Mini-Tutorial Multiple Regression

*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 23:58:00 +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/t1290472699ib9nrjd85lbyagf.htm/, Retrieved Tue, 23 Nov 2010 01:38:19 +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/t1290472699ib9nrjd85lbyagf.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 «

13 26 9 6 25 25 16 20 9 6 25 24 19 21 9 13 19 21 15 31 14 8 18 23 14 21 8 7 18 17 13 18 8 9 22 19 19 26 11 5 29 18 15 22 10 8 26 27 14 22 9 9 25 23 15 29 15 11 23 23 16 15 14 8 23 29 16 16 11 11 23 21 16 24 14 12 24 26 17 17 6 8 30 25 15 19 20 7 19 25 15 22 9 9 24 23 20 31 10 12 32 26 18 28 8 20 30 20 16 38 11 7 29 29 16 26 14 8 17 24 19 25 11 8 25 23 16 25 16 16 26 24 17 29 14 10 26 30 17 28 11 6 25 22 16 15 11 8 23 22 15 18 12 9 21 13 14 21 9 9 19 24 15 25 7 11 35 17 12 23 13 12 19 24 14 23 10 8 20 21 16 19 9 7 21 23 14 18 9 8 21 24 7 18 13 9 24 24 10 26 16 4 23 24 14 18 12 8 19 23 16 18 6 8 17 26 16 28 14 8 24 24 16 17 14 6 15 21 14 29 10 8 25 23 20 12 4 4 27 28 14 25 12 7 29 23 14 28 12 14 27 22 11 20 14 10 18 24 15 17 9 9 25 21 16 17 9 6 22 23 14 20 10 8 26 23 16 31 14 11 23 20 14 21 10 8 16 23 12 19 9 8 27 21 16 23 14 10 25 27 9 15 8 8 14 12 14 24 9 10 19 15 16 28 8 7 20 22 16 16 9 8 16 21 15 19 9 7 18 21 16 21 9 9 22 20 12 21 15 5 21 24 16 20 8 7 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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Selfconfidence[t] = + 12.9244692218402 + 0.0194062852882190ConcernMistakes[t] -0.292329496310611DoubtsActions[t] + 0.0742459719711945ParentalCriticism[t] + 0.0344516405357084PersonalStandards[t] + 0.152496856322935Organization[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) 12.9244692218402 1.424886 9.0705 0 0 ConcernMistakes 0.0194062852882190 0.037126 0.5227 0.601981 0.300991 DoubtsActions -0.292329496310611 0.069094 -4.2309 4.1e-05 2.1e-05 ParentalCriticism 0.0742459719711945 0.068699 1.0807 0.281618 0.140809 PersonalStandards 0.0344516405357084 0.049183 0.7005 0.484762 0.242381 Organization 0.152496856322935 0.049916 3.055 0.002682 0.001341 Multiple Linear Regression - Regression Statistics Multiple R 0.438418729396901 R-squared 0.192210982285993 Adjusted R-squared 0.164162752504256 F-TEST (value) 6.85287391688267 F-TEST (DF numerator) 5 F-TEST (DF denominator) 144 p-value 9.15406172974365e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.07799929532179 Sum Squared Residuals 621.803674275534 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 15.9172554258317 -2.91725542583166 2 16 15.6483208577794 0.351679142220559 3 19 15.5232485346830 3.47675146531703 4 15 14.1549761182663 0.84502388173371 5 14 14.7256631333390 -0.725663133338962 6 13 15.2587364962054 -2.25873649620540 7 19 14.3286790291216 4.67132097087844 8 15 16.0352380854922 -1.03523808549217 9 14 15.7573744879465 -1.75737448794653 10 15 14.2188301699714 0.781169830028633 11 16 14.9317148942709 1.06828510572906 12 16 14.8308727338211 1.16912726617891 13 16 14.9803164213166 1.01968357868341 14 17 16.9403374937905 0.0596625062095173 15 15 12.4333230981544 2.56667690184562 16 15 15.7229228474108 -0.722922847410819 17 20 16.5610915278622 3.43890847213777 18 18 16.6976150213793 1.30238497862067 19 16 16.3875118160749 -0.387511816074863 20 16 14.1759899076124 1.82401009238758 