*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Thu, 19 Nov 2009 06:57:06 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/19/t1258639081gobe752f93qazz2.htm/, Retrieved Thu, 19 Nov 2009 14:58:19 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Nov/19/t1258639081gobe752f93qazz2.htm/}, year = {2009}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

3.88 153.3 3.98 154.5 3.29 155.2 2.88 156.9 3.22 157 3.62 157.4 3.82 157.2 3.54 157.5 2.53 158 2.22 158.5 2.85 159 2.78 159.3 2.28 160 2.26 160.8 2.71 161.9 2.77 162.5 2.77 162.7 2.64 162.8 2.56 162.9 2.07 163 2.32 164 2.16 164.7 2.23 164.8 2.4 164.9 2.84 165 2.77 165.8 2.93 166.1 2.91 167.2 2.69 167.7 2.38 168.3 2.58 168.6 3.19 168.9 2.82 169.1 2.72 169.5 2.53 169.6 2.7 169.7 2.42 169.8 2.5 170.4 2.31 170.9 2.41 171.9 2.56 171.9 2.76 172 2.71 172 2.44 172.4 2.46 173 2.12 173.7 1.99 173.8 1.86 173.8 1.88 173.9 1.82 174.6 1.74 175 1.71 175.9 1.38 176 1.27 175.1 1.19 175.6 1.28 175.9 1.19 176.7 1.22 176.1 1.47 176.1 1.46 176.2 1.96 176.3 1.88 177.8 2.03 178.5 2.04 179.4 1.9 179.5 1.8 179.6 1.92 179.7 1.92 179.7 1.97 179.8 2.46 179.9 2.36 180.2 2.53 180.4 2.31 180.4 1.98 181.3 1.46 181.9 1.26 182.5 1.58 182.7 1.74 183.1 1.89 183.6 1.85 183.7 1.62 183.8 1.3 183.9 1.42 184.1 1.15 184.4 0.42 184.5 0.74 185.9 1.02 186.6 1.51 187.6 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[t] = + 2.46573628773672 -0.00180117407981777X[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) 2.46573628773672 0.547683 4.5021 1.1e-05 5e-06 X -0.00180117407981777 0.002751 -0.6547 0.513324 0.256662 Multiple Linear Regression - Regression Statistics Multiple R 0.0438997676878124 R-squared 0.0019271896030439 Adjusted R-squared -0.00256863386721262 F-TEST (value) 0.428662205220865 F-TEST (DF numerator) 1 F-TEST (DF denominator) 222 p-value 0.513323876544774 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.02226417409436 Sum Squared Residuals 231.995337243375 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3.88 2.18961630130065 1.69038369869935 2 3.98 2.18745489240488 1.79254510759513 3 3.29 2.186194070549 1.103805929451 4 2.88 2.18313207461331 0.696867925386689 5 3.22 2.18295195720533 1.03704804279467 6 3.62 2.1822314875734 1.4377685124266 7 3.82 2.18259172238937 1.63740827761063 8 3.54 2.18205137016542 1.35794862983458 9 2.53 2.18115078312551 0.348849216874488 10 2.22 2.1802501960856 0.0397498039143977 11 2.85 2.17934960904569 0.670650390954306 12 2.78 2.17880925682175 0.601190743178252 13 2.28 2.17754843496588 0.102451565034124 14 2.26 2.17610749570202 0.0838925042979782 15 2.71 2.17412620421422 0.535873795785778 16 2.77 2.17304549976633 0.596954500233669 17 2.77 2.17268526495037 0.597314735049632 18 2.64 2.17250514754239 0.467494852457614 19 2.56 2.17232503013440 0.387674969865596 20 2.07 2.17214491272642 -0.102144912726423 21 2.32 2.17034373864660 0.149656261353395 22 2.16 2.16908291679073 -0.00908291679073216 23 2.23 2.16890279938275 0.0610972006172495 24 2.4 2.16872268197477 0.231277318025231 25 2.84 2.16854256456679 0.671457435433213 26 2.77 2.16710162530293 0.602898374697067 27 2.93 2.16656127307899 0.763438726921013 28 2.91 2.16457998159119 0.745420018408812 29 2.69 2.16367939455128 0.526320605448721 30 2.38 2.16259869010339 0.217401309896612 31 2.58 