*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, 03 Dec 2010 12:53:42 +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/03/t12913807470pk78m9vw7qva75.htm/, Retrieved Fri, 03 Dec 2010 13:52:38 +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/03/t12913807470pk78m9vw7qva75.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:

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4 4 5 4 4 4 4 4 4 4 4 3 4 4 5 5 4 4 5 5 4 3 3 2 3 4 4 3 2 3 2 3 2 4 3 5 4 3 3 4 5 4 4 3 3 3 3 4 4 2 3 4 4 2 4 2 4 4 3 4 4 5 3 4 3 2 3 2 2 3 4 3 2 4 4 4 4 2 3 2 4 2 3 2 5 4 2 5 5 5 4 3 4 2 3 3 4 4 4 3 4 4 4 4 4 4 3 3 4 4 5 4 3 2 3 3 3 3 3 4 4 4 4 4 4 4 2 3 2 2 2 4 2 4 2 4 4 3 4 4 3 3 2 4 4 4 3 3 2 4 4 2 3 4 4 4 2 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 3 3 4 3 4 3 5 4 4 4 4 4 4 3 4 3 2 4 4 4 1 4 4 4 4 4 4 4 2 4 4 4 3 4 4 2 4 4 4 4 4 3 4 3 2 4 4 4 3 2 4 4 4 3 4 4 5 4 4 5 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 3 2 3 3 5 4 4 4 2 4 4 4 4 4 3 3 3 3 4 4 4 4 3 4 3 4 4 3 3 4 4 3 3 3 4 4 4 4 3 4 4 2 3 2 3 2 3 2 2 2 4 2 2 5 2 4 3 4 4 4 5 4 4 4 4 4 2 4 4 5 4 4 4 4 5 5 4 3 2 4 4 4 4 4 3 3 4 3 4 3 4 4 2 4 4 4 4 5 4 2 4 4 4 4 3 3 4 3 3 4 3 2 2 4 2 1 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 3 2 3 4 4 2 4 3 2 2 5 2 2 4 2 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 3 4 4 3 4 4 3 4 4 4 3 4 4 2 3 2 3 1 4 3 4 4 4 4 4 4 4 5 3 4 4 2 4 4 4 4 3 4 4 4 4 5 4 4 5 5 5 5 4 4 2 4 3 4 4 3 3 2 3 3 4 3 3 3 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 11 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation y[t] = + 0.798651349529265 + 0.00472531567739815x1[t] + 0.207076583341754x2[t] + 0.157771782945949x3[t] + 0.149637329469757x4[t] + 0.173326753875179x5[t] + 0.0319795163326446x6[t] -0.0387105943596768M1[t] + 0.0768735256343226M2[t] + 0.112509114385824M3[t] -0.132101853134254M4[t] -0.157713147188171M5[t] + 0.217054121005734M6[t] + 0.16140957424235M7[t] -0.554040474802723M8[t] -0.206280916205303M9[t] + 0.107726425781439M10[t] + 0.377411731782024M11[t] + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 0.798651349529265 0.446895 1.7871 0.07618 0.03809 x1 0.00472531567739815 0.063896 0.074 0.941158 0.470579 x2 0.207076583341754 0.072053 2.8739 0.004716 0.002358 x3 0.157771782945949 0.066102 2.3868 0.018393 0.009197 x4 0.149637329469757 0.083208 1.7984 0.074371 0.037186 x5 0.173326753875179 0.073206 2.3677 0.01933 0.009665 x6 0.0319795163326446 0.063865 0.5007 0.617379 0.308689 M1 -0.0387105943596768 0.259658 -0.1491 0.881712 0.440856 M2 0.0768735256343226 0.253947 0.3027 0.762577 0.381288 M3 0.112509114385824 0.254616 0.4419 0.65929 0.329645 M4 -0.132101853134254 0.261175 -0.5058 0.613829 0.306914 M5 -0.157713147188171 0.253138 -0.623 0.534322 0.267161 M6 0.217054121005734 0.255342 0.8501 0.396812 0.198406 M7 0.16140957424235 0.255943 0.6306 0.529345 0.264673 M8 -0.554040474802723 0.254923 -2.1734 0.031511 0.015755 M9 -0.206280916205303 0.258109 -0.7992 0.425588 0.212794 M10 0.107726425781439 0.260012 0.4143 0.679308 0.339654 M11 0.377411731782024 0.258872 1.4579 0.147205 0.073602 Multiple Linear Regression - Regression Statistics Multiple R 0.631888676545997 R-squared 0.399283299547052 Adjusted R-squared 0.323072971877648 F-TEST (value) 5.23922822217902 F-TEST (DF numerator) 17 