WS7 deterministic trend

*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: Mon, 22 Nov 2010 20:37:40 +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/22/t1290458386mlepjcjv0onjxbf.htm/, Retrieved Mon, 22 Nov 2010 21:39:58 +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/22/t1290458386mlepjcjv0onjxbf.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 25 15 9 3 38 25 15 9 4 37 19 14 9 4 36 18 10 14 2 42 18 10 8 4 44 23 9 14 4 40 23 18 15 3 43 25 14 9 4 40 23 11 11 4 45 24 11 14 4 47 32 9 14 4 45 30 17 6 5 45 32 21 10 4 40 24 16 9 4 49 17 14 14 4 48 30 24 8 5 44 25 7 11 4 29 25 9 10 4 42 26 18 16 4 45 23 11 11 5 32 25 13 11 5 32 25 13 11 5 41 35 18 7 4 29 19 14 13 2 38 20 12 10 4 41 21 12 9 4 38 21 9 9 4 24 23 11 15 3 34 24 8 13 2 38 23 5 16 2 37 19 10 12 3 46 17 11 6 5 48 27 15 4 5 42 27 16 12 4 46 25 12 10 4 43 18 14 14 5 38 22 13 9 4 39 26 10 10 4 34 26 18 14 4 39 23 17 14 4 35 16 12 10 2 41 27 13 9 3 40 25 13 14 3 43 14 11 8 4 37 19 13 9 2 41 20 12 8 4 46 26 12 10 4 26 16 12 9 3 41 18 12 9 3 37 22 9 9 3 39 25 17 9 4 44 29 18 11 5 39 21 7 15 2 36 22 17 8 4 38 22 12 10 2 38 32 12 8 0 38 23 9 14 4 32 31 9 11 4 33 18 13 10 3 46 23 10 12 4 42 24 12 9 4 42 19 10 13 2 43 26 11 14 4 41 14 13 15 2 49 20 6 8 4 45 22 7 7 3 39 24 13 10 4 45 25 11 10 5 31 21 18 13 3 30 21 18 13 3 45 28 9 11 4 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 LeadershipPreference[t] = + 1.63596771428962 + 0.0405311256109401Career[t] + 0.047890142115417PersonalStandards[t] + 0.0137973603388139ParentalExpectations[t] -0.0745266685219804Doubts[t] -0.000855430748768299t + 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) 1.63596771428962 0.734855 2.2262 0.027596 0.013798 Career 0.0405311256109401 0.013929 2.9098 0.004209 0.002104 PersonalStandards 0.047890142115417 0.017885 2.6776 0.008301 0.004151 ParentalExpectations 0.0137973603388139 0.021758 0.6341 0.527036 0.263518 Doubts -0.0745266685219804 0.02579 -2.8898 0.004469 0.002235 t -0.000855430748768299 0.001719 -0.4977 0.619484 0.309742 Multiple Linear Regression - Regression Statistics Multiple R 0.456013921999117 R-squared 0.207948697057017 Adjusted R-squared 0.179661150523339 F-TEST (value) 7.35124542559537 F-TEST (DF numerator) 5 F-TEST (DF denominator) 140 p-value 3.79880482204165e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.8475088091418 Sum Squared Residuals 100.557965420213 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3 4.03036237485918 -1.03036237485918 2 4 3.90791356727761 0.092086432722387 3 4 3.56538879788659 0.434611202113411 4 2 3.04828931544630 -1.04828931544630 5 4 3.73778064949506 0.262219350504939 6 4 3.59648080907456 0.403519190925438 7 3 3.48315045040938 -0.483150450409379 8 4 4.09163925050089 -0.091639250500891 9 4 3.68296474062807 0.317035259371934 10 4 3.70907507448347 0.290924925516527 11 4 4.14480831120229 -0.144808311202293 12 5 4.67370257588717 0.326297424112834 13 4 4.52571019663657 -0.525710196636566 14 4 3.94461786773767 0.0553821322623282 15 4 3.57308350939192 0.426916490608085 16 5 4.73940241505265 0.260597584947350 17 4 3.87883663995726 0.121163360042743 18 4 3.37213571424400 0.627864285756004 19 4 3.62309129047031 0.37690870952969 20 5 3.87621063044631 1.12378936955369 