*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: Fri, 03 Dec 2010 17:49:16 +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/03/t1291398427gylhmifidujvwor.htm/, Retrieved Fri, 03 Dec 2010 18:47:17 +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/03/t1291398427gylhmifidujvwor.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 «

1 26 24 24 14 14 11 11 12 12 24 24 1 23 25 25 11 11 7 7 8 8 25 25 0 25 17 0 6 0 17 0 8 0 30 0 1 23 18 18 12 12 10 10 8 8 19 19 1 20 18 18 8 8 12 12 9 9 22 22 0 29 16 10 0 12 0 7 0 22 1 25 20 20 10 10 11 11 4 4 25 25 1 21 16 16 11 11 11 11 11 11 23 23 1 22 18 18 16 16 12 12 7 7 17 17 1 25 17 17 11 11 13 13 7 7 21 21 1 24 23 23 13 13 14 14 12 12 19 19 1 18 30 30 12 12 16 16 10 10 19 19 1 22 23 23 8 8 11 11 10 10 15 15 1 15 18 18 12 12 10 10 8 8 16 16 1 22 15 15 11 11 11 11 8 8 23 23 1 28 12 12 4 4 15 15 4 4 27 27 1 20 21 21 9 9 9 9 9 9 22 22 1 12 15 15 8 8 11 11 8 8 14 14 1 24 20 20 8 8 17 17 7 7 22 22 1 20 31 31 14 14 17 17 11 11 23 23 1 21 27 27 15 15 11 11 9 9 23 23 1 20 34 34 16 16 18 18 11 11 21 21 1 21 21 21 9 9 14 14 13 13 19 19 1 23 31 31 14 14 10 10 8 8 18 18 1 28 19 19 11 11 11 11 8 8 20 20 1 24 16 16 8 8 15 15 9 9 23 23 1 24 20 20 9 9 15 15 6 6 25 25 1 24 21 21 9 9 13 13 9 9 19 19 1 23 22 22 9 9 16 16 9 9 24 24 1 23 17 17 9 9 13 13 6 6 22 22 1 29 24 24 10 10 9 9 6 6 25 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 10 seconds R Server 'George Udny Yule' @ 72.249.76.132 R Framework error message Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Multiple Linear Regression - Estimated Regression Equation O[t] = -0.578264633807969 + 0.925535412411281B[t] + 0.0132183880731054CM[t] + 0.0160035232163488CM_B[t] -1.31048736184262D[t] + 1.32524772719413D_B[t] + 0.406327339245114PE[t] -0.394585656390907PE_B[t] -0.341990685460128PC[t] + 0.363464570658177PC_B[t] + 0.942105175460255PS[t] + 0.0146495184249106PS_B[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) -0.578264633807969 1.018728 -0.5676 0.57115 0.285575 B 0.925535412411281 0.026458 34.9813 0 0 CM 0.0132183880731054 0.08117 0.1628 0.870862 0.435431 CM_B 0.0160035232163488 0.079044 0.2025 0.839834 0.419917 D -1.31048736184262 0.218181 -6.0064 0 0 D_B 1.32524772719413 0.221044 5.9954 0 0 PE 0.406327339245114 0.143549 2.8306 0.005297 0.002649 PE_B -0.394585656390907 0.151846 -2.5986 0.010314 0.005157 PC -0.341990685460128 0.108022 -3.1659 0.00188 0.00094 PC_B 0.363464570658177 0.109279 3.326 0.001113 0.000556 PS 0.942105175460255 0.048185 19.5519 0 0 PS_B 0.0146495184249106 0.030566 0.4793 0.632459 0.316229 Multiple Linear Regression - Regression Statistics Multiple R 0.986054290328691 R-squared 0.972303063475619 Adjusted R-squared 0.970230503599645 F-TEST (value) 469.131471059976 F-TEST (DF numerator) 11 F-TEST (DF denominator) 147 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.43270045551945 Sum Squared Residuals 301.736697501107 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 26 24.6041995514881 1.39580044851188 2 23 25.4130327883993 -2.41303278839934 3 25 24.2183183396727 0.781681660327342 4 23 19.5179366599762 3.48206334002384 5 20 22.3741165311321 -2.37411653113210 6 29 22.2387016296813 6.76129837031869 7 20 20.2205856699302 -0.220585669930168 8 16 16.6015594595828 -0.601559459582765 9 18 18.4816387188737 -0.481638718873727 10 17 17.4960001377340 -0.496000137733962 11 23 23.0502803334575 -0.0502803334575189 12 30 29.5644417477413 0.435558252258726 13 23 22.7065622191804 0.293437780819597 14 18 18.2815495853943 -0.281549585394319 15 15 15.7286961091583 -0.728696109158334 16 12 12.7283106162804 -0.728310616280424 17 21 20.9498195332017 0.0501804667983168 18 15 15.3891673348079 -0.389167334807897 19 20 20.2068579140039 -0.206857914003871 20 31 30.6461690533045 0.353830946695543 21 27 26.8465542387064 0.153445761293572 22 34 33.4530317080726 0.546968291927387 23 21 21.1673111384559 -0.167311138455917 24 31 30.5027986502654 0.497201349734577 25 19 19.3078180295097 -0.307818029509666 26 16 16.5787508582618 -0.578750858261846 27 20 20.3178371410299 -0.317837141029892 28 21 21.1055840416876 -0.105584041687579 29 22 22.1827699761436 -0.18276997614362 30 17 17.5205361096234 -0.520536109623447 31 24 23.9606385098554 0.0393614901445721 32 25 25.2453422813576 -0.245342281357642 33 26 26.0625779104939 -0.0625779104938919 34 25 24.9901215197081 0.00987848029186378 35 17 17.6352757199115 -0.63527571991151 36 32 31.5968497808248 0.403150219175241 37 33 32.3548017515907 0.645198248409278 38 13 12.8444245603739 0.155575439626085 39 0 2.18794968435403 -2.18794968435403 40 25 25.174433175096 -0.174433175095998 41 29 28.8918376034232 0.108162396576839 42 22 22.0868260200892 -0.0868260200891923 43 18 18.2686093376018 -0.268609337601756 44 17 17.5296000678684 -0.52960006786844 45 20 20.3328639948932 -0.332863994893188 46 15 15.634898291154 -0.634898291154002 47 20 20.3458358671561 -0.345835867156142 48 33 32.5430125446762 0.456987455323814 49 29 28.6121314784000 0.387868521599974 50 23 23.2818153482682 -0.281815348268217 51 26 25.8615682049042 0.138431795095830 52 18 18.4186711187687 -0.418671118768676 53 20 20.1016957485837 -0.101695748583713 54 11 11.4706891159079 -0.470689115907915 55 28 28.1707423952679 -0.170742395267933 56 26 25.9896142003860 0.0103857996140364 57 22 22.1695069951440 -0.169506995144029 58 17 17.5343728156567 -0.534372815656687 59 12 12.5319259276468 -0.53192592764685 60 14 14.7123555505507 -0.712355550550716 61 17 17.5107009711061 -0.510700971106108 62 21 20.3380927470690 0.661907252931049 63 0 -5.25108566558226 5.25108566558226 64 18 18.4794330488443 -0.479433048844267 65 10 10.9799755833075 -0.979975583307487 66 29 28.7346391115354 0.265360888464638 67 31 30.325576459698 0.674423540301971 68 19 19.4438616524450 -0.443861652445022 69 9 9.12373445468246 -0.123734454682457 70 0 -0.37226893878106 0.37226893878106 71 28 27.5383401714152 0.461659828584786 72 19 19.2588847154214 -0.258884715421409 73 30 29.6367145656765 0.3632854343235 74 29 28.8976785788225 0.102321421177502 75 26 25.8271010602228 0.172898939777162 76 23 23.0101476516417 -0.010147651641749 77 13 13.869782539103 -0.869782539102994 78 21 21.3603289070511 -0.360328907051055 79 19 19.3574021941919 -0.357402194191938 80 28 27.7949920874708 0.205007912529245 81 23 22.3451927968144 0.65480720318562 82 0 0.446493779711891 -0.446493779711891 83 21 21.1961576111266 -0.196157611126642 84 20 19.4521857063233 0.547814293676748 85 0 7.23771568007521 -7.23771568007521 86 21 21.2209489982355 -0.220948998235549 87 21 21.296532797793 -0.296532797792993 88 15 15.6989440017742 -0.698944001774219 89 28 26.9753740420348 1.02462595796523 90 0 -0.262612919822329 0.262612919822329 91 26 25.8540910907174 0.145908909282642 92 10 9.75667480922528 0.243325190774718 93 0 0.0342085643549297 -0.0342085643549297 94 22 22.1776567768225 -0.17765677682249 95 19 19.3236304946870 -0.323630494687044 96 31 30.8519275928890 0.148072407111044 97 31 30.5939006437243 0.406099356275668 98 29 28.7494305950021 0.250569404997940 99 19 19.1361975269074 -0.136197526907408 100 22 21.9978267604862 0.00217323951376444 101 23 23.0837356952992 -0.0837356952991858 102 15 15.3413957017525 -0.341395701752491 103 20 20.2871768710127 -0.287176871012683 104 18 18.4718631876671 -0.471863187667068 105 23 22.0471579374471 0.95284206255289 106 0 5.73875916131579 -5.73875916131579 107 21 20.8699276360379 0.130072363962140 108 24 23.8646329249258 0.135367075074194 109 25 24.0998567874755 0.900143212524538 110 0 -1.85640375280188 1.85640375280188 111 13 13.5411151924826 -0.541115192482635 112 28 27.5691937214214 0.430806278578554 113 21 20.1181711746810 0.881828825318958 114 0 -7.15715228035646 7.15715228035646 115 9 10.0905632682401 -1.09056326824014 116 16 16.3128204414968 -0.312820441496799 117 19 19.2843924990371 -0.284392499037124 118 17 17.4037431082757 -0.403743108275679 119 25 24.901282449828 0.0987175501719826 120 20 19.9624893812134 0.0375106187865630 121 29 28.4688111245886 0.531188875411384 122 14 13.6033852267716 0.396614773228388 123 0 -1.15007446225698 1.15007446225698 124 15 15.4353749719552 -0.435374971955153 125 19 19.4786690485831 -0.47866904858306 126 20 19.4012843437678 0.598715656232225 127 0 -4.26985303011458 4.26985303011458 128 20 20.3485480195630 -0.348548019562961 129 18 18.4452068883406 -0.445206888340618 130 33 32.3939257377748 0.60607426222523 131 22 22.1911170315266 -0.191117031526603 132 16 16.4309318311061 -0.430931831106054 133 17 17.4128504707148 -0.412850470714811 134 16 16.3094613074666 -0.309461307466617 135 21 21.0292327307523 -0.0292327307522631 136 26 26.0715816303282 -0.0715816303281492 137 18 18.2493848514483 -0.249384851448318 138 18 18.4742408271431 -0.474240827143107 139 17 17.2852117383983 -0.285211738398313 140 22 22.1127894550919 -0.112789455091947 141 30 28.6516116953374 1.34838830466263 142 0 2.92325184158514 -2.92325184158514 143 24 24.3774196544525 -0.377419654452548 144 21 21.1736848378696 -0.173684837869621 145 21 21.4055415731769 -0.405541573176937 146 29 28.7628679486231 0.2371320513769 147 31 29.5627692076597 1.43723079234029 148 0 0.431084021843937 -0.431084021843937 149 16 16.2259330922225 -0.225933092222508 150 22 22.0352239577883 -0.0352239577882592 151 20 20.2570507908056 -0.257050790805632 152 28 28.0166912573327 -0.0166912573327274 153 38 37.0463235816683 0.953676418331654 154 22 21.966706215613 0.0332937843869896 155 20 20.466852129873 -0.466852129873005 156 17 17.3828668619047 -0.382866861904748 157 28 27.7818989790219 0.218101020978084 158 22 22.2097426131333 -0.209742613133305 159 31 30.7372463017937 0.262753698206324 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 15 0.931890324775148 0.136219350449705 0.0681096752248525 16 0.996805081921695 0.0063898361566104 0.0031949180783052 17 0.992876311439192 0.0142473771216159 0.00712368856080793 18 0.985384367544231 0.0292312649115373 0.0146156324557687 19 0.983095289663175 0.0338094206736501 0.0169047103368250 20 0.97085633205466 0.0582873358906796 0.0291436679453398 21 0.963207522126937 0.0735849557461259 0.0367924778730630 22 0.942149601773135 0.115700796453731 0.0578503982268655 23 0.912732285381901 0.174535429236198 