2.16205833787944 0.417941662120557 32 3.19 2.16151798565550 1.02848201434450 33 2.82 2.16115775083953 0.658842249160466 34 2.72 2.16043728120761 0.559562718792393 35 2.53 2.16025716379963 0.369742836200375 36 2.7 2.16007704639164 0.539922953608357 37 2.42 2.15989692898366 0.260103071016338 38 2.5 2.15881622453577 0.341183775464229 39 2.31 2.15791563749586 0.152084362504138 40 2.41 2.15611446341604 0.253885536583956 41 2.56 2.15611446341604 0.403885536583956 42 2.76 2.15593434600806 0.604065653991937 43 2.71 2.15593434600806 0.554065653991937 44 2.44 2.15521387637614 0.284786123623865 45 2.46 2.15413317192824 0.305866828071755 46 2.12 2.15287235007237 -0.0328723500723722 47 1.99 2.15269223266439 -0.162692232664391 48 1.86 2.15269223266439 -0.292692232664390 49 1.88 2.15251211525641 -0.272512115256409 50 1.82 2.15125129340054 -0.331251293400536 51 1.74 2.15053082376861 -0.410530823768609 52 1.71 2.14890976709677 -0.438909767096773 53 1.38 2.14872964968879 -0.768729649688792 54 1.27 2.15035070636063 -0.880350706360628 55 1.19 2.14945011932072 -0.959450119320719 56 1.28 2.14890976709677 -0.868909767096773 57 1.19 2.14746882783292 -0.95746882783292 58 1.22 2.14854953228081 -0.92854953228081 59 1.47 2.14854953228081 -0.67854953228081 60 1.46 2.14836941487283 -0.688369414872828 61 1.96 2.14818929746485 -0.188189297464846 62 1.88 2.14548753634512 -0.265487536345120 63 2.03 2.14422671448925 -0.114226714489247 64 2.04 2.14260565781741 -0.102605657817411 65 1.9 2.14242554040943 -0.242425540409429 66 1.8 2.14224542300145 -0.342245423001447 67 1.92 2.14206530559347 -0.222065305593466 68 1.92 2.14206530559347 -0.222065305593466 69 1.97 2.14188518818548 -0.171885188185484 70 2.46 2.14170507077750 0.318294929222498 71 2.36 2.14116471855356 0.218835281446443 72 2.53 2.14080448373759 0.389195516262407 73 2.31 2.14080448373759 0.169195516262407 74 1.98 2.13918342706576 -0.159183427065757 75 1.46 2.13810272261787 -0.678102722617867 76 1.26 2.13702201816998 -0.877022018169976 77 1.58 2.13666178335401 -0.556661783354012 78 1.74 2.13594131372209 -0.395941313722085 79 1.89 2.13504072668218 -0.245040726682176 80 1.85 2.13486060927419 -0.284860609274195 81 1.62 2.13468049186621 -0.514680491866213 82 1.3 2.13450037445823 -0.834500374458231 83 1.42 2.13414013964227 -0.714140139642268 84 1.15 2.13359978741832 -0.983599787418322 85 0.42 2.13341967001034 -1.71341967001034 86 0.74 2.13089802629860 -1.39089802629860 87 1.02 2.12963720444272 -1.10963720444272 88 1.51 2.12783603036291 -0.617836030362905 89 1.86 2.12747579554694 -0.267475795546942 90 1.59 2.12729567813896 -0.53729567813896 91 1.03 2.12711556073098 -1.09711556073098 92 0.44 2.12657520850703 -1.68657520850703 93 0.82 2.12639509109905 -1.30639509109905 94 0.86 2.12621497369107 -1.26621497369107 95 0.58 2.12621497369107 -1.54621497369107 96 0.59 2.12603485628309 -1.53603485628309 97 0.95 2.12603485628309 -1.17603485628309 98 0.98 2.12459391701923 -1.14459391701923 99 1.23 2.12351321257134 -0.893513212571343 100 1.17 2.12009098181969 -0.95009098181969 101 0.84 2.1190102773718 -1.27901027737180 102 0.74 2.11810969033189 -1.37810969033189 103 0.65 2.11720910329198 -1.46720910329198 104 0.91 2.11648863366005 -1.20648863366005 105 1.19 2.11594828143611 -0.925948281436108 106 1.3 