Workshop 4

*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, 01 Dec 2010 10:12:58 +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/01/t12911982696yug1ymsupa7ejg.htm/, Retrieved Wed, 01 Dec 2010 11:11:26 +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/01/t12911982696yug1ymsupa7ejg.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 «

2 1 27 5 35 26 49 2 1 36 4 34 25 45 1 1 25 4 13 17 54 4 1 27 3 35 37 36 3 2 25 3 28 35 36 1 2 44 3 32 15 53 2 1 50 4 35 27 46 2 1 41 4 36 36 42 2 1 48 5 27 25 41 2 2 43 4 29 30 45 1 2 47 2 27 27 47 2 2 41 3 28 33 42 3 1 44 2 29 29 45 2 2 47 5 28 30 40 3 2 40 3 30 25 45 3 2 46 3 25 23 40 2 1 28 3 15 26 42 3 1 56 3 33 24 45 2 2 49 4 31 35 47 4 2 25 4 37 39 31 2 2 41 4 37 23 46 3 2 26 3 34 32 34 2 1 50 5 32 29 43 2 1 47 4 21 26 45 3 1 52 2 25 21 42 3 2 37 5 32 35 51 4 2 41 3 28 23 44 2 1 45 4 22 21 47 1 2 26 4 25 28 47 2 1 3 26 30 41 4 1 52 4 34 21 44 1 1 46 2 34 29 51 2 1 58 3 36 28 46 3 1 54 5 36 19 47 2 1 29 3 26 26 46 4 2 50 3 26 33 38 3 1 43 2 34 34 50 3 2 30 3 33 33 48 3 2 47 2 31 40 36 1 1 45 3 33 24 51 2 48 1 22 35 35 2 2 48 3 29 35 49 2 2 26 4 24 32 38 2 1 46 5 37 20 47 4 2 3 32 35 36 2 2 50 3 23 35 47 3 1 25 4 29 21 46 2 1 47 2 35 33 43 5 2 47 2 20 40 53 4 1 41 3 28 22 55 4 2 45 2 26 35 39 2 2 41 4 36 20 55 3 2 45 5 26 28 41 2 2 40 3 33 46 33 3 1 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 11 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 Teamwork33rec[t] = + 56.3578676483602 -0.181121611496331geslacht[t] -0.217858586723552leeftijd[t] -0.403102859125285opleiding[t] -0.309347564888897Openheid[t] -0.308371926580031Neuroticisme[t] -0.526092314808072`Extraversie `[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) 56.3578676483602 4.906956 11.4853 0 0 geslacht -0.181121611496331 0.064002 -2.8299 0.005162 0.002581 leeftijd -0.217858586723552 0.057284 -3.8031 0.000193 9.7e-05 opleiding -0.403102859125285 0.059104 -6.8202 0 0 Openheid -0.309347564888897 0.060651 -5.1004 1e-06 0 Neuroticisme -0.308371926580031 0.057734 -5.3413 0 0 `Extraversie ` -0.526092314808072 0.047006 -11.1919 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.751173541373145 R-squared 0.564261689259072 Adjusted R-squared 0.550355147426915 F-TEST (value) 40.5752699750474 F-TEST (DF numerator) 6 F-TEST (DF denominator) 188 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 8.09104652000884 Sum Squared Residuals 12307.4263523221 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2 3.65569161191305 -1.65569161191305 2 2 4.82015594122822 -2.82015594122822 3 1 11.4450438372218 -10.4450438372218 4 4 7.90900623028884 -3.90900623028884 5 3 10.9457785996221 -7.94577859962208 6 1 2.79294437218239 -1.79294437218239 7 2 0.317951994241523 1.68204800575848 8 2 1.29835362987663 0.70164637012337 9 2 6.07255225487497 -4.07255225487497 10 2 3.11890241421145 -1.11890241421145 11 1 3.54530006546956 -2.54530006546956 12 2 4.92023117635685 -2.92023117635685 13 3 4.19674308381483 -1.19674308381483 14 2 4.78417434712121 -2.78417434712121 15 3 5.40809310151865 -2.40809310151865 16 3 8.89488483282224 -5.89488483282224 17 2 14.1136362448752 -12.1136362448752 18 3 1.48380655735149 1.51619344264851 19 2 -1.40098849842395 3.40098849842395 20 4 9.15552152421692 -5.15552152421692 21 2 2.71235023979952 -0.712350239799518 22 3 10.8491350329213 -7.84913503292135 23 2 1.80442492104712 0.195575078952883 24 2 6.13685790424487 -4.13685790424487 25 3 7.73651700664647 -4.73651700664647 26 3 -1.60350514098780 4.6035051409878 27 4 6.95176581254102 -2.95176581254102 28 2 6.75290251608709 -4.75290251608709 29 