*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Fri, 26 Nov 2010 09:19:18 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/26/t1290763103cz6u52h9qf6vsre.htm/, Retrieved Fri, 26 Nov 2010 10:18:33 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Nov/26/t1290763103cz6u52h9qf6vsre.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 «

9 26 24 14 11 12 24 9 23 25 11 7 8 25 9 25 17 6 17 8 30 9 23 18 12 10 8 19 9 19 18 8 12 9 22 10 29 16 10 12 7 22 10 25 20 10 11 4 25 10 21 16 11 11 11 23 10 22 18 16 12 7 17 10 25 17 11 13 7 21 10 24 23 13 14 12 19 10 18 30 12 16 10 19 10 22 23 8 11 10 15 10 15 18 12 10 8 16 10 22 15 11 11 8 23 10 28 12 4 15 4 27 10 20 21 9 9 9 22 10 12 15 8 11 8 14 10 24 20 8 17 7 22 10 20 31 14 17 11 23 10 21 27 15 11 9 23 10 20 34 16 18 11 21 10 21 21 9 14 13 19 10 23 31 14 10 8 18 10 28 19 11 11 8 20 10 24 16 8 15 9 23 10 24 20 9 15 6 25 10 24 21 9 13 9 19 10 23 22 9 16 9 24 10 23 17 9 13 6 22 10 29 24 10 9 6 25 10 24 25 16 18 16 26 10 18 26 11 18 5 29 10 25 25 8 12 7 32 10 21 17 9 17 9 25 10 26 32 16 9 6 29 10 22 33 11 9 6 28 10 22 13 16 12 5 17 10 22 32 12 18 12 28 10 23 25 12 12 7 29 10 30 29 14 18 10 26 10 23 22 9 14 9 25 10 17 18 10 15 8 14 10 23 17 9 16 5 25 10 23 20 10 10 8 26 10 25 15 12 11 8 20 10 24 20 14 14 10 18 10 24 33 14 9 6 32 10 23 29 10 12 8 25 10 21 23 14 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 10 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation O[t] = + 6.67822358754374 + 1.09089428266750maand[t] -0.0608903034875092CM[t] + 0.214416815593605D[t] -0.142213186036547PE[t] -0.240815534408649PC[t] + 0.399817197705633PS[t] -0.016068024633864t + 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) 6.67822358754374 16.640062 0.4013 0.688742 0.344371 maand 1.09089428266750 1.669545 0.6534 0.514487 0.257243 CM -0.0608903034875092 0.062235 -0.9784 0.329444 0.164722 D 0.214416815593605 0.11107 1.9305 0.055423 0.027711 PE -0.142213186036547 0.103898 -1.3688 0.173102 0.086551 PC -0.240815534408649 0.129923 -1.8535 0.065759 0.03288 PS 0.399817197705633 0.075551 5.292 0 0 t -0.016068024633864 0.006317 -2.5438 0.011971 0.005986 Multiple Linear Regression - Regression Statistics Multiple R 0.504343958942387 R-squared 0.254362828921680 Adjusted R-squared 0.219796867348513 F-TEST (value) 7.35876617762421 F-TEST (DF numerator) 7 F-TEST (DF denominator) 151 p-value 1.34744991164837e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.44924263771775 Sum Squared Residuals 1796.48849085136 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 26 23.1621535271571 2.83784647284293 2 23 24.3738768317412 -1.37387683174123 3 25 24.3498012852021 0.650198714797901 4 23 22.1568469781362 0.843153021863775 5 19 21.9573213777631 -2.9573213777631 6 29 24.0643929427763 4.93560705722375 7 25 25.8688750865718 -0.868875086571769 8 21 23.8254419552097 -2.82544195520972 9 22 23.1818231669331 -1.18182316693311 10 25 23.6116169726047 1.38838302739528 11 24 21.5131155047420 2.48688449525805 12 18 21.0536032368461 -3.05360323684612 13 22 19.7178972136106 2.2821027863894 14 15 21.8876094213482 -6.88760942134818 15 22 24.4963026894861 -2.49630268948613 16 28 25.1556660504705 2.84433394952951 17 20 23.3137848280649 -3.31378482806495 18 12 20.206493389453 -8.20649338945302 19 24 22.4720478472160 1.52795215278396 20 20 22.5092424378522 -2.50924243785224 21 21 24.2860626277986 -3.28606262779861 22 20 21.7814215278614 -1.78142152786138 23 21 20.3435970193275 0.656402980672472 24 23 22.1638232562704 