21 5 3.47182557166379 1.52817442833621 22 5 3.47097014091502 1.52902985908498 23 4 4.68088973760087 -0.680889737600873 24 2 2.92506907318701 -0.925069073187013 25 4 3.53286919994044 0.467130800059564 26 4 3.77602395666189 0.223976043338115 27 4 3.61218306806385 0.387816931936145 28 3 2.72010687253850 0.279893127461495 29 2 3.28011409604207 -1.28011409604207 30 2 3.12852093903926 -1.12852093903926 31 3 3.26266728999988 -0.262667289999880 32 5 3.99176907698943 1.00823092301057 33 5 4.75512009701593 0.244879902984066 34 4 3.9286619247645 0.0713380752355042 35 4 4.08801460791736 -0.0880146079173586 36 5 3.35982285211756 1.64017714788244 37 4 3.70670834404685 0.293291655953155 38 4 3.82202585783226 0.177974142167738 39 4 3.43078700765138 0.569212992348616 40 4 3.47511941827225 0.524880581727749 41 2 3.20602836266565 -1.20602836266565 42 3 4.06347527771291 -1.06347527771291 43 3 3.55367509451246 -0.553675094512464 44 4 3.56718676778118 0.432813232218816 45 2 3.51566334609951 -1.51566334609951 46 4 3.78555186809308 0.214448131906917 47 4 4.12563958104756 -0.125639581047556 48 3 2.90978688544780 0.0902131145522034 49 3 3.61267862309396 -0.612678623093963 50 3 3.59986717734666 -0.599867177346661 51 4 3.93412330687654 0.0658766931234643 52 5 4.19222809593899 0.807771904061011 53 2 3.15571826239731 -1.15571826239731 54 4 3.74081987997314 0.25918012002686 55 2 3.60298656170822 -1.60298656170822 56 0 4.23008588915758 -4.23008588915758 57 4 3.30966708722174 0.690332912778262 58 4 3.67232604529661 0.327673954703394 59 3 3.21914600253559 -0.219146002535593 60 4 3.79420049724573 0.205799502754272 61 4 3.93028543241219 0.0697145675878141 62 2 3.36427789632078 -1.36427789632078 63 4 3.67845527780771 0.321544722192293 64 2 2.9749239426077 -0.974923942607703 65 4 4.01076352672112 -0.0107635267211218 66 3 4.03188790662022 -1.03188790662022 67 4 3.74283016290359 0.257169837096411 68 5 4.00545690725825 0.99454309274175 69 3 3.11860666630041 -0.118606666300410 70 3 3.0772201099407 -0.0772201099407018 71 4 4.04443965215859 -0.0444396521585882 72 5 4.19719703534691 0.802802964653086 73 4 2.54893988322515 1.45106011677485 74 2 3.47797916671655 -1.47797916671655 75 4 3.67516016986471 0.324839830135286 76 4 3.63300989696507 0.366990103034934 77 4 3.64493391501941 0.355066084980590 78 4 3.11585622191688 0.884143778083121 79 4 3.18385333726555 0.816146662734447 80 2 2.81392782005817 -0.813927820058166 81 5 4.60473597150117 0.39526402849883 82 4 3.75682970580975 0.243170294190246 83 2 2.30442307810982 -0.304423078109816 84 3 3.23848583715845 -0.238485837158451 85 3 3.65399869564133 -0.653998695641332 86 5 3.97144812155271 1.02855187844729 87 4 3.66964895550375 0.330351044496247 88 3 4.13734191206221 -1.13734191206221 89 4 3.66862676734431 0.331373232655695 90 3 3.65295606472102 -0.652956064721021 91 4 3.8532061284135 0.146793871586499 92 5 4.04084220558208 0.959157794417918 93 2 2.50476026350089 -0.504760263500894 94 4 3.6103128442474 0.389687155752602 95 4 3.43470354865546 0.565296451344543 96 4 3.30274733669521 0.697252663304788 97 5 3.26231897460657 1.73768102539343 98 2 3.02181835554959 -1.02181835554959 99 3 3.22757076446906 -0.227570764469056 100 4 3.73573563424367 0.264264365756327 101 4 