1 7.62444787161133 -6.62444787161133 30 2 21.0144507437553 -19.0144507437553 31 1 11.7718563464008 -10.7718563464008 32 1 8.13482686884638 -7.13482686884638 33 1 6.26241810889727 -5.26241810889727 34 1 9.5530358536636 -8.5530358536636 35 1 15.6385762485134 -14.6385762485134 36 2 12.6626571803165 -10.6626571803165 37 1 6.91373349066285 -5.91373349066285 38 2 10.3796501305658 -8.37965013056584 39 2 10.9118618344566 -8.91186183445657 40 1 10.0479305771889 -9.04793057718893 41 48 24.7791638056731 23.2208361943269 42 48 18.5610445671710 29.438955432829 43 26 24.6074399952542 1.39256000474576 44 46 22.5044268138869 23.4955731861131 45 3 0.885167893301558 2.11483210669844 46 3 11.2324631782833 -8.23246317828333 47 4 2.33417322167167 1.66582677832833 48 2 -1.39396553185980 3.3939655318598 49 2 -0.458906677415186 2.45890667741519 50 3 -1.20537191242479 4.20537191242479 51 2 5.49741981817633 -3.49741981817633 52 4 -1.90928006605945 5.90928006605945 53 5 6.7423165217987 -1.74231652179870 54 3 10.5638733778826 -7.56387337788265 55 4 7.51509887411194 -3.51509887411194 56 5 5.0902582659543 -0.090258265954297 57 5 -5.2705426828559 10.2705426828559 58 3 2.60549603829008 0.394503961709919 59 4 4.53902564449172 -0.539025644491719 60 3 0.0815332763109033 2.91846672368910 61 3 -1.47484259054303 4.47484259054303 62 2 12.8727825102441 -10.8727825102441 63 3 8.62916684215383 -5.62916684215383 64 4 9.84199377090062 -5.84199377090062 65 4 -1.64146389541344 5.64146389541344 66 4 -2.39069066268417 6.39069066268417 67 4 -1.52371514377462 5.52371514377462 68 3 -1.84539930948934 4.84539930948934 69 3 7.320254476196 -4.320254476196 70 3 -3.08269001301171 6.08269001301171 71 2 5.70609681280954 -3.70609681280954 72 3 13.3300996063586 -10.3300996063586 73 3 6.73316195574574 -3.73316195574574 74 3 7.6046921394136 -4.60469213941360 75 3 11.7621259274492 -8.76212592744922 76 5 -3.58551948501181 8.5855194850118 77 3 12.4529192344847 -9.45291923448468 78 5 -0.695477499003792 5.69547749900379 79 4 2.34299117208896 1.65700882791104 80 4 7.47924173032437 -3.47924173032437 81 4 12.4034753841663 -8.40347538416633 82 5 21.0709082572884 -16.0709082572884 83 4 3.44584030543296 0.554159694567039 84 5 -3.22119099324009 8.2211909932401 85 3 2.31416002034494 0.685839979655059 86 3 -2.43912371299852 5.43912371299852 87 2 14.6916352816308 -12.6916352816308 88 3 0.612734720645915 2.38726527935408 89 4 0.182045246012176 3.81795475398782 90 5 7.46501377248785 -2.46501377248785 91 5 8.87907044584107 -3.87907044584107 92 3 2.70492975941155 0.295070240588451 93 2 -0.381495319681523 2.38149531968152 94 3 -1.95682983407143 4.95682983407143 95 4 9.50835144418757 -5.50835144418757 96 1 5.36997226007593 -4.36997226007593 97 4 10.6497195173875 -6.64971951738749 98 3 -0.479195708298474 3.47919570829847 99 3 10.8557088183521 -7.85570881835206 100 4 5.25674818434468 -1.25674818434468 101 3 12.7053552969696 -9.70535529696955 102 4 3.55291881863552 0.447081181364483 103 2 5.55562272390959 -3.55562272390959 104 3 1.80581386522551 1.19418613477449 105 3 11.7090399878631 -8.70903998786305 106 3 -2.56591763830829 5.5659176383083 107 2 6.50925433892976 -4.50925433892976 108 5 -1.53797811378748 6.53797811378748 109 5 12.6014546122057 -7.60145461220566 110 4 -1.44912315018161 5.44912315018161 111 2 0.61834254713009 1.38165745286991 112 3 14.3794804915105 -11.3794804915105 113 3 8.33901498440335 -5.33901498440335 114 3 5.97507472681706 -2.97507472681706 115 4 -1.63493686946029 5.63493686946029 116 5 1.35421035769127 3.64578964230873 117 4 12.2699350720912 -8.26993507209117 118 30 26.1949428976021 