0.8361767437296 25 28 22.8926096360806 5.10739036391945 26 24 22.8057453896905 1.19425461030954 27 24 24.2826139653374 -0.282613965337378 28 24 21.3687322198294 2.63126778017065 29 23 22.8642203221265 0.135779677873497 30 23 23.5020555808545 -0.502055580854508 31 29 25.0424765846648 3.95752341533522 32 24 22.9637623293953 1.03623767060475 33 18 25.6631423949179 -7.66314239491789 34 25 26.6358138675096 -1.63581386750961 35 21 23.3298677034300 -2.32986770342995 36 26 27.3607837179795 -1.36078371797955 37 22 25.8119241141845 -3.81192411418451 38 22 23.5019330388059 -1.50193303880590 39 22 23.3302833032171 -1.33028330321708 40 23 26.1976213889639 -3.19762138896394 41 30 23.5916484690051 6.40835153099488 42 23 23.339579571665 -0.339579571664999 43 17 19.4821027501849 -2.48210275018491 44 23 24.2907308053963 -1.29073080539632 45 23 24.8370583965925 -1.83705839659250 46 25 23.0131591483130 1.98684085168695 47 24 21.4135682150906 2.58643178490936 48 24 27.8776950808154 -3.87769508081536 49 23 23.5405299968907 -0.540529996890735 50 21 24.2772206597823 -3.27722065978226 51 24 26.1366857961263 -2.13668579612633 52 24 22.3484336549356 1.65156634506439 53 28 22.0251846412147 5.9748153587853 54 16 21.5169173509197 -5.51691735091971 55 20 20.4789198645737 -0.47891986457366 56 29 23.8541579839914 5.1458420160086 57 27 24.2380351219380 2.76196487806198 58 22 23.4951552848874 -1.49515528488743 59 28 24.2466109377594 3.75338906224063 60 16 20.8090179954004 -4.80901799540038 61 25 23.2233477954266 1.77665220457341 62 24 23.7583687896257 0.241631210374305 63 28 23.9098862827089 4.09011371729114 64 24 24.5407734245581 -0.540773424558101 65 23 22.9061139720403 0.0938860279597174 66 30 27.0297797412780 2.97022025872196 67 24 21.6434529082386 2.3565470917614 68 21 24.2871449575035 -3.28714495750353 69 25 23.4473802754011 1.55261972459895 70 25 24.1077442125973 0.892255787402672 71 22 21.0608196731265 0.939180326873492 72 23 22.6336379512891 0.366362048710892 73 26 23.0117695894899 2.98823041051014 74 23 21.8355533441557 1.16444665584433 75 25 23.1460069619868 1.85399303801315 76 21 21.4729491641733 -0.472949164173297 77 25 23.6626865172753 1.33731348272467 78 24 22.2658198419973 1.73418015800268 79 29 23.5810179005989 5.41898209940105 80 22 23.6571462351028 -1.65714623510282 81 27 23.6255180370527 3.37448196294728 82 26 19.7660868643529 6.23391313564712 83 22 21.3690568461563 0.630943153843703 84 24 22.0468444219424 1.95315557805762 85 27 23.0774863545094 3.92251364549055 86 24 21.3204291306657 2.67957086933426 87 24 24.6815444756721 -0.681544475672106 88 29 24.2510137100680 4.74898628993203 89 22 22.1734213910241 -0.173421391024079 90 21 20.532921974541 0.467078025459013 91 24 20.4230471813872 3.57695281861276 92 24 21.5860172526589 2.41398274734108 93 23 21.7900762536225 1.20992374637753 94 20 22.0992409303702 -2.09924093037018 95 27 21.2572004094112 5.74279959058881 96 26 23.2190918041 2.78090819589998 97 25 21.8094744037476 3.1905255962524 98 21 19.9806371919358 1.01936280806420 99 21 20.5737101349482 0.426289865051762 100 19 20.2063592950003 -1.20635929500026 101 21 21.3624295145167 -0.362429514516657 102 21 20.9808663759238 0.0191336240762448 103 16 19.5302432228548 -3.53024322285476 104 22 20.3902089314541 1.60979106854587 105 29 21.5252258293849 7.47477417061509 106 15 21.3920032767024 -6.39200327670237 107 17 20.3933948873818 -3.3933948873818 108 15 19.6598038042491 -4.65980380424906 109 21 21.3291392407309 -0.329139240730866 110 