Workshop

*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 17:12:06 +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/t1291223482q3unjhhi2pfixal.htm/, Retrieved Wed, 01 Dec 2010 18:11:22 +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/t1291223482q3unjhhi2pfixal.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 5 2 3 3 4 4 2 4 2 4 3 4 4 4 4 2 4 2 5 4 2 4 2 2 2 2 4 3 2 2 2 3 2 4 4 5 1 3 2 4 5 3 5 1 2 1 4 4 3 4 3 3 3 4 3 3 3 2 3 2 4 4 2 4 1 3 2 2 4 4 4 4 3 3 3 4 4 2 2 4 2 4 4 3 3 3 2 2 3 4 3 3 2 2 2 4 2 4 4 1 1 3 4 3 4 5 1 1 1 4 4 3 4 2 3 3 4 3 3 2 2 2 2 2 2 3 4 2 2 3 4 4 4 4 2 3 4 4 3 2 4 1 4 2 4 3 5 4 2 4 3 3 4 4 4 4 3 5 2 3 2 4 2 2 2 4 3 3 5 2 3 2 2 4 4 4 2 4 3 3 4 4 4 2 3 2 4 4 3 4 2 2 2 3 4 4 4 3 1 2 4 4 4 4 2 3 2 4 4 1 4 1 2 3 4 5 4 4 4 4 4 4 4 5 2 1 4 1 4 4 2 4 2 5 3 4 4 4 4 2 2 3 4 3 3 5 2 4 2 5 4 2 5 2 4 1 4 3 4 4 2 2 1 2 4 5 3 2 4 2 4 4 4 4 2 4 2 4 3 4 5 2 2 2 5 5 4 4 2 3 1 4 4 3 4 2 2 2 2 3 4 5 2 4 1 4 3 2 4 2 3 2 4 3 2 5 1 1 2 4 4 4 4 2 2 4 2 4 2 4 1 5 2 5 4 4 4 2 2 2 4 4 4 3 1 4 2 4 4 1 4 1 4 1 4 4 4 4 2 2 2 4 4 2 4 2 2 2 4 5 1 2 1 2 1 3 3 4 3 5 4 5 5 3 3 5 2 3 2 4 5 2 4 2 4 2 4 5 4 4 1 2 2 4 4 3 5 1 3 1 4 4 2 3 2 2 3 2 3 2 5 2 2 1 4 4 3 4 1 3 1 4 4 2 5 1 2 2 4 5 1 4 2 3 3 4 4 3 4 1 2 2 3 4 2 5 1 4 2 4 5 3 4 2 2 2 2 4 3 4 1 5 4 4 3 3 5 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 7 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation neat[t] = + 2.66020802501524 -0.0216461795712711standards[t] + 0.317101533122638organization[t] -0.12757403167846punished[t] + 0.0145397512907747secondrate[t] -0.0551812777793777mistakes[t] + 0.0489105933244106competent[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) 2.66020802501524 0.425739 6.2484 0 0 standards -0.0216461795712711 0.065713 -0.3294 0.742303 0.371151 organization 0.317101533122638 0.071239 4.4512 1.6e-05 8e-06 punished -0.12757403167846 0.073232 -1.742 0.083524 0.041762 secondrate 0.0145397512907747 0.062916 0.2311 0.817549 0.408774 mistakes -0.0551812777793777 0.070596 -0.7816 0.435636 0.217818 competent 0.0489105933244106 0.078423 0.6237 0.533776 0.266888 Multiple Linear Regression - Regression Statistics Multiple R 0.41006257220594 R-squared 0.168151313124152 Adjusted R-squared 0.135315180747473 F-TEST (value) 5.12092323161605 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 8.09002176053175e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.73968317220331 Sum Squared Residuals 83.1639416765942 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4 4.0209930619608 -0.0209930619608009 2 4 3.71843128012893 0.281568719871066 3 4 3.77923079209018 0.220769207909820 4 4 3.64671186867794 0.353288131322058 5 4 2.93568134508202 1.06431865491798 6 5 4.16045601227609 0.839543987723907 7 4 4.22274371833597 -0.222743718335967 8 3 3.55467131758843 -0.554671317588429 9 4 3.42032509392363 0.579674906076371 10 4 3.78882565164718 0.211174348352824 11 4 3.35654051301429 0.643459486985713 12 4 3.09611713252050 0.903882867479505 13 4 3.22930071762998 0.770699282370017 14 2 3.40578534263285 -1.40578534263285 15 3 3.75909369879253 -0.759093698792528 16 4 4.18655778747392 -0.186557787473921 17 3 3.68224534926689 -0.682245349266889 18 2 2.99086262286140 -0.990862622861395 19 4 3.66770559797611 0.332294402023886 20 3 3.60541789191624 -0.60541789191624 21 3 3.90118658958677 -0.901186589586772 22 4 3.60458214809071 0.395417851909289 23 3 3.19726736413112 -0.197267364131121 24 3 3.74453305532676 -0.744533055326763 25 4 3.95670697352008 0.0432930264799172 26 4 3.62622832766198 0.373771672338018 27 4 3.71578044747499 