PAPER BAEYENS (Multiple Linear Regression2)

*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: Tue, 21 Dec 2010 14:03:10 +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/21/t1292940331i0n6j1a28j651xv.htm/, Retrieved Tue, 21 Dec 2010 15:05:34 +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/21/t1292940331i0n6j1a28j651xv.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 «

5 13 14 3 12 18 0 15 11 7 12 12 4 10 16 1 12 18 6 15 14 3 9 14 12 12 15 0 11 15 5 11 17 6 11 19 6 15 10 6 7 16 2 11 18 1 11 14 5 10 14 7 14 17 3 10 14 3 6 16 3 11 18 7 15 11 8 11 14 6 12 12 3 14 17 5 15 9 5 9 16 10 13 14 2 13 15 6 16 11 4 13 16 6 12 13 8 14 17 4 11 15 5 9 14 10 16 16 6 12 9 7 10 15 4 13 17 10 16 13 4 14 15 3 15 16 3 5 16 3 8 12 3 11 12 7 16 11 15 17 15 0 9 15 0 9 17 4 13 13 5 10 16 5 6 14 2 12 11 3 8 12 0 14 12 9 12 15 2 11 16 7 16 15 7 8 12 0 15 12 0 7 8 10 16 13 2 14 11 1 16 14 8 9 15 6 14 10 11 11 11 3 13 12 8 15 15 6 5 15 9 15 14 9 13 16 8 11 15 8 11 15 7 12 13 6 12 12 5 12 17 4 12 13 6 14 15 3 6 13 2 7 15 12 14 16 8 14 15 5 10 16 9 13 15 6 12 14 5 9 15 2 12 14 4 16 13 7 10 7 5 14 17 6 10 13 7 16 15 8 15 14 6 12 13 0 10 16 1 8 12 5 8 14 5 11 17 5 13 15 7 16 17 7 16 12 1 14 16 3 11 11 4 4 15 8 14 9 6 9 16 6 14 15 2 8 10 2 8 10 3 11 15 3 12 11 0 11 13 2 14 14 8 15 18 8 16 16 0 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 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation IEP[t] = + 11.9662638811661 + 0.272510555913099WP[t] -0.115233314432733HS[t] + 0.00420713199589517t + 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) 11.9662638811661 1.528418 7.8292 0 0 WP 0.272510555913099 0.072667 3.7502 0.000251 0.000125 HS -0.115233314432733 0.097281 -1.1845 0.238048 0.119024 t 0.00420713199589517 0.005035 0.8355 0.404728 0.202364 Multiple Linear Regression - Regression Statistics Multiple R 0.313673089491999 R-squared 0.0983908070714556 Adjusted R-squared 0.0805958887899713 F-TEST (value) 5.52915194748778 F-TEST (DF numerator) 3 F-TEST (DF denominator) 152 p-value 0.00124948454744112 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.81580162137916 Sum Squared Residuals 1205.16829318615 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 11.7197573906692 1.28024260933077 2 12 10.718010153108 1.28198984689202 3 15 10.7113188183937 4.28868118160629 4 12 12.5078665273486 -0.507866527348564 5 10 11.2336087338742 -1.23360873387423 6 12 10.1898175692654 1.81018243073464 7 15 12.0175107385577 2.98248926144232 8 9 11.2041862028143 -2.20418620281428 9 12 13.5457550235953 -1.54575502359533 10 11 10.279835484634 0.720164515365954 11 11 11.41612876733 -0.416128767329968 12 11 11.4623798263735 -0.462379826373496 13 15 12.503686788264 2.49631321173601 14 7 11.8164940336635 -4.81649403366348 15 11 10.5001923131415 0.49980768685848 16 11 10.6928221469552 0.307177853044752 17 10 11.7870715026035 -1.78707150260354 18 14 11.9905998031274 2.00940019687257 19 10 11.2504646547691 -1.25046465476913 20 6 11.0242051578996 -5.02420515789956 21 11 10.79794566103 0.20205433897001 22 15 12.6988282177074 2.30117178229259 23 11 12.6298459623182 -1.6298459623182 24 12 12.3194986113534 -0.319498611353369 25 14 10.9300075034463 3.0699924965537 26 15 12.4011022627303 2.59889773726974 27 9 11.598676193697 -2.59867619369702 28 13 13.1959027341239 -0.195902734123878 29 13 10.9047921043823 2.09520789561775 30 16 12.4599747177615 3.54002528223853 31 13 