*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, 23 Nov 2010 22:04:55 +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/23/t12905497787bm4v110ez6xlsj.htm/, Retrieved Tue, 23 Nov 2010 23:03:09 +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/23/t12905497787bm4v110ez6xlsj.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 «

41 12 14 12 39 11 18 11 30 15 11 14 31 6 12 12 34 13 16 21 35 10 18 12 39 12 14 22 34 14 14 11 36 12 15 10 37 6 15 13 38 10 17 10 36 12 19 8 38 12 10 15 39 11 16 14 33 15 18 10 32 12 14 14 36 10 14 14 38 12 17 11 39 11 14 10 32 12 16 13 32 11 18 7 31 12 11 14 39 13 14 12 37 11 12 14 39 9 17 11 41 13 9 9 36 10 16 11 33 14 14 15 33 12 15 14 34 10 11 13 31 12 16 9 27 8 13 15 37 10 17 10 34 12 15 11 34 12 14 13 32 7 16 8 29 6 9 20 36 12 15 12 29 10 17 10 35 10 13 10 37 10 15 9 34 12 16 14 38 15 16 8 35 10 12 14 38 10 12 11 37 12 11 13 38 13 15 9 33 11 15 11 36 11 17 15 38 12 13 11 32 14 16 10 32 10 14 14 32 12 11 18 34 13 12 14 32 5 12 11 37 6 15 12 39 12 16 13 29 12 15 9 37 11 12 10 35 10 12 15 30 7 8 20 38 12 13 12 34 14 11 12 31 11 14 14 34 12 15 13 35 13 10 11 36 14 11 17 30 11 12 12 39 12 15 13 35 12 15 14 38 8 14 13 31 11 16 15 34 14 15 13 38 14 15 10 34 12 13 11 39 9 12 19 37 13 17 13 34 11 13 17 28 12 15 13 37 12 13 9 33 12 15 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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Connected[t] = + 33.0875718780359 + 0.0537248567570098Software[t] + 0.152393156666027Happiness[t] -0.0487180136506633Depression[t] -0.0069668331728648t + 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) 33.0875718780359 3.26887 10.122 0 0 Software 0.0537248567570098 0.125827 0.427 0.669984 0.334992 Happiness 0.152393156666027 0.135081 1.1282 0.260971 0.130486 Depression -0.0487180136506633 0.100588 -0.4843 0.628824 0.314412 t -0.0069668331728648 0.005744 -1.2128 0.227014 0.113507 Multiple Linear Regression - Regression Statistics Multiple R 0.184759663662724 R-squared 0.034136133316763 Adjusted R-squared 0.0095281367133685 F-TEST (value) 1.38719676643868 F-TEST (DF numerator) 4 F-TEST (DF denominator) 157 p-value 0.240829939787867 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.35901121152838 Sum Squared Residuals 1771.42414211022 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 41 35.2741913554640 5.72580864453596 2 39 35.8717903058485 3.1282096941515 3 30 34.8668167620895 -4.8668167620895 4 31 34.6261554020709 -3.6261554020709 5 34 35.1663730700052 -1.16637307000524 6 35 35.7414801027494 -0.741480102749372 7 39 34.7452102199198 4.25478978008021 8 34 35.3815912504182 -1.38159125041824 9 36 35.4682858740480 0.531714125951957 10 37 34.9928158593811 2.00718414061887 11 38 35.6516888075203 2.34831119247965 12 36 36.1543940284949 -0.154394028494883 13 38 34.4348626897731 3.56513731022687 14 39 35.3372479534901 3.66275204650992 15 33 36.04483891528 -3.04483891527997 16 32 35.0722528305693 -3.07225283056931 17 36 34.9578362838824 1.04216371611757 18 38 35.6616526751736 2.33834732482635 19 39 35.1924995288964 3.80750047110364 20 32 35.3978898248606 -3.39788982486057 21 32 35.9342925301667 -3.93429253016673 22 31 34.573272361534 -3.57327236153404 23 39 35.1746458824176 3.82535411758241 24 37 34.6580069950973 2.34199300490267 25 39 35.4517102726926 3.54828972730743 26 41 34.5379336405209 6.46206635947915 27 36 35.3391083064378 0.66089169356218 28 33 35.0473825323583 -2.04738253235829 29 33 35.1340771559881 -2.13407715598809 30 34 34.4588059962878 -0.458805996287765 31 31 35.5161267145617 -4.51612671456171 32 27 34.5447729024587 -7.54477290245874 33 37 35.4984184777173 1.50158152228268 34 34 35.2453970310758 -1.24539703107576 35 34 34.9886010139355 -0.988601013935542 36 32 35.261386278563 -3.261386278563 37 29 33.549326328163 -4.54932632816298 38 36 35.1688116847336 0.831188315266362 39 29 35.4566174786801 -6.45661747868013 40 35 34.8400780188432 0.159921981156839 41 37 35.186615512653 1.81338448734699 42 34 35.1959014814069 -1.19590148140688 43 38 35.642417300409 2.35758269959098 44 35 34.464945474883 0.535054525116978 45 38 34.6041326826621 3.39586731733785 46 37 34.4547863790360 2.54521362096405 47 38 35.3059890838869 2.69401091611315 48 33 35.0941365098986 -2.09413650989864 49 36 35.1970839354552 0.80291606454482 50 38 34.8291413869779 3.17085861302213 51 32 35.4355217509678 -3.43552175096777 52 32 34.7139971228322 -2.71399712283216 53 32 34.1624284785726 -2.16242847857258 54 34 34.5564517134254 -0.556451713425404 55 32 34.2658400671484 -2.26584006714845 56 37 34.72105954708 2.27894045291999 57 39 35.1401169974646 3.85988300253543 58 29 35.1756290622283 -6.17562906222833 59 37 34.6090398886497 2.39096011135029 60 35 34.3047581304665 0.695241869533478 61 30 33.2834540321052 -3.2834540321052 62 38 34.6968213752528 3.30317862474717 63 34 34.4925179422619 -0.49251794226193 64 31 34.6841199815148 -3.68411998151479 65 34 34.9319891754156 -0.931989175415625 66 35 34.3142174429710 0.685782557029038 67 36 34.2210605413172 1.77893945868285 68 30 34.4489023627926 -4.4489023627926 69 39 34.9041218427242 4.09587815727583 70 35 34.8484369959006 0.151563004099362 71 38 34.5228955926844 3.47710440731563 72 31 34.8844536158133 -3.88445361581326 73 34 34.9837042235467 -0.983704223546727 74 38 35.1228914313259 2.87710856867415 75 34 34.6549705576562 -0.65497055765625 76 39 33.944691888341 5.05530811165898 77 37 35.2068983474303 1.79310165256969 78 34 34.2880371194767 -0.288037119476666 79 28 34.8344535109955 -6.83445351099552 80 37 34.7175724190933 2.28242758090675 81 33 34.9179558719511 -1.91795587195111 82 37 35.1121002090949 1.88789979090506 83 35 35.0014582329067 -0.0014582329067116 84 37 35.0007305154479 1.99926948455212 85 32 34.787645668852 -2.78764566885198 86 33 34.5258428086054 -1.52584280860542 87 38 34.6175442753416 3.38245572465843 88 33 34.6680768694244 -1.66807686942437 89 29 34.3625628386335 -5.36256283863349 90 33 33.1002109699098 -0.100210969909821 91 31 34.8944632559822 -3.89446325598216 92 36 34.5028369093859 1.49716309061407 93 35 34.7369178465754 0.263082153424589 94 32 34.4801218294352 -2.48012182943519 95 29 34.5643519078496 -5.56435190784962 96 39 34.8583968175101 4.14160318248985 97 37 34.1594418596909 2.84055814030911 98 35 34.4859519810754 0.514048018924644 99 37 35.0973391881716 1.90266081182840 100 32 34.7268543418033 -2.72685434180333 101 38 35.2395732489906 2.76042675100944 102 37 34.0171579803125 2.98284201968745 103 36 35.0295352554345 0.970464744565517 104 32 34.0944212255541 -2.09442122555411 105 33 34.453436950792 -1.45343695079203 106 40 33.439681993428 6.56031800657197 107 38 34.8892113661227 3.11078863387734 108 41 34.4862613080304 6.51373869196955 109 36 33.7123218484211 2.28767815157890 110 43 33.0519934653642 9.94800653463577 111 30 34.5627968358132 -4.56279683581318 112 31 34.0049890758396 -3.00498907583957 113 32 34.3365060403304 -2.33650604033038 114 32 34.2870603092209 -2.28706030922089 115 37 34.9820952869071 2.01790471309289 116 37 34.9289527379745 2.07104726202545 117 33 34.422327536867 -1.42232753686698 