2.11468745958024 -0.814687459580235 107 1.53 2.11468745958024 -0.584687459580235 108 1.94 2.11468745958024 -0.174687459580236 109 1.79 2.11468745958024 -0.324687459580235 110 1.95 2.11360675513234 -0.163606755132345 111 2.26 2.11270616809244 0.147293831907564 112 2.04 2.11234593327647 -0.0723459332764724 113 2.16 2.11234593327647 0.0476540667235277 114 2.75 2.11234593327647 0.637654066723528 115 2.79 2.11234593327647 0.677654066723528 116 2.88 2.11090499401262 0.769095005987382 117 3.36 2.10964417215675 1.25035582784325 118 2.97 2.1091038199328 0.8608961800672 119 3.1 2.10874358511684 0.991256414883163 120 2.49 2.10820323289289 0.381796767107109 121 2.2 2.10802311548491 0.0919768845150904 122 2.25 2.10640205881307 0.143597941186926 123 2.09 2.10550147177316 -0.0155014717731650 124 2.79 2.1031599454694 0.686840054530598 125 3.14 2.10153888879757 1.03846111120243 126 2.93 2.10027806694169 0.829721933058307 127 2.65 2.09919736249380 0.550802637506197 128 2.67 2.09919736249380 0.570802637506197 129 2.26 2.09829677545389 0.161703224546106 130 2.35 2.09811665804591 0.251883341954088 131 2.13 2.09775642322995 0.0322435767700515 132 2.18 2.09739618841398 0.0826038115860153 133 2.9 2.09685583619004 0.80314416380996 134 2.63 2.09631548396609 0.533684516033906 135 2.67 2.09523477951820 0.574765220481796 136 1.81 2.09379384025435 -0.283793840254349 137 1.33 2.09307337062242 -0.763073370622422 138 0.88 2.09271313580646 -1.21271313580646 139 1.28 2.09145231395059 -0.811452313950586 140 1.26 2.09109207913462 -0.831092079134623 141 1.26 2.09019149209471 -0.830191492094714 142 1.29 2.09001137468673 -0.800011374686732 143 1.1 2.08929090505480 -0.989290905054805 144 1.37 2.08911078764682 -0.719110787646823 145 1.21 2.08803008319893 -0.878030083198932 146 1.74 2.08784996579095 -0.347849965790951 147 1.76 2.08766984838297 -0.327669848382969 148 1.48 2.08748973097499 -0.607489730974987 149 1.04 2.08604879171113 -1.04604879171113 150 1.62 2.08496808726324 -0.464968087263242 151 1.49 2.08442773503930 -0.594427735039297 152 1.79 2.08388738281535 -0.293887382815352 153 1.8 2.08352714799939 -0.283527147999388 154 1.58 2.08316691318342 -0.503166913183424 155 1.86 2.08226632614352 -0.222266326143515 156 1.74 2.08136573910361 -0.341365739103607 157 1.59 2.08082538687966 -0.490825386879661 158 1.26 2.08028503465572 -0.820285034655716 159 1.13 2.07974468243177 -0.94974468243177 160 1.92 2.07884409539186 -0.158844095391862 161 2.61 2.0784838605759 0.531516139424102 162 2.26 2.07686280390406 0.183137196095938 163 2.41 2.07596221686415 0.334037783135847 164 2.26 2.07506162982424 0.184938370175755 165 2.03 2.0745212776003 -0.0445212776002994 166 2.86 2.07398092537635 0.786019074623646 167 2.55 2.07326045574443 0.476739544255573 168 2.27 2.07290022092846 0.197099779071537 169 2.26 2.07199963388855 0.188000366111445 170 2.57 2.07145928166461 0.498540718335391 171 3.07 2.07073881203268 0.999261187967318 172 2.76 2.06875752054488 0.691242479455118 173 2.51 2.06785693350497 0.442143066495026 174 2.87 2.06767681609699 0.802323183903008 175 3.14 2.06623587683314 1.07376412316686 176 3.11 2.06587564201717 1.04412435798283 177 3.16 2.06551540720121 1.09448459279879 178 2.47 2.06497505497726 0.405024945022735 179 2.57 2.06425458534534 0.505745414654662 180 