3.58944983986687 0.410550160133135 102 3 3.747132954877 -0.747132954877001 103 3 3.72491134361660 -0.724911343616605 104 5 3.45112605065039 1.54887394934961 105 4 3.70022445072935 0.299775549270649 106 4 4.17079249497086 -0.170792494970860 107 4 2.91242456667424 1.08757543332576 108 4 3.94339076163413 0.0566092383658726 109 2 3.53794226843582 -1.53794226843582 110 4 3.49892877462428 0.501071225375718 111 5 3.26889425908688 1.73110574091312 112 3 3.71615703374106 -0.716157033741063 113 3 3.32626583816336 -0.326265838163360 114 3 3.93739722173602 -0.937397221736016 115 4 3.7136504587594 0.286349541240604 116 4 4.19533525338779 -0.195335253387790 117 4 3.2708886917667 0.729111308233299 118 3 3.19372496442031 -0.193724964420311 119 2 3.23426161468798 -1.23426161468798 120 3 2.96935477002697 0.0306452299730272 121 3 3.46920192415619 -0.469201924156188 122 4 3.46629534439880 0.533704655601196 123 5 4.02178010774030 0.978219892259696 124 4 3.38662881382463 0.613371186175369 125 3 3.85445653084957 -0.854456530849574 126 3 3.45594057709257 -0.455940577092569 127 4 3.38492347698383 0.615076523016172 128 4 3.79640908065132 0.203590919348676 129 4 3.50183417064035 0.498165829359645 130 3 3.30211836732022 -0.30211836732022 131 5 4.08979256846975 0.91020743153025 132 3 3.33208970345019 -0.332089703450193 133 4 3.46400411718577 0.535995882814232 134 4 3.65079456488606 0.349205435113941 135 4 3.52907195224348 0.470928047756515 136 4 3.96656512624409 0.0334348737559073 137 5 3.73559410722948 1.26440589277052 138 3 3.35504603524218 -0.355046035242175 139 2 3.45020288805629 -1.45020288805629 140 3 3.38775719371885 -0.387757193718854 141 3 3.60609457371031 -0.606094573710307 142 3 3.50087212702219 -0.500872127022188 143 4 2.90621393224667 1.09378606775333 144 2 3.4391581522805 -1.4391581522805 145 4 3.32050510505210 0.679494894947896 146 2 3.18711182915104 -1.18711182915104 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.51155136469874 0.97689727060252 0.48844863530126 10 0.343316904458083 0.686633808916167 0.656683095541917 11 0.223754598867411 0.447509197734823 0.776245401132589 12 0.138319635982025 0.276639271964049 0.861680364017975 13 0.0926681930521013 0.185336386104203 0.907331806947899 14 0.0527240967530869 0.105448193506174 0.947275903246913 15 0.0280679835087703 0.0561359670175405 0.97193201649123 16 0.0149888398792221 0.0299776797584442 0.985011160120778 17 0.00948843605408469 0.0189768721081694 0.990511563945915 18 0.00689551237266116 0.0137910247453223 0.993104487627339 19 0.00416358678630374 0.00832717357260747 0.995836413213696 20 0.00267383048227446 0.00534766096454893 0.997326169517726 21 0.00408381796719099 0.00816763593438197 0.99591618203281 22 0.00337318441982156 0.00674636883964312 0.996626815580179 23 0.0156613769428495 0.031322753885699 0.98433862305715 24 0.123332225503015 0.246664451006029 0.876667774496985 25 0.0976011139028435 0.195202227805687 0.902398886097156 26 0.0836545378850253 0.167309075770051 0.916345462114975 27 0.0659458575058846 0.131891715011769 0.934054142494115 28 0.0469953997177304 0.0939907994354609 0.95300460028227 29 0.151228234100562 0.302456468201124 0.848771765899438 30 0.202900253311263 0.405800506622526 0.797099746688737 31 