Workshop 7

*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 00:07:56 +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/t12905572671xw8og12apuht1z.htm/, Retrieved Wed, 24 Nov 2010 01:07:58 +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/t12905572671xw8og12apuht1z.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 «

14 12 53 18 11 86 11 14 66 12 12 67 16 21 76 18 12 78 14 22 53 14 11 80 15 10 74 15 13 76 17 10 79 19 8 54 10 15 67 16 14 54 18 10 87 14 14 58 14 14 75 17 11 88 14 10 64 16 13 57 18 7 66 11 14 68 14 12 54 12 14 56 17 11 86 9 9 80 16 11 76 14 15 69 15 14 78 11 13 67 16 9 80 13 15 54 17 10 71 15 11 84 14 13 74 16 8 71 9 20 63 15 12 71 17 10 76 13 10 69 15 9 74 16 14 75 16 8 54 12 14 52 12 11 69 11 13 68 15 9 65 15 11 75 17 15 74 13 11 75 16 10 72 14 14 67 11 18 63 12 14 62 12 11 63 15 12 76 16 13 74 15 9 67 12 10 73 12 15 70 8 20 53 13 12 77 11 12 77 14 14 52 15 13 54 10 11 80 11 17 66 12 12 73 15 13 63 15 14 69 14 13 67 16 15 54 15 13 81 15 10 69 13 11 84 12 19 80 17 13 70 13 17 69 15 13 77 13 9 54 15 11 79 16 10 30 15 9 71 16 12 73 15 12 72 14 13 77 15 13 75 14 12 69 13 15 54 7 22 70 17 13 73 13 15 54 15 13 77 14 15 82 13 10 80 16 11 80 12 16 69 14 11 78 17 11 81 15 10 76 17 10 76 12 16 73 16 12 85 11 11 66 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 Belonging[t] = + 65.5915982474038 + 0.889722068030321Happiness[t] -0.570504968361378Depression[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) 65.5915982474038 8.598315 7.6284 0 0 Happiness 0.889722068030321 0.411034 2.1646 0.031911 0.015955 Depression -0.570504968361378 0.303472 -1.8799 0.061947 0.030974 Multiple Linear Regression - Regression Statistics Multiple R 0.318675284277338 R-squared 0.101553936809242 Adjusted R-squared 0.0902527284672199 F-TEST (value) 8.98611314257667 F-TEST (DF numerator) 2 F-TEST (DF denominator) 159 p-value 0.000200731161597245 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 10.2279857720870 Sum Squared Residuals 16633.2591796883 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 53 71.2016475794921 -18.2016475794921 2 86 75.3310408199744 10.6689591800256 3 66 67.391471438678 -1.39147143867804 4 67 69.4222034434311 -2.42220344343110 5 76 67.8465470003 8.15345299970001 6 78 74.760535851613 3.23946414838697 7 53 65.496597895878 -12.4965978958780 8 80 71.7721525478531 8.22784745214688 9 74 73.2323795842448 0.767620415755177 10 76 71.5208646791607 4.47913532083931 11 79 75.0118237203055 3.98817627969454 12 54 77.9322777930889 -23.9322777930889 13 67 65.9312444022863 1.06875559771367 14 54 71.8400817788296 -17.8400817788296 15 87 75.9015457883358 11.0984542116642 16 58 70.060637642769 -12.060637642769 17 75 70.060637642769 4.93936235723101 18 88 74.4413187519441 13.5586812480559 19 64 72.3426575162145 -8.3426575162145 20 57 72.410586747191 -15.410586747191 21 66 77.6130606934199 -11.6130606934199 22 68 67.391471438678 0.608528561321973 23 54 71.2016475794917 -17.2016475794917 24 56 68.2811935067083 -12.2811935067083 25 86 74.4413187519441 11.5586812480559 26 80 68.4645521444243 11.5354478555757 27 76 73.5515966839138 2.44840331608623 28 69 69.4901326744076 -0.490132674407613 29 78 70.9503597107993 7.04964028920069 30 67 67.9619764070394 -0.961976407039405 31 80 74.6926066206365 5.30739337936348 32 54 68.6004106063773 -14.6004106063773 33 71 75.0118237203055 -4.01182372030546 34 84 72.6618746158834 11.3381253841166 35 74 70.6311426111304 3.36885738886963 36 71 75.2631115889979 -4.2631115889979 37 63 62.1889974924491 0.811002507550883 38 71 