0.284219552525005 28 4 3.67397628243108 0.326023717568919 29 4 3.55912691321499 0.440873086785014 30 4 3.71578044747499 0.284219552525005 31 5 3.83857198879712 1.16142801120288 32 4 3.36480957985009 0.635190420149906 33 4 3.25722626240706 0.742773737592938 34 4 3.73297103141971 0.267028968580291 35 3 3.64605941840484 -0.646059418404843 36 4 4.11797850478409 -0.117978504784089 37 3 4.14589536881033 -1.14589536881033 38 4 3.65860078731478 0.341399212685223 39 4 3.39157248607186 0.608427513928139 40 3 3.73032019876577 -0.73032019876577 41 5 4.06725282263127 0.932747177368731 42 4 3.77096172525437 0.229038274745627 43 3 3.62506568910667 -0.62506568910667 44 3 4.10260300966779 -1.10260300966779 45 3 3.75907280661754 -0.759072806617537 46 4 4.17466886883709 -0.174668868837086 47 4 3.49305695397664 0.506943046023356 48 4 3.96463693420196 0.0353630657980426 49 4 3.70124069618422 0.298759303815780 50 4 3.54079269732159 0.459207302678408 51 4 3.97801404693742 0.0219859530625790 52 4 3.70124069618422 0.298759303815780 53 5 3.74453305532676 1.25546694467324 54 3 3.26582088478619 -0.265820884786186 55 3 2.91386333059403 0.0861366694059704 56 5 4.0545281601689 0.945471839831096 57 5 3.77361255790831 1.22638744209169 58 4 3.82881472786268 0.171185272137319 59 4 4.23728346962674 -0.237283469626742 60 3 3.27442905777593 -0.274429057775926 61 4 4.11681586622878 -0.116815866228778 62 4 3.92018193650410 0.0798180634958958 63 5 4.18920862012786 0.81079137987214 64 4 3.72553770840943 0.274462291590569 65 4 3.80155031410954 0.198449685890459 66 5 4.21828812270941 0.78171187729059 67 4 3.62506568910667 0.374934310893329 68 3 3.78371760574752 -0.78371760574752 69 4 4.20820396704519 -0.208203967045192 70 4 3.75907280661754 0.240927193382463 71 4 3.53335937431131 0.466640625688686 72 4 3.87210708700522 0.127892912994777 73 4 3.90530794891917 0.0946920510808273 74 4 3.87093710688554 0.129062893114463 75 4 4.10260300966779 -0.102603009667785 76 3 3.74453305532676 -0.744533055326763 77 4 3.86500065872473 0.134999341275274 78 3 3.91984770020995 -0.919847700209948 79 5 4.03998840887813 0.960011591121871 80 4 3.7564219739636 0.243578026036402 81 5 3.98035153547219 1.01964846452781 82 5 3.30796415598403 1.69203584401597 83 4 3.77544853891171 0.224551461088287 84 4 3.49500322615171 0.504996773848289 85 4 3.89291752275096 0.107082477249035 86 4 3.80898363711982 0.191016362880181 87 4 3.886646838296 0.113353161704003 88 5 4.22985014661646 0.770149853383537 89 4 3.46063238411808 0.539367615881925 90 3 3.77806815353487 -0.778068153534869 91 4 3.70124069618422 0.298759303815780 92 3 4.18093955329205 -1.18093955329205 93 4 3.56954530517336 0.43045469482664 94 4 3.53335937431131 0.466640625688686 95 4 3.87177285071107 0.128227149288934 96 4 3.72371527801665 0.276284721983354 97 4 3.55910602103999 0.440893978960005 98 3 3.5692110688792 -0.569211068879203 99 3 3.65860078731478 -0.658600787314777 100 3 3.72915756021046 -0.729157560210459 101 3 3.53929582247212 -0.539295822472124 102 3 3.85673159188892 -0.856731591888919 103 2 3.54013156629765 -1.54013156629765 104 3 3.74453305532676 -0.744533055326763 105 5 3.95670697352008 1.04329302647992 106 2 3.16021992740878 -1.16021992740878 107 2 3.67397628243108 -1.67397628243108 108 3 2.86972167701534 0.130278322984658 109 3 3.64338769357591 -0.643387693575913 110 3 4.07684768218826 -1.07684768218826 111 4 3.44826285012486 0.551737149875142 112 4 3.60541789191624 0.39458210808376 113 3 3.55054995825603 -0.550549958256028 114 2 3.64455033213122 -1.64455033213122 115 3 3.54461837995499 -0.544618379954994 