ws 7 6

*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: Wed, 24 Nov 2010 13:52:28 +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/Nov/24/t1290606692byuh4r21bk445rx.htm/, Retrieved Wed, 24 Nov 2010 14:51:32 +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/Nov/24/t1290606692byuh4r21bk445rx.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 9 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 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] = -0.578264633807956 + 0.92553541241128B[t] + 0.0132183880731032CM[t] + 0.0160035232163502CM_B[t] -1.31048736184262D[t] + 1.32524772719412D_B[t] + 0.406327339245112PE[t] -0.394585656390905PE_B[t] -0.341990685460131PC[t] + 0.363464570658179PC_B[t] + 0.942105175460257PS[t] + 0.0146495184249108PS_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) -0.578264633807956 1.018728 -0.5676 0.57115 0.285575 B 0.92553541241128 0.026458 34.9813 0 0 CM 0.0132183880731032 0.08117 0.1628 0.870862 0.435431 CM_B 0.0160035232163502 0.079044 0.2025 0.839834 0.419917 D -1.31048736184262 0.218181 -6.0064 0 0 D_B 1.32524772719412 0.221044 5.9954 0 0 PE 0.406327339245112 0.143549 2.8306 0.005297 0.002649 PE_B -0.394585656390905 0.151846 -2.5986 0.010314 0.005157 PC -0.341990685460131 0.108022 -3.1659 0.00188 0.00094 PC_B 0.363464570658179 0.109279 3.326 0.001113 0.000556 PS 0.942105175460257 0.048185 19.5519 0 0 PS_B 0.0146495184249108 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) 469.131471059977 F-TEST (DF numerator) 11 F-TEST (DF denominator) 147 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.43270045551944 Sum Squared Residuals 301.736697501106 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 26 24.6041995514881 1.39580044851185 2 23 25.4130327883993 -2.41303278839925 3 25 24.2183183396727 0.78168166032734 4 23 19.5179366599762 3.48206334002381 5 20 22.3741165311321 -2.37411653113214 6 29 22.2387016296813 6.76129837031869 7 20 20.2205856699302 -0.220585669930177 8 16 16.6015594595828 -0.601559459582769 9 18 18.4816387188737 -0.481638718873717 10 17 17.4960001377340 -0.49600013773396 11 23 23.0502803334575 -0.0502803334575275 12 30 29.5644417477413 0.435558252258724 13 23 22.7065622191804 0.293437780819601 14 18 18.2815495853943 -0.281549585394317 15 15 15.7286961091583 -0.728696109158332 16 12 12.7283106162804 -0.728310616280428 17 21 20.9498195332017 0.0501804667983207 18 15 15.3891673348079 -0.389167334807894 19 20 20.2068579140039 -0.206857914003871 20 31 30.6461690533045 0.353830946695542 21 27 26.8465542387064 0.153445761293572 22 34 33.4530317080726 0.546968291927387 23 21 21.1673111384559 -0.167311138455912 24 31 30.5027986502654 0.497201349734574 25 19 19.3078180295097 -0.307818029509666 26 16 16.5787508582618 -0.578750858261844 27 20 20.3178371410299 -0.317837141029893 28 21 21.1055840416876 -0.105584041687578 29 22 22.1827699761436 -0.182769976143621 30 17 17.5205361096234 -0.52053610962345 31 24 23.9606385098554 0.0393614901445705 32 25 25.2453422813576 -0.245342281357636 33 26 26.0625779104939 -0.0625779104938981 34 25 24.9901215197081 0.00987848029186374 35 17 17.6352757199115 -0.635275719911508 36 32 31.5968497808248 0.403150219175239 37 33 32.3548017515907 0.645198248409274 38 13 12.8444245603739 0.155575439626082 39 0 2.18794968435404 -2.18794968435404 40 25 25.174433175096 -0.174433175096001 41 29 28.8918376034232 0.108162396576836 42 22 22.0868260200892 -0.0868260200891926 43 18 18.2686093376018 -0.268609337601757 