workshop 7

*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Thu, 02 Dec 2010 10:14:38 +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/02/t1291284838f7m39gp7biwlt54.htm/, Retrieved Thu, 02 Dec 2010 11:14:08 +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/02/t1291284838f7m39gp7biwlt54.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 «

13 14 3 25 55 147 12 8 5 158 7 71 10 12 6 0 0 0 9 7 6 143 10 0 10 10 5 67 74 43 12 7 3 0 0 0 13 16 8 148 138 8 12 11 4 28 0 0 12 14 4 114 113 34 6 6 4 0 0 0 5 16 6 123 115 103 12 11 6 145 9 0 11 16 5 113 114 73 14 12 4 152 59 159 14 7 6 0 0 0 12 13 4 36 114 113 12 11 6 0 0 0 11 15 6 8 102 44 11 7 4 108 0 0 7 9 4 112 86 0 9 7 2 51 17 41 11 14 7 43 45 74 11 15 5 120 123 0 12 7 4 13 24 0 12 15 6 55 5 0 11 17 6 103 123 32 11 15 7 127 136 126 8 14 5 14 4 154 9 14 6 135 76 129 12 8 4 38 99 98 10 8 4 11 98 82 10 14 7 43 67 45 12 14 7 141 92 8 8 8 4 62 13 0 12 11 4 62 24 129 11 16 6 135 129 31 12 10 6 117 117 117 7 8 5 82 11 99 11 14 6 145 20 55 11 16 7 87 91 132 12 13 6 76 111 58 9 5 3 124 0 0 15 8 3 151 58 0 11 10 4 131 0 0 11 8 6 127 146 101 11 13 7 76 129 31 11 15 5 25 48 147 15 6 4 0 0 0 11 12 5 58 111 132 12 16 6 115 32 123 12 5 6 130 112 39 9 15 6 17 51 136 12 12 5 102 53 141 12 8 4 21 131 0 13 13 5 0 0 0 11 14 5 14 76 135 9 12 4 110 106 118 9 16 6 133 2 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 19 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation FindingFriends[t] = + 9.01508211087726 + 0.173745393657251KnowingPeople[t] + 0.00935140411484961Celebrity[t] + 0.0055986399334022firstbestfriend[t] + 0.0106393108702864secondbestfriend[t] -0.0156929343329173thirdbestfriend[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) 9.01508211087726 0.762899 11.8169 0 0 KnowingPeople 0.173745393657251 0.082966 2.0942 0.037925 0.018963 Celebrity 0.00935140411484961 0.005716 1.6359 0.103963 0.051982 firstbestfriend 0.0055986399334022 0.004705 1.1899 0.235977 0.117988 secondbestfriend 0.0106393108702864 0.00458 2.323 0.021524 0.010762 thirdbestfriend -0.0156929343329173 0.007084 -2.2152 0.028255 0.014127 Multiple Linear Regression - Regression Statistics Multiple R 0.332773506741778 R-squared 0.110738206789220 Adjusted R-squared 0.0810961470155275 F-TEST (value) 3.73584722636247 F-TEST (DF numerator) 5 F-TEST (DF denominator) 150 p-value 0.00323763782245301 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.88804771231853 Sum Squared Residuals 1251.12293829424 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 9.89383858368528 3.10616141631472 2 12 10.2966642286419 1.70333577135806 3 10 11.1561352594534 -1.15613525945336 4 9 11.1944069103465 -2.19440691034649 5 10 11.2869147716477 -1.28691477164771 6 12 10.2593540788226 1.74064592117744 7 13 14.0410997778918 -1.04109977789177 8 12 11.1204489757017 0.879551024298322 9 12 12.7918505519692 -0.79185055196919 10 6 10.0949600892802 -4.09496008928016 11 5 12.1468980596833 -7.14689805968329 12 12 11.8899464539720 0.110053546027988 13 11 12.5417089753517 -1.54170897535165 14 14 10.1209685035139 3.87903149648615 15 14 10.2874082911671 3.71259170883289 16 12 10.9523087420764 1.04769125792361 17 12 10.9823898657961 1.01761013420388 18 11 12.1168811580132 -1.11688115801318 19 11 10.8733585957449 0.126641404255147 20 7 12.1582246776376 -5.15822467763759 21 9 10.0729912884565 -1.07299128845649 22 11 11.0712108165460 -0.07121081654602 23 11 13.6484920653638 -2.64849206536375 24 12 10.5968312629585 1.40316873704148 25 12 12.0384931911137 -0.0384931911136705 26 11 13.4079834792719 -2.40798347927191 27 11 11.8673866684934 -0.867386668493416 28 8 9.19850095793254 -1.19850095793254 29 9 11.0436415349726 -2.0436415349726 30 12 10.1705834055964 1.82941659440359 31 10 10.2598677658509 -0.259867765850937 32 10 11.7603707513469 -1.76037075134692 33 12 13.1556588068954 -1.15565880689543 34 8 10.9278775937793 -2.92787759377932 35 12 9.5417576653779 2.4582423346221 36 11 13.4929233630382 -2.49292336303817 37 12 10.8724113992191 1.12758860078089 38 7 9.47432267586284 -2.47432267586284 39 11 11.6651036662065 -0.665103666206464 40 11 11.2442598696542 -0.244259869654189 41 12 12.0261506033418 -0.0261506033417682 42 9 10.6060946432499 -1.60609464324994 43 15 11.8955741329002 3.10442586709984 44 11 11.5233634951849 -0.523363495184854 45 11 11.1405339758036 -0.140533975803608 46 11 12.6507188301105 -1.65071883011054 47 11 10.0118116094802 0.98818839051977 48 15 10.0949600892802 4.90503991071984 49 11 10.5810011461326 0.418998853867449 50 12 10.9051874513240 1.09481254867604 51 12 11.2473190736832 0.752680926316802 52 9 10.1809141044008 -1.18091410440081 53 12 10.0690248637294 1.93097513627062 54 12 11.9537720392036 0.0462279607963763 55 13 11.3205292489958 1.67947075100423 56 11 10.2626970929186 0.737302907081419 57 9 11.0292835448640 -2.02928354486403 58 9 10.4556461405830 -1.45564614058305 59 11 11.5314333707824 -0.531433370782359 60 15 12.3272830553294 2.67271694467061 61 8 9.34800307985401 -1.34800307985401 62 16 11.9134814337377 4.08651856626225 63 19 11.4717514070302 7.52824859296983 64 14 11.5559862591027 2.44401374089731 65 6 12.1628404454536 -6.1628404454536 66 13 11.8481939461577 1.15180605384229 67 15 10.6620511811186 4.33794881888143 68 7 10.4342547922416 -3.43425479224163 69 13 11.8617306465007 1.13826935349932 70 4 10.8682303434704 -6.8682303434704 71 14 11.7981563199613 2.2018436800387 72 13 11.8082506143608 1.19174938563919 73 11 12.8764432340041 -1.87644323400408 74 14 11.4472309886587 2.55276901134126 75 12 11.7820097559899 0.217990244010121 76 15 11.8100337508591 3.18996624914094 77 14 11.4532370161886 2.54676298381141 78 13 11.4860133707635 1.51398662923648 79 8 12.0549280446279 -4.05492804462788 80 6 9.72599052897288 -3.72599052897288 81 7 10.6606853124895 -3.66068531248951 82 13 11.8784396805979 1.12156031940209 83 13 12.8831225629876 0.116877437012414 84 11 12.5349040926459 -1.53490409264587 85 5 10.6809567472698 -5.68095674726982 86 12 11.9556658275354 0.0443341724646023 87 8 11.2761588909443 -3.27615889094431 88 11 11.8764862117699 -0.876486211769938 89 14 11.9950814068258 2.0049185931742 90 9 11.0833231770439 -2.08332317704388 91 10 11.4473033172173 -1.44730331721730 92 13 12.5020523748200 0.497947625179985 93 16 12.0790979563482 3.92090204365176 94 16 12.4122149694515 3.58778503054846 95 11 10.3098644601560 0.690135539843977 96 8 10.4979479402014 -2.49794794020141 97 4 9.85354632649284 -5.85354632649284 98 7 9.60715430359752 -2.60715430359752 99 14 11.9611016776927 2.03889832230729 100 11 11.8706382097162 -0.870638209716206 101 17 12.4659413971768 4.53405860282324 102 15 12.1110497078284 2.88895029217165 103 17 10.3412349223421 6.65876507765786 104 5 10.2765136167700 -5.27651361677003 105 4 12.0857841145972 -8.08578411459724 106 10 12.6996959101111 -2.69969591011112 107 11 10.3200107318547 0.679989268145262 108 15 12.9077405876710 2.09225941232902 109 10 11.2077384815379 -1.20773848153788 110 9 10.0589677938194 -1.05896779381944 111 12 12.4660636051942 -0.466063605194235 112 15 12.7110809614819 2.28891903851815 113 7 12.3092543946452 -5.30925439464515 114 13 12.1417827687105 0.85821723128954 115 12 13.2009024721173 -1.20090247211731 116 14 12.0753042295089 1.92469577049115 117 14 11.2808424891682 2.71915751083175 118 8 11.7664790750518 -3.76647907505175 119 15 12.0391647609664 2.9608352390336 120 12 11.4935449300286 0.506455069971386 121 12 11.9701722146525 0.0298277853475329 122 16 11.8973897210816 4.1026102789184 123 9 11.9466874403003 -2.94668744030026 124 15 12.3604997834862 2.63950021651376 125 15 12.7337445441219 2.26625545587805 126 6 9.6954938671685 -3.69549386716851 127 14 11.2497341080888 2.75026589191121 128 15 12.4184075107692 2.58159248923077 129 10 12.2075859169522 -2.20758591695223 130 6 9.52174847351126 -3.52174847351126 131 14 12.2317072722876 1.76829272771238 132 12 10.7695565098893 1.23044349011066 133 8 9.68373221736048 -1.68373221736048 134 11 9.86923926082576 1.13076073917424 135 13 10.7371153196462 2.2628846803538 136 9 11.1990339526980 -2.19903395269802 137 15 11.9993044472963 3.00069555270366 138 13 9.34800307985401 3.65199692014599 139 15 11.2760901946083 3.7239098053917 140 14 12.5629269804353 1.43707301956469 141 16 11.2850484629261 4.7149515370739 142 14 12.0535694739878 1.94643052601225 143 14 12.0272247248914 1.9727752751086 144 10 10.2282143206381 -0.228214320638078 145 10 11.4035241720714 -1.4035241720714 146 4 12.1991464216973 -8.19914642169729 147 8 10.3684731810132 -2.36847318101318 148 15 12.2948747427662 2.70512525723376 149 16 10.9832414452442 5.01675855475582 150 12 12.8891921035521 -0.889192103552134 151 12 11.4935305937240 0.506469406275974 152 15 10.6421842003074 4.35781579969259 153 9 10.2026985998068 -1.20269859980682 154 12 11.9288501078919 0.0711498921081077 155 14 11.691656178364 2.30834382163599 156 11 11.4070056110141 -0.40700561101407 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.176701688362858 0.353403376725717 0.823298311637142 10 0.216214433986386 0.432428867972772 0.783785566013614 11 0.750496925650071 0.499006148699858 0.249503074349929 12 0.643970793491136 0.712058413017727 0.356029206508864 13 0.537939452809304 0.924121094381392 0.462060547190696 14 0.517503249405494 0.964993501189013 0.482496750594506 15 0.722396889653368 0.555206220693263 0.277603110346632 16 0.656073425991334 0.687853148017331 0.343926574008666 17 0.577160749113609 0.845678501772782 0.422839250886391 18 0.491164894913154 0.982329789826307 0.508835105086846 19 0.40543651991273 0.81087303982546 0.59456348008727 20 0.413262040593272 0.826524081186545 0.586737959406728 21 0.35010815972842 0.70021631945684 0.64989184027158 22 0.29139017293595 0.5827803458719 0.70860982706405 23 0.245201350096803 0.490402700193606 0.754798649903197 24 0.217776917274023 0.435553834548045 0.782223082725977 25 0.168770752694726 0.337541505389451 0.831229247305274 26 0.136162987084468 0.272325974168936 0.863837012915532 27 0.101400054450785 0.20280010890157 0.898599945549215 28 0.142960008084988 0.285920016169975 0.857039991915012 29 0.123844789444848 0.247689578889696 0.876155210555152 30 0.109001925824809 0.218003851649619 0.89099807417519 31 0.0814715842515424 0.162943168503085 0.918528415748458 32 0.0648220865926526 0.129644173185305 0.935177913407347 33 0.0536559356865913 0.107311871373183 0.946344064313409 34 0.0580284198875619 0.116056839775124 0.941971580112438 35 0.0482870951902044 0.0965741903804087 0.951712904809796 36 0.0453193914969526 0.0906387829939052 0.954680608503047 37 0.036856457233436 0.073712914466872 0.963143542766564 38 0.0459930341237943 0.0919860682475885 0.954006965876206 39 0.0363942419520223 0.0727884839040446 0.963605758047978 40 0.0264372873974029 0.0528745747948057 0.973562712602597 41 0.0208999825892216 0.0417999651784432 0.979100017410778 42 0.0160845315366922 0.0321690630733843 0.983915468463308 43 0.0275282194605323 0.0550564389210646 0.972471780539468 44 0.0226534618771412 0.0453069237542824 0.97734653812286 45 0.0165654984776031 0.0331309969552062 0.983434501522397 46 0.0162050000201964 0.0324100000403928 0.983794999979804 47 0.0115383576921745 0.023076715384349 0.988461642307826 48 0.0228862285194034 0.0457724570388068 0.977113771480597 49 0.0169553255919376 0.0339106511838752 0.983044674408062 50 0.0130714625368336 0.0261429250736671 0.986928537463166 51 0.0101804942528943 0.0203609885057885 0.989819505747106 52 0.00829219156869507 0.0165843831373901 0.991707808431305 53 0.00736694181339918 0.0147338836267984 0.9926330581866 54 0.00568374289598142 0.0113674857919628 0.994316257104018 55 0.00716916443306949 0.0143383288661390 