11.3429941657675 1.65700583423249 32 12 12.2379223528878 -0.237922352887797 33 14 12.326217338979 1.67378266102104 34 11 11.4708488761879 -0.470848876187924 35 9 11.8627998785297 -2.86279987852965 36 16 12.9990931612256 3.00090683877443 37 12 12.7198912705982 -0.719891270598205 38 10 12.3052090719108 -2.3052090719108 39 13 11.2614179073019 1.73858209269807 40 16 13.3616216325074 2.63837836749265 41 14 11.5002988001592 2.49970119984081 42 15 11.1167620618093 3.88323793819075 43 5 11.1209691938051 -6.12096919380515 44 8 11.586109583532 -3.58610958353198 45 11 11.5903167155279 -0.590316715527872 46 16 12.7997993856089 3.20020061439111 47 17 14.5231577071786 2.47684229282135 48 9 10.4397065004781 -1.43970650047806 49 9 10.2134470036085 -1.21344700360849 50 13 11.7686296169877 1.23137038301229 51 10 11.6996473615985 -1.69964736159851 52 6 11.9343211224599 -5.93432112245987 53 12 11.4666965300147 0.533303469985333 54 8 11.6281809034909 -3.62818090349093 55 14 10.8148563677475 3.18514363225247 56 12 12.9259585596631 -0.925958559663111 57 11 10.9073584858346 0.0926415141654167 58 16 12.3893517118287 3.6106482881713 59 8 12.7392587871228 -4.7392587871228 60 15 10.835892027727 4.164107972273 61 7 11.3010324174538 -4.30103241745383 62 16 13.454178536417 2.54582146358295 63 14 11.5087678499736 2.49123215002638 64 16 10.8947644827582 5.10523551724178 65 9 12.6913121917131 -3.69131219171307 66 14 12.7266647840464 1.27333521595357 67 11 13.9781913811751 -2.97819138117509 68 13 11.6870807514335 1.31291924856654 69 15 12.7081407196966 2.29185928030335 70 5 12.1673267398663 -7.16732673986635 71 15 13.1042988540343 1.89570114596573 72 13 12.8780393571647 0.121960642835299 73 11 12.7249692476802 -1.72496924768023 74 11 12.7291763796761 -1.72917637967613 75 12 12.6913395846244 -0.691339584624388 76 12 12.5382694751399 -0.538269475139918 77 12 11.693799479059 0.306200520940951 78 12 11.8864293128728 0.113570687127222 79 14 12.2051909278294 1.7948090721706 80 6 11.6223330209515 -5.62233302095147 81 7 11.1235629681688 -4.1235629681688 82 14 13.7376423448629 0.262357655137052 83 14 12.7670405676392 1.23295943236082 84 10 11.838482717463 -1.83848271746305 85 13 13.0479653875441 -0.047965387544071 86 12 12.3498741662334 -0.349874166233403 87 9 11.9663374278835 -2.96633742788347 88 12 11.2682462065728 0.7317537934272 89 16 11.9327077648276 4.06729223517238 90 10 13.4458464511592 -3.44584645115921 91 14 11.7526993270016 2.24730067299842 92 10 12.4903502726415 -2.49035027264151 93 16 12.536601331685 3.46339866831496 94 15 12.9285523340268 2.07144766597324 95 12 12.5029716686292 -0.502971668629193 96 10 10.5264155218483 -0.526415521848298 97 8 11.2640664674882 -3.26406646748822 98 8 12.127849194271 -4.12784919427105 99 11 11.7863563829687 -0.786356382968743 100 13 12.0210301438301 0.978969856169895 101 16 12.3397917587867 3.66020824121327 102 16 12.9201654629463 3.07983453705371 103 14 10.8283760017327 3.17162399826734 104 11 11.9537708177184 -0.95377081771842 105 4 11.7695552478965 -7.76955524789648 106 14 13.5552044901412 0.444795509858831 107 9 12.2077573092817 -3.20775730928174 108 14 12.3271977557104 1.67280224428964 109 8 11.8175292362175 -3.81752923621753 110 8 11.8217363682134 -3.82173636821343 111 11 11.5222874839588 -0.522287483958754 112 12 11.9874278736856 0.012572126314419 113 11 10.9436367090767 0.0563632909232854 114 14 11.3776316384661 2.62236836153393 