F-TEST (DF denominator) 134 p-value 1.00962128657400e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.624867951380325 Sum Squared Residuals 52.3216341927407 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4 3.86508646508212 0.134913534917875 2 4 3.62395667226457 0.376043327735434 3 5 4.13691898950816 0.863081010491836 4 3 2.95598884132625 0.0440111586737519 5 2 2.63110288833281 -0.63110288833281 6 5 3.72225298469321 1.27774701530679 7 4 3.33891903890749 0.66108096109251 8 2 2.77472099401507 -0.774720994015071 9 4 3.42471021409548 0.575289785904525 10 4 2.54988895355206 1.45011104644794 11 4 3.65525372552112 0.344746274478885 12 2 2.74128154825911 -0.741281548259107 13 5 3.7245925813477 1.27540741865230 14 3 3.05203172263511 -0.0520317226351052 15 4 3.80450427480842 0.195495725191577 16 4 3.52614347782177 0.473856522178231 17 3 2.80976473159175 0.190235268408255 18 4 3.91377459710573 0.086225402894269 19 2 2.76047431048474 -0.760474310484738 20 4 2.98359204047272 1.01640795952728 21 3 3.03958156120114 -0.0395815612011431 22 3 3.32239485771194 -0.322394857711944 23 4 3.65997904119851 0.340020958801487 24 4 3.48964389275824 0.510356107241757 25 4 3.65800988174032 0.34199011825968 26 4 3.38017525691276 0.619824743087236 27 5 3.80922959048582 1.19077040951418 28 3 3.04199847373209 -0.0419984737320906 29 1 3.53900732891183 -2.53900732891183 30 4 3.73099721187576 0.269002788124245 31 4 3.84867941898755 0.15132058101245 32 3 2.62005985206362 0.379940147936378 33 3 3.30766217466472 -0.307662174664718 34 4 3.95880954702859 0.0411904529714089 35 4 4.07413220788202 -0.0741322078820209 36 4 3.72869999243264 0.271300007567358 37 3 3.43334821356758 -0.433348213567577 38 4 3.76414337037952 0.235856629620477 39 3 3.43965590852072 -0.439655908520720 40 4 3.37014200800975 0.62985799199025 41 3 3.05827146262094 -0.0582714626209402 42 4 3.69204378149449 0.307956218505508 43 3 2.76580939986849 0.234190600131508 44 2 2.21596709044127 -0.215967090441266 45 3 3.64007688936445 -0.640076889364452 46 4 3.52088285232218 0.479117147677818 47 4 4.39709629122696 -0.397096291226957 48 3 3.6872698447452 -0.6872698447452 49 3 3.32218602924179 -0.322186029241793 50 4 3.79612288671217 0.203877113287833 51 4 3.76779944279838 0.23220055720162 52 3 2.96248447013757 0.0375155298624292 53 2 2.65153881339047 -0.651538813390471 54 4 3.91377459710573 0.0862254028942692 55 4 3.61611894812448 0.383881051875521 56 3 2.58985064886491 0.410149351135093 57 2 2.41881463524633 -0.418814635246328 58 4 3.80444690188144 0.195553098118565 59 3 4.07413220788202 -1.07413220788202 60 3 3.5069691768214 -0.506969176821403 61 4 3.43627906612908 0.563720933870918 62 3 2.91042468432474 0.0895753156752582 63 4 3.84120910681847 0.158790893181534 64 3 3.24907505707384 -0.249075057073844 65 4 3.56626152956707 0.433738470432928 66 4 4.60158704673837 -0.601587046738371 67 4 3.65892811970896 0.341071880291044 68 3 2.56307473344695 0.43692526655305 69 3 2.46207794208613 0.537922057913871 70 3 3.77246738554879 -0.77246738554879 71 4 3.14089951823272 0.859100481767279 72 3 2.52344684449907 0.476553155500927 73 2 2.54022949372711 -0.540229493727114 74 4 3.94576021618192 0.0542397838180752 75 4 3.98953025840962 0.0104697415903816 76 4 3.89230802198808 0.107691978011922 