*Unverified author*

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

Title produced by software: Multiple Regression

Date of computation: Tue, 21 Dec 2010 13:53:35 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939524dit98g087trgbwo.htm/, Retrieved Tue, 21 Dec 2010 14:52:04 +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/2010/Dec/21/t1292939524dit98g087trgbwo.htm/}, year = {2010}, } @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 = {2010}, 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 «

3.66356 7.74414 -4.4 4.2 0 18 19 116 3.04452 8.03398 -5.7 4.8 -0.3 69.1 9 506 3.71357 4.70048 -13.5 4.3 0.2 80 3 95 2.94444 7.5251 1.4 3 0.1 177 22 161 4.06044 7.7626 4.1 5.6 1.1 287 7 80 3.68888 7.88683 5.8 2.3 -0.1 200 9 33 3.3322 7.81521 2.7 1.9 0.4 228 7 129 3.3673 7.77779 7.1 8.9 0.2 220 15 155 2.07944 6.89163 4.1 2 0.1 183 9 132 1.94591 7.6774 1.1 5.2 0.1 43.1 10 480 3.3322 5.71373 -9 3.4 0 80 6 98 3.21888 8.33471 1.6 4.4 -0.3 78.1 16 558 1.09861 4.65396 -0.4 5.7 0.8 267 3 121 5.3845 7.38895 -4.8 6 0 81 20 122 3.93183 7.81763 -0.9 1.4 -0.3 236 15 51 3.3673 4.96981 -0.5 0.6 1.7 341.1 4 552 2.83321 7.80384 -1 1.8 0 16 7 150 3.04452 7.62168 -2.3 5.2 -0.1 66.1 12 428 2.99573 5.21494 5.8 2.6 -0.2 68.8 3 582 4.21951 7.64204 5.1 2.2 1.1 199 18 538 3.04452 7.77149 10.8 2.4 -1.5 329.8 13 579 3.7612 8.31385 12.2 4 -2.8 230.4 17 572 3.58352 7.63964 -2.8 2.1 -1.6 210.2 11 512 2.48491 7.05531 11.2 3.3 2.3 302.8 23 604 2.48491 7.38275 13.6 0.6 -0.8 159.8 11 602 3.3322 7.56786 -12.3 3.7 -0.2 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 39 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation PM10[t] = + 1.23054751597176 + 0.32678291036685Cars[t] -0.00212248873738100Temp[t] -0.103338779289504Windspeed[t] + 0.0110718232100302Tempdiff[t] -4.56448970049517e-05Winddir[t] + 0.000317930999549815hour[t] + 0.000266198137725166`day `[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) 1.23054751597176 0.296506 4.1502 3.9e-05 2e-05 Cars 0.32678291036685 0.043561 7.5018 0 0 Temp -0.00212248873738100 0.006667 -0.3184 0.750344 0.375172 Windspeed -0.103338779289504 0.02079 -4.9706 1e-06 0 Tempdiff 0.0110718232100302 0.042363 0.2614 0.793927 0.396963 Winddir -4.56448970049517e-05 0.000456 -0.1001 0.920338 0.460169 hour 0.000317930999549815 0.00646 0.0492 0.96077 0.480385 `day ` 0.000266198137725166 0.000185 1.441 0.150227 0.075113 Multiple Linear Regression - Regression Statistics Multiple R 0.420078639159281 R-squared 0.176466063077913 Adjusted R-squared 0.164749116820892 F-TEST (value) 15.060755525115 F-TEST (DF numerator) 7 F-TEST (DF denominator) 492 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.81047251485717 Sum Squared Residuals 323.177923090742 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3.66356 3.37261426571013 0.290945734289873 2 3.04452 3.50306895475311 -0.458548954753114 3 3.71357 2.37568628646686 1.33788371353314 4 2.94444 3.41951419038747 -0.475074190387474 5 4.06044 3.20243345624646 0.858006543753539 6 3.68888 3.55924890571656 0.129631094283437 7 3.3322 3.61293695418916 -0.280736954189165 8 3.3673 2.87561372632352 0.491686273676484 9 2.07944 3.29798836148575 -1.21854836148575 10 1.94591 3.32978854546934 -1.38387854546934 11 3.3322 2.78979079520823 0.542409204791772 12 3.21888 3.64284073940617 -0.423960739406167 13 1.09861 2.19303410177854 -1.09442410177854 14 5.3845 3.07042292786537 2.31407707213463 15 3.93183 3.64670267576235 0.285127324237649 16 3.3673 2.94512018964818 0.422179810351821 17 2.83321 3.63824666852882 -0.80503666852882 18 3.04452 3.30232602497507 -0.257806024975069 19 2.99573 2.80423590132949 0.191494098670508 20 4.21951 3.64169860842918 0.577811391570822 21 3.04452 3.62580209028985 -0.58128209028985 22 3.7612 3.62427460808425 0.136925391915750 23 3.58352 3.62846405430732 -0.044944054307317 24 2.48491 3.35105241254369 -0.866142412543689 25 2.48491 3.69983193987672 -1.21492193987672 26 3.3322 3.46820476803507 -0.136004768035075 27 3.13549 3.69671616846449 -0.561226168464492 28 2.07944 3.30199883611252 -1.22255883611252 29 3.68888 3.0501825122178 0.6386974877822 30 2.99573 2.3133446760978 0.682385323902202 31 3.98898 3.54986153100004 0.439118468999958 32 3.04452 3.05399385879268 -0.00947385879267545 33 3.55535 3.53579275131524 0.0195572486847613 34 1.79176 3.18885260944478 -1.39709260944478 35 3.04452 2.74102374210171 0.303496257898288 36 2.56495 3.56518223106331 -1.00023223106331 37 4.36945 3.59079890549621 0.778651094503793 