115 15 12.5559688482096 2.44403115179037 116 16 12.790642609071 3.20935739092901 117 16 10.8452319226276 5.15476807737244 118 11 12.211991834189 -1.21199183418895 119 14 13.3062411898372 0.69375881016276 120 14 12.4929166540938 1.50708334590616 121 12 12.7275904149552 -0.7275904149552 122 14 11.6837992503463 2.31620074965367 123 8 13.2078364033881 -5.20783640338809 124 13 12.6670224235578 0.332977576442214 125 16 12.9437401114668 3.05625988853322 126 12 10.9983294250234 1.00167057497665 127 16 12.44917719068 3.55082280931999 128 12 10.5458104312842 1.45418956871579 129 11 11.6821037139801 -0.682103713980133 130 4 10.7846913241415 -6.78469132414147 131 16 14.8345128677862 1.16548713221379 132 15 12.8470582542951 2.15294174570485 133 10 11.3423338319553 -1.34233383195535 134 13 12.9816042994298 0.0183957005701641 135 15 11.8957692077733 3.10423079222666 136 12 11.2397219135103 0.760278086489698 137 14 12.9101378413223 1.08986215867774 138 7 11.7511133622807 -4.75111336228066 139 19 12.6460415494009 6.35395845059905 140 12 13.2793576473183 -1.27935764731831 141 12 11.8789680727011 0.121031927298925 142 13 11.6527085758315 1.3472914241685 143 15 10.7241507256554 4.27584927434463 144 8 13.6839300456477 -5.68393004564772 145 12 11.9378405277323 0.0621594722677116 146 10 11.2817932334693 -1.28179323346925 147 8 11.5585109213782 -3.55851092137825 148 10 14.0464585169295 -4.0464585169295 149 15 13.1179006667534 1.88209933324664 150 16 11.5602338506558 4.43976614934423 151 13 12.3928711171011 0.607128882898876 152 16 13.2877993042214 2.71220069577858 153 9 10.7662220456143 -1.76622204561432 154 14 12.3214046589935 1.67859534100646 155 14 14.3063750697662 -0.306375069766229 156 12 12.4870961644657 -0.4870961644657 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.307857534752408 0.615715069504816 0.692142465247592 8 0.430679671492941 0.861359342985881 0.56932032850706 9 0.307240429861632 0.614480859723264 0.692759570138368 10 0.196088955703537 0.392177911407074 0.803911044296463 11 0.121216647898557 0.242433295797114 0.878783352101443 12 0.0756030323175526 0.151206064635105 0.924396967682447 13 0.0636093491146596 0.127218698229319 0.93639065088534 14 0.13651417998175 0.273028359963499 0.86348582001825 15 0.103936000154667 0.207872000309333 0.896063999845333 16 0.0663593864316057 0.132718772863211 0.933640613568394 17 0.0438190028465056 0.0876380056930112 0.956180997153494 18 0.0885295022158275 0.177059004431655 0.911470497784172 19 0.0635505922801605 0.127101184560321 0.93644940771984 20 0.110456728996559 0.220913457993119 0.88954327100344 21 0.0970599526700894 0.194119905340179 0.90294004732991 22 0.112493643098512 0.224987286197025 0.887506356901488 23 0.0814666657366459 0.162933331473292 0.918533334263354 24 0.0569877090088269 0.113975418017654 0.943012290991173 25 0.0966821098655101 0.19336421973102 0.90331789013449 26 0.0821987167119867 0.164397433423973 0.917801283288013 27 0.0698362778543074 0.139672555708615 0.930163722145693 28 0.0530933546399141 0.106186709279828 0.946906645360086 29 0.0467548887652167 0.0935097775304334 0.953245111234783 30 0.0515431003826687 0.103086200765337 0.948456899617331 31 0.0427353807926508 0.0854707615853015 0.957264619207349 32 0.0309373712364388 0.0618747424728776 0.96906262876356 33 0.0308178338470624 0.0616356676941248 0.969182166152938 34 0.0226331415644758 0.0452662831289516 0.977366858435524 35 