77 3 2.34499927544895 0.655000724551051 78 5 4.24487313392686 0.75512686607314 79 3 3.50115633676301 -0.501156336763007 80 2 2.41343740397719 -0.413437403977192 81 3 3.11003622267776 -0.110036222677761 82 3 3.43959853559373 -0.439598535593732 83 4 3.72660912565748 0.273390874342522 84 4 3.15854535593711 0.841454644062886 85 3 3.40950315071112 -0.409503150711124 86 2 2.49804183077516 -0.498041830775164 87 4 3.61134383773104 0.388656162268964 88 4 3.00706395485598 0.992936045144022 89 3 2.64295775650986 0.357042243490141 90 4 3.71457266647234 0.28542733352766 91 3 3.33550990110869 -0.335509901108695 92 2 2.56262059819162 -0.562620598191625 93 3 3.28040797400947 -0.280407974009472 94 3 3.23429226538591 -0.234292265385908 95 3 3.20826768869680 -0.208267688696803 96 4 3.31159182320567 0.688408176794335 97 4 3.65978019487425 0.34021980512575 98 4 3.07941741175942 0.920582588240582 99 3 3.22917018738017 -0.229170187380173 100 4 3.65029691977021 0.349703080229789 101 4 2.99610689307154 1.00389310692845 102 3 2.83742435677997 0.162575643220034 103 4 3.99831674845731 0.00168325154269271 104 3 3.16179974847633 -0.161799748476328 105 4 3.33089746381482 0.669102536185184 106 4 4.15466518588162 -0.154665185881618 107 3 3.91163510925867 -0.911635109258673 108 3 3.51394309087002 -0.513943090870021 109 3 3.45880795110693 -0.458807951106929 110 3 3.54241255476828 -0.542412554768284 111 3 3.10544673070509 -0.105446730705092 112 2 2.48826838263998 -0.488268382639978 113 4 3.47301818234478 0.526981817655222 114 2 3.02335107904091 -1.02335107904091 115 3 3.33550990110869 -0.335509901108695 116 3 2.80685614879875 0.193143851201253 117 3 2.94753912405441 0.0524608759455865 118 4 3.82000187281067 0.179998127189335 119 4 3.52294168011452 0.477058319885483 120 3 2.99132294163637 0.00867705836363157 121 4 3.62130504973028 0.378694950269723 122 3 3.09188589167611 -0.0918858916761129 123 3 3.64673249186247 -0.646732491862474 124 3 3.3494075861478 -0.349407586147797 125 4 3.61996031003890 0.380039689961104 126 2 3.21946651866176 -1.21946651866176 127 4 3.67489852985705 0.325101470142954 128 3 2.94347807066388 0.0565219293361169 129 3 2.89527932111514 0.104720678884860 130 4 3.79143149427681 0.208568505723186 131 4 3.55492119644716 0.445078803552838 132 4 3.66001564408995 0.339984355910046 133 3 3.28495552714287 -0.284955527142873 134 2 2.25662186492651 -0.256621864926505 135 4 3.80922959048582 0.190770409514178 136 2 3.50065959030045 -1.50065959030045 137 3 3.16943364694672 -0.169433646946724 138 4 3.87366062729689 0.126339372703106 139 3 3.4427921942493 -0.4427921942493 140 3 2.52932490398038 0.470675096019625 141 3 3.14291647767015 -0.142916477670151 142 3 3.63112014800626 -0.631120148006256 143 4 4.07413220788202 -0.0741322078820209 144 3 3.6872698447452 -0.6872698447452 145 3 3.58591639559884 -0.585916395598839 146 2 3.05900563668372 -1.05900563668372 147 2 3.80922959048582 -1.80922959048582 148 3 3.00616321619623 -0.00616321619623199 149 4 3.49757718122438 0.502422818775616 150 3 3.51222139880798 -0.512221398807985 151 4 3.72288715237425 0.277112847625754 152 3 3.83521776660731 -0.835217766607312 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.120596712705617 0.241193425411233 0.879403287294383 22 0.819856175840086 