38 3.46574 3.3718274832979 0.0939125167021008 39 4.60517 3.38894391089748 1.21622608910252 40 3.09104 3.21798961453139 -0.126949614531385 41 4.15888 3.43532026341395 0.72355973658605 42 1.79176 3.23238567361750 -1.44062567361750 43 2.48491 3.34875621972375 -0.863846219723751 44 3.21888 3.36946155975178 -0.150581559751777 45 3.73767 3.29237737464006 0.445292625359943 46 4.2485 3.18914827127870 1.05935172872130 47 3.8712 2.83860884400759 1.03259115599241 48 4.00733 3.42311006313825 0.584219936861753 49 2.94444 2.84789235602249 0.096547643977513 50 3.09104 2.17225556625099 0.918784433749007 51 1.94591 2.54677682585091 -0.600866825850913 52 3.52636 3.41608018391302 0.110279816086979 53 3.8712 3.56754866186391 0.303651338136093 54 2.99573 3.56120317272594 -0.565473172725938 55 4.07754 3.68208976596850 0.395450234031496 56 3.21888 3.36135748926800 -0.142477489268004 57 3.49651 3.53222673309843 -0.0357167330984298 58 3.2581 2.57777906944691 0.680320930553086 59 2.99573 3.39807901302201 -0.402349013022008 60 2.70805 3.17136249222854 -0.463312492228538 61 3.09104 3.25736393858322 -0.166323938583223 62 4.06044 3.60022763179766 0.460212368202338 63 3.61092 3.61769077435327 -0.00677077435327486 64 2.56495 3.10147583831473 -0.536525838314729 65 1.60944 3.03934574483264 -1.42990574483264 66 5.0876 3.71171904579472 1.37588095420528 67 2.30259 3.28942028862513 -0.986830288625135 68 3.2581 3.42798031550935 -0.169880315509354 69 3.66356 3.30340568272434 0.360154317275656 70 3.04452 3.57192815051480 -0.527408150514795 71 3.4012 3.45867816293088 -0.0574781629308787 72 3.04452 3.05480961651745 -0.0102896165174459 73 3.4012 3.79764439379578 -0.396444393795776 74 3.55535 3.12978992432364 0.425560075676362 75 3.97029 3.72606697964271 0.24422302035729 76 4.72739 3.31252425066683 1.41486574933317 77 4.30407 3.29314121550153 1.01092878449847 78 2.56495 3.21273119633899 -0.64778119633899 79 3.78419 3.24707062930082 0.537119370699184 80 4.95583 3.29440468136066 1.66142531863934 81 3.66356 3.35104770918684 0.312512290813165 82 5.26786 3.50613722167475 1.76172277832525 83 3.46574 2.73550555644094 0.730234443559064 84 2.07944 2.89747885297113 -0.818038852971127 85 3.3673 3.52903123987403 -0.161731239874031 86 3.29584 3.47118772696543 -0.175347726965426 87 2.19722 3.32627529947194 -1.12905529947194 88 3.43399 3.76672374585954 -0.332733745859536 89 3.2581 3.52710921074039 -0.269009210740386 90 2.83321 3.20288407169552 -0.369674071695523 91 3.63759 3.98739749215343 -0.349807492153426 92 2.70805 3.10824645950444 -0.400196459504444 93 2.99573 3.65257617214376 -0.656846172143764 94 4.00733 3.76987974451658 0.237450255483415 95 3.43399 3.22709958229402 0.206890417705977 96 0.69315 3.26748997682473 -2.57433997682473 97 3.52636 3.60649074219999 -0.0801307421999939 98 2.63906 3.51250153341184 -0.873441533411836 99 1.94591 3.45625111662678 -1.51034111662678 100 3.71357 3.61173017566083 0.101839824339168 101 2.83321 3.17955048614001 -0.346340486140005 102 3.43399 3.44035777504435 -0.00636777504435337 103 3.29584 3.85679512635679 -0.560955126356788 104 3.17805 3.47075136328789 -0.29270136328789 105 4.81218 3.68121077118895 1.13096922881105 106 4.63473 3.9182062025476 0.716523797452402 107 3.04452 2.82335926606517 0.221160733934829 108 3.8712 3.46594817108398 0.405251828916016 109 3.68888 3.68460819212117 0.0042718078788268 110 4.33073 3.15202587406749 1.17870412593251 111 4.61512 3.40470792650623 1.21041207349377 112 4.43082 3.04298516105466 1.38783483894534 113 3.4012 2.96710772926129 0.434092270738706 114 2.48491 3.62585336617278 -1.14094336617278 115 3.29584 3.78756316872347 -0.491723168723473 116 2.94444 3.56024859947109 -0.615808599471088 117 3.3673 3.26218087703616 0.105119122963836 118 2.89037 3.27399509585958 -0.383625095859577 119 4.90527 3.31114496453436 1.59412503546564 120 2.63906 3.22086395521298 -0.581803955212983 121 3.29584 3.28646099545881 0.00937900454118726 122 3.71357 3.22622433208720 0.487345667912803 123 4.39445 3.80786164856396 0.58658835143604 124 3.82864 3.48495007284181 0.343689927158195 125 2.56495 2.72179217436529 -0.15684217436529 126 3.3322 3.45553498145376 -0.123334981453763 127 3.13549 3.21713274662683 -0.0816427466268335 128 0.69315 2.95422751802715 -2.26107751802715 129 4.00733 3.74244855522445 0.264881444775547 130 3.2581 2.96733059008503 0.290769409914967 131 3.2581 3.20981584094257 0.0482841590574256 132 4.84419 3.84374396145869 1.00044603854131 133 2.63906 2.77648598040609 -0.137425980406094 134 1.38629 2.23318675141557 -0.84689675141557 135 3.2581 2.95604945071353 0.302050549286475 136 2.30259 3.51543013352702 -1.21284013352702 137 3.09104 2.71980492002587 0.371235079974129 138 2.94444 3.04513166109217 -0.100691661092167 139 3.4012 3.07546365441053 0.325736345589467 140 2.99573 2.82670789306411 0.169022106935885 141 3.82864 3.24065280199193 0.587987198008065 142 2.30259 3.59154331525355 -1.28895331525355 143 4.29046 3.32165980327959 0.96880019672041 144 4.41884 3.61974113627139 0.799098863728608 145 3.3673 3.44132677187325 -0.0740267718732475 146 2.30259 2.27292486406351 0.029665135936492 147 3.98898 3.6090269783062 0.379953021693802 148 4.12713 2.55485663912379 1.57227336087621 149 3.68888 3.11963992631705 0.569240073682952 150 2.30259 2.67114060869048 -0.368550608690480 151 3.29584 3.53610635543966 -0.240266355439659 152 3.13549 3.18220289103497 -0.046712891034975 153 2.07944 3.30500190337161 -1.22556190337161 154 5.25227 3.85790012111362 1.39436987888638 155 3.78419 3.49992000402474 0.284269995975265 156 3.97029 3.11208095170735 0.858209048292646 157 2.99573 2.76513545772413 0.230594542275867 158 2.56495 3.22513266100679 -0.660182661006795 159 3.21888 3.18755345026419 0.0313265497358109 160 1.38629 3.69920465410332 -2.31291465410332 161 3.13549 3.31655757826776 -0.181067578267758 162 4.06044 3.45197781141938 0.60846218858062 163 4.27667 3.56042544602430 0.716244553975696 164 3.49651 3.87200987255104 -0.375499872551043 165 3.21888 3.42536076953830 -0.206480769538296 166 4.07754 3.45195738506421 0.62558261493579 167 4.20469 3.02211576361082 1.18257423638918 168 4.18965 3.06929365718400 1.12035634281600 169 2.48491 3.49991806693173 -1.01500806693173 170 1.09861 3.01901122926141 -1.92040122926141 171 2.48491 3.41237827926239 -0.927468279262386 172 2.48491 3.54566220961134 -1.06075220961134 173 0.69315 3.52008422041535 -2.82693422041535 174 4.34381 3.89245530942895 0.451354690571047 175 2.63906 3.51505576036003 -0.875995760360028 176 3.29584 3.45446810226272 -0.158628102262721 177 4.17439 3.37749706213737 0.796892937862625 178 3.71357 3.94896380444413 -0.235393804444129 179 4.02535 3.35268518490412 0.672664815095884 180 4.85203 3.47091470494862 1.38111529505138 181 4.64439 3.28666804150141 1.35772195849859 182 3.63759 3.10174141260339 0.535848587396606 183 3.4012 3.41722800003298 -0.0160280000329785 184 1.79176 2.93270644425858 -1.14094644425858 185 4.11087 3.12757377064339 0.983296229356613 186 3.3673 3.63043301189004 -0.263133011890042 187 4.44265 3.58445718460009 0.858192815399908 188 2.77259 3.36651549809148 -0.593925498091483 189 3.71357 3.34019214629553 0.37337785370447 190 5.17048 3.24031409885593 1.93016590114407 191 3.09104 3.48253012213513 -0.391490122135130 192 2.70805 2.79426623249857 -0.0862162324985663 193 4.11087 3.38841811903960 0.722451880960396 194 4.79579 3.64551084136453 1.15027915863547 195 2.3979 3.12885297314528 -0.73095297314528 196 2.99573 2.84894151028301 0.146788489716992 197 3.13549 3.39179669448550 -0.256306694485495 198 3.43399 3.54402226822102 -0.110032268221020 199 3.4012 3.05688562364058 0.344314376359425 200 3.09104 3.76416840035499 -0.67312840035499 201 4.45435 3.34170794884952 1.11264205115048 202 4.18965 3.74568055870844 0.443969441291562 203 3.73767 3.57518265740067 0.16248734259933 204 4.20469 2.98956187448242 1.21512812551758 205 2.56495 2.88262463423447 -0.317674634234473 206 2.56495 3.14611801411747 -0.581168014117466 207 4.85981 3.47164866368105 1.38816133631895 208 5.25227 2.96804065351769 2.28422934648231 209 2.63906 3.15447120314681 -0.515411203146808 210 3.13549 2.93534338938119 0.200146610618805 211 1.94591 3.30540210760479 -1.35949210760479 212 3.4012 3.1387710030535 0.262428996946498 213 4.72739 3.59394509449509 1.13344490550491 214 3.3673 2.91536625715423 0.451933742845774 215 3.2581 3.57028938248245 -0.312189382482454 216 3.73767 3.84477804839344 -0.107108048393443 217 1.79176 3.26229573458224 -1.47053573458224 218 4.06044 3.25874733601814 0.801692663981858 219 3.91202 3.87864765166365 0.033372348336351 220 0.69315 3.09984761203875 -2.40669761203875 221 1.60944 2.76830998158047 -1.15886998158047 222 4.46591 3.07286059695557 1.39304940304443 223 3.17805 3.85132952815137 -0.673279528151367 224 2.89037 3.36361479632846 -0.473244796328457 225 4.17439 3.50784736602154 0.666542633978463 226 3.73767 3.83702314372922 -0.0993531437292243 227 4.00733 3.31589296023466 0.691437039765342 228 3.04452 3.38864477581191 -0.344124775811912 229 2.63906 2.91591206032718 -0.276852060327181 230 4.11087 3.70945984619802 0.401410153801976 231 4.47734 3.59195620036844 0.885383799631562 232 3.17805 3.33387718691563 -0.155827186915628 233 3.3322 3.65845838432179 -0.326258384321794 234 0.69315 2.53247287702073 -1.83932287702073 235 4.58497 3.6751074314897 0.909862568510302 236 0.69315 2.21338236861897 -1.52023236861897 237 3.4012 3.46809739136932 -0.0668973913693187 238 2.07944 3.73072312469563 -1.65128312469563 239 4.55388 3.14304253260818 1.41083746739182 240 3.21888 2.85581445694595 0.363065543054045 241 2.77259 2.74824547888693 0.0243445211130687 242 3.29584 3.11928801460807 0.176551985391930 243 3.3322 3.24107267301529 0.0911273269847122 244 4.02535 3.5963601689712 0.428989831028802 245 4.38203 3.60439833003718 0.777631669962816 246 2.99573 2.73885803230002 0.256871967699979 247 3.55535 3.19680152358694 0.358548476413056 248 3.2581 3.40713507974006 -0.149035079740058 249 4.47734 3.77579605030257 0.701543949697426 250 4.06044 2.90998931146505 1.15045068853495 251 3.21888 3.40237469288508 -0.183494692885082 252 4.46591 3.35773106649896 1.10817893350104 253 3.13549 3.0818242483842 0.0536657516157972 254 2.30259 2.28976694588200 0.0128230541180041 255 3.61092 3.45039163222534 0.160528367774661 256 3.13549 3.18414121794353 -0.0486512179435268 257 3.89182 3.87990114596708 0.0119188540329179 258 3.21888 3.46388506647288 -0.245005066472879 259 3.17805 2.4833051318649 0.694744868135099 260 3.73767 3.63722936985765 0.100440630142353 261 2.3979 3.47157306683045 -1.07367306683045 262 3.68888 3.8858245038922 -0.196944503892202 263 4.26268 3.55849175130938 0.704188248690617 264 4.94164 3.74622735476612 1.19541264523388 265 3.29584 3.44495951226678 -0.149119512266777 266 2.07944 2.79794311257719 -0.718503112577186 267 2.19722 3.50945394456123 -1.31223394456123 268 2.07944 2.96776511047247 -0.888325110472475 269 4.54329 3.3589835855812 1.18430641441880 270 2.07944 3.60490037447673 -1.52546037447673 271 4.36945 3.55344750893982 0.816002491060177 272 3.97029 3.53324027621657 0.437049723783434 273 3.98898 3.19942667637309 0.789553323626913 274 2.99573 3.01965451823610 -0.0239245182360963 275 3.52636 3.18359022104522 0.342769778954779 276 2.99573 3.51310527158511 -0.517375271585115 277 5.39363 3.09556634648576 2.29806365351424 278 3.63759 3.378744479772 0.258845520228003 279 2.30259 2.72578524862604 -0.423195248626043 280 4.92725 3.86044556970327 1.06680443029673 281 2.94444 3.36782069053123 -0.423380690531226 282 2.70805 3.44401939192998 -0.735969391929975 283 2.07944 3.6648804906697 -1.5854404906697 284 3.4012 3.53779933786704 -0.136599337867040 285 5.05625 3.57095684854471 1.48529315145529 286 4.93447 3.61747595334579 1.31699404665421 287 2.56495 3.38626058525621 -0.82131058525621 288 3.04452 3.73532513036665 -0.690805130366649 289 1.38629 2.34345979015862 -0.957169790158617 290 2.77259 2.73507996829079 0.0375100317092106 291 3.91202 2.87482671722474 1.03719328277526 292 4.35671 3.80606588836221 0.550644111637788 293 3.4012 3.73265323056083 -0.331453230560835 294 4.02535 3.36372111884689 0.661628881153114 295 3.73767 3.42030794703106 0.317362052968945 296 2.94444 3.54024220252199 -0.595802202521985 297 4.09434 3.02009180954923 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1.34649727745855 319 4.39445 3.31692535901467 1.07752464098533 320 2.63906 2.91583643434338 -0.276776434343378 321 3.2581 3.53811395851495 -0.280013958514945 322 1.94591 2.98473263302033 -1.03882263302033 323 2.94444 3.19136326112840 -0.246923261128403 324 2.56495 3.18809779470572 -0.623147794705718 325 3.21888 2.89056626293482 0.32831373706518 326 2.77259 3.33560476844357 -0.563014768443572 327 4.61512 3.42512548315791 1.18999451684209 328 1.60944 2.62824745753836 -1.01880745753836 329 2.07944 2.67828919544767 -0.598849195447675 330 3.8712 3.06531116401529 0.805888835984706 331 3.17805 3.61782136671866 -0.439771366718657 332 3.58352 3.37862536151626 0.204894638483739 333 4.68213 3.53859170203875 1.14353829796125 334 2.56495 3.30455238670421 -0.739602386704215 335 2.30259 2.89932758781601 -0.596737587816005 336 3.55535 3.61577129342301 -0.0604212934230136 337 3.46574 3.32783858077353 0.137901419226468 338 2.48491 3.53050067640921 -1.04559067640921 339 4.21951 2.84393568742139 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-0.480497180771996 382 3.3322 3.40883946342121 -0.0766394634212073 383 2.70805 2.47278292817015 0.235267071829852 