0.087267714618099 24 0.965010013242333 0.0699799735153345 0.0349899867576673 25 0.94760064853572 0.104798702928561 0.0523993514642806 26 0.924726268691785 0.150547462616429 0.0752737313082147 27 0.895200219936103 0.209599560127793 0.104799780063897 28 0.858080979736357 0.283838040527287 0.141919020263643 29 0.813311838739202 0.373376322521597 0.186688161260798 30 0.7697783746988 0.460443250602399 0.230221625301199 31 0.762113147402695 0.475773705194609 0.237886852597305 32 0.722634649881768 0.554730700236463 0.277365350118232 33 0.663850487204165 0.67229902559167 0.336149512795835 34 0.620709085408414 0.758581829183172 0.379290914591586 35 0.560556487990152 0.878887024019696 0.439443512009848 36 0.513812575763891 0.972374848472218 0.486187424236109 37 0.470394142827484 0.94078828565497 0.529605857172516 38 0.413657578173373 0.827315156346747 0.586342421826627 39 0.598974369708282 0.802051260583435 0.401025630291718 40 0.554492920001726 0.891014159996548 0.445507079998274 41 0.495662276774661 0.991324553549321 0.504337723225339 42 0.43930558874277 0.87861117748554 0.56069441125723 43 0.385478527407006 0.770957054814012 0.614521472592994 44 0.336057625432361 0.672115250864723 0.663942374567638 45 0.28756728351969 0.57513456703938 0.71243271648031 46 0.242217504440554 0.484435008881109 0.757782495559446 47 0.201131976603972 0.402263953207944 0.798868023396028 48 0.167170787342460 0.334341574684920 0.83282921265754 49 0.136007451573169 0.272014903146338 0.863992548426831 50 0.110051711244625 0.220103422489251 0.889948288755375 51 0.0863358334372093 0.172671666874419 0.91366416656279 52 0.0676583074721679 0.135316614944336 0.932341692527832 53 0.0529175410391101 0.105835082078220 0.94708245896089 54 0.0398030850049678 0.0796061700099357 0.960196914995032 55 0.0304749236788783 0.0609498473577567 0.969525076321122 56 0.0224820192074435 0.044964038414887 0.977517980792556 57 0.0161687035770375 0.0323374071540749 0.983831296422963 58 0.0117099067954443 0.0234198135908886 0.988290093204556 59 0.00829445004929689 0.0165889000985938 0.991705549950703 60 0.00599323754579779 0.0119864750915956 0.994006762454202 61 0.00411199622777645 0.0082239924555529 0.995888003772224 62 0.00440994293701585 0.0088198858740317 0.995590057062984 63 0.0113828213699638 0.0227656427399276 0.988617178630036 64 0.0080651253522124 0.0161302507044248 0.991934874647788 65 0.00598443901853486 0.0119688780370697 0.994015560981465 66 0.00420360259308408 0.00840720518616816 0.995796397406916 67 0.00307682744066831 0.00615365488133662 0.996923172559332 68 0.0021003958185277 0.0042007916370554 0.997899604181472 69 0.00184308630197766 0.00368617260395532 0.998156913698022 70 0.0857341924375482 0.171468384875096 0.914265807562452 71 0.0704593620542214 0.140918724108443 0.929540637945779 72 0.055587751999073 0.111175503998146 0.944412248000927 73 0.0434785609220826 0.0869571218441652 0.956521439077917 74 0.0332179696396098 0.0664359392792195 0.96678203036039 75 0.0251676357556351 0.0503352715112702 0.974832364244365 76 0.0188414936432211 0.0376829872864422 0.98115850635678 77 0.0153803488780289 0.0307606977560578 0.98461965112197 78 0.0115565990717314 0.0231131981434629 0.988443400928269 79 0.00836004005565155 0.0167200801113031 0.991639959944348 80 0.0060007309433662 0.0120014618867324 0.993999269056634 81 0.00569693894171976 0.0113938778834395 0.99430306105828 82 0.0193095068878416 