CaseStatistiek - Multipele Regressie

*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 17:22:47 -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/30/t1262132822ccdl2j2jucgoga3.htm/, Retrieved Wed, 30 Dec 2009 01:27:16 +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/30/t1262132822ccdl2j2jucgoga3.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:

CaseStatistiek - Multipele Regressie

Dataseries X:

» Textbox « » Textfile « » CSV «

15 2.1 14.4 2.1 13.5 2.6 12.8 2.6 12.3 2.7 12.2 2.5 14.5 2.4 17.2 1.9 18 2.2 18.1 1.9 18 2 18.3 2.2 18.7 2.5 18.6 2.5 18.3 2.7 17.9 2.6 17.4 2.3 17.4 2 20.1 2.3 23.2 2.9 24.2 2.5 24.2 2.5 23.9 2.3 23.8 2.5 23.8 2.3 23.3 2.4 22.4 2.2 21.5 2.4 20.5 2.6 19.9 2.8 22 2.8 24.9 2.5 25.7 2.5 25.3 2.2 24.4 2.1 23.8 1.9 23.5 1.9 23 1.7 22.2 1.7 21.4 1.6 20.3 1.4 19.5 1.1 21.7 0.8 24.7 0.9 25.3 1 24.9 1 24.1 1.1 23.4 1.3 23.1 1.4 22.4 1.4 21.3 1.6 20.3 2 19.3 2.1 18.7 1.9 21 1.5 24 1.2 24.8 1.5 24.2 2.2 23.3 2.1 22.7 2.1 22.3 2.1 21.8 1.9 21.2 1.3 20.5 1.1 19.7 1.4 19.2 1.6 21.2 1.9 23.9 1.7 24.8 1.6 24.2 1.2 23 1.3 22.2 0.9 21.8 0.5 21.2 0.8 20.5 1 19.7 1.3 19 1.3 18.4 1.2 20.7 1.2 24.5 1 26 0.8 25.2 0.7 24.1 0.6 23.7 0.7 23.5 1 23.1 1 22.7 1.3 22.5 1.1 21.7 0.8 20.5 0.7 21.9 0.7 22.9 0.9 21.5 1.3 19 1.4 17 1.6 16.1 2.1 15.9 0.3 15.7 2.1 15.1 2.5 14.8 2.3 14.3 2.4 14.5 3 18.9 1.7 21.6 3.5 20.4 4 17.9 3.7 15.7 3.7 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 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y(Werkloosheid)[t] = + 21.9148726937865 -0.898005613316569`X(inflatie)`[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) 21.9148726937865 0.435075 50.3704 0 0 `X(inflatie)` -0.898005613316569 0.195376 -4.5963 7e-06 4e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.301031438385647 R-squared 0.0906199268965314 Adjusted R-squared 0.0863303982498169 F-TEST (value) 21.1258472340407 F-TEST (DF numerator) 1 F-TEST (DF denominator) 212 p-value 7.38328562854829e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.01212920578624 Sum Squared Residuals 1923.4595386983 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 15 20.0290609058211 -5.02906090582111 2 14.4 20.0290609058216 -5.62906090582164 3 13.5 19.5800580991634 -6.08005809916335 4 12.8 19.5800580991634 -6.78005809916335 5 12.3 19.4902575378317 -7.1902575378317 6 12.2 19.669858660495 -7.46985866049501 7 14.5 19.7596592218267 -5.25965922182667 8 17.2 20.2086620284850 -3.00866202848495 9 18 19.9392603444900 -1.93926034448998 10 18.1 20.2086620284850 -2.10866202848495 11 18 20.1188614671533 -2.11886146715329 12 18.3 19.9392603444900 -1.63926034448998 13 18.7 19.669858660495 -0.96985866049501 14 18.6 19.669858660495 -1.06985866049501 15 18.3 19.4902575378317 -1.19025753783169 16 17.9 19.5800580991634 -1.68005809916335 17 17.4 19.8494597831583 -2.44945978315832 18 17.4 20.1188614671533 -2.71886146715329 19 20.1 19.8494597831583 0.250540216841679 20 23.2 19.3106564151684 3.88934358483162 21 24.2 19.669858660495 4.53014133950499 22 24.2 19.669858660495 4.53014133950499 23 23.9 19.8494597831583 4.05054021684168 24 23.8 19.669858660495 4.13014133950499 25 23.8 19.8494597831583 3.95054021684168 26 23.3 19.7596592218267 3.54034077817334 27 22.4 19.9392603444900 2.46073965551002 28 21.5 19.7596592218267 1.74034077817333 29 20.5 19.5800580991634 0.919941900836649 30 19.9 19.4004569765000 0.49954302349996 31 22 19.4004569765000 2.59954302349996 