118 34 34.1954544335597 -0.195454433559724 119 33 34.5445342252605 -1.54453422526054 120 38 34.2989841669407 3.70101583305929 121 33 33.9335061636788 -0.93350616367878 122 31 34.3874933710026 -3.38749337100265 123 38 34.6253488786908 3.37465112130921 124 37 34.8719857999839 2.12801420001606 125 33 34.6651400691021 -1.66514006910207 126 31 34.4608366361112 -3.46083663611117 127 39 34.9409721867694 4.05902781323064 128 44 34.8902941830522 9.10970581694782 129 33 35.0319459360467 -2.03194593604668 130 35 34.4254201624224 0.574579837577597 131 32 34.1573781864618 -2.1573781864618 132 28 33.1561014605259 -5.15610146052587 133 40 34.3894991335848 5.61050086641523 134 27 34.3001168024296 -7.30011680242962 135 37 34.4930288669658 2.50697113303425 136 32 34.5410191631576 -2.54101916315759 137 28 33.1724498535276 -5.17244985352759 138 34 34.1685743267228 -0.168574326722795 139 30 33.5532671394935 -3.55326713949351 140 35 34.2920132877241 0.707986712275948 141 31 33.9852669843255 -2.98526698432548 142 32 34.326797635029 -2.32679763502899 143 30 34.3310767606765 -4.33107676067650 144 30 34.4391087820150 -4.43910878201497 145 31 34.3696356784801 -3.36963567848009 146 40 34.4026054453529 5.59739455464711 147 32 34.6155448823144 -2.61554488231441 148 36 33.7441693954037 2.25583060459626 149 32 33.9870317461982 -1.98703174619823 150 35 32.9719667635509 2.02803323644905 151 38 34.2653284090809 3.73467159091911 152 42 33.8799411781987 8.1200588218013 153 34 34.5049984972012 -0.504998497201173 154 35 33.5811304261412 1.41886957385882 155 35 32.8834077409296 2.11659225907039 156 33 33.5347315480715 -0.534731548071519 157 36 34.0499927531497 1.95000724685029 158 32 33.7606133794804 -1.76061337948045 159 33 34.8229409408607 -1.82294094086074 160 34 34.1065009085071 -0.106500908507059 161 32 33.3475042255412 -1.34750422554117 162 34 33.5903665763357 0.409633423664343 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.896243975502255 0.207512048995491 0.103756024497745 9 0.84528901255469 0.30942197489062 0.15471098744531 10 0.791714619151272 0.416570761697456 0.208285380848728 11 0.706705044633178 0.586589910733643 0.293294955366822 12 0.626597325214464 0.746805349571072 0.373402674785536 13 0.684994276282729 0.630011447434543 0.315005723717271 14 0.613831543404358 0.772336913191284 0.386168456595642 15 0.63455636204455 0.730887275910901 0.365443637955451 16 0.634536739437591 0.730926521124819 0.365463260562409 17 0.551711143945734 0.896577712108532 0.448288856054266 18 0.496655416322394 0.993310832644787 0.503344583677606 19 0.496697531311349 0.993395062622698 0.503302468688651 20 0.540453535429793 0.919092929140414 0.459546464570207 21 0.554275904981595 0.891448190036811 0.445724095018405 22 0.526917072779886 0.946165854440228 0.473082927220114 23 0.591767586124115 0.81646482775177 0.408232413875885 24 0.55082687651951 0.89834624696098 0.44917312348049 25 0.522485386334229 0.955029227331543 0.477514613665771 26 0.665434258713658 0.669131482572685 0.334565741286342 27 0.608449770634369 0.783100458731262 0.391550229365631 28 0.583246840750686 0.833506318498629 0.416753159249314 29 0.555684517165594 0.888630965668813 0.444315482834406 30 0.508122134787662 0.983755730424677 0.491877865212338 31 0.541546516799155 0.91690696640169 0.458453483200845 32 0.736455617609043 0.527088764781914 0.263544382390957 33 0.713197222400873 0.573605555198255 0.286802777599127 34 0.662461364485479 0.675077271029043 0.337538635514521 35 0.608718909144263 0.782562181711473 0.391281090855737 36 0.581841280484485 