21 19 15.1566883792188 3.84331162078123 22 16 14.4759571702939 1.52404282970609 23 17 15.6077466101785 1.39225338982155 24 17 14.9139184348181 2.0860815651819 25 16 14.7412253889422 1.25877461105777 26 15 13.1399857324896 1.86001426751036 27 14 15.683755215767 -1.68375521576699 28 15 15.9782795477943 -0.97827954779427 29 12 14.7759877170146 -2.77598771701457 30 14 14.9329533896285 -0.93295338962853 31 16 15.4128571259966 0.587142874003353 32 14 15.6201936690026 -1.62019366900256 33 7 14.6284765773384 -7.62847657733843 34 10 13.5010568703207 -3.50105687032067 35 14 14.5218050426764 -0.521805042676374 36 16 16.6643693084374 -0.664369308437427 37 16 14.4559639619388 1.54403603806118 38 16 13.3264475460358 2.67355245396416 39 14 15.5266430166823 -1.52664301668225 40 20 17.4851168194475 2.51488318055249 41 14 14.9279194730798 -0.927919473079796 42 14 15.2844599953485 -1.28445999534846 43 11 14.2424957803612 -3.24249578036120 44 15 15.3553493488596 -0.355349348859563 45 16 15.3342502239847 0.665749776015276 46 14 15.386438089624 -1.38643808962399 47 16 14.0924816678896 1.90751833211039 48 14 15.0613279695551 -1.06132796955513 49 12 15.3888192285362 -3.38881922853622 50 16 14.9993666889446 1.00063331105537 51 9 13.7831805498233 -4.78318054982334 52 14 14.4437483366964 -0.443748336696430 53 16 15.6928946930426 0.307105306957414 54 16 14.9516323267788 1.04836767322123 55 15 15.0045084917437 -0.00450849174365286 56 16 15.1771227120824 0.822877287917622 57 12 13.7016976310900 -1.70169763108997 58 16 15.9115414044541 0.0884585955458791 59 16 16.0117415522947 -0.0117415522946973 60 14 16.5055860925752 -2.50558609257523 61 16 13.0096023007214 2.99039769927861 62 17 16.2857634419329 0.714236558067145 63 18 14.5396501106230 3.46034988937698 64 18 15.5939990280450 2.40600097195496 65 12 14.7743955257743 -2.77439552577426 66 16 15.9308851336156 0.0691148663844061 67 10 14.2113207474753 -4.21132074747527 68 14 12.3274552156526 1.67254478434742 69 18 15.8238575812933 2.17614241870665 70 18 16.4358701278371 1.56412987216286 71 16 15.3409460062213 0.65905399377866 72 16 15.3599962738494 0.640003726150624 73 16 14.5038381408465 1.49616185915350 74 13 15.1143047828663 -2.11430478286632 75 16 15.6868474334068 0.313152566593205 76 16 14.8030315399933 1.19696846000671 77 20 16.2455824672020 3.75441753279803 78 16 15.1848002551780 0.815199744821957 79 15 12.8242848152350 2.17571518476495 80 15 15.4826958812108 -0.482695881210769 81 16 15.707103857309 0.292896142690989 82 14 14.0529117318693 -0.0529117318692575 83 15 13.0568409480684 1.94315905193162 84 12 14.7376000015362 -2.73760000153625 85 17 16.6683797742167 0.331620225783264 86 16 15.3646506654235 0.635349334576457 87 15 13.1984752704858 1.80152472951423 88 13 13.8616476350934 -0.861647635093433 89 16 15.3633591736207 0.636640826379345 90 16 15.0943792754449 0.905620724555142 91 16 16.0168598477793 -0.0168598477793425 92 16 16.1992565145957 -0.199256514595724 93 14 15.4717480117765 -1.47174801177651 94 16 13.8713049693176 2.12869503068240 95 16 14.6218824000409 1.37811759995907 96 20 16.2376342419748 3.76236575802517 97 15 15.6304767464256 -0.630476746425586 98 16 14.0940891719475 1.90591082805248 99 13 14.0192246946814 -1.01922469468144 100 17 15.9422125280244 1.05778747197558 101 16 14.6801165687232 1.31988343127681 