116 4 3.74369731150123 0.256302688498766 117 2 3.08157738122972 -1.08157738122972 118 4 2.94871935166355 1.05128064833645 119 4 3.51764964290085 0.482350357099147 120 2 3.49071946544187 -1.49071946544187 121 3 3.92018193650410 -0.920181936504104 122 3 3.35687474930844 -0.356874749308444 123 3 3.30729081353594 -0.307290813535944 124 4 4.11054518177381 -0.110545181773811 125 4 3.81692580922584 0.183074190774155 126 4 3.36430807231872 0.635691927681278 127 3 3.8641649148992 -0.864164914899197 128 4 3.68851603372186 0.311483966278144 129 4 3.81609006540032 0.183909934599684 130 4 3.68224534926689 0.317754650733111 131 2 3.28564463396467 -1.28564463396467 132 4 3.67397628243108 0.326023717568919 133 5 3.71645378992308 1.28354621007692 134 4 3.84962516360842 0.150374836391578 135 4 3.64671186867794 0.353288131322058 136 4 3.71578044747499 0.284219552525005 137 3 3.55500555388259 -0.555005553882585 138 1 3.64605941840484 -2.64605941840484 139 4 3.66503387314718 0.334966126852816 140 3 2.77835446837392 0.221645531626081 141 3 3.02904693610428 -0.0290469361042816 142 3 3.5673750878758 -0.567375087875803 143 1 2.44821492866975 -1.44821492866975 144 4 3.9272883647846 0.0727116352153995 145 5 3.2711048826739 1.72889511732610 146 4 3.69678510055766 0.303214899442337 147 3 3.48377543853881 -0.483775438538814 148 4 3.06885271876736 0.931147281232645 149 3 3.04871562546970 -0.0487156254697031 150 4 3.47517213540885 0.52482786459115 151 4 3.4194893500981 0.580510649901901 152 4 3.71578044747499 0.284219552525005 153 5 3.66321878431877 1.33678121568123 154 2 3.14570106829300 -1.14570106829300 155 3 3.63745611527488 -0.637456115274879 156 3 3.67397628243108 -0.673976282431081 157 4 3.78633722037068 0.213662779629323 158 4 3.46063238411808 0.539367615881925 159 3 2.93534710878786 0.064652891212139 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.213016949510012 0.426033899020024 0.786983050489988 11 0.165618609423038 0.331237218846077 0.834381390576962 12 0.0833825626351159 0.166765125270232 0.916617437364884 13 0.068499888504255 0.13699977700851 0.931500111495745 14 0.363035208139982 0.726070416279964 0.636964791860018 15 0.276900226815828 0.553800453631657 0.723099773184172 16 0.201012610787272 0.402025221574544 0.798987389212728 17 0.185781789660773 0.371563579321546 0.814218210339227 18 0.45839656758859 0.91679313517718 0.54160343241141 19 0.469548847724083 0.939097695448167 0.530451152275917 20 0.463855218936452 0.927710437872905 0.536144781063548 21 0.502276917298609 0.995446165402783 0.497723082701391 22 0.463507108078647 0.927014216157294 0.536492891921353 23 0.430016193214655 0.86003238642931 0.569983806785345 24 0.379501236949507 0.759002473899015 0.620498763050493 25 0.332624173049723 0.665248346099445 0.667375826950278 26 0.271262294385563 0.542524588771127 0.728737705614437 27 0.216419125372383 0.432838250744765 0.783580874627617 28 0.178269677657195 0.35653935531439 0.821730322342805 29 0.152116145045779 0.304232290091558 0.847883854954221 30 0.115853620720073 0.231707241440145 0.884146379279927 31 0.333053110580321 0.666106221160643 0.666946889419679 32 0.297145368854654 0.594290737709307 0.702854631145346 33 0.263083999000837 0.526167998001674 0.736916000999163 34 0.215835583282193 0.431671166564386 0.784164416717807 35 0.198192296978967 0.396384593957934 0.801807703021033 36 0.161758585773032 0.323517171546064 0.838241414226968 37 0.239199264546884 0.478398529093769 0.760800735453116 38 0.19890072228861 0.39780144457722 0.80109927771139 39 0.169660482511332 0.339320965022663 