2.89 2.06389435052937 0.826105649470626 181 2.63 2.06335399830543 0.566646001694571 182 2.38 2.06227329385754 0.317726706142462 183 1.69 2.06029200236974 -0.370292002369739 184 1.96 2.05957153273781 -0.0995715327378117 185 2.19 2.05885106310588 0.131148936894115 186 1.87 2.05813059347396 -0.188130593473957 187 1.6 2.05777035865799 -0.457770358657994 188 1.63 2.05686977161808 -0.426869771618085 189 1.22 2.05632941939414 -0.83632941939414 190 1.21 2.05542883235423 -0.84542883235423 191 1.49 2.05488848013029 -0.564888480130285 192 1.64 2.05434812790634 -0.41434812790634 193 1.66 2.05416801049836 -0.394168010498358 194 1.77 2.05362765827441 -0.283627658274413 195 1.82 2.05326742345845 -0.233267423458449 196 1.78 2.05308730605047 -0.273087306050468 197 1.28 2.05272707123450 -0.772727071234504 198 1.29 2.05218671901056 -0.762186719010559 199 1.37 2.05164636678661 -0.681646366786613 200 1.12 2.05146624937863 -0.931466249378631 201 1.51 2.05110601456267 -0.541106014562668 202 2.24 2.05002531011478 0.189974689885223 203 2.94 2.04966507529881 0.890334924701186 204 3.09 2.04840425344294 1.04159574655706 205 3.46 2.04804401862698 1.41195598137302 206 3.64 2.04606272713918 1.59393727286082 207 4.39 2.04228026157156 2.34771973842844 208 4.15 2.04065920489972 2.10934079510028 209 5.21 2.03903814822789 3.17096185177211 210 5.8 2.03867791341193 3.76132208658807 211 5.91 2.03795744378 3.87204255622 212 5.39 2.03669662192413 3.35330337807587 213 5.46 2.03543580006825 3.42456419993175 214 4.72 2.03507556525229 2.68492443474771 215 3.14 2.03345450858045 1.10654549141955 216 2.63 2.03309427376449 0.59690572623551 217 2.32 2.03255392154055 0.287446078459455 218 1.93 2.03219368672458 -0.102193686724582 219 0.62 2.03147321709265 -1.41147321709265 220 0.6 2.03093286486871 -1.43093286486871 221 -0.37 2.02949192560485 -2.39949192560485 222 -1.1 2.02823110374898 -3.12823110374898 223 -1.68 2.02769075152504 -3.70769075152504 224 -0.78 2.02642992966916 -2.80642992966916 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0236954574572773 0.0473909149145545 0.976304542542723 6 0.0263421566458947 0.0526843132917895 0.973657843354105 7 0.0209895500036243 0.0419791000072486 0.979010449996376 8 0.00810453254429183 0.0162090650885837 0.991895467455708 9 0.0113690764952041 0.0227381529904082 0.988630923504796 10 0.0135705068326868 0.0271410136653737 0.986429493167313 11 0.0059822296932875 0.011964459386575 0.994017770306713 12 0.00249861935549060 0.00499723871098121 0.99750138064451 13 0.00112659133450835 0.00225318266901670 0.998873408665492 14 0.000428956462365636 0.000857912924731271 0.999571043537634 15 0.000394548766369662 0.000789097532739324 0.99960545123363 16 0.000344888826394417 0.000689777652788834 0.999655111173606 17 0.000229908259012922 0.000459816518025845 0.999770091740987 18 0.000109666590394971 0.000219333180789941 0.999890333409605 19 4.62496788174078e-05 9.24993576348156e-05 0.999953750321183 20 2.27816817943743e-05 4.55633635887485e-05 0.999977218318206 21 8.89041313699628e-06 1.77808262739926e-05 0.999991109586863 22 3.28705710254488e-06 6.57411420508975e-06 0.999996712942897 23 1.22322372953518e-06 2.44644745907036e-06 0.99999877677627 24 5.3863705171531e-07 1.07727410343062e-06 0.999999461362948 25 7.27282898904727e-07 