ws 7 3

*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, 24 Nov 2010 13:24:17 +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/24/t12906049958hlkqgp8s96msv5.htm/, Retrieved Wed, 24 Nov 2010 14:23:18 +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/24/t12906049958hlkqgp8s96msv5.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 9 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 7.9 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 1 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 9 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation O[t] = + 28.2113145628772 -1.21076082808973M[t] -0.0662441512071262CM[t] + 0.219982378476393D[t] -0.138042493202292PE[t] -0.267683206546857PC[t] + 0.415179865256042PS[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) 28.2113145628772 14.945756 1.8876 0.060988 0.030494 M -1.21076082808973 1.484819 -0.8154 0.416104 0.208052 CM -0.0662441512071262 0.063225 -1.0478 0.296415 0.148207 D 0.219982378476393 0.112769 1.9507 0.052927 0.026464 PE -0.138042493202292 0.105255 -1.3115 0.191667 0.095833 PC -0.267683206546857 0.1315 -2.0356 0.043526 0.021763 PS 0.415179865256042 0.076265 5.4439 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.475107146524304 R-squared 0.225726800678466 Adjusted R-squared 0.195163384915774 F-TEST (value) 7.38552269259134 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 6.01600129157553e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.50327124217684 Sum Squared Residuals 1865.48222823202 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 26 24.0380116421256 1.96198835787441 2 23 25.3499030197419 -2.34990301974193 3 25 25.4754187312743 -0.475418731274265 4 23 23.1283877855251 -0.12838778552508 5 19 22.9502296744362 -3.95022967443619 6 29 24.0580491468969 4.94195085310305 7 25 24.7689434225897 0.231056577410299 8 21 22.5497602295545 -1.54976022955451 9 22 21.9587949609711 0.0412050390288902 10 25 22.4478041876181 2.55219581238185 11 24 20.1834857808795 3.81651421912049 12 18 19.7590757706424 -1.75907577064237 13 22 18.372348320174 3.62765167982603 14 15 20.6720873616672 -5.67208736166723 15 22 23.4458223210569 -1.4458223210569 16 28 24.2571921190913 3.74280788090873 17 20 22.1748462508084 -2.17484625080835 18 12 19.0224880776687 -7.02248807766866 19 24 21.4521344910145 2.54786550898554 20 20 21.387790137663 -1.38779013766304 21 21 23.2363704932754 -2.23637049327541 22 20 20.6606202172801 -0.660620217280076 23 21 19.1683613628413 1.83163863715866 24 23 21.0812378834395 1.91876211656055 25 28 21.9085377998056 6.09146220019442 26 24 21.8730095344099 2.12699046559012 27 24 23.4614246582104 0.538575341789576 28 24 20.3771366822311 3.62286331776894 29 23 21.9726643776973 1.02733562230273 30 23 22.6907025024683 0.309297497531739 31 29 24.2446853910721 4.75531460892794 32 24 21.9943008716901 2.00569912830987 33 18 25.0181996958846 -7.0181996958846 34 25 25.9629248535507 -0.962924853550713 35 21 22.5810225057866 -1.58102250578665 36 26 26.6953459132976 -0.695345913297579 37 22 25.1140100044524 -3.11401000445245 38 22 22.8253821301005 -0.825382130100455 39 22 22.5517548560342 -0.551754856034193 40 23 25.5973147716882 -2.59731477168816 41 30 22.89545874919 7.10454125081001 42 23 22.6639292293579 0.336070770642108 43 17 18.7115504081909 -1.71155040819089 44 23 23.7897978251764 -0.789797825176368 45 23 24.2514329548606 -1.2514329548606 46 25 22.3934967831105 2.60650321688952 47 24 20.722387160815 3.27761283918504 48 24 27.4346766009058 -3.43467660090579 49 23 22.9639707423358 0.0360292576641573 50 21 23.8188359040196 -2.81883590401957 51 24 25.689268014907 -1.68926801490697 52 24 21.8119545661137 2.18804543388633 53 28 21.4842687769198 6.51573122308023 54 16 21.0236250829993 -5.02362508299931 55 20 19.7974410658806 0.202558934119401 56 29 23.4074704661304 5.59252953386964 57 27 23.8428596660418 3.15714033395823 58 22 23.1630373613017 -1.16303736130166 59 28 23.9455798738586 4.05442012614143 60 16 20.3525238918059 -4.35252389180595 61 25 22.8560551065421 2.14394489345794 62 24 23.4760680066282 0.523931993371767 63 28 23.6427953662461 4.35720463375388 64 