0.830339517488669 40 0.186961770552265 0.373923541104531 0.813038229447735 41 0.233162257893540 0.466324515787079 0.76683774210646 42 0.193673142895542 0.387346285791084 0.806326857104458 43 0.187300188083803 0.374600376167605 0.812699811916197 44 0.236482931518568 0.472965863037136 0.763517068481432 45 0.229200782154032 0.458401564308064 0.770799217845968 46 0.192629505990322 0.385259011980643 0.807370494009679 47 0.166216995611345 0.332433991222689 0.833783004388655 48 0.136366294444464 0.272732588888927 0.863633705555537 49 0.112691692600822 0.225383385201643 0.887308307399178 50 0.0942252813182614 0.188450562636523 0.905774718681739 51 0.0767883720304845 0.153576744060969 0.923211627969516 52 0.0618315795656061 0.123663159131212 0.938168420434394 53 0.108726505436542 0.217453010873084 0.891273494563458 54 0.0910934729915393 0.182186945983079 0.90890652700846 55 0.0744102194891806 0.148820438978361 0.92558978051082 56 0.092774292149161 0.185548584298322 0.907225707850839 57 0.137933341416044 0.275866682832088 0.862066658583956 58 0.113329043188246 0.226658086376492 0.886670956811754 59 0.092541002671041 0.185082005342082 0.907458997328959 60 0.0774763391238501 0.154952678247700 0.92252366087615 61 0.0614464737117671 0.122892947423534 0.938553526288233 62 0.0478623062903147 0.0957246125806294 0.952137693709685 63 0.0529964042200023 0.105992808440005 0.947003595779998 64 0.0422330943255416 0.0844661886510833 0.957766905674458 65 0.0328238805268432 0.0656477610536865 0.967176119473157 66 0.0340862786969688 0.0681725573939376 0.965913721303031 67 0.0275373226653875 0.0550746453307749 0.972462677334613 68 0.0306808201851784 0.0613616403703568 0.969319179814822 69 0.0237432788162414 0.0474865576324827 0.976256721183759 70 0.0181668749832962 0.0363337499665923 0.981833125016704 71 0.0149464661706068 0.0298929323412136 0.985053533829393 72 0.0110569202578568 0.0221138405157136 0.988943079742143 73 0.00804251393430083 0.0160850278686017 0.9919574860657 74 0.00579411285907851 0.0115882257181570 0.994205887140922 75 0.00413934690644545 0.0082786938128909 0.995860653093555 76 0.004382959889463 0.008765919778926 0.995617040110537 77 0.00311521554106667 0.00623043108213334 0.996884784458933 78 0.00390793028938342 0.00781586057876684 0.996092069710617 79 0.00513293509641129 0.0102658701928226 0.994867064903589 80 0.00375572279913246 0.00751144559826492 0.996244277200868 81 0.00543364809897377 0.0108672961979475 0.994566351901026 82 0.0186437423856554 0.0372874847713108 0.981356257614345 83 0.0146871428599218 0.0293742857198435 0.985312857140078 84 0.0122497017577745 0.024499403515549 0.987750298242225 85 0.00903623832187661 0.0180724766437532 0.990963761678123 86 0.00684093633755256 0.0136818726751051 0.993159063662447 87 0.00499670413327902 0.00999340826655803 0.99500329586672 88 0.00539340356956929 0.0107868071391386 0.99460659643043 89 0.00448937159311437 0.00897874318622873 0.995510628406886 90 0.00483215648066965 0.0096643129613393 0.99516784351933 91 0.00368717677805907 0.00737435355611813 0.99631282322194 92 0.00598176985003513 0.0119635397000703 0.994018230149965 93 0.00484313351940352 0.00968626703880703 0.995156866480597 94 0.00406660196195837 0.00813320392391673 0.995933398038042 95 0.00294242669439799 0.00588485338879597 0.997057573305602 96 0.00241001275714701 0.00482002551429403 0.997589987242853 97 0.00180361841223770 0.00360723682447540 0.998196381587762 98 0.00154944914234327 0.00309889828468655 0.998450550857657 99 0.00147634439327331 0.00295268878654662 0.998523655606727 100 0.00149537221923969 