384 3.78419 3.45654244966306 0.327647550336942 385 3.78419 3.61515287343302 0.169037126566983 386 1.60944 3.54654470375942 -1.93710470375942 387 3.3673 3.4791420663459 -0.111842066345897 388 3.04452 2.77713116683005 0.267388833169953 389 4.45435 3.47622135628151 0.978128643718488 390 1.94591 2.94849255233157 -1.00258255233157 391 2.63906 2.61799974893890 0.0210602510610969 392 3.3322 3.49141205082772 -0.159212050827723 393 3.43399 2.77689272714344 0.65709727285656 394 3.89182 3.20837636334211 0.683443636657885 395 2.19722 3.54307248651152 -1.34585248651152 396 4.59512 3.35122860112076 1.24389139887924 397 3.49651 2.99134180021268 0.505168199787321 398 2.83321 3.37172585727866 -0.538515857278663 399 2.19722 3.15251209784754 -0.955292097847535 400 2.89037 2.94266467639002 -0.0522946763900218 401 3.4012 3.49608684920465 -0.0948868492046484 402 2.99573 3.12206817900645 -0.126338179006452 403 3.73767 3.51182460295778 0.225845397042217 404 2.94444 2.83114779272358 0.113292207276419 405 3.58352 3.64862755672633 -0.0651075567263265 406 3.29584 3.48668499612859 -0.190844996128589 407 4.8752 3.49046690907261 1.38473309092739 408 4.33073 3.57479352532751 0.755936474672493 409 3.29584 3.38887690466521 -0.0930369046652127 410 3.78419 3.57797473575513 0.206215264244874 411 3.61092 2.49423764620803 1.11668235379197 412 2.83321 3.15160703205219 -0.318397032052192 413 3.7612 3.07228684813963 0.688913151860374 414 3.58352 2.87821387359292 0.70530612640708 415 3.17805 2.79537375132831 0.382676248671688 416 3.52636 2.86117025718982 0.66518974281018 417 4.21951 3.52810028848623 0.69140971151377 418 3.93183 3.54716990417114 0.384660095828861 419 2.30259 2.84336056223226 -0.540770562232265 420 3.2581 2.72079321547499 0.537306784525005 421 2.70805 3.30112752473515 -0.593077524735149 422 3.55535 2.79997917462219 0.75537082537781 423 1.94591 2.93313267202192 -0.987222672021918 424 4.36945 2.82239663514964 1.54705336485036 425 4.70048 3.11370927526001 1.58677072473999 426 2.48491 2.81552250156380 -0.330612501563804 427 1.60944 3.15775357841319 -1.54831357841319 428 3.78419 3.74704791084165 0.0371420891583493 429 1.94591 2.55061452509379 -0.60470452509379 430 3.09104 3.7084938789866 -0.617453878986601 431 3.21888 3.32984884315862 -0.110968843158616 432 2.48491 3.39322551571586 -0.90831551571586 433 2.19722 2.96938244534641 -0.77216244534641 434 4.93447 3.53937891282213 1.39509108717787 435 4.04305 3.53392128738162 0.509128712618379 436 4.51086 3.71909137892365 0.791768621076354 437 1.94591 2.19447016692617 -0.248560166926170 438 3.09104 3.88573643322791 -0.794696433227908 439 4.60517 3.54852259177420 1.05664740822580 440 3.63759 3.14475302587045 0.492836974129546 441 3.46574 3.42390229430193 0.041837705698065 442 3.8712 3.91048373197228 -0.0392837319722808 443 5.15329 3.66717830323186 1.48611169676814 444 3.04452 3.39705155237952 -0.352531552379522 445 3.49651 3.65021537334007 -0.153705373340071 446 2.56495 2.5635298963074 0.00142010369260253 447 3.85015 3.45404668388003 0.396103316119968 448 2.48491 2.73835408192363 -0.253444081923633 449 2.07944 3.29977088289596 -1.22033088289596 450 2.99573 3.71433728451629 -0.718607284516291 451 1.38629 3.08948811659787 -1.70319811659787 452 3.17805 3.56443769859199 -0.386387698591988 453 2.19722 2.65871731878204 -0.461497318782044 454 3.55535 3.59370944540704 -0.0383594454070413 455 3.8712 3.75087940926709 0.120320590732908 456 3.4012 3.48384246311578 -0.0826424631157822 457 3.04452 3.44368293686847 -0.399162936868474 458 4.34381 3.34519447424815 0.998615525751849 459 2.3979 3.06154402687230 -0.663644026872297 460 2.63906 3.53103595518752 -0.891975955187524 461 2.56495 2.73979857701213 -0.174848577012134 462 3.3322 2.69541242322991 0.636787576770086 463 2.56495 3.53920119566180 -0.974251195661796 464 3.68888 3.22405959413498 0.46482040586502 465 2.3979 3.56369759058502 -1.16579759058502 466 2.3979 2.81956257297870 -0.421662572978696 467 4.68213 3.81155065543755 0.870579344562446 468 3.04452 3.51189661651613 -0.467376616516134 469 3.04452 3.41196351434744 -0.36744351434744 470 2.19722 2.42592485820441 -0.228704858204410 471 3.17805 3.55127830022768 -0.373228300227675 472 4.48864 3.70027426080182 0.788365739198184 473 2.30259 3.53318113150615 -1.23059113150615 474 3.29584 3.85740656023556 -0.561566560235555 475 3.17805 3.43283474834439 -0.254784748344390 476 4.06044 2.92509897026089 1.13534102973911 477 4.15888 3.12885884248724 1.03002115751276 478 3.09104 