24 24.2219104420497 -0.221910442049678 65 23 22.6726225365779 0.327377463422147 66 30 26.8922094115959 3.10779058840406 67 24 21.284020580403 2.71597941959703 68 21 24.0987471132405 -3.0987471132405 69 25 23.2691731098696 1.73082689013041 70 25 23.9181929748787 1.08180702512134 71 22 20.7820340168568 1.21796598314317 72 23 22.4275211010603 0.572478898939722 73 26 22.8262932570107 3.17370674298933 74 23 21.6022183253514 1.3977816746486 75 25 23.0639597509677 1.93604024903233 76 21 21.2855363232984 -0.28553632329839 77 25 23.6404111344227 1.35958886557731 78 24 22.1445809202261 1.85541907977393 79 29 23.5121022672524 5.48789773274761 80 22 23.6475211919108 -1.64752119191078 81 27 23.5679562571882 3.43204374281184 82 26 19.6293304628626 6.37066953713738 83 22 21.3047670242071 0.695232975792906 84 24 22.0326669603443 1.96733303965569 85 27 23.1055055643977 3.89449443560234 86 24 21.3535202379267 2.64647976207328 87 24 24.8501959300918 -0.850195930091758 88 29 24.355086122236 4.64491387776403 89 22 22.1422701689175 -0.142270168917526 90 21 20.5726565389056 0.427343461094374 91 24 20.4451088014099 3.55489119859013 92 24 21.7191549172559 2.28084508274409 93 23 21.940865263704 1.05913473629601 94 20 22.3033791385044 -2.30337913850444 95 27 21.3483864950151 5.65161350498488 96 26 23.4246262317058 2.57537376829418 97 25 21.9468890568043 3.05311094319566 98 21 20.0642106313397 0.935789368660329 99 21 20.7678540256853 0.232145974314724 100 19 20.3833782507911 -1.38337825079114 101 21 21.5815820263659 -0.581582026365925 102 21 21.2757289453639 -0.275728945363894 103 16 19.7626225329336 -3.76262253293362 104 22 20.6424782949367 1.35752170506331 105 29 21.7681419173125 7.23185808268746 106 15 21.7285300518644 -6.72853005186445 107 17 20.6914683311992 -3.69146833119922 108 15 19.9107210220628 -4.91072102206282 109 21 21.6461601660543 -0.646160166054345 110 21 21.0223978312602 -0.0223978312602242 111 19 19.2846170934275 -0.284617093427472 112 24 18.0610882808013 5.93891171919871 113 20 22.2498571897503 -2.24985718975033 114 17 25.0894942854413 -8.08949428544126 115 23 24.8187640667656 -1.81876406676556 116 24 22.3894676164898 1.61053238351019 117 14 22.0562702744901 -8.05627027449007 118 19 22.8524775017181 -3.85247750171813 119 24 22.1815265791481 1.81847342085194 120 13 20.4208948976005 -7.42089489760047 121 22 25.3600782782672 -3.36007827826717 122 16 21.1238596734176 -5.12385967341765 123 19 23.2284747086461 -4.22847470864614 124 25 22.7391461483101 2.26085385168992 125 25 24.1550100269908 0.844989973009194 126 23 21.4292185546407 1.57078144535926 127 24 23.5527023191067 0.447297680893288 128 26 23.5030131096226 2.49698689037738 129 26 21.4881687516386 4.51183124836138 130 25 24.1321460098712 0.867853990128757 131 18 22.2913902011632 -4.29139020116321 132 21 19.8685435422477 1.13145645775229 133 26 23.6496505606757 2.35034943932426 134 23 21.9637812000777 1.03621879992229 135 23 19.7573051646885 3.24269483531153 136 22 22.5981238379304 -0.59812383793039 137 20 22.3968907626009 -2.39689076260087 138 13 22.0661760017937 -9.0661760017937 139 24 21.3905331322975 2.60946686770245 140 15 21.5036713077125 -6.50367130771249 141 14 23.0937406475822 -9.09374064758223 142 22 24.0489169164051 -2.04891691640508 143 10 17.6456931542631 -7.64569315426308 144 24 24.4263784690027 -0.426378469002681 145 22 21.8302492712579 0.169750728742086 146 24 25.7876336500023 -1.78763365000229 147 19 21.6536043888869 -2.65360438888688 148 20 22.0851919634486 -2.08519196344857 149 13 17.1097811441646 -4.10978114416461 150 20 20.1003643180544 -0.100364318054432 151 22 23.1857601196823 -1.18576011968228 152 24 23.3827593263361 0.617240673663885 153 29 23.2737759886985 5.72622401130151 154 12 20.9758996574622 -8.97589965746221 155 20 20.9222146380677 -0.922214638067705 156 21 21.4451629067001 -0.445162906700136 157 24 23.6330070353948 0.36699296460521 158 22 21.8925934477462 0.107406552253813 159 20 17.7221746839407 2.27782531605929 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.527011339441509 0.945977321116983 0.472988660558491 11 0.562050758269063 0.875898483461873 0.437949241730937 