32 24.9 19.669858660495 5.23014133950499 33 25.7 19.669858660495 6.03014133950499 34 25.3 19.9392603444900 5.36073965551002 35 24.4 20.0290609058216 4.37093909417836 36 23.8 20.2086620284850 3.59133797151505 37 23.5 20.2086620284850 3.29133797151505 38 23 20.3882631511483 2.61173684885174 39 22.2 20.3882631511483 1.81173684885174 40 21.4 20.4780637124799 0.921936287520079 41 20.3 20.6576648351432 -0.357664835143233 42 19.5 20.9270665191382 -1.42706651913820 43 21.7 21.1964682031332 0.503531796866824 44 24.7 21.1066676418015 3.59333235819848 45 25.3 21.0168670804699 4.28313291953014 46 24.9 21.0168670804699 3.88313291953014 47 24.1 20.9270665191382 3.1729334808618 48 23.4 20.7474653964749 2.65253460352511 49 23.1 20.6576648351432 2.44233516485677 50 22.4 20.6576648351432 1.74233516485677 51 21.3 20.4780637124799 0.821936287520081 52 20.3 20.1188614671533 0.181138532846708 53 19.3 20.0290609058216 -0.729060905821635 54 18.7 20.2086620284849 -1.50866202848495 55 21 20.5678642738116 0.432135726188423 56 24 20.8372659578065 3.16273404219345 57 24.8 20.5678642738116 4.23213572618842 58 24.2 19.9392603444900 4.26073965551002 59 23.3 20.0290609058216 3.27093909417836 60 22.7 20.0290609058216 2.67093909417836 61 22.3 20.0290609058216 2.27093909417836 62 21.8 20.2086620284849 1.59133797151505 63 21.2 20.7474653964749 0.452534603525109 64 20.5 20.9270665191382 -0.427066519138204 65 19.7 20.6576648351432 -0.957664835143234 66 19.2 20.4780637124799 -1.27806371247992 67 21.2 20.2086620284849 0.99133797151505 68 23.9 20.3882631511483 3.51173684885174 69 24.8 20.4780637124799 4.32193628752008 70 24.2 20.8372659578065 3.36273404219345 71 23 20.7474653964749 2.25253460352511 72 22.2 21.1066676418015 1.09333235819848 73 21.8 21.4658698871281 0.334130112871856 74 21.2 21.1964682031332 0.00353179686682453 75 20.5 21.0168670804699 -0.516867080469861 76 19.7 20.7474653964749 -1.04746539647489 77 19 20.7474653964749 -1.74746539647489 78 18.4 20.8372659578065 -2.43726595780655 79 20.7 20.8372659578065 -0.137265957806548 80 24.5 21.0168670804699 3.48313291953014 81 26 21.1964682031332 4.80353179686683 82 25.2 21.2862687644648 3.91373123553517 83 24.1 21.3760693257965 2.72393067420351 84 23.7 21.2862687644648 2.41373123553517 85 23.5 21.0168670804699 2.48313291953014 86 23.1 21.0168670804699 2.08313291953014 87 22.7 20.7474653964749 1.95253460352511 88 22.5 20.9270665191382 1.57293348086180 89 21.7 21.1964682031332 0.503531796866824 90 20.5 21.2862687644648 -0.786268764464832 91 21.9 21.2862687644648 0.613731235535167 92 22.9 21.1066676418015 1.79333235819848 93 21.5 20.7474653964749 0.75253460352511 94 19 20.6576648351432 -1.65766483514323 95 17 20.4780637124799 -3.47806371247992 96 16.1 20.0290609058216 -3.92906090582163 97 15.9 21.6454710097915 -5.74547100979146 98 15.7 20.0290609058216 -4.32906090582164 99 15.1 19.669858660495 -4.56985866049501 100 14.8 19.8494597831583 -5.04945978315832 101 14.3 19.7596592218267 -5.45965922182666 102 14.5 19.2208558538367 -4.72085585383672 103 18.9 20.3882631511483 -1.48826315114826 104 21.6 18.7718530471784 2.82814695282156 105 20.4 18.3228502405202 2.07714975947984 106 17.9 18.5922519245151 -0.692251924515128 107 15.7 18.5922519245151 -2.89225192451513 108 14.5 19.2208558538367 -4.72085585383672 109 14 19.4902575378317 -5.4902575378317 110 13.9 19.669858660495 -5.76985866049501 111 14.4 19.9392603444900 -5.53926034448998 