44 17 17.5296000678684 -0.529600067868443 45 20 20.3328639948932 -0.332863994893188 46 15 15.634898291154 -0.634898291154 47 20 20.3458358671561 -0.345835867156141 48 33 32.5430125446762 0.456987455323809 49 29 28.6121314784000 0.38786852159997 50 23 23.2818153482682 -0.281815348268219 51 26 25.8615682049042 0.138431795095829 52 18 18.4186711187687 -0.418671118768677 53 20 20.1016957485837 -0.101695748583711 54 11 11.4706891159079 -0.470689115907916 55 28 28.1707423952679 -0.170742395267928 56 26 25.9896142003860 0.0103857996140351 57 22 22.1695069951440 -0.169506995144028 58 17 17.5343728156567 -0.53437281565669 59 12 12.5319259276469 -0.531925927646852 60 14 14.7123555505507 -0.712355550550712 61 17 17.5107009711061 -0.510700971106106 62 21 20.3380927470690 0.661907252931047 63 0 -5.25108566558226 5.25108566558226 64 18 18.4794330488443 -0.479433048844261 65 10 10.9799755833075 -0.979975583307488 66 29 28.7346391115354 0.265360888464633 67 31 30.3255764596980 0.67442354030197 68 19 19.4438616524450 -0.443861652445022 69 9 9.12373445468246 -0.123734454682459 70 0 -0.372268938781072 0.372268938781072 71 28 27.5383401714152 0.461659828584786 72 19 19.2588847154214 -0.258884715421411 73 30 29.6367145656765 0.363285434323499 74 29 28.8976785788225 0.102321421177499 75 26 25.8271010602228 0.172898939777158 76 23 23.0101476516417 -0.0101476516417497 77 13 13.869782539103 -0.869782539102996 78 21 21.3603289070511 -0.360328907051057 79 19 19.3574021941919 -0.357402194191937 80 28 27.7949920874708 0.205007912529240 81 23 22.3451927968144 0.654807203185622 82 0 0.446493779711898 -0.446493779711898 83 21 21.1961576111266 -0.196157611126643 84 20 19.4521857063232 0.54781429367675 85 0 7.2377156800752 -7.2377156800752 86 21 21.2209489982356 -0.220948998235552 87 21 21.296532797793 -0.296532797792997 88 15 15.6989440017742 -0.698944001774215 89 28 26.9753740420348 1.02462595796524 90 0 -0.262612919822320 0.262612919822320 91 26 25.8540910907174 0.145908909282640 92 10 9.75667480922528 0.243325190774723 93 0 0.0342085643549303 -0.0342085643549303 94 22 22.1776567768225 -0.177656776822495 95 19 19.3236304946870 -0.323630494687042 96 31 30.8519275928890 0.148072407111043 97 31 30.5939006437243 0.406099356275664 98 29 28.7494305950021 0.250569404997940 99 19 19.1361975269074 -0.136197526907407 100 22 21.9978267604862 0.0021732395137644 101 23 23.0837356952992 -0.083735695299185 102 15 15.3413957017525 -0.341395701752489 103 20 20.2871768710127 -0.287176871012682 104 18 18.4718631876671 -0.471863187667068 105 23 22.0471579374471 0.952842062552895 106 0 5.73875916131579 -5.73875916131579 107 21 20.8699276360379 0.130072363962143 108 24 23.8646329249258 0.135367075074196 109 25 24.0998567874755 0.90014321252454 110 0 -1.85640375280187 1.85640375280187 111 13 13.5411151924826 -0.541115192482634 112 28 27.5691937214214 0.430806278578555 113 21 20.1181711746810 0.881828825318965 114 0 -7.15715228035647 7.15715228035647 115 9 10.0905632682401 -1.09056326824013 116 16 16.3128204414968 -0.312820441496799 117 19 19.2843924990371 -0.284392499037124 118 17 17.4037431082757 -0.40374310827568 119 25 24.901282449828 0.0987175501719828 120 20 19.9624893812134 0.0375106187865633 121 29 28.4688111245886 0.531188875411382 122 14 13.6033852267716 0.396614773228392 123 0 -1.15007446225698 1.15007446225698 124 15 15.4353749719551 -0.435374971955149 125 19 19.4786690485831 -0.47866904858306 126 20 19.4012843437678 0.598715656232224 127 0 -4.26985303011458 4.26985303011458 128 20 20.3485480195630 -0.348548019562960 129 18 18.4452068883406 -0.445206888340618 130 33 32.3939257377748 0.606074262225229 131 22 22.1911170315266 -0.191117031526600 132 16 16.4309318311061 -0.430931831106053 133 17 17.4128504707148 -0.412850470714814 134 16 16.3094613074666 -0.309461307466619 135 21 21.0292327307523 -0.029232730752263 136 26 26.0715816303282 -0.0715816303281501 137 18 18.2493848514483 -0.249384851448318 138 18 18.4742408271431 -0.474240827143106 139 17 17.2852117383983 -0.285211738398310 140 22 22.1127894550919 -0.11278945509194 141 30 28.6516116953374 1.34838830466263 142 0 2.92325184158514 -2.92325184158514 143 24 24.3774196544525 -0.377419654452538 144 21 21.1736848378696 -0.173684837869617 145 21 21.4055415731769 -0.405541573176936 146 29 28.7628679486231 0.237132051376895 147 31 29.5627692076597 1.43723079234029 148 0 0.431084021843932 -0.431084021843932 149 16 16.2259330922225 -0.225933092222503 150 22 22.0352239577883 -0.0352239577882566 151 20 20.2570507908056 -0.25705079080563 152 28 28.0166912573327 -0.0166912573327332 153 38 37.0463235816684 0.953676418331649 154 22 21.966706215613 0.0332937843869862 155 20 20.466852129873 -0.466852129872996 156 17 17.3828668619047 -0.38286686190475 157 28 27.7818989790219 0.218101020978083 158 22 22.2097426131333 -0.209742613133305 159 31 30.7372463017937 0.262753698206326 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 15 0.931890324775149 0.136219350449703 0.0681096752248514 16 0.996805081921695 0.0063898361566105 0.00319491807830525 17 0.992876311439192 0.0142473771216161 0.00712368856080807 18 0.98538436754423 0.0292312649115383 0.0146156324557692 19 0.983095289663174 0.0338094206736516 0.0169047103368258 20 0.97085633205466 0.0582873358906794 0.0291436679453397 21 0.963207522126936 0.0735849557461287 0.0367924778730644 22 0.94214960177313 0.115700796453739 0.0578503982268694 23 0.9127322853819 0.174535429236199 0.0872677146180996 24 0.965010013242332 0.0699799735153369 0.0349899867576685 25 0.94760064853572 0.104798702928559 0.0523993514642797 26 0.924726268691788 0.150547462616425 0.0752737313082124 27 0.895200219936097 0.209599560127806 0.104799780063903 28 0.858080979736361 0.283838040527277 0.141919020263639 29 0.813311838739206 0.373376322521589 0.186688161260794 30 0.7697783746988 0.460443250602399 0.230221625301199 31 0.762113147402687 0.475773705194627 0.237886852597313 32 0.722634649881769 0.554730700236463 0.277365350118231 33 0.663850487204168 0.672299025591664 0.336149512795832 34 0.620709085408403 0.758581829183194 0.379290914591597 35 0.560556487990136 0.878887024019728 0.439443512009864 36 0.513812575763877 0.972374848472245 0.486187424236123 37 0.470394142827472 0.940788285654945 0.529605857172528 38 0.413657578173338 0.827315156346676 0.586342421826662 39 0.598974369708297 0.802051260583405 0.401025630291703 40 0.554492920001728 0.891014159996544 0.445507079998272 41 0.495662276774656 0.991324553549312 0.504337723225344 42 0.439305588742755 0.87861117748551 0.560694411257245 43 0.385478527406998 0.770957054813996 0.614521472593002 44 0.336057625432369 0.672115250864738 0.663942374567631 45 0.287567283519701 0.575134567039403 0.712432716480299 46 0.242217504440564 0.484435008881128 0.757782495559436 47 0.201131976603976 0.402263953207952 0.798868023396024 48 0.167170787342452 0.334341574684905 0.832829212657548 49 0.136007451573175 0.272014903146351 0.863992548426824 50 