12 0.488797048040874 0.977594096081748 0.511202951959126 13 0.540312608910689 0.919374782178622 0.459687391089311 14 0.741606301267105 0.516787397465791 0.258393698732895 15 0.654975316425638 0.690049367148725 0.345024683574362 16 0.62434981409628 0.751300371807439 0.37565018590372 17 0.538687106536786 0.922625786926427 0.461312893463214 18 0.676523849957849 0.646952300084302 0.323476150042151 19 0.601787714256701 0.796424571486598 0.398212285743299 20 0.58900929980256 0.82198140039488 0.41099070019744 21 0.525027626121065 0.94994474775787 0.474972373878935 22 0.455644610275876 0.911289220551752 0.544355389724124 23 0.404802514498525 0.809605028997049 0.595197485501475 24 0.409292695949613 0.818585391899226 0.590707304050387 25 0.571837157525293 0.856325684949414 0.428162842474707 26 0.510576212129371 0.978847575741259 0.489423787870629 27 0.443519562686602 0.887039125373204 0.556480437313398 28 0.437932035294218 0.875864070588437 0.562067964705782 29 0.373771831625196 0.747543663250391 0.626228168374804 30 0.313336025758917 0.626672051517833 0.686663974241083 31 0.347263297377555 0.694526594755111 0.652736702622445 32 0.296163153698189 0.592326307396377 0.703836846301811 33 0.521927365358015 0.95614526928397 0.478072634641985 34 0.470812921787909 0.941625843575818 0.529187078212091 35 0.432862899334544 0.865725798669089 0.567137100665456 36 0.375546236339171 0.751092472678343 0.624453763660829 37 0.348910287323424 0.697820574646848 0.651089712676576 38 0.297272496870143 0.594544993740286 0.702727503129857 39 0.249904028542291 0.499808057084582 0.750095971457709 40 0.222560825336939 0.445121650673878 0.777439174663061 41 0.375203931367904 0.750407862735809 0.624796068632096 42 0.323419485366195 0.64683897073239 0.676580514633805 43 0.291372184891437 0.582744369782875 0.708627815108563 44 0.247786889016575 0.49557377803315 0.752213110983425 45 0.211393904844775 0.422787809689551 0.788606095155225 46 0.191987017977891 0.383974035955782 0.80801298202211 47 0.179547882285088 0.359095764570176 0.820452117714912 48 0.164459892538351 0.328919785076702 0.83554010746165 49 0.134369240006066 0.268738480012132 0.865630759993934 50 0.12472845629302 0.24945691258604 0.87527154370698 51 0.102954440158643 0.205908880317287 0.897045559841357 52 0.0878329701028204 0.175665940205641 0.91216702989718 53 0.147392747581937 0.294785495163874 0.852607252418063 54 0.176759866229267 0.353519732458535 0.823240133770733 55 0.165314066746353 0.330628133492706 0.834685933253647 56 0.222746328051184 0.445492656102369 0.777253671948816 57 0.215184324890159 0.430368649780318 0.78481567510984 58 0.184195410631713 0.368390821263425 0.815804589368287 59 0.197396035986441 0.394792071972881 0.80260396401356 60 0.225127634390959 0.450255268781918 0.774872365609041 61 0.198905633976573 0.397811267953146 0.801094366023427 62 0.167144063564596 0.334288127129193 0.832855936435404 63 0.18238401406996 0.364768028139921 0.81761598593004 64 0.153297483576505 0.306594967153011 0.846702516423495 65 0.126476444675909 0.252952889351819 0.87352355532409 66 0.122928310183972 0.245856620367944 0.877071689816028 67 0.112290924195902 0.224581848391803 0.887709075804098 68 0.111389708749007 0.222779417498014 0.888610291250993 69 0.0947978505473057 0.189595701094611 0.905202149452694 70 0.077395403456274 0.154790806912548 0.922604596543726 71 0.0628992200876906 0.125798440175381 0.93710077991231 72 0.0496820132984475 0.099364026596895 0.950317986701553 73 0.0466400462749178 0.0932800925498357 0.953359953725082 74 0.0373621752075984 0.0747243504151968 0.962637824792402 75 0.0310517330200508 0.0621034660401016 0.96894826697995 76 0.0238172017328579 0.0476344034657159 0.976182798267142 77 0.0187002305121635 0.037400461024327 0.981299769487836 78 0.0149689403621708 0.0299378807243416 0.98503105963783 79 0.0224924007048703 0.0449848014097406 0.97750759929513 80 0.017931427030847 0.0358628540616939 0.982068572969153 81 0.0175338942105028 0.0350677884210056 0.982466105789497 82 0.0313614803069281 0.0627229606138562 0.968638519693072 83 0.0241862122156632 0.0483724244313264 0.975813787784337 84 0.0201798986454488 