87084939385624 0.829150606143763 112 7.8 6.96882348740718 0.831176512592821 113 7.8 6.95242694160039 0.847573058399615 114 7.7 6.82341830611737 0.876581693882633 115 7.5 6.68711226127925 0.812887738720747 116 7.3 6.52391398837586 0.776086011624143 117 7.1 6.35359930805472 0.746400691945276 118 7.1 6.63734058677019 0.462659413229809 119 7.2 6.86562936064227 0.334370639357735 120 6.8 6.87058618322717 -0.0705861832271697 121 6.6 6.65234473290867 -0.0523447329086721 122 6.4 6.56662487129773 -0.16662487129773 123 6.4 6.58257305839961 -0.182573058399613 124 6.5 6.6084780680864 -0.108478068086398 125 6.3 6.52001243841545 -0.220012438415449 126 5.9 6.39100380293243 -0.49100380293243 127 5.5 6.34478411292451 -0.844784112924512 128 5.2 6.18158584002112 -0.981585840021116 129 4.9 6.01127115969998 -1.11127115969998 130 5.4 6.34906425131357 -0.949064251313566 131 5.8 6.59537029615168 -0.79537029615168 132 5.7 6.61834438970262 -0.918344389702623 133 5.6 6.4361374813162 -0.836137481316204 134 5.5 6.35041761970526 -0.850417619705262 135 5.4 6.3483485358411 -0.948348535841105 136 5.4 6.35623627456185 -0.956236274561852 137 5.4 6.28578791585694 -0.885787915856941 138 5.5 6.17479655133996 -0.674796551339963 139 5.8 6.12857686133204 -0.328576861332044 140 5.7 5.98339585939469 -0.283395859394687 141 5.4 5.77704663714148 -0.377046637141475 142 5.6 6.0427706448909 -0.442770644890904 143 5.8 6.25304214779694 -0.453042147796939 144 6.2 6.38411986714412 -0.184119867144116 145 6.8 6.34605112648601 0.453948873513991 146 6.7 6.33240034873922 0.367599651260777 147 6.7 6.47446943260338 0.225530567396621 148 6.4 6.64451261001848 -0.244512610018476 149 6.3 6.62811606421168 -0.328116064211683 150 6.3 6.48109015776263 -0.181090157762626 151 6.4 6.27271502906036 0.127284970939644 152 6.3 6.10951675615696 0.190483243843040 153 6 5.9752366177679 0.0247633822320956 154 6.3 6.43915060614376 -0.139150606143762 155 6.3 6.63140483808376 -0.331404838083759 156 6.6 6.6543789316347 -0.0543789316347017 157 7.5 6.40010293938413 1.09989706061587 158 7.8 6.33240034873922 1.46759965126078 159 7.9 6.4384348906713 1.4615651093287 160 7.8 6.62649533905244 1.17350466094756 161 7.6 6.64613333517772 0.953866664822278 162 7.5 6.49910742872866 1.00089257127134 163 7.6 6.32676684195847 1.27323315804153 164 7.5 6.14555129808904 1.35444870191096 165 7.3 5.99325388873394 1.30674611126606 166 7.6 6.42113333517772 1.17886666482228 167 7.5 6.63140483808376 0.868595161916241 168 7.6 6.69041347356678 0.90958652643322 169 7.9 6.47217202324828 1.42782797675172 170 7.9 6.44050397453546 1.45949602546454 171 8.1 6.56455578743357 1.53544421256643 172 8.2 6.78865077774679 1.41134922225321 173 8 6.77225423194 1.22774576806001 174 7.5 6.6072110545249 0.892788945475102 175 6.8 6.34478411292451 0.455215887075488 176 6.5 6.16356856905508 0.336431430944923 177 6.6 6.10135751453018 0.498642485469822 178 7.6 6.65535785773623 0.94464214226377 179 8 6.93769844450642 1.06230155549358 180 8.1 6.96067253805736 1.13932746194264 181 7.7 6.63432746194263 1.06567253805737 182 7.5 6.47653851646754 1.02346148353247 183 7.6 6.54653851646753 1.05346148353247 184 7.8 6.71658169388263 1.08341830611737 185 7.8 6.73621969000792 1.06378030999208 186 7.8 6.64324559645698 1.15675440354302 187 7.5 6.48892228065282 1.01107771934718 188 7.5 6.32572400774943 1.17427599225057 189 7.1 6.19144386936037 0.908556130639627 190 7.5 6.60130604483811 0.898693955161887 191 7.5 6.79356027677811 0.70643972322189 192 7.6 6.83455164129509 0.765448358704909 193 7.7 6.56225837807848 1.13774162192152 194 7.7 6.47653851646754 1.22346148353247 195 7.9 6.56455578743357 1.33544421256643 196 8.1 6.69856442291659 1.40143557708341 197 8.2 6.70018514807584 1.49981485192416 198 