112 15.8 19.3106564151684 -3.51065641516838 113 15.6 19.1310552925051 -3.53105529250507 114 14.7 19.2208558538367 -4.52085585383672 115 16.7 19.4004569765000 -2.70045697650004 116 17.9 19.669858660495 -1.76985866049501 117 18.7 20.2086620284849 -1.50866202848495 118 20.1 20.2086620284849 -0.108662028484948 119 19.5 20.2984625898166 -0.798462589816606 120 19.4 20.1188614671533 -0.718861467153294 121 18.6 19.5800580991634 -0.98005809916335 122 17.8 19.669858660495 -1.86985866049501 123 17.1 19.669858660495 -2.56985866049501 124 16.5 20.4780637124799 -3.97806371247992 125 15.5 20.6576648351432 -5.15766483514323 126 14.9 21.1964682031332 -6.29646820313317 127 18.6 20.9270665191382 -2.32706651913820 128 19.1 20.7474653964749 -1.64746539647489 129 18.8 20.8372659578065 -2.03726595780655 130 18.2 20.7474653964749 -2.54746539647489 131 18 20.9270665191382 -2.92706651913820 132 19 20.7474653964749 -1.74746539647489 133 20.7 20.8372659578065 -0.137265957806548 134 21.2 20.4780637124799 0.72193628752008 135 20.7 20.3882631511483 0.311736848851736 136 19.6 20.5678642738116 -0.967864273811575 137 18.6 21.1066676418015 -2.50666764180152 138 18.7 20.5678642738116 -1.86786427381158 139 23.8 20.6576648351432 3.14233516485677 140 24.9 20.4780637124799 4.42193628752008 141 24.8 20.3882631511483 4.41173684885174 142 23.8 20.6576648351432 3.14233516485677 143 22.3 20.2984625898166 2.00153741018339 144 21.7 20.3882631511483 1.31173684885174 145 20.7 20.6576648351432 0.0423351648567656 146 19.7 20.8372659578065 -1.13726595780655 147 18.4 21.0168670804699 -2.61686708046986 148 17.4 20.3882631511483 -2.98826315114826 149 17 19.7596592218267 -2.75965922182667 150 18 20.1188614671533 -2.11886146715329 151 23.8 20.0290609058216 3.77093909417836 152 25.5 20.1188614671533 5.38113853284671 153 25.6 20.2984625898166 5.3015374101834 154 23.7 19.4902575378317 4.20974246216830 155 22 19.8494597831583 2.15054021684168 156 21.3 20.2086620284849 1.09133797151505 157 20.7 20.1188614671533 0.581138532846707 158 20.4 19.8494597831583 0.550540216841676 159 20.3 19.4004569765000 0.899543023499963 160 20.4 19.7596592218267 0.640340778173333 161 19.8 19.8494597831583 -0.0494597831583216 162 19.5 19.4902575378317 0.00974246216830549 163 23.1 19.4902575378317 3.60974246216831 164 23.5 19.3106564151684 4.18934358483162 165 23.5 19.2208558538367 4.27914414616328 166 22.9 19.9392603444900 2.96073965551002 167 21.9 19.8494597831583 2.05054021684168 168 21.5 19.4004569765000 2.09954302349996 169 20.5 19.4004569765000 1.09954302349996 170 20.2 19.4004569765000 0.799543023499961 171 19.4 19.9392603444900 -0.53926034448998 172 19.2 19.5800580991634 -0.380058099163352 173 18.8 19.4004569765000 -0.600456976500037 174 18.8 19.669858660495 -0.869858660495008 175 22.6 19.7596592218267 2.84034077817334 176 23.3 19.8494597831583 3.45054021684168 177 23 20.2086620284850 2.79133797151505 178 21.4 20.3882631511483 1.01173684885174 179 19.9 20.1188614671533 -0.218861467153294 180 18.8 20.0290609058216 -1.22906090582163 181 18.6 20.3882631511483 -1.78826315114826 182 18.4 20.2984625898166 -1.89846258981661 183 18.6 20.2984625898166 -1.69846258981660 184 19.9 20.2984625898166 -0.398462589816608 185 19.2 20.7474653964749 -1.54746539647489 186 18.4 20.7474653964749 -2.34746539647489 187 21.1 20.7474653964749 0.352534603525111 188 20.5 20.8372659578065 -0.337265957806547 189 19.1 20.6576648351432 -1.55766483514323 