0.836317439031031 0.418158719515515 37 0.572787613341393 0.854424773317215 0.427212386658607 38 0.541026068543331 0.917947862913339 0.458973931456669 39 0.606916690783954 0.786166618432092 0.393083309216046 40 0.565934826865656 0.868130346268688 0.434065173134344 41 0.557955183491693 0.884089633016614 0.442044816508307 42 0.510887067876624 0.978225864246751 0.489112932123376 43 0.497398443418637 0.994796886837274 0.502601556581363 44 0.460472280995517 0.920944561991033 0.539527719004483 45 0.482223368399948 0.964446736799897 0.517776631600052 46 0.466435033987339 0.932870067974677 0.533564966012661 47 0.45026378540302 0.90052757080604 0.54973621459698 48 0.410440511115477 0.820881022230953 0.589559488884523 49 0.381880291225459 0.763760582450918 0.618119708774541 50 0.377457148820271 0.754914297640542 0.622542851179729 51 0.377479874396902 0.754959748793804 0.622520125603098 52 0.347140362307554 0.694280724615109 0.652859637692446 53 0.311463816946187 0.622927633892373 0.688536183053813 54 0.268931770790320 0.537863541580641 0.73106822920968 55 0.237975326163818 0.475950652327636 0.762024673836182 56 0.244376588144022 0.488753176288045 0.755623411855978 57 0.275354502943971 0.550709005887942 0.724645497056029 58 0.368665132082861 0.737330264165721 0.63133486791714 59 0.349922257771217 0.699844515542434 0.650077742228783 60 0.312418153965361 0.624836307930722 0.687581846034639 61 0.299815039529396 0.599630079058792 0.700184960470604 62 0.30391632737986 0.60783265475972 0.69608367262014 63 0.264874496088185 0.529748992176369 0.735125503911815 64 0.262645454867974 0.525290909735948 0.737354545132026 65 0.227391639852245 0.454783279704489 0.772608360147755 66 0.194592306055635 0.389184612111270 0.805407693944365 67 0.175773494523714 0.351546989047427 0.824226505476286 68 0.194699834660068 0.389399669320135 0.805300165339932 69 0.223265474868613 0.446530949737226 0.776734525131387 70 0.191356441059961 0.382712882119922 0.808643558940039 71 0.203311899881824 0.406623799763647 0.796688100118176 72 0.208995023545914 0.417990047091828 0.791004976454086 73 0.178993739408189 0.357987478816377 0.821006260591811 74 0.171718679972787 0.343437359945575 0.828281320027213 75 0.144546911642980 0.289093823285961 0.85545308835702 76 0.190238242038343 0.380476484076686 0.809761757961657 77 0.168962660139537 0.337925320279075 0.831037339860463 78 0.141682635665457 0.283365271330914 0.858317364334543 79 0.234119555974352 0.468239111948704 0.765880444025648 80 0.216121084218065 0.432242168436129 0.783878915781935 81 0.193086815011431 0.386173630022862 0.806913184988569 82 0.172986941979495 0.345973883958989 0.827013058020505 83 0.145079157373775 0.290158314747550 0.854920842626225 84 0.129259958779881 0.258519917559763 0.870740041220119 85 0.121153879831551 0.242307759663102 0.878846120168449 86 0.104007931706148 0.208015863412296 0.895992068293852 87 0.104876604388980 0.209753208777959 0.89512339561102 88 0.0898371943641422 0.179674388728284 0.910162805635858 89 0.121612624498080 0.243225248996161 0.87838737550192 90 0.100717185211400 0.201434370422799 0.8992828147886 91 0.114277516895701 0.228555033791403 0.885722483104299 92 0.0971911879368542 0.194382375873708 0.902808812063146 93 0.0796733427361246 0.159346685472249 0.920326657263875 94 0.0749299288282982 0.149859857656596 0.925070071171702 95 0.112247636050102 0.224495272100204 0.887752363949898 96 0.120120457955684 0.240240915911368 0.879879542044316 97 0.111174572486849 0.222349144973699 0.88882542751315 98 0.092620014613736 