1.45456579780945e-06 0.999999272717101 26 7.59242130399879e-07 1.51848426079976e-06 0.99999924075787 27 1.10449402617948e-06 2.20898805235895e-06 0.999998895505974 28 1.46616329256213e-06 2.93232658512426e-06 0.999998533836707 29 9.6262399158567e-07 1.92524798317134e-06 0.999999037376008 30 4.15136974060486e-07 8.30273948120973e-07 0.999999584863026 31 2.2282354394207e-07 4.4564708788414e-07 0.999999777176456 32 5.81107959565134e-07 1.16221591913027e-06 0.99999941889204 33 4.0052781756108e-07 8.0105563512216e-07 0.999999599472182 34 2.25801325689048e-07 4.51602651378096e-07 0.999999774198674 35 1.01897199496772e-07 2.03794398993544e-07 0.9999998981028 36 5.35212206684752e-08 1.07042441336950e-07 0.99999994647878 37 2.2777168529579e-08 4.5554337059158e-08 0.999999977222831 38 9.89440945720025e-09 1.97888189144005e-08 0.99999999010559 39 4.11055167259240e-09 8.22110334518479e-09 0.999999995889448 40 1.71743974984819e-09 3.43487949969638e-09 0.99999999828256 41 8.07797449929404e-10 1.61559489985881e-09 0.999999999192203 42 5.22906459684762e-10 1.04581291936952e-09 0.999999999477094 43 2.92890082159423e-10 5.85780164318846e-10 0.99999999970711 44 1.21100704063667e-10 2.42201408127334e-10 0.999999999878899 45 5.06801656942499e-11 1.01360331388500e-10 0.99999999994932 46 2.21040036397904e-11 4.42080072795807e-11 0.999999999977896 47 1.10381679490933e-11 2.20763358981866e-11 0.999999999988962 48 6.72192675990233e-12 1.34438535198047e-11 0.999999999993278 49 3.65571028703176e-12 7.31142057406351e-12 0.999999999996344 50 1.97235909230504e-12 3.94471818461009e-12 0.999999999998028 51 1.13206945921819e-12 2.26413891843639e-12 0.999999999998868 52 5.87584115527815e-13 1.17516823105563e-12 0.999999999999412 53 6.66870195959581e-13 1.33374039191916e-12 0.999999999999333 54 1.13372990081182e-12 2.26745980162363e-12 0.999999999998866 55 1.84731928932048e-12 3.69463857864097e-12 0.999999999998153 56 1.76203896775156e-12 3.52407793550313e-12 0.999999999998238 57 1.66231016200552e-12 3.32462032401104e-12 0.999999999998338 58 1.45806183779796e-12 2.91612367559592e-12 0.999999999998542 59 7.218944115413e-13 1.4437888230826e-12 0.999999999999278 60 3.49494451782893e-13 6.98988903565786e-13 0.99999999999965 61 1.51754314838830e-13 3.03508629677659e-13 0.999999999999848 62 6.6260214383419e-14 1.32520428766838e-13 0.999999999999934 63 3.83002821045388e-14 7.66005642090775e-14 0.999999999999962 64 2.44629732698592e-14 4.89259465397184e-14 0.999999999999976 65 1.16870386804490e-14 2.33740773608979e-14 0.999999999999988 66 4.86438718926842e-15 9.72877437853684e-15 0.999999999999995 67 2.33147176381711e-15 4.66294352763421e-15 0.999999999999998 68 1.08972739067170e-15 2.17945478134339e-15 0.999999999999999 69 5.44210719905558e-16 1.08842143981112e-15 1 70 1.07117816216937e-15 2.14235632433875e-15 0.999999999999999 71 1.33504704077367e-15 2.67009408154734e-15 0.999999999999999 72 2.80025129623952e-15 5.60050259247905e-15 0.999999999999997 73 2.51965353794073e-15 5.03930707588146e-15 0.999999999999998 74 1.22169793782694e-15 2.44339587565389e-15 0.999999999999999 75 5.11988412998345e-16 1.02397682599669e-15 1 76 2.56471645788598e-16 5.12943291577197e-16 1 77 9.76953000969466e-17 1.95390600193893e-16 1 78 3.97021609338788e-17 7.94043218677576e-17 