2.82286203944694 0.268177960553062 479 4.41884 3.86538791053739 0.553452089462615 480 2.89037 3.29214562722978 -0.401775627229782 481 1.09861 2.37901076491087 -1.28040076491087 482 3.43399 3.35844070296421 0.0755492970357948 483 3.52636 3.62522987423169 -0.0988698742316937 484 3.13549 3.31501002438850 -0.179520024388505 485 2.19722 3.44595453258393 -1.24873453258393 486 3.13549 3.62415604710286 -0.48866604710286 487 2.07944 2.86074691608603 -0.78130691608603 488 3.63759 2.72584304572836 0.911746954271641 489 3.73767 3.08908507595247 0.648584924047529 490 2.48491 2.89805608950403 -0.413146089504025 491 1.94591 2.73578439580118 -0.789874395801181 492 1.94591 3.05520170354835 -1.10929170354835 493 2.77259 2.58443071210413 0.188159287895875 494 2.70805 3.33699030109203 -0.628940301092035 495 1.79176 2.56218100739247 -0.770421007392468 496 2.30259 2.90502961310921 -0.602439613109213 497 4.11087 3.71900654193257 0.391863458067428 498 3.4012 3.20543216101029 0.195767838989705 499 3.68888 3.29917339452086 0.389706605479139 500 4.17439 3.86428563132368 0.310104368676324 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.0526869268378438 0.105373853675688 0.947313073162156 12 0.266114761145501 0.532229522291002 0.7338852388545 13 0.271199590031095 0.54239918006219 0.728800409968905 14 0.365481051150901 0.730962102301801 0.634518948849099 15 0.298463607626666 0.596927215253333 0.701536392373334 16 0.621005485305211 0.757989029389578 0.378994514694789 17 0.524370887082578 0.951258225834845 0.475629112917422 18 0.42824398518027 0.85648797036054 0.57175601481973 19 0.849607705396088 0.300784589207825 0.150392294603912 20 0.819863577418134 0.360272845163732 0.180136422581866 21 0.772032225113229 0.455935549773543 0.227967774886771 22 0.749247802855808 0.501504394288385 0.250752197144192 23 0.687386118396392 0.625227763207215 0.312613881603608 24 0.684277872187349 0.631444255625302 0.315722127812651 25 0.625145476625848 0.749709046748304 0.374854523374152 26 0.586960177958999 0.826079644082001 0.413039822041001 27 0.521379478854006 0.957241042291989 0.478620521145994 28 0.632709971065317 0.734580057869367 0.367290028934683 29 0.604268668245125 0.79146266350975 0.395731331754875 30 0.550694770474593 0.898610459050813 0.449305229525407 31 0.513037259473815 0.97392548105237 0.486962740526185 32 0.468776090728313 0.937552181456627 0.531223909271687 33 0.411276990546275 0.82255398109255 0.588723009453725 34 0.573490091675373 0.853019816649253 0.426509908324627 35 0.539092569918608 0.921814860162783 0.460907430081392 36 0.540134402729745 0.919731194540511 0.459865597270255 37 0.534346268236369 0.931307463527262 0.465653731763631 38 0.488630694352654 0.977261388705308 0.511369305647346 39 0.563825385993268 0.872349228013464 0.436174614006732 40 0.51763038889517 0.96473922220966 0.48236961110483 41 0.502840380661878 0.994319238676243 0.497159619338122 42 0.670657696005323 0.658684607989354 0.329342303994677 43 0.670453440280198 0.659093119439603 0.329546559719802 44 0.626932807071701 0.746134385856599 0.373067192928299 45 0.595379401649976 0.809241196700048 0.404620598350024 46 0.592297685097504 0.815404629804992 0.407702314902496 47 0.601804583492589 0.796390833014821 0.398195416507411 48 0.588273487922875 0.823453024154249 0.411726512077125 49 0.552982846665424 0.894034306669151 0.447017153334576 50 0.517317644083845 0.96536471183231 0.482682355916155 51 0.510757628556782 0.978484742886436 0.489242371443218 52 0.465898097323218 0.931796194646437 0.534101902676782 53 0.445530151947416 0.891060303894833 0.554469848052584 54 0.404115853574483 0.808231707148966 0.595884146425517 55 0.379707899971298 0.759415799942597 0.620292100028702 56 0.339133715625818 0.678267431251635 0.660866284374182 57 0.303173697999878 0.606347395999756 0.696826302000122 58 0.272810689600195 0.545621379200391 0.727189310399805 59 0.25004855609858 0.50009711219716 0.74995144390142 60 0.242019870084158 0.484039740168316 0.757980129915842 61 0.216428461644598 0.432856923289196 0.783571538355402 62 0.196741530084653 0.393483060169305 0.803258469915347 63 0.170190619400863 0.340381238801726 0.829809380599137 64 0.152423961676284 0.304847923352568 0.847576038323716 65 0.225127357531815 0.450254715063631 0.774872642468185 66 0.293017414399995 0.58603482879999 0.706982585600005 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0.967938262319151 0.0641234753616974 0.0320617376808487 373 0.97432228376305 0.0513554324739007 0.0256777162369503 