0.0403597972908976 0.97982010135455 85 0.0221020803926987 0.0442041607853975 0.977897919607301 86 0.0195896963605926 0.0391793927211851 0.980410303639407 87 0.0148920824096965 0.0297841648193931 0.985107917590303 88 0.0194432873314935 0.038886574662987 0.980556712668507 89 0.0152908309903176 0.0305816619806353 0.984709169009682 90 0.0114418907049145 0.0228837814098289 0.988558109295086 91 0.0115015183841046 0.0230030367682092 0.988498481615895 92 0.0100556605744892 0.0201113211489783 0.98994433942551 93 0.00771186522967607 0.0154237304593521 0.992288134770324 94 0.00637459672667729 0.0127491934533546 0.993625403273323 95 0.0116799873633403 0.0233599747266806 0.98832001263666 96 0.0105781200811642 0.0211562401623283 0.989421879918836 97 0.0100612562765504 0.0201225125531008 0.98993874372345 98 0.0076991130418428 0.0153982260836856 0.992300886958157 99 0.00568082481582092 0.0113616496316418 0.99431917518418 100 0.00434897856817229 0.00869795713634458 0.995651021431828 101 0.00321348308435686 0.00642696616871372 0.996786516915643 102 0.00228647225577791 0.00457294451155582 0.997713527744222 103 0.00244472023349373 0.00488944046698746 0.997555279766506 104 0.00191524517799058 0.00383049035598117 0.99808475482201 105 0.00811448135931826 0.0162289627186365 0.991885518640682 106 0.0181618719205614 0.0363237438411228 0.981838128079439 107 0.0180245037378091 0.0360490074756183 0.98197549626219 108 0.0227179481921592 0.0454358963843184 0.97728205180784 109 0.0175277218388999 0.0350554436777998 0.9824722781611 110 0.0128020488841614 0.0256040977683228 0.987197951115839 111 0.00926861401690118 0.0185372280338024 0.9907313859831 112 0.0227283733594769 0.0454567467189538 0.977271626640523 113 0.0205971811202097 0.0411943622404194 0.97940281887979 114 0.057200293841469 0.114400587682938 0.942799706158531 115 0.0484627048912367 0.0969254097824734 0.951537295108763 116 0.0392764367838187 0.0785528735676373 0.960723563216181 117 0.115731466764412 0.231462933528825 0.884268533235588 118 0.110887113341823 0.221774226683646 0.889112886658177 119 0.098312791055947 0.196625582111894 0.901687208944053 120 0.171833930614441 0.343667861228881 0.82816606938556 121 0.163712493436824 0.327424986873648 0.836287506563176 122 0.195066967106405 0.39013393421281 0.804933032893595 123 0.188054053203409 0.376108106406818 0.811945946796591 124 0.187235424914874 0.374470849829748 0.812764575085126 125 0.170002447239331 0.340004894478661 0.82999755276067 126 0.138341398877432 0.276682797754863 0.861658601122568 127 0.10817856804368 0.21635713608736 0.89182143195632 128 0.111630464935295 0.22326092987059 0.888369535064705 129 0.160133500921297 0.320267001842595 0.839866499078703 130 0.137951852096966 0.275903704193932 0.862048147903034 131 0.120423104329633 0.240846208659267 0.879576895670367 132 0.104299007980801 0.208598015961602 0.8957009920192 133 0.0956741758549074 0.191348351709815 0.904325824145093 134 0.0781005925981874 0.156201185196375 0.921899407401813 135 0.10658043524578 0.21316087049156 0.89341956475422 136 0.0790287321188472 0.158057464237694 0.920971267881153 137 0.0576357982509478 0.115271596501896 0.942364201749052 138 0.146870833753746 0.293741667507492 0.853129166246254 139 0.20813414994964 0.416268299899281 0.79186585005036 140 0.188534489726447 0.377068979452894 0.811465510273553 141 0.406055845705897 0.812111691411795 0.593944154294103 142 0.356404340277385 0.712808680554769 0.643595659722615 143 0.666036975633689 0.667926048732622 0.333963024366311 144 0.604830923460291 0.790338153079417 0.395169076539709 145 0.494206523128987 0.988413046257973 0.505793476871013 146 0.423316957865472 0.846633915730945 0.576683042134528 147 0.433611033957533 0.867222067915066 0.566388966042467 148 0.30330721814227 0.60661443628454 0.69669278185773 149 0.211421302306707 0.422842604613414 0.788578697693293 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 5 0.0357142857142857 NOK 5% type I error level 37 0.264285714285714 NOK 10% type I error level 44 0.314285714285714 NOK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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