8.2 6.58919378355886 1.61080621644114 199 8.2 6.47090500968678 1.72909499031321 200 7.9 6.34374127871547 1.55625872128453 201 7.3 6.19144386936037 1.10855613063963 202 6.9 6.54725423194 0.352745768060004 203 6.6 6.73950846387999 -0.139508463879993 204 6.7 6.76248255743094 -0.0624825574309356 205 6.9 6.50820656518036 0.391793434819640 206 7 6.44050397453546 0.559496025464543 207 7.1 6.51050397453546 0.589496025464543 208 7.2 6.64451261001848 0.555487389981524 209 7.1 6.64613333517772 0.453866664822278 210 6.9 6.57117651259282 0.328823487407179 211 7 6.50693955161886 0.493060448381137 212 6.8 6.30770673678339 0.49229326321661 213 6.4 6.0653229725981 0.334677027401901 214 6.7 6.29501243841545 0.404987561584551 215 6.6 6.39718031552525 0.202819684474748 216 6.4 6.38411986714412 0.0158801328558843 217 6.3 6.25596477165581 0.0440352283441861 218 6.2 6.24231399390903 -0.0423139939090281 219 6.5 6.33033126487507 0.169668735124933 220 6.8 6.428305358426 0.371694641573992 221 6.8 6.37587427068714 0.424125729312863 222 6.4 6.21083109327204 0.189168906727960 223 6.1 6.07452504843393 0.025474951566073 224 5.8 5.89330950456449 -0.093309504564492 225 6.1 5.81308117907355 0.286918820926446 226 7.2 6.25897789648337 0.941022103516629 227 7.3 6.50528394132149 0.794716058678514 228 6.9 6.49222349294035 0.40777650705965 229 6.1 6.25596477165581 -0.155964771655814 230 5.8 6.17024491004487 -0.370244910044872 231 6.2 6.29429672294299 -0.0942967229429881 232 7.1 6.50037444229016 0.599625557709835 233 7.7 6.52001243841545 1.17998756158455 234 7.9 6.40902107389847 1.49097892610153 235 7.7 6.23668048712828 1.46331951287172 236 7.4 6.01943040132677 1.38056959867324 237 7.5 5.88515026293771 1.61484973706229 238 8 6.24096062551733 1.75903937448267 239 8.1 6.46924939938941 1.63075060061059 240 8 6.51024076390639 1.48975923609361 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.000104131163267682 0.000208262326535364 0.999895868836732 17 1.58960369558944e-05 3.17920739117888e-05 0.999984103963044 18 4.9494050823811e-06 9.8988101647622e-06 0.999995050594918 19 3.77801047775776e-06 7.55602095551551e-06 0.999996221989522 20 2.97076593538797e-06 5.94153187077594e-06 0.999997029234065 21 3.43403494175652e-06 6.86806988351304e-06 0.999996565965058 22 1.47070546263599e-06 2.94141092527197e-06 0.999998529294537 23 1.03530260862348e-06 2.07060521724695e-06 0.999998964697391 24 1.91286255831437e-06 3.82572511662874e-06 0.999998087137442 25 1.77367472289486e-06 3.54734944578971e-06 0.999998226325277 26 1.38134666218810e-06 2.76269332437621e-06 0.999998618653338 27 1.86922526969480e-06 3.73845053938961e-06 0.99999813077473 28 3.33602206710436e-06 6.67204413420872e-06 0.999996663977933 29 5.87754872802942e-06 1.17550974560588e-05 0.999994122451272 30 1.14701683381148e-05 2.29403366762295e-05 0.999988529831662 31 4.01184540750343e-05 8.02369081500687e-05 0.999959881545925 32 0.000204208969006712 0.000408417938013424 0.999795791030993 33 0.000621594475959028 0.00124318895191806 0.99937840552404 34 0.00237302753544248 0.00474605507088496 0.997626972464557 35 0.0073468530350193 0.0146937060700386 0.99265314696498 36 0.0189070666353376 0.0378141332706752 0.981092933364662 37 0.0447705041046141 0.0895410082092282 0.955229495895386 38 0.0939065813435961 0.187813162687192 0.906093418656404 39 0.211344888160674 0.422689776321348 0.788655111839326 40 0.422728538052592 0.845457076105184 0.577271461947408 41 0.658579951449352 0.682840097101296 0.341420048550648 42 0.830817359499773 0.338365281000454 0.169182640500227 43 0.914048035403175 0.171903929193650 0.0859519645968248 44 0.952875757584823 0.0942484848303533 0.0471242424151767 45 0.969765788082847 0.0604684238343051 0.0302342119171526 46 0.97840689194408 