1 79 1.97184130645294e-17 3.94368261290588e-17 1 80 9.07470982262487e-18 1.81494196452497e-17 1 81 3.38777907578339e-18 6.77555815156678e-18 1 82 1.44051492294481e-18 2.88102984588963e-18 1 83 5.3840032086916e-19 1.07680064173832e-18 1 84 2.66058013505788e-19 5.32116027011577e-19 1 85 1.45786345690265e-18 2.91572691380530e-18 1 86 1.36787507673527e-18 2.73575015347055e-18 1 87 6.27818394114343e-19 1.25563678822869e-18 1 88 2.75141541886039e-19 5.50283083772078e-19 1 89 2.36715310587458e-19 4.73430621174917e-19 1 90 1.10905747910266e-19 2.21811495820532e-19 1 91 4.79240554573309e-20 9.58481109146618e-20 1 92 8.28730124835647e-20 1.65746024967129e-19 1 93 4.62922803997995e-20 9.2584560799599e-20 1 94 2.36698748186838e-20 4.73397496373676e-20 1 95 2.22759967294803e-20 4.45519934589607e-20 1 96 1.95572092573719e-20 3.91144185147439e-20 1 97 8.78774865821209e-21 1.75754973164242e-20 1 98 3.78916603991302e-21 7.57833207982603e-21 1 99 1.66008521554054e-21 3.32017043108107e-21 1 100 7.912765781472e-22 1.5825531562944e-21 1 101 3.73676104537108e-22 7.47352209074215e-22 1 102 1.93691214507565e-22 3.87382429015131e-22 1 103 1.12529235505838e-22 2.25058471011676e-22 1 104 5.75441537698296e-23 1.15088307539659e-22 1 105 3.77244762453888e-23 7.54489524907776e-23 1 106 3.21770803017672e-23 6.43541606035344e-23 1 107 4.56252092101486e-23 9.12504184202971e-23 1 108 2.49705649948773e-22 4.99411299897545e-22 1 109 5.61037606559084e-22 1.12207521311817e-21 1 110 2.09185596843676e-21 4.18371193687351e-21 1 111 2.35666851371155e-20 4.7133370274231e-20 1 112 7.4974012674133e-20 1.49948025348266e-19 1 113 2.82337494448655e-19 5.64674988897311e-19 1 114 8.69587339948773e-18 1.73917467989755e-17 1 115 1.58421723696279e-16 3.16843447392557e-16 1 116 2.66478373440962e-15 5.32956746881924e-15 0.999999999999997 117 1.90123127923443e-13 3.80246255846885e-13 0.99999999999981 118 1.50029435310632e-12 3.00058870621264e-12 0.9999999999985 119 1.23315057051500e-11 2.46630114103000e-11 0.999999999987669 120 1.83489696402606e-11 3.66979392805212e-11 0.99999999998165 121 1.63686795634679e-11 3.27373591269358e-11 0.999999999983631 122 1.55112326478565e-11 3.10224652957129e-11 0.999999999984489 123 1.18897969027219e-11 2.37795938054438e-11 0.99999999998811 124 2.83508563425677e-11 5.67017126851354e-11 0.99999999997165 125 1.35917832307751e-10 2.71835664615503e-10 0.999999999864082 126 3.38118260895138e-10 6.76236521790275e-10 0.999999999661882 127 4.62019465157659e-10 9.24038930315317e-10 0.99999999953798 128 6.1157759796389e-10 1.22315519592778e-09 0.999999999388422 129 4.7072710708555e-10 9.414542141711e-10 0.999999999529273 130 3.88204352634806e-10 7.76408705269613e-10 0.999999999611796 131 2.58380188375233e-10 5.16760376750466e-10 0.99999999974162 132 1.763802459699e-10 3.527604919398e-10 0.99999999982362 133 2.99962810909563e-10 5.99925621819126e-10 0.999999999700037 134 3.21685554667214e-10 6.43371109334429e-10 0.999999999678314 135 3.58438359732916e-10 7.16876719465831e-10 0.999999999641562 136 1.97464971275583e-10 3.94929942551167e-10 0.999999999802535 137 1.13805225229508e-10 2.27610450459016e-10 0.999999999886195 138 9.18897466638972e-11 1.83779493327794e-10 0.99999999990811 139 5.3818289180313e-11 1.07636578360626e-10 0.999999999946182 