3.80505710239792 119 24 25.0122969624971 -1.01229696249706 120 27 20.4975014656477 6.50249853435233 121 26 28.2320701741048 -2.23207017410476 122 30 26.3141292065638 3.68587079343617 123 15 29.6137540617741 -14.6137540617741 124 28 24.8403728761144 3.15962712388556 125 34 22.5371948902184 11.4628051097816 126 29 23.2113771728050 5.78862282719503 127 26 23.4282469278012 2.57175307219876 128 31 28.3094156936942 2.69058430630583 129 28 21.3834552040163 6.61654479598372 130 33 29.4961410229925 3.50385897700755 131 32 27.0108666566815 4.98913334331848 132 33 22.1864471979522 10.8135528020478 133 31 21.9423000316417 9.05769996835832 134 37 23.6037814139099 13.3962185860901 135 27 32.2822536819512 -5.28225368195118 136 19 26.2717367879828 -7.27173678798282 137 27 24.9686420962191 2.03135790378086 138 31 23.6584695985582 7.3415304014418 139 38 32.0913940540965 5.90860594590349 140 22 24.4479836716564 -2.44798367165635 141 35 23.3335958903925 11.6664041096075 142 35 23.7079418370744 11.2920581629256 143 30 20.0870464377978 9.91295356220222 144 41 33.2172340993747 7.78276590062526 145 25 23.0814777429305 1.91852225706950 146 26 6.06639299318345 19.9336070068165 147 30 20.1770277380129 9.82297226198715 148 25 18.4878688353637 6.51213116463625 149 38 24.4308688895714 13.5691311104286 150 35 11.0594666552484 23.9405333447516 151 49 9.54425043594733 39.4557495640527 152 40 15.2662916434498 24.7337083565502 153 3 3.86117843611636 -0.86117843611636 154 2 -0.965547721967873 2.96554772196787 155 5 11.6273636758047 -6.62736367580469 156 5 8.32480193613167 -3.32480193613167 157 1 3.52043819858354 -2.52043819858354 158 2 3.45440122958215 -1.45440122958215 159 3 7.62762208407335 -4.62762208407335 160 3 3.03428154667045 -0.0342815466704533 161 2 2.77867170394853 -0.778671703948527 162 3 1.09451721009500 1.905482789905 163 4 13.1985215817832 -9.19852158178318 164 5 4.55939612852537 0.440603871474633 165 5 8.06870341105964 -3.06870341105965 166 1 -0.508987162257075 1.50898716225707 167 2 -0.714597107767927 2.71459710776793 168 3 9.5909729928579 -6.5909729928579 169 2 5.3028760002612 -3.3028760002612 170 1 7.25410691762637 -6.25410691762637 171 2 -0.769950705580802 2.7699507055808 172 2 12.5795772448798 -10.5795772448798 173 4 0.559501027559275 3.44049897244073 174 3 3.70550563002747 -0.705505630027472 175 2 1.06264540380316 0.937354596196836 176 3 4.83379723069364 -1.83379723069364 177 2 1.75750379395207 0.242496206047933 178 3 3.29274131959690 -0.292741319596895 179 2 6.05171463634383 -4.05171463634383 180 5 3.07237866227357 1.92762133772643 181 4 2.97239935289229 1.02760064710771 182 3 -6.13020788062198 9.13020788062198 183 3 1.59824809833087 1.40175190166913 184 1 -6.80982388264441 7.80982388264441 185 2 -2.82755020950619 4.82755020950619 186 3 1.03869448638095 1.96130551361905 187 3 1.44624821915758 1.55375178084242 188 3 7.56579694002818 -4.56579694002818 189 3 9.28822176585219 -6.28822176585219 190 2 6.77196077450595 -4.77196077450595 191 3 8.9126312915485 -5.9126312915485 192 4 10.4912633383816 -6.49126333838164 193 2 0.754419924558933 1.24558007544107 194 4 5.03335514991107 -1.03335514991107 195 2 3.65569161191377 -1.65569161191377 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.000246815876147257 0.000493631752294515 0.999753184123853 11 1.75749591610434e-05 3.51499183220868e-05 0.999982425040839 12 8.1197712034293e-07 1.62395424068586e-06 0.99999918802288 13 1.87550414495736e-07 3.75100828991472e-07 0.999999812449585 14 1.20708398580669e-08 2.41416797161337e-08 0.99999998792916 15 5.01273743468723e-09 1.00254748693745e-08 