0.110051711244626 0.220103422489251 0.889948288755374 51 0.0863358334372096 0.172671666874419 0.91366416656279 52 0.0676583074721739 0.135316614944348 0.932341692527826 53 0.0529175410391086 0.105835082078217 0.947082458960891 54 0.0398030850049655 0.079606170009931 0.960196914995035 55 0.0304749236788772 0.0609498473577544 0.969525076321123 56 0.0224820192074422 0.0449640384148845 0.977517980792558 57 0.0161687035770383 0.0323374071540765 0.983831296422962 58 0.0117099067954447 0.0234198135908894 0.988290093204555 59 0.00829445004929892 0.0165889000985978 0.991705549950701 60 0.0059932375457984 0.0119864750915968 0.994006762454202 61 0.00411199622777575 0.0082239924555515 0.995888003772224 62 0.00440994293701509 0.00881988587403018 0.995590057062985 63 0.0113828213699662 0.0227656427399324 0.988617178630034 64 0.00806512535221193 0.0161302507044239 0.991934874647788 65 0.00598443901853502 0.0119688780370700 0.994015560981465 66 0.00420360259308469 0.00840720518616938 0.995796397406915 67 0.00307682744066801 0.00615365488133603 0.996923172559332 68 0.00210039581852808 0.00420079163705617 0.997899604181472 69 0.00184308630197776 0.00368617260395552 0.998156913698022 70 0.0857341924375413 0.171468384875083 0.914265807562459 71 0.0704593620542171 0.140918724108434 0.929540637945783 72 0.055587751999065 0.11117550399813 0.944412248000935 73 0.0434785609220866 0.0869571218441731 0.956521439077913 74 0.0332179696396098 0.0664359392792195 0.96678203036039 75 0.0251676357556353 0.0503352715112706 0.974832364244365 76 0.0188414936432232 0.0376829872864463 0.981158506356777 77 0.0153803488780306 0.0307606977560612 0.98461965112197 78 0.0115565990717313 0.0231131981434626 0.988443400928269 79 0.00836004005565288 0.0167200801113058 0.991639959944347 80 0.00600073094336713 0.0120014618867343 0.993999269056633 81 0.00569693894172114 0.0113938778834423 0.994303061058279 82 0.019309506887842 0.038619013775684 0.980690493112158 83 0.0143201485575349 0.0286402971150698 0.985679851442465 84 0.0133472797826577 0.0266945595653153 0.986652720217342 85 0.969588942760994 0.0608221144780117 0.0304110572390058 86 0.9605088840681 0.0789822318638016 0.0394911159319008 87 0.951200002698601 0.097599994602797 0.0487999973013985 88 0.939805350546437 0.120389298907126 0.060194649453563 89 0.927099247634885 0.14580150473023 0.072900752365115 90 0.935662044259217 0.128675911481566 0.064337955740783 91 0.91865226035956 0.162695479280880 0.0813477396404401 92 0.903973950830475 0.192052098339049 0.0960260491695245 93 0.925192040220129 0.149615919559742 0.0748079597798712 94 0.909344025117669 0.181311949764663 0.0906559748823313 95 0.88845986458147 0.223080270837061 0.111540135418531 96 0.862500288799537 0.274999422400926 0.137499711200463 97 0.833935874719888 0.332128250560223 0.166064125280112 98 0.801463296405597 0.397073407188807 0.198536703594403 99 0.764136060724027 0.471727878551947 0.235863939275974 100 0.722561571165965 0.55487685766807 0.277438428834035 101 0.677870534591829 0.644258930816342 0.322129465408171 102 0.633106556527083 0.733786886945834 0.366893443472917 103 0.584624927846848 0.830750144306303 0.415375072153152 104 0.549708908710682 0.900582182578636 0.450291091289318 105 0.509341852295823 0.981316295408355 0.490658147704177 106 0.999533615326094 0.000932769347812684 0.000466384673906342 107 0.999336540552618 0.00132691889476335 0.000663459447381676 108 0.998921075126882 0.00215784974623607 0.00107892487311803 109 