0.360287648319828 0.180143824159914 23 0.727401674404558 0.545196651190883 0.272598325595442 24 0.735848125168934 0.528303749662131 0.264151874831066 25 0.638881711980294 0.722236576039413 0.361118288019706 26 0.643761144904137 0.712477710191725 0.356238855095863 27 0.73866996609184 0.522660067816321 0.261330033908161 28 0.672574882863675 0.65485023427265 0.327425117136325 29 0.99330949522015 0.0133810095597004 0.00669050477985021 30 0.99048206995373 0.0190358600925384 0.0095179300462692 31 0.984573306334867 0.0308533873302671 0.0154266936651335 32 0.983138752393599 0.0337224952128017 0.0168612476064009 33 0.97675997981445 0.0464800403711017 0.0232400201855508 34 0.966455276605355 0.0670894467892901 0.0335447233946450 35 0.955293405905152 0.0894131881896969 0.0447065940948484 36 0.938572472350592 0.122855055298816 0.061427527649408 37 0.970152101179867 0.0596957976402661 0.0298478988201331 38 0.959394330785664 0.0812113384286721 0.0406056692143361 39 0.976981205785999 0.0460375884280023 0.0230187942140011 40 0.984166388725778 0.0316672225484445 0.0158336112742222 41 0.98614695217077 0.0277060956584599 0.0138530478292299 42 0.982259337610773 0.0354813247784547 0.0177406623892274 43 0.977170465385994 0.0456590692280118 0.0228295346140059 44 0.975495878550832 0.0490082428983365 0.0245041214491682 45 0.973904518549158 0.0521909629016847 0.0260954814508423 46 0.967146601747463 0.0657067965050747 0.0328533982525373 47 0.957083165969415 0.0858336680611691 0.0429168340305845 48 0.952182861345168 0.0956342773096631 0.0478171386548316 49 0.941524501758432 0.116950996483136 0.058475498241568 50 0.926049613564687 0.147900772870627 0.0739503864353135 51 0.908420096191636 0.183159807616728 0.0915799038083639 52 0.883230656703387 0.233538686593227 0.116769343296613 53 0.883411297158847 0.233177405682306 0.116588702841153 54 0.86924869124371 0.261502617512579 0.130751308756290 55 0.856483577678623 0.287032844642753 0.143516422321377 56 0.849155743059736 0.301688513880529 0.150844256940264 57 0.83271123126086 0.334577537478281 0.167288768739141 58 0.807411985876758 0.385176028246483 0.192588014123242 59 0.859369637245766 0.281260725508467 0.140630362754234 60 0.847495277775198 0.305009444449604 0.152504722224802 61 0.846762583873187 0.306474832253626 0.153237416126813 62 0.815113733276374 0.369772533447251 0.184886266723626 63 0.79223040931662 0.41553918136676 0.20776959068338 64 0.757286198925834 0.485427602148331 0.242713801074166 65 0.783937270501097 0.432125458997806 0.216062729498903 66 0.805787907124655 0.388424185750691 0.194212092875345 67 0.782982094870347 0.434035810259305 0.217017905129653 68 0.765323296550487 0.469353406899025 0.234676703449512 69 0.771401649667709 0.457196700664582 0.228598350332291 70 0.796798855444865 0.40640228911027 0.203201144555135 71 0.84449706690231 0.311005866195381 0.155502933097691 72 0.825385359882324 0.349229280235352 0.174614640117676 73 0.831855635545813 0.336288728908374 0.168144364454187 74 0.801690506769823 0.396618986460354 0.198309493230177 75 0.787899529816719 0.424200940366563 0.212100470183281 76 0.750945190553662 0.498109618892675 0.249054809446338 77 0.741645312636007 0.516709374727986 0.258354687363993 78 0.801405604114154 0.397188791771693 0.198594395885846 79 