0.999999994987263 16 3.89466743549885e-10 7.7893348709977e-10 0.999999999610533 17 4.22568707590942e-11 8.45137415181883e-11 0.999999999957743 18 4.95454520985085e-12 9.9090904197017e-12 0.999999999995046 19 7.71489264802238e-13 1.54297852960448e-12 0.999999999999229 20 5.22455248481107e-14 1.04491049696221e-13 0.999999999999948 21 3.36737965708210e-15 6.73475931416421e-15 0.999999999999997 22 4.21652457672521e-16 8.43304915345042e-16 1 23 2.72649062621617e-17 5.45298125243233e-17 1 24 1.72047124066403e-18 3.44094248132806e-18 1 25 1.06593615638218e-19 2.13187231276435e-19 1 26 4.91715672150619e-19 9.83431344301239e-19 1 27 1.19565503431552e-18 2.39131006863105e-18 1 28 1.04539750310065e-19 2.0907950062013e-19 1 29 2.16104172264669e-20 4.32208344529337e-20 1 30 2.84117319373774e-21 5.68234638747548e-21 1 31 2.83275794674141e-22 5.66551589348283e-22 1 32 2.43219697568112e-23 4.86439395136224e-23 1 33 2.1252352747663e-24 4.2504705495326e-24 1 34 2.17532915864978e-25 4.35065831729956e-25 1 35 1.07727023181189e-25 2.15454046362379e-25 1 36 1.44561490963593e-26 2.89122981927187e-26 1 37 1.65782159459822e-27 3.31564318919644e-27 1 38 5.38229533982967e-28 1.07645906796593e-27 1 39 1.46121926418044e-28 2.92243852836087e-28 1 40 1.41076615984121e-28 2.82153231968242e-28 1 41 2.57845244805132e-05 5.15690489610264e-05 0.99997421547552 42 7.86704036787008e-05 0.000157340807357402 0.999921329596321 43 0.000763427930990744 0.00152685586198149 0.99923657206901 44 0.0151041770611924 0.0302083541223848 0.984895822938808 45 0.0118013005385746 0.0236026010771492 0.988198699461425 46 0.038344205008222 0.076688410016444 0.961655794991778 47 0.0299114023122001 0.0598228046244002 0.9700885976878 48 0.0219174857649989 0.0438349715299978 0.978082514235001 49 0.0204209817187675 0.040841963437535 0.979579018281233 50 0.0148670676194347 0.0297341352388694 0.985132932380565 51 0.0109953583498038 0.0219907166996075 0.989004641650196 52 0.00859215785704406 0.0171843157140881 0.991407842142956 53 0.00603391676779579 0.0120678335355916 0.993966083232204 54 0.005429300676497 0.010858601352994 0.994570699323503 55 0.00431570300902211 0.00863140601804423 0.995684296990978 56 0.00333796855050973 0.00667593710101947 0.99666203144949 57 0.00307210195264178 0.00614420390528356 0.996927898047358 58 0.00213645583028494 0.00427291166056988 0.997863544169715 59 0.00146340604493298 0.00292681208986596 0.998536593955067 60 0.000976577627260363 0.00195315525452073 0.99902342237274 61 0.000733941135957442 0.00146788227191488 0.999266058864043 62 0.00108108455156754 0.00216216910313508 0.998918915448432 63 0.000959394552936383 0.00191878910587277 0.999040605447064 64 0.000777754961294104 0.00155550992258821 0.999222245038706 65 0.000560318037553286 0.00112063607510657 0.999439681962447 66 0.000436832817129287 0.000873665634258573 0.99956316718287 67 0.000314293091645482 0.000628586183290965 0.999685706908354 68 0.000246369043781938 0.000492738087563875 0.999753630956218 69 0.000171896417734236 0.000343792835468471 0.999828103582266 70 0.000135119012874794 0.000270238025749589 0.999864880987125 71 0.000110234874615167 0.000220469749230333 0.999889765125385 72 8.1232198873726e-05 0.000162464397747452 0.999918767801126 73 5.21638636383846e-05 0.000104327727276769 0.999947836136362 74 4.23600352405474e-05 8.47200704810949e-05 0.99995763996476 75 3.0934629338428e-05 6.1869258676856e-05 0.999969065370662 76 2.29161306724798e-05 4.58322613449596e-05 0.999977083869328 77 1.56163749688743e-05 3.12327499377486e-05 0.99998438362503 78 1.03137720562639e-05 2.06275441125278e-05 