374 0.969412854703068 0.0611742905938647 0.0305871452969323 375 0.964485312816952 0.0710293743660963 0.0355146871830482 376 0.959208916339544 0.0815821673209127 0.0407910836604564 377 0.952593746015176 0.094812507969649 0.0474062539848245 378 0.951837680692876 0.0963246386142485 0.0481623193071243 379 0.945496681125166 0.109006637749667 0.0545033188748336 380 0.938618866729262 0.122762266541476 0.0613811332707381 381 0.92972665864585 0.140546682708301 0.0702733413541504 382 0.918701311809335 0.162597376381330 0.0812986881906649 383 0.906596468795818 0.186807062408364 0.093403531204182 384 0.89754663050837 0.204906738983262 0.102453369491631 385 0.882974297457787 0.234051405084426 0.117025702542213 386 0.936867403857722 0.126265192284557 0.0631325961422783 387 0.92713339829253 0.145733203414942 0.0728666017074709 388 0.918846447941639 0.162307104116723 0.0811535520583613 389 0.931797926107567 0.136404147784866 0.068202073892433 390 0.941142330898837 0.117715338202326 0.0588576691011628 391 0.933640128756322 0.132719742487357 0.0663598712436783 392 0.922889448313233 0.154221103373534 0.0771105516867668 393 0.922152711663463 0.155694576673074 0.077847288336537 394 0.926301924334641 0.147396151330717 0.0736980756653587 395 0.9504162928981 0.0991674142037988 0.0495837071018994 396 0.964883608282382 0.0702327834352368 0.0351163917176184 397 0.95864779706385 0.0827044058723004 0.0413522029361502 398 0.95241734009211 0.0951653198157815 0.0475826599078907 399 0.96571307132123 0.0685738573575414 0.0342869286787707 400 0.958990308888628 0.0820193822227439 0.0410096911113719 401 0.951308825450476 0.0973823490990476 0.0486911745495238 402 0.943046675285013 0.113906649429973 0.0569533247149866 403 0.932989804056466 0.134020391887068 0.067010195943534 404 0.921380146067922 0.157239707864156 0.0786198539320781 405 0.90800309058131 0.183993818837379 0.0919969094186896 406 0.893163660449984 0.213672679100032 0.106836339550016 407 0.929635786784258 0.140728426431483 0.0703642132157417 408 0.926145909130266 0.147708181739468 0.073854090869734 409 0.913170906401247 0.173658187197506 0.086829093598753 410 0.902285232098681 0.195429535802638 0.097714767901319 411 0.912787222480036 0.174425555039929 0.0872127775199644 412 0.907031284147462 0.185937431705077 0.0929687158525384 413 0.903074080520079 0.193851838959843 0.0969259194799214 414 0.895460659309488 0.209078681381024 0.104539340690512 415 0.888067542730856 0.223864914538289 0.111932457269144 416 0.886358997794428 0.227282004411145 0.113641002205572 417 0.881974360676482 0.236051278647036 0.118025639323518 418 0.867797992351666 0.264404015296667 0.132202007648334 419 0.8617300338822 0.276539932235601 0.138269966117801 420 0.846984161729812 0.306031676540377 0.153015838270188 421 0.826911659616577 0.346176680766847 0.173088340383423 422 0.824892580235334 0.350214839529333 0.175107419764666 423 0.840493550577349 0.319012898845302 0.159506449422651 424 0.897776986474284 0.204446027051431 0.102223013525716 425 0.955201920592635 0.0895961588147292 0.0447980794073646 426 0.94552688920738 0.108946221585240 0.0544731107926201 427 0.954480068496786 0.091039863006429 0.0455199315032145 428 0.946643090938338 0.106713818123323 0.0533569090616616 429 0.936802705344778 0.126394589310444 0.0631972946552218 430 0.930479682516298 0.139040634967404 0.069520317483702 431 0.916376360744788 0.167247278510425 0.0836236392552124 432 0.913051524618906 0.173896950762188 0.0869484753810938 433 0.907167737235613 0.185664525528773 0.0928322627643866 434 0.96548913856934 0.0690217228613198 0.0345108614306599 435 0.960671929165294 0.0786561416694116 0.0393280708347058 436 0.96247300715005 0.0750539856999007 0.0375269928499503 437 0.953542683887631 0.0929146322247373 0.0464573161123686 438 0.947928632175398 0.104142735649204 0.052071367824602 439 0.975477306086606 0.0490453878267887 0.0245226939133943 440 0.979677317113013 0.0406453657739738 0.0203226828869869 441 0.976244940737622 0.0475101185247557 0.0237550592623779 442 0.969853599171495 0.0602928016570103 0.0301464008285051 443 0.985673235994035 0.0286535280119306 0.0143267640059653 444 0.981359100957893 0.0372817980842145 0.0186408990421072 445 0.975426607037656 0.0491467859246869 0.0245733929623435 446 0.96837152301566 0.0632569539686796 0.0316284769843398 447 0.972337911393451 0.0553241772130976 0.0276620886065488 448 0.965320824995349 0.0693583500093025 0.0346791750046513 449 0.985824185201697 0.0283516295966057 