0.172547600713286 0.345095201426572 0.827452399286714 32 0.149722230158842 0.299444460317684 0.850277769841158 33 0.122600954365595 0.245201908731190 0.877399045634405 34 0.0933831295994378 0.186766259198876 0.906616870400562 35 0.0723900194055771 0.144780038811154 0.927609980594423 36 0.126644466627294 0.253288933254588 0.873355533372706 37 0.100758121625004 0.201516243250009 0.899241878374996 38 0.0773199534468932 0.154639906893786 0.922680046553107 39 0.0635012154420845 0.127002430884169 0.936498784557915 40 0.0499507375308445 0.099901475061689 0.950049262469155 41 0.118497439007396 0.236994878014793 0.881502560992603 42 0.150130855808945 0.300261711617889 0.849869144191056 43 0.132300948768256 0.264601897536512 0.867699051231744 44 0.109131116815744 0.218262233631488 0.890868883184256 45 0.195103915004607 0.390207830009214 0.804896084995393 46 0.162296352858348 0.324592705716697 0.837703647141652 47 0.131289170397810 0.262578340795620 0.86871082960219 48 0.105199652358292 0.210399304716583 0.894800347641708 49 0.0948216853213517 0.189643370642703 0.905178314678648 50 0.0798653425674775 0.159730685134955 0.920134657432522 51 0.062549089456253 0.125098178912506 0.937450910543747 52 0.066029878839054 0.132059757678108 0.933970121160946 53 0.072755815383631 0.145511630767262 0.927244184616369 54 0.0590302027908902 0.118060405581780 0.94096979720911 55 0.0969023589879625 0.193804717975925 0.903097641012037 56 0.89770579749334 0.204588405013321 0.102294202506661 57 0.909744850151857 0.180510299696285 0.0902551498481425 58 0.921168303127764 0.157663393744472 0.0788316968722358 59 0.902325152252951 0.195349695494098 0.0976748477470488 60 0.884775911209549 0.230448177580902 0.115224088790451 61 0.863035131613026 0.273929736773947 0.136964868386974 62 0.89510678219806 0.20978643560388 0.10489321780194 63 0.881831575852768 0.236336848294464 0.118168424147232 64 0.885574666993362 0.228850666013276 0.114425333006638 65 0.86431269119685 0.271374617606299 0.135687308803150 66 0.88196661240358 0.236066775192840 0.118033387596420 67 0.865554260442351 0.268891479115298 0.134445739557649 68 0.882123055664248 0.235753888671504 0.117876944335752 69 0.856976976152263 0.286046047695474 0.143023023847737 70 0.828617122585875 0.342765754828251 0.171382877414125 71 0.808013606306116 0.383972787387768 0.191986393693884 72 0.80581725233085 0.3883654953383 0.19418274766915 73 0.868452768630194 0.263094462739611 0.131547231369806 74 0.924210212108328 0.151579575783344 0.0757897878916718 75 0.908323706002411 0.183352587995177 0.0916762939975886 76 0.892318323633376 0.215363352733249 0.107681676366624 77 0.871343868588696 0.257312262822607 0.128656131411304 78 0.872059897806777 0.255880204386446 0.127940102193223 79 0.871218892645683 0.257562214708634 0.128781107354317 80 0.869408734645642 0.261182530708716 0.130591265354358 81 0.851987437275883 0.296025125448233 0.148012562724117 82 0.824825839817204 0.350348320365592 0.175174160182796 83 0.811212668879054 0.377574662241893 0.188787331120946 84 0.786759775950248 0.426480448099503 0.213240224049752 85 0.778678131538861 0.442643736922279 0.221321868461139 86 0.78487593167907 0.430248136641861 0.215124068320930 87 0.749662129654598 0.500675740690804 