0.0386190137756832 0.980690493112159 83 0.0143201485575354 0.0286402971150708 0.985679851442465 84 0.0133472797826582 0.0266945595653163 0.986652720217342 85 0.969588942760993 0.060822114478013 0.0304110572390065 86 0.960508884068098 0.0789822318638042 0.0394911159319021 87 0.9512000026986 0.0975999946028014 0.0487999973014007 88 0.939805350546436 0.120389298907128 0.0601946494535639 89 0.927099247634887 0.145801504730226 0.0729007523651132 90 0.935662044259216 0.128675911481569 0.0643379557407845 91 0.918652260359559 0.162695479280883 0.0813477396404414 92 0.903973950830475 0.192052098339049 0.0960260491695246 93 0.92519204022013 0.149615919559741 0.0748079597798703 94 0.909344025117669 0.181311949764662 0.090655974882331 95 0.88845986458147 0.223080270837058 0.111540135418529 96 0.862500288799538 0.274999422400924 0.137499711200462 97 0.833935874719891 0.332128250560217 0.166064125280109 98 0.8014632964056 0.397073407188798 0.198536703594399 99 0.764136060724023 0.471727878551954 0.235863939275977 100 0.722561571165964 0.554876857668072 0.277438428834036 101 0.677870534591828 0.644258930816345 0.322129465408172 102 0.633106556527079 0.733786886945843 0.366893443472921 103 0.584624927846856 0.830750144306287 0.415375072153143 104 0.549708908710689 0.900582182578622 0.450291091289311 105 0.509341852295822 0.981316295408356 0.490658147704178 106 0.999533615326094 0.000932769347812665 0.000466384673906333 107 0.999336540552618 0.00132691889476325 0.000663459447381625 108 0.998921075126882 0.002157849746236 0.001078924873118 109 0.998317423490455 0.00336515301908946 0.00168257650954473 110 0.999676731032704 0.000646537934592825 0.000323268967296413 111 0.999455626054086 0.00108874789182888 0.000544373945914438 112 0.999142714328052 0.00171457134389676 0.00085728567194838 113 0.998775299868177 0.00244940026364506 0.00122470013182253 114 1 0 0 115 1 0 0 116 1 0 0 117 1 0 0 118 1 0 0 119 1 0 0 120 1 0 0 121 1 0 0 122 1 0 0 123 1 0 0 124 1 2.29027722876273e-314 1.14513861438137e-314 125 1 2.19100778923149e-298 1.09550389461574e-298 126 1 2.86460374522558e-294 1.43230187261279e-294 127 1 1.57053833308214e-271 7.85269166541068e-272 128 1 5.08887628966546e-253 2.54443814483273e-253 129 1 1.92395357690118e-247 9.61976788450588e-248 130 1 3.04916765780649e-231 1.52458382890324e-231 131 1 5.81868681185882e-221 2.90934340592941e-221 132 1 5.49809410317547e-203 2.74904705158774e-203 133 1 2.46216708404559e-192 1.23108354202280e-192 134 1 9.46371938403483e-175 4.73185969201742e-175 135 1 1.01279277441768e-163 5.06396387208839e-164 136 1 2.02976563452989e-151 1.01488281726494e-151 137 1 7.76901729438546e-137 3.88450864719273e-137 138 1 1.17106859273505e-124 5.85534296367523e-125 139 1 3.26959676519298e-111 1.63479838259649e-111 140 1 3.38936234798622e-95 1.69468117399311e-95 141 1 4.7380306538587e-82 2.36901532692935e-82 142 1 3.33581610477523e-72 1.66790805238761e-72 143 1 5.27979005315606e-57 2.63989502657803e-57 144 1 6.40295872702784e-43 3.20147936351392e-43 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 46 0.353846153846154 NOK 5% type I error level 66 0.507692307692308 NOK 10% type I error level 77 0.592307692307692 NOK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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Software written by Ed van Stee & Patrick Wessa

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