*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 11:20:41 +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/t12912023761ayg83hp2n6dw8l.htm/, Retrieved Wed, 01 Dec 2010 12:19:36 +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/t12912023761ayg83hp2n6dw8l.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 «

4 4 3 3 2 2 2 2 2 4 2 4 2 3 1 1 2 3 3 2 2 1 2 2 5 4 4 3 4 3 2 2 4 4 4 2 2 1 1 2 4 4 4 4 2 3 3 3 4 4 4 4 4 4 2 2 1 1 2 3 4 4 2 3 3 2 3 3 4 4 3 4 1 2 2 2 2 3 2 2 1 3 1 2 4 3 4 3 4 3 4 4 1 2 2 2 4 4 4 3 5 4 4 4 4 4 4 3 4 4 3 3 4 4 3 3 2 2 2 2 2 2 2 2 4 4 2 4 4 3 4 3 2 2 1 3 3 2 4 2 4 4 4 4 3 3 1 3 2 2 2 2 4 4 3 3 4 4 4 4 3 3 3 4 1 1 1 2 2 2 3 1 4 2 2 2 2 2 1 3 3 4 3 3 4 3 4 4 1 2 1 2 3 2 4 3 4 4 4 4 1 1 1 2 4 5 4 2 3 2 4 3 1 3 2 2 1 4 4 4 4 4 3 3 4 3 2 3 4 4 4 4 2 2 2 4 4 3 4 4 2 2 2 2 4 4 4 4 5 5 5 4 3 3 4 4 2 1 1 2 4 3 3 3 4 4 4 3 2 2 1 2 3 3 3 4 1 1 1 1 4 3 4 3 4 2 4 3 4 3 2 2 4 4 4 2 3 3 3 3 4 4 4 3 3 4 4 3 3 3 4 3 2 2 1 3 1 1 2 2 2 2 1 2 4 3 3 3 3 4 3 3 5 1 3 2 1 1 1 2 3 3 3 3 2 2 2 2 3 2 3 3 4 3 4 3 3 2 2 2 3 2 2 3 4 3 3 3 4 4 4 4 4 4 4 4 2 2 4 3 2 2 2 2 1 1 1 1 1 2 2 2 4 3 4 3 2 3 3 3 4 4 4 5 3 4 4 4 5 4 3 5 1 NA 2 2 1 1 1 1 2 3 2 3 4 2 2 3 4 3 4 4 3 3 2 2 4 2 1 2 4 3 2 3 5 2 4 4 1 2 2 2 4 3 3 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 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation Q4 [t] = + 0.865045701430835 + 0.145400006160318Q1[t] + 0.252561146567979Q2[t] + 0.220272402114639Q3[t] -0.0776944496009527M1[t] -0.135576717001389M2[t] + 0.0716598829398656M3[t] + 0.0976981103730005M4[t] + 0.278051810260123M5[t] + 0.0567419658771181M6[t] + 0.133278071817606M7[t] + 0.0873192329729293M8[t] + 0.12122700224052M9[t] + 0.207612182563193M10[t] + 0.230802626594899M11[t] + 0.00207493155891959t + 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) 0.865045701430835 0.261534 3.3076 0.0012 6e-04 Q1 0.145400006160318 0.067585 2.1514 0.03319 0.016595 Q2 0.252561146567979 0.076826 3.2874 0.001282 0.000641 Q3 0.220272402114639 0.072113 3.0546 0.002706 0.001353 M1 -0.0776944496009527 0.258216 -0.3009 0.763951 0.381976 M2 -0.135576717001389 0.259051 -0.5234 0.601564 0.300782 M3 0.0716598829398656 0.256919 0.2789 0.780724 0.390362 M4 0.0976981103730005 0.259071 0.3771 0.706672 0.353336 M5 0.278051810260123 0.255952 1.0863 0.279221 0.139611 M6 0.0567419658771181 0.255813 0.2218 0.82479 0.412395 M7 0.133278071817606 0.25755 0.5175 0.605646 0.302823 M8 0.0873192329729293 0.265127 0.3293 0.742391 0.371196 M9 0.12122700224052 0.259243 0.4676 0.640794 0.320397 M10 0.207612182563193 0.261986 0.7925 0.429456 0.214728 M11 0.230802626594899 0.256484 0.8999 0.369756 0.184878 t 0.00207493155891959 0.001186 1.75 0.082333 0.041166 Multiple Linear Regression - Regression Statistics Multiple R 0.701482221157589 R-squared 0.492077306600185 Adjusted R-squared 0.436868318187161 F-TEST (value) 8.91299262574619 F-TEST (DF numerator) 15 F-TEST (DF denominator) 138 p-value 3.71924713249427e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.646445212137204 Sum Squared Residuals 57.6690148967258 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3 3.0420880006459 -0.042088000645902 2 2 1.97008595723316 0.0299140427668448 3 4 2.68451978186929 1.31548021813071 4 1 2.23979939217872 -1.23979939217872 5 2 2.86277282785404 -0.862772827854045 6 2 1.91814321977936 0.0818567802206368 7 3 3.63118251969294 -0.631182519692938 8 2 2.74879265544961 -0.748792655449606 9 2 3.47788130707337 -1.47788130707337 10 2 1.85704076058648 0.142959239413523 11 4 3.59160679454559 0.408393205454409 12 3 2.59924553850636 0.400754461493641 13 4 3.28725958146758 0.712740418532421 14 2 2.79090744139678 -0.790907441396783 15 3 1.80633551471207 1.19366448528793 16 3 3.02833213188901 -0.0283321318890123 17 3 2.78051086615342 0.219489133846581 18 4 3.21179825262561 0.788201747374392 19 2 2.12881457639347 -0.128814576393467 20 2 2.48289182183601 -0.482891821836005 21 2 2.15320211438756 -0.153202114387559 22 3 3.33867945109402 -0.338679451094022 23 4 3.36394482668465 0.636055173315352 24 2 2.00591116237046 -0.0059111623704582 25 3 3.31215876017461 -0.312158760174614 26 4 3.40175143049341 0.598248569506586 27 3 3.46566295583327 -0.465662955833271 28 3 3.27350371271069 -0.273503712710687 29 3 3.45593234415673 -0.455932344156728 30 2 2.22050272376141 -0.220502723761412 31 2 2.29911376126082 -0.299113761260819 32 4 3.05115215943166 0.948847840568345 33 3 3.27511851791946 -0.275118517919465 34 3 2.15940026456853 0.840599735431475 35 2 2.99088285266339 -0.990882852663387 36 4 3.41267745692368 0.587322543076318 37 3 2.27827957980944 0.721720420190565 38 2 2.04478349335426 -0.0447834933542608 39 3 3.27028973242567 -0.270289732425667 40 4 3.51867529353236 0.481324706467639 41 4 3.08287037013547 0.917129629864532 42 2 1.62716834762551 0.372831652374489 43 1 2.54428534208249 -1.54428534208249 44 2 2.57092904500273 -0.570929045002733 45 3 2.09583933139397 0.904160668606032 46 3 3.27536654680111 -0.275366546801114 47 4 3.41374318409872 0.586256815901282 48 2 1.83543711766989 0.164562882330111 49 3 2.71143481829241 0.288565181707591 50 4 3.30614978174717 0.693850218252833 51 2 1.66076064871854 0.339239351281465 52 2 3.79613561880737 -1.79613561880737 53 3 3.07548080438916 -0.0754808043891635 54 2 2.37746222158314 -0.377462221583143 55 4 3.14917920987981 0.850820790120193 56 3 3.32122291896036 -0.321222918960364 57 3 2.88437207110426 0.115627928895743 58 4 3.66593813378311 0.334061866216893 59 4 2.45473639968786 1.54526360031214 60 4 3.20991466776977 0.790085332230226 61 2 2.15038918660985 -0.150389186609848 62 4 3.3310489604542 0.668951039545798 63 4 4.15859404679731 -0.158594046797312 64 4 3.17051249821814 0.829487501781865 65 2 2.04160162402398 -0.0416016240239844 66 3 3.05883382088577 -0.0588338208857702 67 3 3.61027840706780 -0.610278407067795 68 2 2.10965498798153 -0.109654987981528 69 4 2.98414364576561 1.01585635423439 70 1 1.83613664796134 -0.836136647961335 71 3 3.46354154151279 -0.463541541512788 72 3 2.98225269990883 0.0177473000911697 73 2 2.7186495242055 -0.718649524205497 74 2 3.35594813916124 -1.35594813916124 75 3 2.94702611581848 0.0529738841815237 76 3 3.59337282965347 -0.593372829653466 77 3 3.63040145493919 -0.63040145493919 78 3 3.15860539554713 -0.158605395547127 79 3 2.17843807397432 0.82156192602568 80 2 1.95686541607491 0.0431345839250939 81 2 2.17053686751507 -0.170536867515074 82 3 3.24290294251456 -0.242902942514559 83 3 3.37532945851284 -0.375329458512845 84 2 2.67971833609357 -0.679718336093565 85 2 1.58195398918098 0.418046010819017 86 3 2.76261376302534 0.237386236974663 87 2 2.35369173968258 -0.353691739682576 88 3 2.74747730694959 0.252522693050413 89 3 3.54813949323856 -0.548139493238565 90 2 2.49039862345691 -0.490398623456905 91 3 2.56900966095631 0.430990339043687 92 3 3.14335930851349 -0.143359308513491 93 4 3.65217555802262 0.347824441977381 94 4 3.74063566990421 0.259364330095788 95 3 2.96997874003824 0.0300212599617556 96 2 2.30070624077299 -0.300706240772987 97 1 1.60685316788802 -0.606853167888018 98 2 2.02387938072912 -0.0238793807291185 99 3 3.36249688150750 -0.362496881507503 100 3 2.87953762606428 0.120462373935717 101 5 3.82559981851358 1.17440018148642 102 4 3.46096489952918 0.539035100470824 103 5 3.61010354723458 1.38989645276542 104 2 2.82237407220085 -0.822374072200847 105 1 0.781628885493354 0.218371114506646 106 3 2.84513312683664 0.154866873163363 107 3 2.30951138259791 0.690488617402086 108 