0.250337870345402 88 0.793260965890764 0.413478068218471 0.206739034109236 89 0.761828035367716 0.476343929264568 0.238171964632284 90 0.770441336894993 0.459117326210014 0.229558663105007 91 0.730112387531975 0.53977522493605 0.269887612468025 92 0.723693823464946 0.552612353070107 0.276306176535054 93 0.725905479682883 0.548189040634234 0.274094520317117 94 0.702327463348946 0.595345073302108 0.297672536651054 95 0.668813573522135 0.66237285295573 0.331186426477865 96 0.634997025519278 0.730005948961444 0.365002974480722 97 0.74334998493652 0.513300030126958 0.256650015063479 98 0.770683545833899 0.458632908332201 0.229316454166101 99 0.739483936890286 0.521032126219428 0.260516063109714 100 0.702855925394763 0.594288149210473 0.297144074605237 101 0.6590838099692 0.681832380061601 0.340916190030800 102 0.632887486310937 0.734225027378125 0.367112513689062 103 0.627901062696384 0.744197874607231 0.372098937303616 104 0.671608014733712 0.656783970532576 0.328391985266288 105 0.621418937725443 0.757162124549114 0.378581062274557 106 0.568008865825753 0.863982268348494 0.431991134174247 107 0.599506091308548 0.800987817382905 0.400493908691452 108 0.545451761055033 0.909096477889934 0.454548238944967 109 0.748571788800733 0.502856422398534 0.251428211199267 110 0.710077392187293 0.579845215625414 0.289922607812707 111 0.850955143896615 0.298089712206769 0.149044856103385 112 0.83641314392898 0.327173712142041 0.163586856071020 113 0.79720113736554 0.405597725268922 0.202798862634461 114 0.822952699793298 0.354094600413403 0.177047300206702 115 0.77979900718009 0.440401985639819 0.220200992819909 116 0.793077776570898 0.413844446858204 0.206922223429102 117 0.763709357719836 0.472581284560329 0.236290642280164 118 0.714843807671635 0.57031238465673 0.285156192328365 119 0.791926687233604 0.416146625532792 0.208073312766396 120 0.759444351589987 0.481111296820026 0.240555648410013 121 0.748935147905466 0.502129704189067 0.251064852094534 122 0.708100207842764 0.583799584314473 0.291899792157236 123 0.659974656890276 0.680050686219448 0.340025343109724 124 0.598175833676856 0.803648332646288 0.401824166323144 125 0.588490003687115 0.823019992625771 0.411509996312885 126 0.632563337351165 0.73487332529767 0.367436662648835 127 0.576255296708701 0.847489406582597 0.423744703291299 128 0.507078687179924 0.985842625640153 0.492921312820077 129 0.457739507123953 0.915479014247905 0.542260492876047 130 0.369108114547222 0.738216229094445 0.630891885452778 131 0.365306538552278 0.730613077104556 0.634693461447722 132 0.312983210694960 0.625966421389921 0.68701678930504 133 0.444011226992897 0.888022453985795 0.555988773007103 134 0.3571750233353 0.7143500466706 0.6428249766647 135 0.253500828090029 0.507001656180059 0.74649917190997 136 0.171939618351557 0.343879236703115 0.828060381648443 137 0.382671608067734 0.765343216135468 0.617328391932266 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 4 0.0310077519379845 NOK 5% type I error level 8 0.062015503875969 NOK 10% type I error level 11 0.0852713178294574 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 = 5 ; 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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