0.999989686227944 79 6.17392934902525e-06 1.23478586980505e-05 0.99999382607065 80 4.29047582573303e-06 8.58095165146605e-06 0.999995709524174 81 3.75454794309432e-06 7.50909588618865e-06 0.999996245452057 82 6.24882552254615e-06 1.24976510450923e-05 0.999993751174477 83 3.7333047478164e-06 7.4666094956328e-06 0.999996266695252 84 3.15407226931965e-06 6.30814453863931e-06 0.99999684592773 85 1.97337188204139e-06 3.94674376408278e-06 0.999998026628118 86 1.17715767373167e-06 2.35431534746334e-06 0.999998822842326 87 1.24601388921746e-06 2.49202777843491e-06 0.99999875398611 88 7.7553230367802e-07 1.55106460735604e-06 0.999999224467696 89 4.60369427306326e-07 9.20738854612652e-07 0.999999539630573 90 2.64645251706388e-07 5.29290503412776e-07 0.999999735354748 91 1.68074764122134e-07 3.36149528244268e-07 0.999999831925236 92 1.00744210046500e-07 2.01488420093001e-07 0.99999989925579 93 7.14001520403878e-08 1.42800304080776e-07 0.999999928599848 94 3.94840740872115e-08 7.89681481744231e-08 0.999999960515926 95 2.5890289048557e-08 5.1780578097114e-08 0.99999997410971 96 1.48533781725720e-08 2.97067563451441e-08 0.999999985146622 97 8.501872510237e-09 1.7003745020474e-08 0.999999991498127 98 5.42071592579504e-09 1.08414318515901e-08 0.999999994579284 99 9.46017673733332e-09 1.89203534746666e-08 0.999999990539823 100 5.10392474275223e-09 1.02078494855045e-08 0.999999994896075 101 6.6029229130572e-09 1.32058458261144e-08 0.999999993397077 102 3.67509364883900e-09 7.35018729767801e-09 0.999999996324906 103 2.04182769578397e-09 4.08365539156795e-09 0.999999997958172 104 1.09464825371894e-09 2.18929650743788e-09 0.999999998905352 105 1.57029037066103e-09 3.14058074132206e-09 0.99999999842971 106 9.50130844616383e-10 1.90026168923277e-09 0.99999999904987 107 5.92349080738795e-10 1.18469816147759e-09 0.99999999940765 108 3.75392862512793e-10 7.50785725025585e-10 0.999999999624607 109 2.76492087272946e-10 5.52984174545893e-10 0.999999999723508 110 1.46351239905726e-10 2.92702479811453e-10 0.999999999853649 111 7.44106160029434e-11 1.48821232005887e-10 0.99999999992559 112 5.42191175419206e-10 1.08438235083841e-09 0.999999999457809 113 5.21430280550079e-10 1.04286056110016e-09 0.99999999947857 114 5.89058775232142e-10 1.17811755046428e-09 0.999999999410941 115 4.15997005748042e-10 8.31994011496083e-10 0.999999999584003 116 7.85665950673627e-10 1.57133190134725e-09 0.999999999214334 117 4.74958089109058e-06 9.49916178218115e-06 0.99999525041911 118 0.182338969682438 0.364677939364875 0.817661030317562 119 0.390269112024607 0.780538224049215 0.609730887975393 120 0.628524030724401 0.742951938551198 0.371475969275599 121 0.729966763763832 0.540066472472335 0.270033236236168 122 0.768481480485063 0.463037039029873 0.231518519514936 123 0.914166273677518 0.171667452644965 0.0858337263224823 124 0.925491075216427 0.149017849567146 0.074508924783573 125 0.953871096055783 0.092257807888433 0.0461289039442165 126 0.976160487050296 0.0476790258994083 0.0238395129497041 127 0.971376963472777 0.0572460730544451 0.0286230365272225 128 0.968597479509252 0.0628050409814966 0.0314025204907483 129 0.964337385676871 0.0713252286462573 0.0356626143231287 130 0.960540898482722 0.0789182030345563 0.0394591015172781 131 0.961090173375953 0.0778196532480938 0.0389098266240469 132 0.96216362587417 0.0756727482516606 0.0378363741258303 133 0.958625273893242 0.0827494522135165 0.0413747261067582 134 0.97042499331353 0.0591500133729411 0.0295750066864705 135 0.967611376736717 0.064777246526565 0.0323886232632825 136 0.978355023654817 0.0432899526903661 