190 18.1 19.9392603444900 -1.83926034448998 191 17 19.3106564151684 -2.31065641516838 192 17.1 19.1310552925051 -2.03105529250507 193 17.4 18.7718530471784 -1.37185304717844 194 16.8 18.6820524858468 -1.88205248584678 195 15.3 17.9636479951935 -2.66364799519353 196 14.3 18.2330496791885 -3.9330496791885 197 13.4 17.3350440658719 -3.93504406587193 198 15.3 16.7064401365503 -1.40644013655033 199 22.1 16.6166395752187 5.48336042478133 200 23.7 17.0656423818770 6.63435761812304 201 22.2 16.9758418205453 5.2241581794547 202 19.5 17.6044457498669 1.89555425013310 203 16.6 19.0412547311734 -2.44125473117341 204 17.3 19.4902575378317 -2.19025753783169 205 19.8 20.0290609058216 -0.229060905821635 206 21.2 20.2086620284849 0.99133797151505 207 21.5 21.3760693257965 0.123930674203512 208 20.6 21.2862687644648 -0.68626876446483 209 19.1 22.0944738164497 -2.99447381644974 210 19.6 22.812878307103 -3.212878307103 211 23.5 23.4414822364246 0.0585177635754046 212 24 22.5434766231080 1.45652337689197 213 23.2 22.812878307103 0.387121692897002 214 21.2 22.7230777457713 -1.52307774577134 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.00494777123011235 0.00989554246022469 0.995052228769888 6 0.00470829246491591 0.00941658492983182 0.995291707535084 7 0.00261603570011133 0.00523207140022266 0.997383964299889 8 0.00207114303402469 0.00414228606804938 0.997928856965975 9 0.0208010092299449 0.0416020184598898 0.979198990770055 10 0.0108732355682521 0.0217464711365042 0.989126764431748 11 0.0065321659565697 0.0130643319131394 0.99346783404343 12 0.0124762100791447 0.0249524201582893 0.987523789920855 13 0.088760725930664 0.177521451861328 0.911239274069336 14 0.165263106411268 0.330526212822535 0.834736893588732 15 0.248628455025438 0.497256910050875 0.751371544974562 16 0.249105894390147 0.498211788780293 0.750894105609853 17 0.201452947436843 0.402905894873685 0.798547052563157 18 0.153216168964185 0.306432337928370 0.846783831035815 19 0.197603123971221 0.395206247942442 0.802396876028779 20 0.579495800340597 0.841008399318807 0.420504199659403 21 0.828507623069147 0.342984753861706 0.171492376930853 22 0.931352539012438 0.137294921975125 0.0686474609875624 23 0.969700605800192 0.0605987883996151 0.0302993941998075 24 0.98428562199623 0.0314287560075402 0.0157143780037701 25 0.991807198506433 0.016385602987135 0.0081928014935675 26 0.994386525586464 0.0112269488270726 0.00561347441353631 27 0.994940963440368 0.0101180731192637 0.00505903655963183 28 0.994100855959331 0.0117982880813371 0.00589914404066853 29 0.99194131677058 0.0161173664588408 0.0080586832294204 30 0.988547958414795 0.0229040831704105 0.0114520415852052 31 0.986808642971152 0.0263827140576956 0.0131913570288478 32 0.993237233480139 0.0135255330397225 0.00676276651986124 33 0.997422593924616 0.00515481215076816 0.00257740607538408 34 0.999006200293367 0.00198759941326579 0.000993799706632895 35 0.999420310648204 0.00115937870359115 0.000579689351795573 36 0.999546101241589 0.000907797516821791 0.000453898758410896 37 0.999568661046438 0.000862677907123252 0.000431338953561626 38 0.999489571106204 0.00102085778759308 0.00051042889379654 39 0.99929421127198 0.00141157745604031 0.000705788728020154 40 0.998955424140182 0.00208915171963588 0.00104457585981794 41 0.99848955225023 0.00302089549954108 0.00151044774977054 42 0.997999223165738 0.00400155366852454 0.00200077683426227 43 