72.091369647522 -1.09136964752207 39 76 75.0118237203055 0.988176279694535 40 69 71.4529354481842 -2.45293544818418 41 74 73.8028845526062 0.197115447393799 42 75 71.8400817788296 3.15991822117037 43 54 75.2631115889979 -21.2631115889979 44 52 68.2811935067083 -16.2811935067083 45 69 69.9927084117925 -0.992708411792482 46 68 67.9619764070394 0.038023592960595 47 65 73.8028845526062 -8.8028845526062 48 75 72.6618746158834 2.33812538411655 49 74 72.1592988784986 1.84070112150142 50 75 70.8824304798228 4.1175695201772 51 72 74.1221016522751 -2.12210165227514 52 67 70.060637642769 -3.06063764276899 53 63 65.1094515652325 -2.10945156523252 54 62 68.2811935067083 -6.28119350670835 55 63 69.9927084117925 -6.99270841179248 56 76 72.091369647522 3.90863035247793 57 74 72.410586747191 1.58941325280899 58 67 73.8028845526062 -6.8028845526062 59 73 70.5632133801539 2.43678661984614 60 70 67.710688538347 2.28931146165303 61 53 61.2992754244188 -8.2992754244188 62 77 70.3119255114614 6.68807448853858 63 77 68.5324813754008 8.46751862459922 64 52 70.060637642769 -18.060637642769 65 54 71.5208646791607 -17.5208646791607 66 80 68.2132642757318 11.7867357242682 67 66 65.6799565335939 0.320043466406106 68 73 69.4222034434311 3.57779655656890 69 63 71.5208646791607 -8.52086467916069 70 69 70.9503597107993 -1.95035971079931 71 67 70.6311426111304 -3.63114261113037 72 54 71.2695768104683 -17.2695768104683 73 81 71.5208646791607 9.4791353208393 74 69 73.2323795842448 -4.23237958424482 75 84 70.8824304798228 13.1175695201772 76 80 65.4286686649015 14.5713313350985 77 70 73.3003088152213 -3.30030881522133 78 69 67.4594006696545 1.54059933034546 79 77 71.5208646791607 5.47913532083931 80 54 72.0234404165456 -18.0234404165456 81 79 72.6618746158834 6.33812538411655 82 30 74.1221016522751 -44.1221016522751 83 71 73.8028845526062 -2.8028845526062 84 73 72.9810917155524 0.0189082844476121 85 72 72.091369647522 -0.0913696475220673 86 77 70.6311426111304 6.36885738886963 87 75 71.5208646791607 3.47913532083931 88 69 71.2016475794917 -2.20164757949175 89 54 68.6004106063773 -14.6004106063773 90 70 59.2685434196657 10.7314565803343 91 73 73.3003088152213 -0.300308815221332 92 54 68.6004106063773 -14.6004106063773 93 77 71.5208646791607 5.47913532083931 94 82 69.4901326744076 12.5098673255924 95 80 71.4529354481842 8.54706455181582 96 80 73.5515966839138 6.44840331608623 97 69 67.1401835699856 1.85981643001441 98 78 71.7721525478531 6.22784745214688 99 81 74.4413187519441 6.55868124805591 100 76 73.2323795842448 2.76762041575518 101 76 75.0118237203055 0.988176279694535 102 73 67.1401835699856 5.8598164300144 103 85 72.9810917155524 12.0189082844476 104 66 69.1029863437622 -3.10298634376216 105 79 69.8093497740766 9.19065022592344 106 68 62.7595024608105 5.2404975391895 107 76 73.5515966839138 2.44840331608623 108 71 69.8093497740766 1.19065022592344 109 54 65.9312444022863 -11.9312444022863 110 46 60.7966996870339 -14.7966996870339 111 82 70.9503597107993 11.0496402892007 112 74 66.8209664703166 7.17903352968335 113 88 70.8824304798228 17.1175695201772 114 38 69.4901326744076 -31.4901326744076 115 76 74.760535851613 1.23946414838697 116 86 74.1221016522751 11.8778983477249 117 54 70.060637642769 -16.060637642769 118 70 70.6311426111304 -0.631142611130368 119 69 72.9131624845759 -3.91316248457588 120 90 69.4901326744076 20.5098673255924 121 54 67.710688538347 -13.7106885383470 122 76 70.060637642769 5.93936235723101 123 89 72.6618746158834 16.3381253841166 124 76 74.3733895209676 1.62661047903242 125 73 