21 20.6321904902105 0.36780950978947 111 19 18.9325500538508 0.0674499461492126 112 24 17.8294658515374 6.17053414846262 113 20 21.8748409742144 -1.87484097421436 114 17 24.5188654204699 -7.5188654204699 115 23 24.2858541101743 -1.28585411017425 116 24 21.8076772869391 2.19232271306088 117 14 21.4880741641059 -7.48807416410592 118 19 22.2861213929966 -3.28612139299661 119 24 21.6500900632095 2.34990993679048 120 13 19.8964383041808 -6.89643830418077 121 22 24.6721943043691 -2.6721943043691 122 16 20.5376135192885 -4.53761351928849 123 19 22.6285225854727 -3.62852258547275 124 25 22.0948829634973 2.90511703650273 125 25 23.4831964078493 1.51680359215074 126 23 20.7553869260591 2.24461307394087 127 24 22.7590916096781 1.24090839032195 128 26 22.7759815861276 3.22401841387242 129 26 20.8003706672399 5.19962933276006 130 25 23.3951564337143 1.60484356628568 131 18 21.5991239299519 -3.59912392995193 132 21 19.1856863026733 1.81431369732666 133 26 22.7721081477539 3.22789185224611 134 23 21.1286695289675 1.87133047103249 135 23 19.0474475269278 3.95255247307219 136 22 21.7490138515839 0.250986148416131 137 20 21.5223154968376 -1.52231549683762 138 13 21.2268052627589 -8.22680526275892 139 24 20.5561734652747 3.44382653472530 140 15 20.7442930612423 -5.74429306124235 141 14 22.2452383177519 -8.24523831775189 142 22 23.1051451975367 -1.10514519753668 143 10 16.9966410249546 -6.9966410249546 144 24 23.4075179051279 0.592482094872091 145 22 20.8952255779007 1.10477442209927 146 24 24.6919111512327 -0.691911151232673 147 19 20.6777846956121 -1.67778469561205 148 20 21.0671514035548 -1.06715140355484 149 13 16.2728111632552 -3.2728111632552 150 20 19.1499145726773 0.850085427322734 151 22 22.1075686181769 -0.107568618176907 152 24 22.2642447148001 1.73575528519994 153 29 22.0960251700772 6.90397482992284 154 12 19.8635042296644 -7.86350422966438 155 20 19.8581485746411 0.141851425358916 156 21 20.2780328838707 0.721967116129256 157 24 22.4661368906263 1.53386310937373 158 22 20.7508756629491 1.24912433705090 159 20 16.8172134145822 3.18278658541778 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.354919788605346 0.709839577210691 0.645080211394655 12 0.471916456698003 0.943832913396006 0.528083543301997 13 0.40773722736221 0.81547445472442 0.59226277263779 14 0.303674340651244 0.607348681302488 0.696325659348756 15 0.500835723595075 0.998328552809851 0.499164276404925 16 0.600440248575707 0.799119502848587 0.399559751424293 17 0.506189591311773 0.987620817376454 0.493810408688227 18 0.595563491827326 0.808873016345348 0.404436508172674 19 0.590404733432485 0.81919053313503 0.409595266567515 20 0.50916440938167 0.98167118123666 0.49083559061833 21 0.450081358015266 0.900162716030533 0.549918641984734 22 0.374747174117748 0.749494348235496 0.625252825882252 23 0.387038999847178 0.774077999694357 0.612961000152822 24 0.487274808402724 0.974549616805447 0.512725191597276 25 0.700172667718112 0.599654664563775 0.299827332281888 26 0.639033131861522 0.721933736276955 0.360966868138478 27 0.57363975287631 0.85272049424738 0.42636024712369 28 0.557957298944463 0.884085402111074 0.442042701055537 29 0.491851753114904 0.983703506229808 0.508148246885096 30 0.427096774395021 0.854193548790043 0.572903225604979 31 0.426368422041865 0.85273684408373 0.573631577958135 32 0.36357490224991 0.72714980449982 0.63642509775009 33 0.618536706351569 0.762926587296861 0.381463293648431 34 0.581391977051942 0.837216045896116 0.418608022948058 35 