0.997133977300467 0.00573204539906542 0.00286602269953271 44 0.99712424801715 0.00575150396570225 0.00287575198285112 45 0.997369804808968 0.00526039038206388 0.00263019519103194 46 0.997257154229396 0.00548569154120826 0.00274284577060413 47 0.996755982028332 0.00648803594333677 0.00324401797166839 48 0.99595865556035 0.00808268887930082 0.00404134443965041 49 0.994909220804818 0.0101815583903641 0.00509077919518206 50 0.993288934343183 0.0134221313136336 0.0067110656568168 51 0.991000180903412 0.0179996381931762 0.0089998190965881 52 0.987980388365386 0.0240392232692271 0.0120196116346135 53 0.984531649656379 0.0309367006872426 0.0154683503436213 54 0.981733221738234 0.0365335565235316 0.0182667782617658 55 0.97654884586219 0.0469023082756178 0.0234511541378089 56 0.973807001402116 0.0523859971957682 0.0261929985978841 57 0.975715761387206 0.0485684772255876 0.0242842386127938 58 0.980007245833884 0.0399855083322316 0.0199927541661158 59 0.979763140738933 0.0404737185221335 0.0202368592610667 60 0.977656444332846 0.0446871113343074 0.0223435556671537 61 0.974230426019863 0.0515391479602749 0.0257695739801375 62 0.968485421621064 0.0630291567578717 0.0315145783789358 63 0.961492819098069 0.0770143618038628 0.0385071809019314 64 0.95563947381385 0.0887210523723011 0.0443605261861505 65 0.949419024162181 0.101161951675637 0.0505809758378187 66 0.942863745317546 0.114272509364907 0.0571362546824535 67 0.930886942945487 0.138226114109025 0.0691130570545126 68 0.931224587922063 0.137550824155874 0.0687754120779368 69 0.938865570553497 0.122268858893006 0.061134429446503 70 0.93636089567219 0.127278208655621 0.0636391043278104 71 0.927573540608996 0.144852918782008 0.072426459391004 72 0.915507004195922 0.168985991608157 0.0844929958040783 73 0.904828328630184 0.190343342739632 0.095171671369816 74 0.891808663035816 0.216382673928369 0.108191336964184 75 0.878426952662169 0.243146094675662 0.121573047337831 76 0.865347544300204 0.269304911399592 0.134652455699796 77 0.857775737363683 0.284448525272633 0.142224262636317 78 0.858902424619923 0.282195150760154 0.141097575380077 79 0.837965927882270 0.324068144235461 0.162034072117730 80 0.839412527803076 0.321174944393849 0.160587472196924 81 0.864451210677797 0.271097578644407 0.135548789322203 82 0.871865734753436 0.256268530493128 0.128134265246564 83 0.8648108034775 0.270378393044999 0.135189196522499 84 0.855131267577665 0.289737464844669 0.144868732422335 85 0.846216978955464 0.307566042089072 0.153783021044536 86 0.833426164083704 0.333147671832591 0.166573835916296 87 0.81894111729009 0.362117765419818 0.181058882709909 88 0.801010939386938 0.397978121226125 0.198989060613062 89 0.779706428539186 0.440587142921629 0.220293571460814 90 0.76388216190103 0.47223567619794 0.23611783809897 91 0.740620856656252 0.518758286687496 0.259379143343748 92 0.72288403202201 0.554231935955978 0.277115967977989 93 0.695231484777525 0.60953703044495 0.304768515222475 94 0.679072347693444 0.641855304613111 0.320927652306556 95 0.700539325603797 0.598921348792407 0.299460674396203 96 0.727243694238393 0.545512611523214 0.272756305761607 97 0.829815660819218 0.340368678361565 0.170184339180782 98 0.855867047218285 0.288265905563430 0.144132952781715 99 0.881249255556591 0.237501488886818 0.118750744443409 100 0.911634129406621 0.176731741186757 0.0883658705933786 101 0.940714299308367 0.118571401383266 0.0592857006916329 