0.99283083556693 56 0.0053322466721082 0.0106644933442164 0.994667753327892 57 0.00438878370568868 0.00877756741137736 0.995611216294311 58 0.00330562039920414 0.00661124079840828 0.996694379600796 59 0.00387884847137987 0.00775769694275974 0.99612115152862 60 0.00277188833769017 0.00554377667538033 0.99722811166231 61 0.00266406261071017 0.00532812522142034 0.99733593738929 62 0.0023298933184891 0.0046597866369782 0.99767010668151 63 0.00348781810709336 0.00697563621418673 0.996512181892907 64 0.00250790886549088 0.00501581773098177 0.99749209113451 65 0.00998298547704088 0.0199659709540818 0.99001701452296 66 0.038925390069457 0.077850780138914 0.961074609930543 67 0.0472097882212088 0.0944195764424176 0.952790211778791 68 0.141034172510859 0.282068345021719 0.85896582748914 69 0.124604685076566 0.249209370153132 0.875395314923434 70 0.342274584318185 0.68454916863637 0.657725415681815 71 0.329796594209915 0.659593188419831 0.670203405790085 72 0.295919121074315 0.591838242148631 0.704080878925685 73 0.267830919398994 0.535661838797987 0.732169080601006 74 0.249338986697130 0.498677973394259 0.75066101330287 75 0.213390524242933 0.426781048485866 0.786609475757067 76 0.220541584070749 0.441083168141499 0.77945841592925 77 0.209199356205470 0.418398712410941 0.79080064379453 78 0.184316223438394 0.368632446876788 0.815683776561606 79 0.202701872466568 0.405403744933135 0.797298127533432 80 0.226418524237215 0.45283704847443 0.773581475762785 81 0.242423019750063 0.484846039500126 0.757576980249937 82 0.219765909710600 0.439531819421201 0.7802340902894 83 0.190151579390761 0.380303158781522 0.80984842060924 84 0.164105745509560 0.328211491019120 0.83589425449044 85 0.23431059936336 0.46862119872672 0.76568940063664 86 0.204790841596158 0.409581683192317 0.795209158403842 87 0.211676270519884 0.423352541039769 0.788323729480116 88 0.184028437174001 0.368056874348002 0.815971562825999 89 0.162548153606388 0.325096307212777 0.837451846393612 90 0.144164294036662 0.288328588073324 0.855835705963338 91 0.132409170692458 0.264818341384916 0.867590829307542 92 0.109627944015720 0.219255888031441 0.89037205598428 93 0.124195316072315 0.248390632144629 0.875804683927685 94 0.152096993681625 0.30419398736325 0.847903006318375 95 0.126465040732893 0.252930081465786 0.873534959267107 96 0.118967756363122 0.237935512726244 0.881032243636878 97 0.250098341160801 0.500196682321602 0.749901658839199 98 0.238640285091686 0.477280570183372 0.761359714908314 99 0.221739375613355 0.44347875122671 0.778260624386645 100 0.190474616031644 0.380949232063288 0.809525383968356 101 0.237942603209298 0.475885206418596 0.762057396790702 102 0.237328964758319 0.474657929516638 0.762671035241681 103 0.372484086030734 0.744968172061468 0.627515913969266 104 0.492550213353636 0.985100426707272 0.507449786646364 105 0.701656488535636 0.596687022928728 0.298343511464364 106 0.706432512948459 0.587134974103082 0.293567487051541 107 0.663066037145203 0.673867925709595 0.336933962854797 108 0.626758927660688 0.746482144678623 0.373241072339312 109 0.581498533150739 0.837002933698522 0.418501466849261 110 0.545177852002475 0.90964429599505 0.454822147997525 111 0.517586550607751 0.964826898784498 0.482413449392249 112 0.488651585581818 0.977303171163636 0.511348414418182 113 0.620336749201309 0.759326501597382 0.379663250798691 114 0.570353683275966 0.859292633448067 0.429646316724034 115 0.545781278284308 0.908437443431384 0.454218721715692 116 0.529415614440987 0.941168771118027 0.470584385559013 117 0.512449667976811 0.975100664046377 0.487550332023189 118 0.57254938968662 0.854901220626759 0.427450610313379 119 0.564685037367017 0.870629925265966 0.435314962632983 120 0.522849188459567 0.954301623080865 0.477150811540433 121 0.465063024739482 0.930126049478963 0.534936975260518 122 0.513536584365759 0.972926831268482 0.486463415634241 123 