4 4.64794705416629 -0.647947054166285 109 2 2.26470617580247 -0.264706175802468 110 2 1.94685125598526 0.0531487440147399 111 3 2.30834807879893 0.691651921201068 112 4 4.46863188137442 -0.468631881374425 113 2 2.15843053571391 -0.158430535713911 114 3 2.98448042664534 0.0155195733546601 115 3 2.19315766592756 0.80684233407244 116 4 3.41117390311605 0.588826096883946 117 4 4.55396691763241 -0.553966917632411 118 2 2.81569940290891 -0.815699402908907 119 3 4.18901055514463 -1.18901055514463 120 2 1.89311863498796 0.106881365012041 121 3 2.45554485398938 0.544455146010622 122 4 4.64866167791832 -0.64866167791832 123 2 1.44040839791363 0.559591602086372 124 4 3.65512577381301 0.344874226186990 125 4 4.0217350006894 -0.0217350006893962 126 2 2.51450189848833 -0.514501898488332 127 3 3.69089039331721 -0.690890393317214 128 3 2.63580599061817 0.364194009381829 129 3 1.96063254149651 1.03936745850349 130 3 2.40005377738666 0.599946222613336 131 4 3.96134858728369 0.0386514127163119 132 3 3.29978425885206 -0.299784258852059 133 2 1.64193807573884 0.358061924261162 134 3 3.21692201551397 -0.216922015513970 135 3 2.48140161350277 0.518598386497229 136 3 2.64773620806671 0.352263791933295 137 4 4.20822889312798 -0.208228893127981 138 3 2.61427347314969 0.385726526850311 139 4 3.24295602334163 0.757043976658369 140 4 3.75177227285076 0.248227727149241 141 4 4.58767123816437 -0.587671238164373 142 3 3.64522535820834 -0.645225358208338 143 3 3.79826410832942 -0.798264108329423 144 2 1.47008344371941 0.529916556280588 145 3 3.65064254687464 -0.650642546874641 146 1 1.47818763321775 -0.478187633217751 147 2 1.52249549978104 0.477504500218962 148 4 3.92519653334172 0.074803466658281 149 4 4.0877280656747 -0.0877280656746981 150 3 3.16633910317411 -0.166339103174106 151 3 2.48812760416331 0.511872395836695 152 4 4.68560434803224 -0.685604348032241 153 2 2.67012453691537 -0.670124536915373 154 4 3.7160021466288 0.283997853371202 155 3 NA NA 156 3 NA NA Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.661928744714834 0.676142510570332 0.338071255285166 20 0.531888007174701 0.936223985650599 0.468111992825299 21 0.55676172694791 0.88647654610418 0.44323827305209 22 0.471386535495319 0.942773070990638 0.528613464504681 23 0.368247978311205 0.73649595662241 0.631752021688795 24 0.393728139493427 0.787456278986854 0.606271860506573 25 0.45879327737091 0.91758655474182 0.54120672262909 26 0.470658478855072 0.941316957710144 0.529341521144928 27 0.76873701282131 0.462525974357379 0.231262987178690 28 0.716415823839952 0.567168352320096 0.283584176160048 29 0.660266595049818 0.679466809900364 0.339733404950182 30 0.668565124515494 0.662869750969012 0.331434875484506 31 0.600314166185512 0.799371667628975 0.399685833814488 32 0.722068360545392 0.555863278909216 0.277931639454608 33 0.683101873368574 0.633796253262852 0.316898126631426 34 0.648397163236929 0.703205673526142 0.351602836763071 35 0.800736429511335 0.398527140977329 0.199263570488665 36 0.761438656415732 0.477122687168536 0.238561343584268 37 0.723490808002726 0.553018383994548 0.276509191997274 38 0.666312052510807 0.667375894978387 0.333687947489193 39 0.725891679798901 0.548216640402198 0.274108320201099 40 0.75769064676132 0.484618706477359 0.242309353238680 41 0.790561036977505 0.418877926044991 0.209438963022495 42 0.751555624260349 0.496888751479302 0.248444375739651 43 0.876668304487178 0.246663391025645 0.123331695512822 44 0.864593003680123 0.270813992639755 0.135406996319877 45 0.893481353494578 0.213037293010843 0.106518646505422 46 0.879246036966696 0.241507926066608 0.120753963033304 47 0.858180332733436 0.283639334533127 0.141819667266564 48 0.844824083324463 0.310351833351073 0.155175916675537 49 