102 0.952933956867196 0.0941320862656078 0.0470660431328039 103 0.94527586117924 0.109448277641520 0.0547241388207601 104 0.948785033724855 0.102429932550291 0.0512149662751454 105 0.946826746212502 0.106346507574996 0.0531732537874982 106 0.935801425623983 0.128397148752034 0.0641985743760168 107 0.932904563171685 0.13419087365663 0.067095436828315 108 0.94784298135463 0.104314037290740 0.0521570186453699 109 0.967224275899714 0.0655514482005725 0.0327757241002862 110 0.982158862409947 0.0356822751801056 0.0178411375900528 111 0.99035839981855 0.0192832003628988 0.0096416001814494 112 0.991114244422763 0.0177715111544751 0.00888575557723753 113 0.991926533987366 0.0161469320252677 0.00807346601263386 114 0.994401236231817 0.0111975275363655 0.00559876376818273 115 0.994124444037273 0.0117511119254546 0.00587555596272728 116 0.992951191719527 0.0140976165609464 0.00704880828047319 117 0.9913580803608 0.0172838392783983 0.00864191963919916 118 0.98872641620994 0.0225471675801186 0.0112735837900593 119 0.985670975030938 0.0286580499381243 0.0143290249690621 120 0.981839307717423 0.0363213845651532 0.0181606922825766 121 0.977537920295113 0.0449241594097749 0.0224620797048874 122 0.974168471489927 0.0516630570201464 0.0258315285100732 123 0.972844865389503 0.054310269220995 0.0271551346104975 124 0.978360472932043 0.043279054135913 0.0216395270679565 125 0.98804941042682 0.0239011791463589 0.0119505895731795 126 0.996288825646322 0.00742234870735574 0.00371117435367787 127 0.995978515199297 0.00804296960140622 0.00402148480070311 128 0.995151652174814 0.00969669565037134 0.00484834782518567 129 0.994495533739703 0.0110089325205938 0.00550446626029688 130 0.994298674093204 0.0114026518135919 0.00570132590679593 131 0.994575773629114 0.0108484527417726 0.00542422637088629 132 0.993615283202744 0.0127694335945130 0.00638471679725652 133 0.991523029084595 0.0169539418308092 0.0084769709154046 134 0.988944882140195 0.0221102357196108 0.0110551178598054 135 0.985557797953932 0.0288844040921358 0.0144422020460679 136 0.981989661408099 0.0360206771838022 0.0180103385919011 137 0.981453979323313 0.0370920413533738 0.0185460206766869 138 0.979057964741858 0.041884070516284 0.020942035258142 139 0.979608531778838 0.0407829364423235 0.0203914682211617 140 0.985524518358477 0.0289509632830467 0.0144754816415234 141 0.99006705937215 0.0198658812557000 0.00993294062784999 142 0.99070163022823 0.0185967395435390 0.00929836977176949 143 0.989233485812087 0.0215330283758259 0.0107665141879129 144 0.986562610014756 0.0268747799704881 0.0134373899852441 145 0.982369396569098 0.0352612068618034 0.0176306034309017 146 0.978030561819929 0.043938876360142 0.021969438180071 147 0.977267472919817 0.0454650541603653 0.0227325270801827 148 0.97841313688384 0.0431737262323205 0.0215868631161603 149 0.979154682662613 0.0416906346747740 0.0208453173373870 150 0.97735256754931 0.04529486490138 0.02264743245069 151 0.981062166731108 0.0378756665377839 0.0189378332688920 152 0.991087246866025 0.017825506267949 0.0089127531339745 153 0.996293268319233 0.00741346336153452 0.00370673168076726 154 0.997641326972802 0.00471734605439698 0.00235867302719849 155 0.99729018835969 0.00541962328062015 0.00270981164031007 156 0.99637254950368 0.00725490099263925 0.00362745049631962 157 0.994969865704866 0.0100602685902688 0.00503013429513438 158 0.993071792608312 0.0138564147833763 