102 12 13.0309795743121 -1.03097957431206 103 16 14.6814615851464 1.31853841485360 104 16 15.2480448330947 0.751955166905341 105 17 15.3220436302488 1.67795636975124 106 13 12.8113175776849 0.188682422315101 107 12 15.7560213966097 -3.75602139660969 108 18 15.7519464615180 2.24805353848196 109 14 13.8455742322706 0.154425767729449 110 14 14.4064506967452 -0.406450696745218 111 13 13.6234930334546 -0.623493033454569 112 16 15.494201184581 0.505798815419014 113 13 12.5613739995042 0.438626000495795 114 16 14.9389446031291 1.06105539687087 115 13 14.9747728423161 -1.97477284231606 116 16 15.9673628519961 0.0326371480038552 117 15 14.4957420239639 0.504257976036098 118 16 15.4719651692877 0.528034830712334 119 15 14.7284758370783 0.27152416292174 120 17 15.5917720620994 1.40822793790056 121 15 16.1851756942041 -1.18517569420409 122 12 13.5258821505310 -1.52588215053095 123 16 14.4836807714255 1.51631922857445 124 10 14.4214269858744 -4.4214269858744 125 16 14.6376695792344 1.36233042076565 126 14 14.6777273548973 -0.677727354897334 127 15 16.4390186202925 -1.4390186202925 128 13 14.4275270422181 -1.42752704221810 129 15 14.9218503906348 0.0781496093651607 130 11 13.8342315250441 -2.83423152504412 131 12 14.1406881284627 -2.14068812846272 132 8 14.4030877969739 -6.40308779697394 133 16 16.300214984473 -0.300214984473012 134 15 15.1321021989120 -0.132102198911953 135 17 15.6463429798365 1.35365702016347 136 16 14.9850559197391 1.01494408026091 137 10 15.0951919591115 -5.09519195911154 138 18 13.6504613092664 4.34953869073359 139 13 14.2776900818525 -1.27769008185249 140 15 14.5242715171173 0.475728482882688 141 16 14.7412253889422 1.25877461105777 142 16 14.9101216484423 1.08987835155771 143 14 13.7265319428067 0.27346805719333 144 10 13.5617106183983 -3.56171061839826 145 17 16.6683797742167 0.331620225783264 146 13 14.8192844166996 -1.81928441669964 147 15 16.1851756942041 -1.18517569420409 148 16 15.6509726788231 0.349027321176853 149 12 15.3208749289219 -3.32087492892189 150 13 13.5991936049522 -0.599193604952239 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.839406595619847 0.321186808760306 0.160593404380153 10 0.877892026226054 0.244215947547892 0.122107973773946 11 0.810467274039897 0.379065451920206 0.189532725960103 12 0.736584115475692 0.526831769048615 0.263415884524308 13 0.640184453197918 0.719631093604165 0.359815546802082 14 0.570107319249919 0.859785361500162 0.429892680750081 15 0.482680220694549 0.965360441389098 0.517319779305451 16 0.390312151162189 0.780624302324377 0.609687848837811 17 0.376084736529409 0.752169473058818 0.623915263470591 18 0.378485201781400 0.756970403562799 0.6215147982186 19 0.298200671986401 0.596401343972803 0.701799328013599 20 0.284695190200338 0.569390380400676 0.715304809799662 21 0.384285033003676 0.768570066007351 0.615714966996325 22 0.377020245490686 0.754040490981371 0.622979754509315 23 0.320933877062018 0.641867754124036 0.679066122937982 24 0.273790174262498 0.547580348524996 0.726209825737502 25 0.221176124607349 0.442352249214698 0.778823875392651 26 0.189694346846511 0.379388693693022 0.810305653153489 27 0.152038094918750 0.304076189837501 0.84796190508125 28 0.204939124212455 0.40987824842491 0.795060875787545 29 0.300192559465584 0.600385118931167 0.699807440534416 30 0.255399957789471 