0.509994749853180 0.980010500293639 0.490005250146820 124 0.486809002638292 0.973618005276585 0.513190997361708 125 0.438353004275165 0.87670600855033 0.561646995724835 126 0.488772538074590 0.977545076149179 0.511227461925410 127 0.456280665115092 0.912561330230184 0.543719334884908 128 0.412379973730382 0.824759947460765 0.587620026269618 129 0.380576876855739 0.761153753711479 0.619423123144261 130 0.447283653869721 0.894567307739442 0.552716346130279 131 0.385074955987900 0.770149911975801 0.6149250440121 132 0.324817360181243 0.649634720362486 0.675182639818757 133 0.296360065908994 0.592720131817989 0.703639934091006 134 0.240635594370802 0.481271188741605 0.759364405629198 135 0.193995744095210 0.387991488190421 0.80600425590479 136 0.294244309989339 0.588488619978678 0.705755690010661 137 0.291118719208701 0.582237438417401 0.7088812807913 138 0.265104972475257 0.530209944950513 0.734895027524743 139 0.217103748557582 0.434207497115164 0.782896251442418 140 0.164034116902803 0.328068233805606 0.835965883097197 141 0.158622409057566 0.317244818115132 0.841377590942434 142 0.134328125934156 0.268656251868313 0.865671874065844 143 0.100297039067023 0.200594078134046 0.899702960932977 144 0.0655006383820761 0.131001276764152 0.934499361617924 145 0.0500815645739186 0.100163129147837 0.949918435426081 146 0.291558151897403 0.583116303794807 0.708441848102596 147 0.423915610587416 0.847831221174832 0.576084389412584 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 8 0.0575539568345324 NOK 5% type I error level 24 0.172661870503597 NOK 10% type I error level 33 0.237410071942446 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284838f7m39gp7biwlt54/10rbup1291284858.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284838f7m39gp7biwlt54/10rbup1291284858.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284838f7m39gp7biwlt54/1ksfd1291284858.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284838f7m39gp7biwlt54/1ksfd1291284858.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284838f7m39gp7biwlt54/2ksfd1291284858.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284838f7m39gp7biwlt54/2ksfd1291284858.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284838f7m39gp7biwlt54/3v1eg1291284858.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284838f7m39gp7biwlt54/3v1eg1291284858.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284838f7m39gp7biwlt54/4v1eg1291284858.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284838f7m39gp7biwlt54/4v1eg1291284858.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284838f7m39gp7biwlt54/5v1eg1291284858.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284838f7m39gp7biwlt54/5v1eg1291284858.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284838f7m39gp7biwlt54/65sdi1291284858.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284838f7m39gp7biwlt54/65sdi1291284858.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284838f7m39gp7biwlt54/7ykvm1291284858.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284838f7m39gp7biwlt54/7ykvm1291284858.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284838f7m39gp7biwlt54/8ykvm1291284858.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284838f7m39gp7biwlt54/8ykvm1291284858.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284838f7m39gp7biwlt54/9ykvm1291284858.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291284838f7m39gp7biwlt54/9ykvm1291284858.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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

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

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

Copyright

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

Software written by Ed van Stee & Patrick Wessa

Disclaimer

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.

FreeStatistics.org is powered by