72.6618746158834 0.338125384116555 126 79 70.8824304798228 8.1175695201772 127 90 76.1528336570282 13.8471663429718 128 74 75.0118237203055 -1.01182372030547 129 81 76.2207628880047 4.77923711199527 130 72 71.5208646791607 0.47913532083931 131 71 70.8824304798228 0.117569520177197 132 66 62.1889974924491 3.81100250755088 133 77 73.2323795842448 3.76762041575518 134 65 70.379854742438 -5.37985474243793 135 74 72.091369647522 1.90863035247793 136 82 71.8400817788296 10.1599182211704 137 54 62.2569267234256 -8.25692672342563 138 63 70.060637642769 -7.06063764276899 139 54 66.2504615019553 -12.2504615019553 140 64 72.6618746158834 -8.66187461588345 141 69 70.3119255114614 -1.31192551146142 142 54 73.2323795842448 -19.2323795842448 143 84 71.8400817788296 12.1599182211704 144 86 71.2016475794917 14.7983524205083 145 77 72.091369647522 4.90863035247793 146 89 73.5515966839138 15.4484033160862 147 76 72.9810917155524 3.01890828444761 148 60 67.9619764070394 -7.9619764070394 149 75 69.9927084117925 5.00729158820752 150 73 62.7595024608105 10.2404975391895 151 85 72.9810917155524 12.0189082844476 152 79 67.4594006696545 11.5405993303455 153 71 74.6926066206365 -3.69260662063652 154 72 69.4222034434311 2.57779655656890 155 69 62.7595024608105 6.2404975391895 156 78 66.8888957012932 11.1111042987068 157 54 68.6004106063773 -14.6004106063773 158 69 70.060637642769 -1.06063764276899 159 81 76.2207628880047 4.77923711199527 160 84 72.0234404165456 11.9765595834544 161 84 65.9991736332628 18.0008263667372 162 69 68.0299056380159 0.970094361984086 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.627800612163592 0.744398775672816 0.372199387836408 7 0.666406205155663 0.667187589688674 0.333593794844337 8 0.635918433089962 0.728163133820075 0.364081566910038 9 0.51073579479163 0.97852841041674 0.48926420520837 10 0.407148068765248 0.814296137530497 0.592851931234752 11 0.303865075601501 0.607730151203003 0.696134924398499 12 0.814769629789204 0.370460740421592 0.185230370210796 13 0.749315088564422 0.501369822871156 0.250684911435578 14 0.819358258646258 0.361283482707484 0.180641741353742 15 0.84051997586439 0.318960048271218 0.159480024135609 16 0.831991329649691 0.336017340700617 0.168008670350309 17 0.800394352943246 0.399211294113509 0.199605647056754 18 0.833794712434333 0.332410575131334 0.166205287565667 19 0.805310040192938 0.389379919614124 0.194689959807062 20 0.837464631818143 0.325070736363713 0.162535368181857 21 0.830734479059394 0.338531041881211 0.169265520940606 22 0.788102453041817 0.423795093916366 0.211897546958183 23 0.827677853654329 0.344644292691342 0.172322146345671 24 0.816192037779036 0.367615924441928 0.183807962220964 25 0.83923902489764 0.32152195020472 0.16076097510236 26 0.867914437217962 0.264171125564076 0.132085562782038 27 0.83743945200007 0.325121095999861 0.162560547999930 28 0.7983471115103 0.403305776979399 0.201652888489699 29 0.783726758206316 0.432546483587367 0.216273241793684 30 0.737653016187678 0.524693967624643 0.262346983812322 31 0.70449972850464 0.59100054299072 0.29550027149536 32 0.728732450632513 0.542535098734975 0.271267549367487 33 0.683946989855047 0.632106020289906 0.316053010144953 34 0.70217763920379 0.595644721592421 0.297822360796210 35 0.661851164593846 0.676297670812307 0.338148835406154 36 0.617977197553547 0.764045604892906 0.382022802446453 37 0.569773357558837 0.860453284882325 0.430226642441163 38 0.515630976494514 0.968738047010971 0.484369023505486 39 0.462971167878528 0.925942335757055 0.537028832121472 40 