0.810878092498214 0.378243815003572 0.189121907501786 50 0.809118298274472 0.381763403451056 0.190881701725528 51 0.789447397747515 0.421105204504971 0.210552602252485 52 0.936473344532813 0.127053310934374 0.0635266554671868 53 0.918038401826802 0.163923196346396 0.081961598173198 54 0.90559428027429 0.188811439451421 0.0944057197257105 55 0.949886942571512 0.100226114856977 0.0501130574284885 56 0.939610632398013 0.120778735203974 0.0603893676019871 57 0.922402712139681 0.155194575720638 0.0775972878603188 58 0.904300231511105 0.19139953697779 0.095699768488895 59 0.960409689995648 0.0791806200087036 0.0395903100043518 60 0.96452776554655 0.0709444689068982 0.0354722344534491 61 0.96084488690336 0.0783102261932812 0.0391551130966406 62 0.960403011064763 0.0791939778704733 0.0395969889352367 63 0.953633670726624 0.0927326585467526 0.0463663292733763 64 0.968867627024477 0.0622647459510459 0.0311323729755230 65 0.960702335295448 0.0785953294091046 0.0392976647045523 66 0.949764368529425 0.10047126294115 0.050235631470575 67 0.950247356557502 0.0995052868849962 0.0497526434424981 68 0.93695164406825 0.126096711863499 0.0630483559317495 69 0.957180952282703 0.0856380954345948 0.0428190477172974 70 0.970361108131088 0.0592777837378244 0.0296388918689122 71 0.97052354583492 0.0589529083301594 0.0294764541650797 72 0.963637649234399 0.0727247015312022 0.0363623507656011 73 0.968868131006179 0.0622637379876423 0.0311318689938212 74 0.99087907117093 0.0182418576581396 0.00912092882906981 75 0.988294224697656 0.0234115506046872 0.0117057753023436 76 0.991102914792074 0.0177941704158515 0.00889708520792575 77 0.99201826529669 0.0159634694066209 0.00798173470331045 78 0.988905640701226 0.0221887185975475 0.0110943592987738 79 0.99079068687266 0.0184186262546813 0.00920931312734064 80 0.987126827971741 0.0257463440565171 0.0128731720282586 81 0.982822037800577 0.0343559243988455 0.0171779621994227 82 0.979031544582582 0.0419369108348368 0.0209684554174184 83 0.975451839452904 0.0490963210941923 0.0245481605470961 84 0.976368102156104 0.0472637956877925 0.0236318978438962 85 0.974565330565851 0.050869338868298 0.025434669434149 86 0.96623015344489 0.0675396931102219 0.0337698465551110 87 0.959147067900253 0.0817058641994931 0.0408529320997466 88 0.951289612501369 0.0974207749972625 0.0487103874986313 89 0.959151659023119 0.0816966819537622 0.0408483409768811 90 0.956460006698845 0.0870799866023102 0.0435399933011551 91 0.948532050766015 0.10293589846797 0.051467949233985 92 0.94460791429422 0.110784171411560 0.0553920857057798 93 0.930540269364754 0.138919461270492 0.0694597306352459 94 0.913848043896709 0.172303912206582 0.0861519561032911 95 0.901032932302957 0.197934135394087 0.0989670676970435 96 0.880977469413442 0.238045061173116 0.119022530586558 97 0.87262350882535 0.254752982349300 0.127376491174650 98 0.842781256593949 0.314437486812103 0.157218743406051 99 0.816032938837112 0.367934122325776 0.183967061162888 100 0.787961521824953 0.424076956350095 0.212038478175047 101 0.833313412717427 0.333373174565147 0.166686587282573 102 0.81999263593724 0.360014728125519 0.180007364062760 103 0.895365343743458 0.209269312513084 0.104634656256542 104 0.91388095929191 0.172238081416180 0.0861190407080898 105 0.890915216274405 0.218169567451191 0.109084783725595 106 0.866452816915675 0.267094366168650 0.133547183084325 107 0.898239669249282 0.203520661501436 0.101760330750718 108 0.906794964882848 0.186410070234304 0.0932050351171518 109 0.901513108049871 0.196973783900257 0.0984868919501287 110 0.87325556258433 0.253488874831339 0.126744437415670 111 0.85435959584641 0.29128080830718 0.14564040415359 112 0.85002704427733 0.299945911445339 0.149972955722669 113 0.813173249558997 