0.0141758147983029 450 0.981245917089629 0.0375081658207427 0.0187540829103713 451 0.98616960667381 0.0276607866523793 0.0138303933261896 452 0.981258632710083 0.0374827345798348 0.0187413672899174 453 0.97743710204841 0.0451257959031791 0.0225628979515896 454 0.970395949991471 0.0592081000170574 0.0296040500085287 455 0.960747285296711 0.0785054294065772 0.0392527147032886 456 0.948341863022659 0.103316273954683 0.0516581369773413 457 0.933545024027253 0.132909951945493 0.0664549759727467 458 0.935259301846438 0.129481396307123 0.0647406981535616 459 0.917884921003498 0.164230157993003 0.0821150789965015 460 0.910713467366314 0.178573065267373 0.0892865326336864 461 0.894158960195512 0.211682079608976 0.105841039804488 462 0.894427474822856 0.211145050354288 0.105572525177144 463 0.894396062596816 0.211207874806368 0.105603937403184 464 0.92501363667448 0.149972726651039 0.0749863633255193 465 0.96046175483629 0.0790764903274182 0.0395382451637091 466 0.948442749604758 0.103114500790485 0.0515572503952423 467 0.938535741772324 0.122928516455351 0.0614642582276756 468 0.917881301715214 0.164237396569572 0.082118698284786 469 0.898539266284156 0.202921467431688 0.101460733715844 470 0.866394696134029 0.267210607731942 0.133605303865971 471 0.834807724257285 0.330384551485430 0.165192275742715 472 0.795433984330114 0.409132031339772 0.204566015669886 473 0.840771430382092 0.318457139235816 0.159228569617908 474 0.837427727282819 0.325144545434362 0.162572272717181 475 0.813291062516846 0.373417874966308 0.186708937483154 476 0.863876249239013 0.272247501521975 0.136123750760988 477 0.910804652500367 0.178390694999266 0.089195347499633 478 0.94889989686035 0.102200206279299 0.0511001031396497 479 0.923461405793664 0.153077188412673 0.0765385942063363 480 0.886861417913852 0.226277164172295 0.113138582086148 481 0.846881324345009 0.306237351309983 0.153118675654991 482 0.786794584493695 0.426410831012609 0.213205415506305 483 0.737634912017364 0.524730175965273 0.262365087982636 484 0.645396952343834 0.709206095312332 0.354603047656166 485 0.705131009315543 0.589737981368915 0.294868990684458 486 0.719023076923238 0.561953846153523 0.280976923076762 487 0.602590850231261 0.794818299537478 0.397409149768739 488 0.546019167700662 0.907961664598677 0.453980832299338 489 0.868295471472984 0.263409057054032 0.131704528527016 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 8 0.0167014613778706 NOK 5% type I error level 110 0.229645093945720 NOK 10% type I error level 181 0.377870563674321 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939524dit98g087trgbwo/10bm3r1292939567.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939524dit98g087trgbwo/10bm3r1292939567.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939524dit98g087trgbwo/1fcn01292939567.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939524dit98g087trgbwo/1fcn01292939567.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939524dit98g087trgbwo/2fcn01292939567.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939524dit98g087trgbwo/2fcn01292939567.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939524dit98g087trgbwo/3fcn01292939567.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939524dit98g087trgbwo/3fcn01292939567.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939524dit98g087trgbwo/4fcn01292939567.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939524dit98g087trgbwo/4fcn01292939567.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939524dit98g087trgbwo/584431292939567.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939524dit98g087trgbwo/584431292939567.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939524dit98g087trgbwo/684431292939567.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939524dit98g087trgbwo/684431292939567.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939524dit98g087trgbwo/7jvlo1292939567.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939524dit98g087trgbwo/7jvlo1292939567.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939524dit98g087trgbwo/8bm3r1292939567.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939524dit98g087trgbwo/8bm3r1292939567.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939524dit98g087trgbwo/9bm3r1292939567.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292939524dit98g087trgbwo/9bm3r1292939567.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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