0.00692820739168815 159 0.990733780971392 0.0185324380572164 0.0092662190286082 160 0.987534574483236 0.0249308510335278 0.0124654255167639 161 0.983132144205455 0.0337357115890899 0.0168678557945450 162 0.97749684662142 0.0450063067571593 0.0225031533785797 163 0.981490538510126 0.0370189229797477 0.0185094614898738 164 0.987577405910706 0.0248451881785885 0.0124225940892942 165 0.992389142881295 0.0152217142374103 0.00761085711870517 166 0.993352871089336 0.0132942578213289 0.00664712891066447 167 0.992676517738786 0.014646964522428 0.007323482261214 168 0.991898551010486 0.0162028979790288 0.0081014489895144 169 0.989426583962835 0.0211468320743304 0.0105734160371652 170 0.985878677877233 0.0282426442455337 0.0141213221227669 171 0.980480748320655 0.0390385033586898 0.0195192516793449 172 0.97332921913451 0.0533415617309785 0.0266707808654892 173 0.964221479937325 0.0715570401253502 0.0357785200626751 174 0.952970845051353 0.0940583098972943 0.0470291549486471 175 0.957072894126625 0.0858542117467509 0.0429271058733754 176 0.968357000226151 0.0632859995476979 0.0316429997738489 177 0.973776446632156 0.0524471067356885 0.0262235533678443 178 0.968478499857729 0.0630430002845421 0.0315215001422711 179 0.957435087708729 0.0851298245825426 0.0425649122912713 180 0.94350249603874 0.112995007922521 0.0564975039612606 181 0.928196455902927 0.143607088194146 0.071803544097073 182 0.910703192114179 0.178593615771643 0.0892968078858214 183 0.888469644224284 0.223060711551431 0.111530355775716 184 0.85782210520735 0.284355789585301 0.142177894792650 185 0.824512169389831 0.350975661220337 0.175487830610169 186 0.7969404952444 0.406119009511201 0.203059504755600 187 0.757723384815067 0.484553230369865 0.242276615184933 188 0.707926470891642 0.584147058216716 0.292073529108358 189 0.656057268720878 0.687885462558245 0.343942731279122 190 0.607471531810602 0.785056936378796 0.392528468189398 191 0.573395648353159 0.853208703293682 0.426604351646841 192 0.53336334560418 0.93327330879164 0.46663665439582 193 0.480157789350691 0.960315578701382 0.519842210649309 194 0.442422720445915 0.88484544089183 0.557577279554085 195 0.453576292015821 0.907152584031642 0.546423707984179 196 0.566187761413843 0.867624477172314 0.433812238586157 197 0.780505299328097 0.438989401343807 0.219494700671903 198 0.880582541328337 0.238834917343326 0.119417458671663 199 0.87038021549811 0.25923956900378 0.12961978450189 200 0.93884341167794 0.122313176644121 0.0611565883220606 201 0.980650993657963 0.0386980126840744 0.0193490063420372 202 0.98413332174336 0.0317333565132808 0.0158666782566404 203 0.976715682625749 0.0465686347485024 0.0232843173742512 204 0.972662298133314 0.0546754037333713 0.0273377018666856 205 0.945947523918826 0.108104952162348 0.0540524760811742 206 0.91211594814021 0.175768103719579 0.0878840518597895 207 0.85868920115578 0.282621597688438 0.141310798844219 208 0.78612324565489 0.42775350869022 0.21387675434511 209 0.695841315945763 0.608317368108474 0.304158684054237 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 27 0.131707317073171 NOK 5% type I error level 107 0.521951219512195 NOK 10% type I error level 126 0.614634146341463 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

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

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

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