0.544726822311973 0.910546355376054 0.455273177688027 36 0.488700881720023 0.977401763440046 0.511299118279977 37 0.47397407341028 0.94794814682056 0.52602592658972 38 0.42266111365919 0.84532222731838 0.57733888634081 39 0.372538606214632 0.745077212429264 0.627461393785368 40 0.347706064692882 0.695412129385764 0.652293935307118 41 0.524496840865871 0.951006318268259 0.475503159134129 42 0.469843656948026 0.939687313896052 0.530156343051974 43 0.436007891245913 0.872015782491825 0.563992108754087 44 0.387783054411890 0.775566108823779 0.61221694558811 45 0.347261726035618 0.694523452071237 0.652738273964382 46 0.323095827094319 0.646191654188638 0.676904172905681 47 0.301448151242985 0.602896302485969 0.698551848757015 48 0.296878814039139 0.593757628078279 0.70312118596086 49 0.259055512992681 0.518111025985362 0.740944487007319 50 0.256624033905839 0.513248067811678 0.74337596609416 51 0.236112890427241 0.472225780854483 0.763887109572759 52 0.206391706240348 0.412783412480697 0.793608293759652 53 0.277768768455559 0.555537536911119 0.72223123154444 54 0.355967741394077 0.711935482788154 0.644032258605923 55 0.339436207686296 0.678872415372592 0.660563792313704 56 0.401634448221716 0.803268896443431 0.598365551778284 57 0.377971364465174 0.755942728930348 0.622028635534826 58 0.346554906663464 0.693109813326928 0.653445093336536 59 0.346166462769420 0.692332925538839 0.65383353723058 60 0.423439817522322 0.846879635044643 0.576560182477678 61 0.379191710505946 0.758383421011892 0.620808289494054 62 0.336952134466271 0.673904268932543 0.663047865533729 63 0.339445417533123 0.678890835066245 0.660554582466877 64 0.305288310534378 0.610576621068757 0.694711689465622 65 0.265987342467539 0.531974684935078 0.734012657532461 66 0.249527994697488 0.499055989394975 0.750472005302512 67 0.221389367646431 0.442778735292862 0.778610632353569 68 0.243638209215617 0.487276418431233 0.756361790784383 69 0.210155767961261 0.420311535922522 0.789844232038739 70 0.177471690697583 0.354943381395165 0.822528309302417 71 0.148776901146771 0.297553802293541 0.851223098853229 72 0.123683108282613 0.247366216565226 0.876316891717387 73 0.107657988989492 0.215315977978984 0.892342011010508 74 0.0875428904657325 0.175085780931465 0.912457109534268 75 0.0712485454452075 0.142497090890415 0.928751454554793 76 0.0595115531753168 0.119023106350634 0.940488446824683 77 0.0471412507791547 0.0942825015583094 0.952858749220845 78 0.0367301186332546 0.0734602372665091 0.963269881366746 79 0.0417420020136821 0.0834840040273643 0.958257997986318 80 0.0382410118168574 0.0764820236337149 0.961758988183143 81 0.0320173348063516 0.0640346696127032 0.967982665193648 82 0.0422328403359399 0.0844656806718798 0.95776715966406 83 0.0329524518656972 0.0659049037313944 0.967047548134303 84 0.0257589105813041 0.0515178211626083 0.974241089418696 85 0.0235650947291346 0.0471301894582693 0.976434905270865 86 0.0185940566397445 0.037188113279489 0.981405943360256 87 0.0151210998071831 0.0302421996143662 0.984878900192817 88 0.0154803270183074 0.0309606540366148 0.984519672981693 89 0.0129878819700141 0.0259757639400282 0.987012118029986 90 0.0098022519233165 0.019604503846633 0.990197748076683 91 0.00833281719119403 0.0166656343823881 0.991667182808806 92 0.00678435126045641 0.0135687025209128 0.993215648739544 93 0.00498570699695856 0.00997141399391712 0.995014293003041 94 0.00473501134319883 0.00947002268639765 0.995264988656801 95 0.00701762230194567 0.0140352446038913 