0.41154263506721 0.82308527013442 0.58845736493279 41 0.360383889808767 0.720767779617535 0.639616110191233 42 0.320745395501026 0.641490791002052 0.679254604498974 43 0.474263410250183 0.948526820500367 0.525736589749817 44 0.53221509496057 0.93556981007886 0.46778490503943 45 0.481757117469672 0.963514234939345 0.518242882530328 46 0.432805365436511 0.865610730873023 0.567194634563489 47 0.411468021853911 0.822936043707822 0.588531978146089 48 0.369624922794451 0.739249845588901 0.630375077205549 49 0.327049645253696 0.654099290507393 0.672950354746304 50 0.295883893221119 0.591767786442238 0.704116106778881 51 0.255334754198501 0.510669508397001 0.744665245801499 52 0.218838000290221 0.437676000580441 0.781161999709779 53 0.184581028920836 0.369162057841671 0.815418971079164 54 0.161398716811213 0.322797433622425 0.838601283188787 55 0.142525596777764 0.285051193555527 0.857474403222236 56 0.1232516073354 0.2465032146708 0.8767483926646 57 0.101703894346751 0.203407788693503 0.898296105653249 58 0.088627345786843 0.177254691573686 0.911372654213157 59 0.0736964787297675 0.147392957459535 0.926303521270232 60 0.0602264629547096 0.120452925909419 0.93977353704529 61 0.0532024111407584 0.106404822281517 0.946797588859242 62 0.0486711827312047 0.0973423654624093 0.951328817268795 63 0.0478397849988057 0.0956795699976114 0.952160215001194 64 0.0759886154750654 0.151977230950131 0.924011384524935 65 0.110489256037214 0.220978512074427 0.889510743962787 66 0.122196739698059 0.244393479396118 0.877803260301941 67 0.100957523460073 0.201915046920146 0.899042476539927 68 0.0849760179899104 0.169952035979821 0.91502398201009 69 0.0780555393948009 0.156111078789602 0.921944460605199 70 0.0631398161898766 0.126279632379753 0.936860183810123 71 0.0512637817561778 0.102527563512356 0.948736218243822 72 0.0748950920272416 0.149790184054483 0.925104907972758 73 0.0769169815143366 0.153833963028673 0.923083018485663 74 0.0639524887871246 0.127904977574249 0.936047511212875 75 0.076697727788887 0.153395455577774 0.923302272211113 76 0.102674342631075 0.205348685262150 0.897325657368925 77 0.0863785970789504 0.172757194157901 0.91362140292105 78 0.0708020733893181 0.141604146778636 0.929197926610682 79 0.0616022785692453 0.123204557138491 0.938397721430755 80 0.0965738871988602 0.193147774397720 0.90342611280114 81 0.0863781429385428 0.172756285877086 0.913621857061457 82 0.757527697650848 0.484944604698304 0.242472302349152 83 0.727970867532501 0.544058264934998 0.272029132467499 84 0.692699116078577 0.614601767842846 0.307300883921423 85 0.654649709293039 0.690700581413923 0.345350290706961 86 0.62878836020055 0.7424232795989 0.37121163979945 87 0.59138770822902 0.81722458354196 0.40861229177098 88 0.551995014934709 0.896009970130582 0.448004985065291 89 0.60781242499266 0.78437515001468 0.39218757500734 90 0.622023426018375 0.75595314796325 0.377976573981625 91 0.584570938660633 0.830858122678735 0.415429061339367 92 0.641947263951387 0.716105472097227 0.358052736048613 93 0.610379099423635 0.77924180115273 0.389620900576365 94 0.628904586405482 0.742190827189035 0.371095413594518 95 0.612801048033695 0.774397903932609 0.387198951966305 96 0.583820613512308 0.832358772975384 0.416179386487692 97 0.539224295575337 0.921551408849325 0.460775704424662 98 0.507399863084537 0.985200273830926 0.492600136915463 99 0.477205741940656 0.954411483881312 0.522794258059344 100 0.434631743721534 0.869263487443067 0.565368256278466 101 0.394580308626363 0.789160617252726 0.605419691373637 102 0.363333897406754 