0.373653500882007 0.186826750441003 114 0.767690325151492 0.464619349697015 0.232309674848508 115 0.74462049934664 0.510759001306719 0.255379500653360 116 0.793396962889083 0.413206074221834 0.206603037110917 117 0.79763937086761 0.404721258264779 0.202360629132389 118 0.787574576622231 0.424850846755538 0.212425423377769 119 0.831459740335892 0.337080519328215 0.168540259664108 120 0.780246734604794 0.439506530790413 0.219753265395206 121 0.774618620876481 0.450762758247038 0.225381379123519 122 0.729892569962016 0.540214860075968 0.270107430037984 123 0.669975567033452 0.660048865933097 0.330024432966548 124 0.595258421811809 0.809483156376382 0.404741578188191 125 0.514682216078486 0.970635567843028 0.485317783921514 126 0.580732728740025 0.83853454251995 0.419267271259975 127 0.802273688108276 0.395452623783447 0.197726311891723 128 0.730535539966569 0.538928920066862 0.269464460033431 129 0.891109099166985 0.21778180166603 0.108890900833015 130 0.959663826723787 0.0806723465524269 0.0403361732762134 131 0.929500961835798 0.140998076328404 0.0704990381642022 132 0.919460385136665 0.161079229726670 0.0805396148633351 133 0.90667942847662 0.186641143046758 0.0933205715233792 134 0.842107591376955 0.315784817246089 0.157892408623045 135 0.752511058952942 0.494977882094116 0.247488941047058 136 0.55657683537395 0.886846329252099 0.443423164626049 137 0.5918122316753 0.8163755366494 0.4081877683247 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 11 0.092436974789916 NOK 10% type I error level 31 0.260504201680672 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/01/t12912023761ayg83hp2n6dw8l/10ieea1291202429.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t12912023761ayg83hp2n6dw8l/10ieea1291202429.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t12912023761ayg83hp2n6dw8l/1tdzz1291202429.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t12912023761ayg83hp2n6dw8l/1tdzz1291202429.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t12912023761ayg83hp2n6dw8l/2tdzz1291202429.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t12912023761ayg83hp2n6dw8l/2tdzz1291202429.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t12912023761ayg83hp2n6dw8l/34myk1291202429.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t12912023761ayg83hp2n6dw8l/34myk1291202429.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t12912023761ayg83hp2n6dw8l/44myk1291202429.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t12912023761ayg83hp2n6dw8l/44myk1291202429.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t12912023761ayg83hp2n6dw8l/54myk1291202429.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t12912023761ayg83hp2n6dw8l/54myk1291202429.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t12912023761ayg83hp2n6dw8l/6evgm1291202429.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t12912023761ayg83hp2n6dw8l/6evgm1291202429.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t12912023761ayg83hp2n6dw8l/77nfp1291202429.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t12912023761ayg83hp2n6dw8l/77nfp1291202429.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t12912023761ayg83hp2n6dw8l/87nfp1291202429.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t12912023761ayg83hp2n6dw8l/87nfp1291202429.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t12912023761ayg83hp2n6dw8l/97nfp1291202429.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t12912023761ayg83hp2n6dw8l/97nfp1291202429.ps (open in new window)

Parameters (Session):

par1 = 4 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 4 ; par2 = Include Monthly 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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