0.0278010371401768 0.0556020742803537 0.972198962859823 36 0.039951421536499 0.079902843072998 0.9600485784635 37 0.0342679488197021 0.0685358976394042 0.965732051180298 38 0.0306770335684287 0.0613540671368575 0.969322966431571 39 0.0265448673815292 0.0530897347630583 0.97345513261847 40 0.0268689801737172 0.0537379603474345 0.973131019826283 41 0.0241537313621368 0.0483074627242736 0.975846268637863 42 0.0296839415795228 0.0593678831590456 0.970316058420477 43 0.118165386293976 0.236330772587953 0.881834613706024 44 0.150658293180066 0.301316586360132 0.849341706819934 45 0.12324815956385 0.2464963191277 0.87675184043615 46 0.12997240746347 0.259944814926939 0.87002759253653 47 0.124159433028361 0.248318866056721 0.87584056697164 48 0.103122954828889 0.206245909657778 0.896877045171111 49 0.0826381280066388 0.165276256013278 0.917361871993361 50 0.068327823585776 0.136655647171552 0.931672176414224 51 0.056760061720816 0.113520123441632 0.943239938279184 52 0.123599995007066 0.247199990014132 0.876400004992934 53 0.101430231234825 0.202860462469651 0.898569768765175 54 0.110359114205561 0.220718228411121 0.889640885794439 55 0.1306345090786 0.261269018157201 0.8693654909214 56 0.10671971447483 0.213439428949659 0.89328028552517 57 0.0876359363745504 0.175271872749101 0.91236406362545 58 0.111238709919464 0.222477419838927 0.888761290080537 59 0.156633722257651 0.313267444515301 0.84336627774235 60 0.207158197250958 0.414316394501916 0.792841802749042 61 0.251977069949269 0.503954139898538 0.74802293005073 62 0.251552438949638 0.503104877899276 0.748447561050362 63 0.251927084616129 0.503854169232259 0.74807291538387 64 0.369445935490664 0.738891870981329 0.630554064509336 65 0.389837041409568 0.779674082819136 0.610162958590432 66 0.360122011377542 0.720244022755084 0.639877988622458 67 0.35655015070145 0.713100301402901 0.64344984929855 68 0.330555401208624 0.661110802417248 0.669444598791376 69 0.327605825529384 0.655211651058769 0.672394174470615 70 0.53516119899306 0.92967760201388 0.46483880100694 71 0.521746199047448 0.956507601905104 0.478253800952552 72 0.477322494445634 0.954644988891268 0.522677505554366 73 0.439464526439979 0.878929052879959 0.560535473560021 74 0.402165418856374 0.804330837712749 0.597834581143626 75 0.357851686203635 0.71570337240727 0.642148313796365 76 0.315344701219787 0.630689402439574 0.684655298780213 77 0.279211866125486 0.558423732250972 0.720788133874514 78 0.243225899983503 0.486451799967006 0.756774100016497 79 0.231143328629508 0.462286657259015 0.768856671370492 80 0.316797767858962 0.633595535717925 0.683202232141038 81 0.340843852821876 0.681687705643752 0.659156147178124 82 0.302588073837234 0.605176147674468 0.697411926162766 83 0.277366460184706 0.554732920369412 0.722633539815294 84 0.24862130962264 0.49724261924528 0.75137869037736 85 0.214087204407265 0.428174408814529 0.785912795592735 86 0.181937444806572 0.363874889613144 0.818062555193428 87 0.176408742378633 0.352817484757267 0.823591257621367 88 0.153316750602426 0.306633501204851 0.846683249397574 89 0.198177765217814 0.396355530435628 0.801822234782186 90 0.203375632553585 0.40675126510717 0.796624367446415 91 0.198593789712572 0.397187579425144 0.801406210287428 92 0.184930674751779 0.369861349503559 0.81506932524822 93 0.209392339061485 0.41878467812297 0.790607660938515 94 0.199825228583964 0.399650457167929 0.800174771416036 