0.998317423490455 0.0033651530190893 0.00168257650954465 110 0.999676731032704 0.000646537934592852 0.000323268967296426 111 0.999455626054085 0.0010887478918291 0.00054437394591455 112 0.999142714328052 0.00171457134389647 0.000857285671948233 113 0.998775299868178 0.00244940026364421 0.00122470013182210 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 0 0 125 1 4.25610936260445e-304 2.12805468130223e-304 126 1 4.84385149583064e-294 2.42192574791532e-294 127 1 8.7512927611759e-278 4.37564638058795e-278 128 1 5.65416621894546e-263 2.82708310947273e-263 129 1 2.30484563619042e-245 1.15242281809521e-245 130 1 3.05972870069150e-230 1.52986435034575e-230 131 1 1.32410842359731e-223 6.62054211798654e-224 132 1 3.79293484597089e-209 1.89646742298545e-209 133 1 8.4189297430175e-195 4.20946487150875e-195 134 1 1.01646719401544e-182 5.08233597007721e-183 135 1 5.71862489918074e-168 2.85931244959037e-168 136 1 2.35328575929728e-154 1.17664287964864e-154 137 1 4.30226771089198e-142 2.15113385544599e-142 138 1 9.92764614521413e-126 4.96382307260707e-126 139 1 1.06614260278708e-112 5.33071301393539e-113 140 1 1.9543900810254e-97 9.771950405127e-98 141 1 7.62792043350856e-82 3.81396021675428e-82 142 1 2.03877361448461e-73 1.01938680724230e-73 143 1 5.91295474588529e-59 2.95647737294264e-59 144 1 2.51294829863939e-45 1.25647414931970e-45 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:

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606692byuh4r21bk445rx/10vdhz1290606735.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606692byuh4r21bk445rx/10vdhz1290606735.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606692byuh4r21bk445rx/16uko1290606735.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606692byuh4r21bk445rx/16uko1290606735.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606692byuh4r21bk445rx/26uko1290606735.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606692byuh4r21bk445rx/26uko1290606735.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606692byuh4r21bk445rx/36uko1290606735.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606692byuh4r21bk445rx/36uko1290606735.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606692byuh4r21bk445rx/4zl1r1290606735.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606692byuh4r21bk445rx/4zl1r1290606735.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606692byuh4r21bk445rx/5zl1r1290606735.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606692byuh4r21bk445rx/5zl1r1290606735.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606692byuh4r21bk445rx/6suit1290606735.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606692byuh4r21bk445rx/6suit1290606735.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606692byuh4r21bk445rx/7340e1290606735.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606692byuh4r21bk445rx/7340e1290606735.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606692byuh4r21bk445rx/8340e1290606735.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606692byuh4r21bk445rx/8340e1290606735.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606692byuh4r21bk445rx/9vdhz1290606735.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290606692byuh4r21bk445rx/9vdhz1290606735.ps (open in new window)

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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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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