0.0431862161118417 0.0215931080559208 47 0.982493210676332 0.035013578647337 0.0175067893236685 48 0.983781703712259 0.0324365925754828 0.0162182962877414 49 0.985919639036993 0.0281607219260142 0.0140803609630071 50 0.98685248285668 0.0262950342866387 0.0131475171433194 51 0.985815749168263 0.0283685016634733 0.0141842508317366 52 0.984027895669296 0.0319442086614079 0.0159721043307040 53 0.98004738057213 0.0399052388557412 0.0199526194278706 54 0.974082207897878 0.051835584204243 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0.50556365074781 0.98887269850438 0.49443634925219 73 0.462370351084285 0.92474070216857 0.537629648915715 74 0.419860072118449 0.839720144236898 0.580139927881551 75 0.378969361605857 0.757938723211714 0.621030638394143 76 0.339643185012426 0.679286370024851 0.660356814987574 77 0.304298859975419 0.608597719950837 0.695701140024581 78 0.271622911847015 0.543245823694029 0.728377088152985 79 0.243952099401467 0.487904198802934 0.756047900598533 80 0.21662444086628 0.43324888173256 0.78337555913372 81 0.193028916927672 0.386057833855344 0.806971083072328 82 0.171722756986207 0.343445513972414 0.828277243013793 83 0.150367316638773 0.300734633277547 0.849632683361227 84 0.129724572301014 0.259449144602027 0.870275427698986 85 0.115104287260022 0.230208574520045 0.884895712739978 86 0.105399467684552 0.210798935369105 0.894600532315448 87 0.0974490613772513 0.194898122754503 0.902550938622749 88 0.0933229848136912 0.186645969627382 0.906677015186309 89 0.0910448332626698 0.182089666525340 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107 0.119735863917310 0.239471727834619 0.88026413608269 108 0.149685030459081 0.299370060918161 0.85031496954092 109 0.229581430819842 0.459162861639684 0.770418569180158 110 0.331498314059773 0.662996628119546 0.668501685940227 111 0.461853869366083 0.923707738732165 0.538146130633917 112 0.600064209586541 0.799871580826917 0.399935790413459 113 0.713949113089239 0.572101773821522 0.286050886910761 114 0.811408412711557 0.377183174576885 0.188591587288443 115 0.88132207385583 0.237355852288341 0.118677926144170 116 0.925254170634363 0.149491658731273 0.0747458293656366 117 0.951503280176955 0.0969934396460894 0.0484967198230447 118 0.9664407967706 0.067118406458802 0.033559203229401 119 0.975958686983982 0.0480826260320361 0.0240413130160181 120 0.983373944980771 0.0332521100384571 0.0166260550192286 121 0.989881928859787 0.0202361422804262 0.0101180711402131 122 0.994199013917249 0.0116019721655021 0.00580098608275104 123 0.996913992346623 0.0061720153067549 0.00308600765337745 124 0.998548319116404 0.00290336176719258 0.00145168088359629 125 0.999334353774582 0.00133129245083605 0.000665646225418024 126 0.999660892030046 0.00067821593990732 0.00033910796995366 127 0.999849727350684 0.000300545298632596 0.000150272649316298 128 0.999943564459687 0.000112871080626463 5.64355403132313e-05 129 0.999980218610302 3.95627793954677e-05 1.97813896977339e-05 130 0.999991063138904 1.78737221929681e-05 8.93686109648403e-06 131 0.999994923387665 1.01532246700737e-05 5.07661233503685e-06 132 0.999997561460549 4.87707890207662e-06 2.43853945103831e-06 133 0.999999135660227 1.72867954623256e-06 8.6433977311628e-07 134 0.999999724602744 5.50794512774769e-07 2.75397256387385e-07 135 0.999999914419448 1.71161102965506e-07 8.55805514827529e-08 136 0.999999962033586 7.59328284885785e-08 3.79664142442892e-08 137 0.999999980459972 3.9080056646137e-08 1.95400283230685e-08 138 0.999999988749667 2.25006664516526e-08 1.12503332258263e-08 139 0.99999999314161 1.37167790695222e-08 6.8583895347611e-09 140 0.999999995541475 8.91705030010686e-09 4.45852515005343e-09 141 0.999999996693819 6.6123623684032e-09 