0.726667794813509 0.636666102593246 103 0.368773492021713 0.737546984043427 0.631226507978287 104 0.330243739638688 0.660487479277375 0.669756260361312 105 0.316260278130850 0.632520556261701 0.68373972186915 106 0.289629082827581 0.579258165655162 0.710370917172419 107 0.252792866856312 0.505585733712625 0.747207133143688 108 0.216444948959499 0.432889897918997 0.783555051040501 109 0.22848789405831 0.45697578811662 0.77151210594169 110 0.262238811293822 0.524477622587643 0.737761188706178 111 0.258936887093362 0.517873774186725 0.741063112906638 112 0.236355402922266 0.472710805844532 0.763644597077734 113 0.295899498478121 0.591798996956243 0.704100501521879 114 0.743663450566094 0.512673098867812 0.256336549433906 115 0.708429011561247 0.583141976877505 0.291570988438753 116 0.707576014000258 0.584847971999484 0.292423985999742 117 0.802072530137226 0.395854939725549 0.197927469862774 118 0.767446325598247 0.465107348803507 0.232553674401753 119 0.736281084015391 0.527437831969218 0.263718915984609 120 0.829114702466917 0.341770595066165 0.170885297533083 121 0.873135100551238 0.253729798897523 0.126864899448762 122 0.847607023857486 0.304785952285029 0.152392976142514 123 0.881370807740652 0.237258384518696 0.118629192259348 124 0.851475799137123 0.297048401725755 0.148524200862877 125 0.818223122279291 0.363553755441417 0.181776877720709 126 0.79937732332971 0.401245353340582 0.200622676670291 127 0.819255127500834 0.361489744998332 0.180744872499166 128 0.78350666334914 0.432986673301721 0.216493336650860 129 0.740406027193141 0.519187945613718 0.259593972806859 130 0.692728306493556 0.614543387012888 0.307271693506444 131 0.638197880108284 0.723604239783431 0.361802119891716 132 0.584110825185605 0.83177834962879 0.415889174814395 133 0.527298596544129 0.945402806911742 0.472701403455871 134 0.512895801636292 0.974208396727415 0.487104198363708 135 0.451170060837366 0.902340121674732 0.548829939162634 136 0.414031621613112 0.828063243226224 0.585968378386888 137 0.490195631290096 0.980391262580192 0.509804368709904 138 0.49610177787343 0.99220355574686 0.50389822212657 139 0.595258782468067 0.809482435063865 0.404741217531933 140 0.604284720412977 0.791430559174046 0.395715279587023 141 0.541017721379169 0.917964557241663 0.458982278620831 142 0.80318420373978 0.39363159252044 0.19681579626022 143 0.766340437161036 0.467319125677928 0.233659562838964 144 0.784646265615082 0.430707468769835 0.215353734384918 145 0.72071630213408 0.55856739573184 0.27928369786592 146 0.759592003433977 0.480815993132046 0.240407996566023 147 0.686325897205368 0.627348205589264 0.313674102794632 148 0.717161466476863 0.565677067046274 0.282838533523137 149 0.634130638729912 0.731738722540176 0.365869361270088 150 0.54964136094937 0.90071727810126 0.45035863905063 151 0.526993414896247 0.946013170207507 0.473006585103753 152 0.459251806228762 0.918503612457523 0.540748193771238 153 0.371811214674754 0.743622429349509 0.628188785325246 154 0.264106604552904 0.528213209105807 0.735893395447096 155 0.167449889236602 0.334899778473204 0.832550110763398 156 0.115286820959986 0.230573641919971 0.884713179040014 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 0 0 OK 10% type I error level 2 0.0132450331125828 OK

Charts produced by software:

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Parameters (Session):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 3 ; 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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