140 3.17423268435293e-11 6.34846536870586e-11 0.999999999968258 141 1.86804953976921e-11 3.73609907953842e-11 0.99999999998132 142 1.08074142954845e-11 2.16148285909689e-11 0.999999999989193 143 7.10265294409145e-12 1.42053058881829e-11 0.999999999992897 144 3.9727127676393e-12 7.9454255352786e-12 0.999999999996027 145 2.43130785146040e-12 4.86261570292079e-12 0.999999999997569 146 1.29098833688910e-12 2.58197667377820e-12 0.99999999999871 147 6.81934949504243e-13 1.36386989900849e-12 0.999999999999318 148 3.66557116544713e-13 7.33114233089426e-13 0.999999999999633 149 2.65849466091498e-13 5.31698932182996e-13 0.999999999999734 150 1.41665251706223e-13 2.83330503412445e-13 0.999999999999858 151 7.78382005985138e-14 1.55676401197028e-13 0.999999999999922 152 4.17546292645371e-14 8.35092585290743e-14 0.999999999999958 153 2.23348241256519e-14 4.46696482513038e-14 0.999999999999978 154 1.20815044096235e-14 2.4163008819247e-14 0.999999999999988 155 6.53774634278097e-15 1.30754926855619e-14 0.999999999999993 156 3.49574397272067e-15 6.99148794544134e-15 0.999999999999996 157 1.92473370065269e-15 3.84946740130538e-15 0.999999999999998 158 1.32097385037601e-15 2.64194770075202e-15 0.999999999999999 159 1.09181278003636e-15 2.18362556007272e-15 0.999999999999999 160 6.3764299876906e-16 1.27528599753812e-15 1 161 6.30728421728375e-16 1.26145684345675e-15 1 162 4.20529819092911e-16 8.41059638185822e-16 1 163 3.12765337027568e-16 6.25530674055137e-16 1 164 2.00660157108624e-16 4.01320314217248e-16 1 165 1.13894697995451e-16 2.27789395990903e-16 1 166 1.41574687198182e-16 2.83149374396363e-16 1 167 1.08847523556531e-16 2.17695047113062e-16 1 168 6.42195819033215e-17 1.28439163806643e-16 1 169 3.71582819678039e-17 7.43165639356078e-17 1 170 2.70219485893120e-17 5.40438971786241e-17 1 171 3.92834559583255e-17 7.8566911916651e-17 1 172 3.33498797793294e-17 6.66997595586588e-17 1 173 2.07411275934956e-17 4.14822551869911e-17 1 174 1.91118206242974e-17 3.82236412485947e-17 1 175 2.67728488543320e-17 5.35456977086641e-17 1 176 3.36614034616374e-17 6.73228069232749e-17 1 177 4.4516111608991e-17 8.9032223217982e-17 1 178 2.32363302392274e-17 4.64726604784549e-17 1 179 1.2958721346035e-17 2.591744269207e-17 1 180 1.03504346619356e-17 2.07008693238711e-17 1 181 5.92444864873863e-18 1.18488972974773e-17 1 182 2.71638592133124e-18 5.43277184266247e-18 1 183 1.16628127119406e-18 2.33256254238812e-18 1 184 4.62303607501425e-19 9.24607215002851e-19 1 185 1.85607209828709e-19 3.71214419657418e-19 1 186 7.2842296375152e-20 1.45684592750304e-19 1 187 3.26553332375291e-20 6.53106664750582e-20 1 188 1.45278782248971e-20 2.90557564497942e-20 1 189 1.05320896569686e-20 2.10641793139373e-20 1 190 8.3664793259896e-21 1.67329586519792e-20 1 191 4.93072289647008e-21 9.86144579294016e-21 1 192 2.64178857212926e-21 5.28357714425852e-21 1 193 1.49450617286886e-21 2.98901234573772e-21 1 194 8.21245835982006e-22 1.64249167196401e-21 1 195 4.71194758998378e-22 9.42389517996757e-22 1 196 3.20005011823829e-22 6.40010023647657e-22 1 197 6.37980548625264e-22 1.27596109725053e-21 1 198 2.00456137319741e-21 4.00912274639481e-21 1 199 9.95121432803607e-21 1.99024286560721e-20 1 200 3.40946330220314e-19 6.81892660440627e-19 1 201 1.94862094207815e-17 