0.0216449763451830 137 0.975168704982887 0.0496625900342261 0.0248312950171131 138 0.97288165359916 0.0542366928016793 0.0271183464008397 139 0.974949801854908 0.0501003962901832 0.0250501981450916 140 0.987897378375887 0.0242052432482268 0.0121026216241134 141 0.987279225830732 0.0254415483385363 0.0127207741692682 142 0.991637374575915 0.0167252508481691 0.00836262542408457 143 0.99037732840146 0.0192453431970780 0.00962267159853898 144 0.995565997309274 0.0088680053814522 0.0044340026907261 145 0.993668890189114 0.0126622196217716 0.00633110981088578 146 0.996859572546635 0.00628085490672994 0.00314042745336497 147 0.997682559852319 0.00463488029536273 0.00231744014768136 148 0.998141712679771 0.00371657464045769 0.00185828732022884 149 0.999419648292084 0.00116070341583250 0.000580351707916252 150 0.99983221019012 0.000335579619759233 0.000167789809879617 151 0.99999170921751 1.65815649813597e-05 8.29078249067985e-06 152 1 7.01682646413588e-27 3.50841323206794e-27 153 1 5.845013852657e-26 2.9225069263285e-26 154 1 4.75523848568593e-25 2.37761924284297e-25 155 1 1.88939491957205e-24 9.44697459786026e-25 156 1 1.75321910424696e-24 8.7660955212348e-25 157 1 4.88613898395969e-24 2.44306949197985e-24 158 1 3.8289299765845e-23 1.91446498829225e-23 159 1 3.16670099316466e-22 1.58335049658233e-22 160 1 2.78942466727984e-21 1.39471233363992e-21 161 1 2.35204795495301e-20 1.17602397747651e-20 162 1 1.89291014110312e-19 9.4645507055156e-20 163 1 1.35354676572101e-18 6.76773382860506e-19 164 1 4.72603060387511e-18 2.36301530193756e-18 165 1 2.52444454031183e-18 1.26222227015591e-18 166 1 1.18848344097491e-17 5.94241720487456e-18 167 1 1.02581841079045e-16 5.12909205395224e-17 168 1 8.64342043510031e-16 4.32171021755016e-16 169 0.999999999999996 7.66492913589777e-15 3.83246456794888e-15 170 0.99999999999998 4.08033110047915e-14 2.04016555023958e-14 171 0.999999999999871 2.57568304152799e-13 1.28784152076400e-13 172 0.999999999999587 8.26717026780455e-13 4.13358513390227e-13 173 0.999999999998635 2.73048291618847e-12 1.36524145809423e-12 174 0.999999999988272 2.34551276645789e-11 1.17275638322894e-11 175 0.99999999992976 1.40480781631680e-10 7.02403908158399e-11 176 0.99999999944975 1.10049959804398e-09 5.50249799021991e-10 177 0.999999996958013 6.08397411751767e-09 3.04198705875884e-09 178 0.999999977674126 4.46517476354363e-08 2.23258738177182e-08 179 0.99999992393316 1.52133678610535e-07 7.60668393052674e-08 180 0.999999827831453 3.44337093274774e-07 1.72168546637387e-07 181 0.999998912337874 2.17532425240695e-06 1.08766212620348e-06 182 0.99999769265952 4.61468095915202e-06 2.30734047957601e-06 183 0.99998226044685 3.54791063014154e-05 1.77395531507077e-05 184 0.99984485401602 0.00031029196796154 0.00015514598398077 185 0.998292124969072 0.00341575006185682 0.00170787503092841 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 138 0.784090909090909 NOK 5% type I error level 155 0.880681818181818 NOK 10% type I error level 169 0.960227272727273 NOK

Charts produced by software:

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Parameters (Session):

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

Parameters (R input):

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

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

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

Copyright

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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Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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