95 0.168225150365585 0.33645030073117 0.831774849634415 96 0.140081431574838 0.280162863149677 0.859918568425162 97 0.141051300866465 0.282102601732929 0.858948699133535 98 0.164226989742768 0.328453979485536 0.835773010257232 99 0.137965138697323 0.275930277394645 0.862034861302677 100 0.117500679749566 0.235001359499131 0.882499320250434 101 0.139011328696649 0.278022657393298 0.860988671303351 102 0.148970242901332 0.297940485802664 0.851029757098668 103 0.163052889704916 0.326105779409833 0.836947110295084 104 0.135890813038088 0.271781626076175 0.864109186961912 105 0.348724064938136 0.697448129876271 0.651275935061864 106 0.305500149005042 0.611000298010084 0.694499850994958 107 0.313986115816777 0.627972231633554 0.686013884183223 108 0.286022738286403 0.572045476572805 0.713977261713597 109 0.335715092367548 0.671430184735096 0.664284907632452 110 0.43146647803921 0.86293295607842 0.56853352196079 111 0.394814843662279 0.789629687324558 0.605185156337721 112 0.369810849287953 0.739621698575905 0.630189150712047 113 0.349023476976546 0.698046953953091 0.650976523023454 114 0.322506425173166 0.645012850346332 0.677493574826834 115 0.316561853921729 0.633123707843459 0.683438146078271 116 0.331971054794478 0.663942109588957 0.668028945205521 117 0.392905285753814 0.785810571507629 0.607094714246186 118 0.358952832868018 0.717905665736035 0.641047167131982 119 0.31077671172809 0.621553423456179 0.68922328827191 120 0.271664823914106 0.543329647828211 0.728335176085894 121 0.241273983798035 0.482547967596069 0.758726016201965 122 0.213678749651465 0.42735749930293 0.786321250348535 123 0.319609799996024 0.639219599992049 0.680390200003976 124 0.269833558663099 0.539667117326198 0.730166441336901 125 0.26796880381726 0.535937607634521 0.73203119618274 126 0.224352426111894 0.448704852223787 0.775647573888106 127 0.281641879963537 0.563283759927075 0.718358120036463 128 0.250728044860888 0.501456089721775 0.749271955139112 129 0.219151032799219 0.438302065598439 0.780848967200781 130 0.561840708262953 0.876318583474094 0.438159291737047 131 0.562484003274022 0.875031993451955 0.437515996725978 132 0.509153797373111 0.981692405253778 0.490846202626889 133 0.492139654939986 0.984279309879971 0.507860345060014 134 0.433488241605513 0.866976483211027 0.566511758394487 135 0.447874845826553 0.895749691653107 0.552125154173447 136 0.382097003625756 0.764194007251513 0.617902996374244 137 0.313378905490302 0.626757810980605 0.686621094509698 138 0.570345239464495 0.85930952107101 0.429654760535505 139 0.700689639605461 0.598620720789077 0.299310360394539 140 0.64815433901147 0.703691321977062 0.351845660988531 141 0.569421545255564 0.861156909488872 0.430578454744436 142 0.500017734528726 0.999964530942549 0.499982265471274 143 0.65026780145645 0.6994643970871 0.34973219854355 144 0.658225028259604 0.683549943480792 0.341774971740396 145 0.577496400796659 0.845007198406681 0.422503599203341 146 0.458948453866703 0.917896907733406 0.541051546133297 147 0.443301277246322 0.886602554492645 0.556698722753678 148 0.882686229602798 0.234627540794404 0.117313770397202 149 0.82833285229489 0.34333429541022 0.17166714770511 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 2 0.013986013986014 OK 10% type I error level 14 0.097902097902098 OK

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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