0.00299074443847937 0.99850462778076 101 0.00124308549139659 0.00248617098279317 0.998756914508603 102 0.00139453842630344 0.00278907685260688 0.998605461573697 103 0.00450453367680533 0.00900906735361067 0.995495466323195 104 0.00449144064111274 0.00898288128222547 0.995508559358887 105 0.00656822809130592 0.0131364561826118 0.993431771908694 106 0.0108389148685921 0.0216778297371842 0.989161085131408 107 0.0338997252686675 0.0677994505373351 0.966100274731332 108 0.0259541243937639 0.0519082487875277 0.974045875606236 109 0.0246025676232567 0.0492051352465135 0.975397432376743 110 0.0377148695159905 0.075429739031981 0.96228513048401 111 0.0344214062961022 0.0688428125922044 0.965578593703898 112 0.0409452751506975 0.081890550301395 0.959054724849302 113 0.0345927755626037 0.0691855511252075 0.965407224437396 114 0.0633504378994519 0.126700875798904 0.936649562100548 115 0.0535139679824928 0.107027935964986 0.946486032017507 116 0.0416915632121133 0.0833831264242265 0.958308436787887 117 0.0485976072372024 0.0971952144744049 0.951402392762798 118 0.050173804023858 0.100347608047716 0.949826195976142 119 0.0420401353129323 0.0840802706258647 0.957959864687068 120 0.116879782107015 0.233759564214030 0.883120217892985 121 0.140559791247765 0.281119582495531 0.859440208752235 122 0.124850587323556 0.249701174647113 0.875149412676444 123 0.107226722201333 0.214453444402666 0.892773277798667 124 0.0833906245453877 0.166781249090775 0.916609375454612 125 0.0721839234328154 0.144367846865631 0.927816076567185 126 0.0643576437169036 0.128715287433807 0.935642356283096 127 0.0854106088063593 0.170821217612719 0.91458939119364 128 0.0651075208207044 0.130215041641409 0.934892479179296 129 0.0482667233556155 0.096533446711231 0.951733276644384 130 0.0476484690325767 0.0952969380651535 0.952351530967423 131 0.107825061317501 0.215650122635003 0.892174938682499 132 0.0832440351584872 0.166488070316974 0.916755964841513 133 0.180012178141031 0.360024356282062 0.819987821858969 134 0.140349078456601 0.280698156913201 0.8596509215434 135 0.111340365300301 0.222680730600601 0.8886596346997 136 0.0904485281809226 0.180897056361845 0.909551471819077 137 0.068860728623527 0.137721457247054 0.931139271376473 138 0.352747394442035 0.705494788884071 0.647252605557965 139 0.292214523018714 0.584429046037428 0.707785476981286 140 0.230094865286782 0.460189730573565 0.769905134713218 141 0.206722873218501 0.413445746437002 0.793277126781499 142 0.299433173675835 0.598866347351671 0.700566826324165 143 0.424388631073864 0.848777262147728 0.575611368926136 144 0.329578447926173 0.659156895852346 0.670421552073827 145 0.500783291117362 0.998433417765275 0.499216708882638 146 0.516710522395299 0.966578955209401 0.483289477604701 147 0.56650208326282 0.86699583347436 0.43349791673718 148 0.453492301736241 0.906984603472481 0.546507698263759 149 0.470471186993388 0.940942373986777 0.529528813006612 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 21 0.15 NOK 5% type I error level 39 0.278571428571429 NOK 10% type I error level 56 0.4 NOK

Charts produced by software:

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Parameters (Session):

par1 = 7 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 7 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

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

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

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Software written by Ed van Stee & Patrick Wessa

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