3.89724188415630e-17 1 202 6.4641573420457e-16 1.29283146840914e-15 1 203 2.78593368647831e-14 5.57186737295662e-14 0.999999999999972 204 4.20382126599161e-12 8.40764253198323e-12 0.999999999995796 205 9.24059878849942e-09 1.84811975769988e-08 0.999999990759401 206 0.000222414208901255 0.00044482841780251 0.999777585791099 207 0.0170756732595167 0.0341513465190334 0.982924326740483 208 0.483583335912164 0.967166671824328 0.516416664087836 209 0.746797096459466 0.506405807081069 0.253202903540534 210 0.835769396076116 0.328461207847769 0.164230603923884 211 0.845909515978057 0.308180968043887 0.154090484021943 212 0.815502915811535 0.368994168376930 0.184497084188465 213 0.87906992314691 0.241860153706182 0.120930076853091 214 0.900457066322482 0.199085867355036 0.099542933677518 215 0.878865660598207 0.242268678803586 0.121134339401793 216 0.833450051534579 0.333099896930842 0.166549948465421 217 0.816311849506288 0.367376300987425 0.183688150493712 218 0.845371619647841 0.309256760704317 0.154628380352159 219 0.715540146423523 0.568919707152953 0.284459853576477 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 195 0.906976744186046 NOK 5% type I error level 202 0.93953488372093 NOK 10% type I error level 203 0.944186046511628 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/19/t1258639081gobe752f93qazz2/10bvcz1258639019.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258639081gobe752f93qazz2/10bvcz1258639019.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258639081gobe752f93qazz2/15u301258639019.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258639081gobe752f93qazz2/15u301258639019.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258639081gobe752f93qazz2/2plht1258639019.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258639081gobe752f93qazz2/2plht1258639019.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258639081gobe752f93qazz2/33pot1258639019.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258639081gobe752f93qazz2/33pot1258639019.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258639081gobe752f93qazz2/4wcya1258639019.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258639081gobe752f93qazz2/4wcya1258639019.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258639081gobe752f93qazz2/50e6n1258639019.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258639081gobe752f93qazz2/50e6n1258639019.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258639081gobe752f93qazz2/6uqfo1258639019.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258639081gobe752f93qazz2/6uqfo1258639019.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258639081gobe752f93qazz2/7pwxq1258639019.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258639081gobe752f93qazz2/7pwxq1258639019.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258639081gobe752f93qazz2/8wxlt1258639019.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258639081gobe752f93qazz2/8wxlt1258639019.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258639081gobe752f93qazz2/94be11258639019.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258639081gobe752f93qazz2/94be11258639019.ps (open in new window)

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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