0.185240029227472 0.907379985386264 99 0.0788329708196358 0.157665941639272 0.921167029180364 100 0.0793339639275654 0.158667927855131 0.920666036072435 101 0.0714096341974177 0.142819268394835 0.928590365802582 102 0.0649962817352087 0.129992563470417 0.935003718264791 103 0.0520355387346255 0.104071077469251 0.947964461265374 104 0.0476376296000335 0.095275259200067 0.952362370399966 105 0.041004611443989 0.082009222887978 0.95899538855601 106 0.0705130738724881 0.141026147744976 0.929486926127512 107 0.0646687113985582 0.129337422797116 0.935331288601442 108 0.109572436625036 0.219144873250072 0.890427563374964 109 0.0959880204486227 0.191976040897245 0.904011979551377 110 0.402829861307932 0.805659722615863 0.597170138692068 111 0.423046306515666 0.846092613031332 0.576953693484334 112 0.398434690966872 0.796869381933744 0.601565309033128 113 0.372251424778786 0.744502849557572 0.627748575221214 114 0.339168228051008 0.678336456102016 0.660831771948992 115 0.309664018029331 0.619328036058662 0.690335981970669 116 0.281825577333725 0.563651154667449 0.718174422666275 117 0.243722958333035 0.487445916666070 0.756277041666965 118 0.204948142272811 0.409896284545622 0.79505185772719 119 0.181300095200203 0.362600190400407 0.818699904799797 120 0.209826488935500 0.419652977871001 0.7901735110645 121 0.175568024752830 0.351136049505660 0.82443197524717 122 0.161328914297278 0.322657828594556 0.838671085702722 123 0.164079272409849 0.328158544819698 0.835920727590151 124 0.143791541571797 0.287583083143594 0.856208458428203 125 0.118081002159431 0.236162004318861 0.88191899784057 126 0.111826720973737 0.223653441947474 0.888173279026263 127 0.114621112203591 0.229242224407182 0.88537888779641 128 0.433148840693403 0.866297681386806 0.566851159306597 129 0.383146096862203 0.766292193724406 0.616853903137797 130 0.359699427898234 0.719398855796468 0.640300572101766 131 0.313306314180362 0.626612628360723 0.686693685819638 132 0.318837060905164 0.637674121810328 0.681162939094836 133 0.502363670512949 0.995272658974102 0.497636329487051 134 0.597713398369677 0.804573203260646 0.402286601630323 135 0.642205375370989 0.715589249258022 0.357794624629011 136 0.583844002913121 0.832311994173758 0.416155997086879 137 0.617019114701172 0.765961770597656 0.382980885298828 138 0.556092770673833 0.887814458652335 0.443907229326167 139 0.551064504274096 0.897870991451807 0.448935495725903 140 0.502976445544264 0.994047108911472 0.497023554455736 141 0.462072103673701 0.924144207347402 0.537927896326299 142 0.401042920741143 0.802085841482287 0.598957079258857 143 0.456388096806596 0.912776193613193 0.543611903193404 144 0.554956081416462 0.890087837167076 0.445043918583538 145 0.682430244348413 0.635139511303175 0.317569755651587 146 0.749214869365823 0.501570261268354 0.250785130634177 147 0.860256144519559 0.279487710960881 0.139743855480441 148 0.796744470723162 0.406511058553675 0.203255529276838 149 0.92745220591782 0.145095588164362 0.0725477940821809 150 0.93769708685101 0.124605826297978 0.062302913148989 151 0.918394946551103 0.163210106897794 0.0816050534488968 152 0.99409115994436 0.0118176801112804 0.00590884005564021 153 0.981497406017036 0.0370051879659289 0.0185025939829644 154 0.95681886166919 0.0863622766616217 0.0431811383308109 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 0.0136054421768707 OK 10% type I error level 5 0.0340136054421769 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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