3.3061811842016e-09 142 0.999999997185732 5.62853562950225e-09 2.81426781475112e-09 143 0.99999999710239 5.79521788105109e-09 2.89760894052554e-09 144 0.99999999683974 6.32051950177211e-09 3.16025975088606e-09 145 0.999999996787713 6.42457351750567e-09 3.21228675875283e-09 146 0.999999996542853 6.91429436415779e-09 3.45714718207889e-09 147 0.99999999660011 6.79977832742143e-09 3.39988916371072e-09 148 0.999999998211951 3.57609736929854e-09 1.78804868464927e-09 149 0.999999999249926 1.50014890342658e-09 7.5007445171329e-10 150 0.999999999568264 8.63470972962869e-10 4.31735486481434e-10 151 0.99999999958741 8.25180711605138e-10 4.12590355802569e-10 152 0.999999999571297 8.57405379651369e-10 4.28702689825684e-10 153 0.999999999593486 8.1302802778123e-10 4.06514013890615e-10 154 0.999999999756312 4.87375919085769e-10 2.43687959542885e-10 155 0.99999999984653 3.06940197896375e-10 1.53470098948187e-10 156 0.99999999983291 3.3417948874349e-10 1.67089744371745e-10 157 0.999999999857947 2.8410529696251e-10 1.42052648481255e-10 158 0.999999999942705 1.14589793944765e-10 5.72948969723823e-11 159 0.999999999968457 6.30867613941891e-11 3.15433806970946e-11 160 0.99999999996273 7.45405950520101e-11 3.72702975260051e-11 161 0.999999999944781 1.10437339687670e-10 5.52186698438352e-11 162 0.999999999919722 1.60555350867906e-10 8.02776754339528e-11 163 0.999999999916516 1.6696870769279e-10 8.3484353846395e-11 164 0.999999999926576 1.46847962961838e-10 7.3423981480919e-11 165 0.999999999930572 1.38856908173012e-10 6.94284540865061e-11 166 0.999999999904432 1.91135284405105e-10 9.55676422025526e-11 167 0.999999999837933 3.24133285554516e-10 1.62066642777258e-10 168 0.999999999732248 5.35504869899392e-10 2.67752434949696e-10 169 0.999999999820419 3.59161509637496e-10 1.79580754818748e-10 170 0.999999999874582 2.50835984507921e-10 1.25417992253960e-10 171 0.999999999896929 2.06142708782503e-10 1.03071354391252e-10 172 0.999999999848768 3.02463174131204e-10 1.51231587065602e-10 173 0.999999999731481 5.37037296886987e-10 2.68518648443493e-10 174 0.999999999506567 9.86865015645416e-10 4.93432507822708e-10 175 0.9999999991927 1.61460217310105e-09 8.07301086550524e-10 176 0.999999998751345 2.49730889198201e-09 1.24865444599101e-09 177 0.999999997879097 4.24180626966584e-09 2.12090313483292e-09 178 0.999999996134945 7.73010916406653e-09 3.86505458203327e-09 179 0.99999999245734 1.50853212165345e-08 7.54266060826724e-09 180 0.999999985727072 2.85458557249366e-08 1.42729278624683e-08 181 0.999999976116647 4.77667054598958e-08 2.38833527299479e-08 182 0.999999963294847 7.34103053968371e-08 3.67051526984186e-08 183 0.999999939642514 1.20714972820842e-07 6.03574864104208e-08 184 0.999999889360887 2.21278226832623e-07 1.10639113416311e-07 185 0.999999792457623 4.15084753354108e-07 2.07542376677054e-07 186 0.999999617672645 7.64654710343927e-07 3.82327355171963e-07 187 0.999999291828322 1.41634335590861e-06 7.08171677954304e-07 188 0.999998726395763 2.54720847308598e-06 1.27360423654299e-06 189 0.999997650886372 4.69822725580204e-06 2.34911362790102e-06 190 0.999995853417506 8.29316498842452e-06 4.14658249421226e-06 191 0.999992453542117 1.50929157665068e-05 7.54645788325342e-06 192 0.99998587734855 2.82453028984513e-05 1.41226514492257e-05 193 0.9999823232807 3.53534386002181e-05 1.76767193001090e-05 194 0.999982354906633 3.52901867346475e-05 1.76450933673237e-05 195 0.999982161226354 3.56775472920966e-05 1.78387736460483e-05 196 0.999977994295869 4.40114082625543e-05 2.20057041312772e-05 197 0.999971295238278 5.74095234444861e-05 2.87047617222430e-05 198 0.999968049340712 6.39013185753663e-05 3.19506592876831e-05 199 0.999971195406461 5.76091870773296e-05 2.88045935386648e-05 200 