0.992982377698054 96 0.00570568070229904 0.0114113614045981 0.994294319297701 97 0.0048582976313875 0.009716595262775 0.995141702368612 98 0.00370982406489181 0.00741964812978363 0.996290175935108 99 0.00279243516048257 0.00558487032096514 0.997207564839517 100 0.00231229150212311 0.00462458300424623 0.997687708497877 101 0.00181201691437998 0.00362403382875996 0.99818798308562 102 0.00132547390397148 0.00265094780794296 0.998674526096029 103 0.00161138565242602 0.00322277130485204 0.998388614347574 104 0.00125266947585096 0.00250533895170192 0.998747330524149 105 0.00549530781737645 0.0109906156347529 0.994504692182623 106 0.0131215320632556 0.0262430641265112 0.986878467936744 107 0.0137420253251103 0.0274840506502206 0.98625797467489 108 0.0185735697640732 0.0371471395281464 0.981426430235927 109 0.0143844689314596 0.0287689378629193 0.98561553106854 110 0.0103918414164169 0.0207836828328338 0.989608158583583 111 0.00747423951515109 0.0149484790303022 0.992525760484849 112 0.0218603042549018 0.0437206085098036 0.978139695745098 113 0.0219589601411376 0.0439179202822753 0.978041039858862 114 0.0546760849789303 0.109352169957861 0.94532391502107 115 0.0468892658509958 0.0937785317019916 0.953110734149004 116 0.0393580569194592 0.0787161138389183 0.96064194308054 117 0.102523948514164 0.205047897028328 0.897476051485836 118 0.0963281456713693 0.192656291342739 0.90367185432863 119 0.0860205876962038 0.172041175392408 0.913979412303796 120 0.149104401189883 0.298208802379766 0.850895598810117 121 0.146065449219176 0.292130898438351 0.853934550780824 122 0.185090803488405 0.370181606976811 0.814909196511595 123 0.184133922154256 0.368267844308513 0.815866077845744 124 0.174401104619243 0.348802209238485 0.825598895380757 125 0.150958814572763 0.301917629145526 0.849041185427237 126 0.121150887699949 0.242301775399898 0.878849112300051 127 0.0947742915519483 0.189548583103897 0.905225708448052 128 0.0924262901788672 0.184852580357734 0.907573709821133 129 0.130226845149648 0.260453690299295 0.869773154850352 130 0.112616517090961 0.225233034181922 0.887383482909039 131 0.0941978249292126 0.188395649858425 0.905802175070787 132 0.0836187819287552 0.167237563857510 0.916381218071245 133 0.0819450988731638 0.163890197746328 0.918054901126836 134 0.0729533502478809 0.145906700495762 0.92704664975212 135 0.171512038868157 0.343024077736314 0.828487961131843 136 0.136628566990416 0.273257133980831 0.863371433009585 137 0.114239841788961 0.228479683577923 0.885760158211039 138 0.160955313934112 0.321910627868224 0.839044686065888 139 0.391954458218437 0.783908916436875 0.608045541781563 140 0.337750603767427 0.675501207534855 0.662249396232573 141 0.48140814054873 0.96281628109746 0.51859185945127 142 0.390283213132021 0.780566426264042 0.609716786867979 143 0.553431960036677 0.893136079926645 0.446568039963323 144 0.499741685279348 0.999483370558696 0.500258314720652 145 0.403076750935159 0.806153501870319 0.596923249064841 146 0.298613380818744 0.597226761637487 0.701386619181256 147 0.290180448483953 0.580360896967905 0.709819551516047 148 0.172902385860861 0.345804771721721 0.82709761413914 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 10 0.072463768115942 NOK 5% type I error level 29 0.210144927536232 NOK 10% type I error level 39 0.282608695652174 NOK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = 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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