0.787628222180902 0.424743555638197 0.212371777819098 80 0.769852713627121 0.460294572745759 0.230147286372879 81 0.729591412716395 0.540817174567209 0.270408587283605 82 0.710059745462653 0.579880509074694 0.289940254537347 83 0.674788046638109 0.650423906723782 0.325211953361891 84 0.702947639459116 0.594104721081769 0.297052360540884 85 0.66654717251719 0.66690565496562 0.33345282748281 86 0.662217412151691 0.675565175696618 0.337782587848309 87 0.648043746358969 0.703912507282062 0.351956253641031 88 0.735880262832959 0.528239474334082 0.264119737167041 89 0.703999993592751 0.592000012814497 0.296000006407249 90 0.703659138826989 0.592681722346022 0.296340861173011 91 0.677949620345982 0.644100759308036 0.322050379654018 92 0.68339459499325 0.6332108100135 0.31660540500675 93 0.643897711988507 0.712204576022987 0.356102288011494 94 0.606882229452262 0.786235541095476 0.393117770547738 95 0.573204019539217 0.853591960921567 0.426795980460783 96 0.602573801277901 0.794852397444197 0.397426198722099 97 0.586697120191213 0.826605759617575 0.413302879808787 98 0.710569357695275 0.578861284609449 0.289430642304725 99 0.670143463027311 0.659713073945378 0.329856536972689 100 0.724426389279881 0.551147221440238 0.275573610720119 101 0.76469760201538 0.470604795969241 0.235302397984620 102 0.779314272746687 0.441371454506625 0.220685727253313 103 0.732233845075927 0.535532309848147 0.267766154924073 104 0.680532817891012 0.638934364217977 0.319467182108988 105 0.698733599563034 0.602532800873932 0.301266400436966 106 0.642487211312252 0.715025577375497 0.357512788687748 107 0.748784658643063 0.502430682713874 0.251215341356937 108 0.715939337396693 0.568121325206613 0.284060662603307 109 0.700794109408353 0.598411781183294 0.299205890591647 110 0.651488387910083 0.697023224179833 0.348511612089916 111 0.61893901688278 0.762121966234439 0.381060983117219 112 0.588115304762031 0.823769390475938 0.411884695237969 113 0.558650887538726 0.882698224922548 0.441349112461274 114 0.622825255048906 0.754349489902188 0.377174744951094 115 0.574159335992738 0.851681328014525 0.425840664007262 116 0.50687250666637 0.98625498666726 0.49312749333363 117 0.433558984155095 0.86711796831019 0.566441015844905 118 0.367958298520107 0.735916597040215 0.632041701479893 119 0.308700802634704 0.617401605269408 0.691299197365296 120 0.260660853414836 0.521321706829672 0.739339146585164 121 0.308626994152307 0.617253988304614 0.691373005847693 122 0.243650467065881 0.487300934131762 0.756349532934119 123 0.196359537422571 0.392719074845142 0.803640462577429 124 0.145048158830950 0.290096317661900 0.85495184116905 125 0.100800168028716 0.201600336057433 0.899199831971284 126 0.133044094542255 0.26608818908451 0.866955905457745 127 0.0946326899678296 0.189265379935659 0.90536731003217 128 0.0571646801305799 0.114329360261160 0.94283531986942 129 0.0313533158994947 0.0627066317989893 0.968646684100505 130 0.0314363100635211 0.0628726201270423 0.968563689936479 131 0.0153812784353617 0.0307625568707234 0.984618721564638 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 12 0.108108108108108 NOK 10% type I error level 22 0.198198198198198 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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