0.999970364330402 5.92713391961715e-05 2.96356695980858e-05 201 0.999946749890653 0.000106500218694617 5.32501093473083e-05 202 0.999924498063467 0.000151003873066517 7.55019365332585e-05 203 0.999940311541403 0.000119376917193147 5.96884585965734e-05 204 0.999938976208173 0.000122047583653345 6.10237918266727e-05 205 0.999872834123773 0.000254331752452992 0.000127165876226496 206 0.999783926230559 0.000432147538883036 0.000216073769441518 207 0.999600804527664 0.000798390944671653 0.000399195472335826 208 0.999196635603306 0.00160672879338828 0.000803364396694142 209 0.99863206092833 0.00273587814334082 0.00136793907167041 210 0.998150459256664 0.00369908148667242 0.00184954074333621 211 0.997685504239843 0.00462899152031403 0.00231449576015701 212 0.998317224592992 0.00336555081401681 0.00168277540700840 213 0.999822268889704 0.000355462220592655 0.000177731110296327 214 0.999953676648282 9.26467034366133e-05 4.63233517183067e-05 215 0.999880965438234 0.000238069123531522 0.000119034561765761 216 0.999648140745407 0.000703718509186859 0.000351859254593429 217 0.99903763500779 0.00192472998442217 0.000962364992211085 218 0.997478018431437 0.00504396313712528 0.00252198156856264 219 0.99340846085191 0.0131830782961781 0.00659153914808903 220 0.984914032728998 0.0301719345420038 0.0150859672710019 221 0.96804259651257 0.0639148069748582 0.0319574034874291 222 0.936877300546756 0.126245398906488 0.0631226994532441 223 0.867759067801547 0.264481864396907 0.132240932198453 224 0.738816572165209 0.522366855669582 0.261183427834791 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 115 0.550239234449761 NOK 5% type I error level 131 0.626794258373206 NOK 10% type I error level 140 0.669856459330144 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/28/t1262021332ghmyfyued1fxe2e/107dpi1262021262.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262021332ghmyfyued1fxe2e/107dpi1262021262.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262021332ghmyfyued1fxe2e/1apew1262021262.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262021332ghmyfyued1fxe2e/1apew1262021262.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262021332ghmyfyued1fxe2e/2pelp1262021262.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262021332ghmyfyued1fxe2e/2pelp1262021262.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262021332ghmyfyued1fxe2e/3ijxu1262021262.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262021332ghmyfyued1fxe2e/3ijxu1262021262.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262021332ghmyfyued1fxe2e/45o681262021262.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262021332ghmyfyued1fxe2e/45o681262021262.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262021332ghmyfyued1fxe2e/5irm91262021262.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262021332ghmyfyued1fxe2e/5irm91262021262.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262021332ghmyfyued1fxe2e/6ashq1262021262.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262021332ghmyfyued1fxe2e/6ashq1262021262.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262021332ghmyfyued1fxe2e/7205c1262021262.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262021332ghmyfyued1fxe2e/7205c1262021262.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262021332ghmyfyued1fxe2e/8issd1262021262.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262021332ghmyfyued1fxe2e/8issd1262021262.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262021332ghmyfyued1fxe2e/9tei01262021262.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262021332ghmyfyued1fxe2e/9tei01262021262.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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