0.510799915578942 0.744600042210529 31 0.221141518174618 0.442283036349235 0.778858481825382 32 0.187502949680778 0.375005899361555 0.812497050319222 33 0.907460909601488 0.185078180797025 0.0925390903985125 34 0.95963341529059 0.0807331694188188 0.0403665847094094 35 0.945768762971858 0.108462474056284 0.0542312370281419 36 0.933301186469834 0.133397627060332 0.0666988135301659 37 0.919105657494833 0.161788685010333 0.0808943425051667 38 0.929364027607019 0.141271944785962 0.070635972392981 39 0.92284882135416 0.154302357291681 0.0771511786458406 40 0.951341659562348 0.0973166808753041 0.0486583404376521 41 0.942031185700585 0.115937628598830 0.0579688142994148 42 0.935283651152039 0.129432697695923 0.0647163488479613 43 0.952993899664985 0.0940122006700296 0.0470061003350148 44 0.939019155077905 0.121961689844191 0.0609808449220953 45 0.923816579535725 0.152366840928550 0.0761834204642748 46 0.912600998304644 0.174798003390713 0.0873990016953565 47 0.903277606468952 0.193444787062095 0.0967223935310476 48 0.883809025546829 0.232381948906343 0.116190974453171 49 0.917113703509634 0.165772592980732 0.0828862964903662 50 0.900652609162264 0.198694781675472 0.099347390837736 51 0.955801592119583 0.0883968157608345 0.0441984078804173 52 0.943356648400162 0.113286703199676 0.0566433515998382 53 0.928672707224073 0.142654585551853 0.0713272927759266 54 0.92039207138818 0.159215857223638 0.0796079286118192 55 0.901391855579454 0.197216288841091 0.0986081444205456 56 0.882986461168553 0.234027077662894 0.117013538831447 57 0.873946245417115 0.252107509165771 0.126053754582885 58 0.847282819471214 0.305434361057571 0.152717180528786 59 0.816671955106788 0.366656089786424 0.183328044893212 60 0.832140011463428 0.335719977073145 0.167859988536572 61 0.85484480682211 0.290310386355778 0.145155193177889 62 0.82817881771833 0.343642364563339 0.171821182281669 63 0.877162753591611 0.245674492816777 0.122837246408389 64 0.887735741575225 0.224528516849549 0.112264258424775 65 0.908097248837835 0.183805502324331 0.0919027511621654 66 0.886649013757977 0.226701972484046 0.113350986242023 67 0.939152920427661 0.121694159144678 0.0608470795723389 68 0.933913072845168 0.132173854309665 0.0660869271548323 69 0.937298153438762 0.125403693122475 0.0627018465612377 70 0.93223891045251 0.13552217909498 0.06776108954749 71 0.916737931933217 0.166524136133566 0.0832620680667829 72 0.898574787131802 0.202850425736397 0.101425212868198 73 0.88976945636665 0.220461087266701 0.110230543633350 74 0.890526654479395 0.218946691041210 0.109473345520605 75 0.866744421632086 0.266511156735829 0.133255578367914 76 0.848658697186031 0.302682605627937 0.151341302813969 77 0.90662320359226 0.18675359281548 0.09337679640774 78 0.889012915451997 0.221974169096005 0.110987084548003 79 0.888938341983281 0.222123316033437 0.111061658016719 80 0.865296993936307 0.269406012127386 0.134703006063693 81 0.838284675962851 0.323430648074298 0.161715324037149 82 0.80981725009318 0.38036549981364 0.19018274990682 83 0.811989755796598 0.376020488406804 0.188010244203402 84 0.835048408236778 0.329903183526444 0.164951591763222 85 0.804073726116609 0.391852547766782 0.195926273883391 86 0.77233084751484 0.455338304970321 0.227669152485161 87 0.765167952485139 0.469664095029722 0.234832047514861 88 0.731895543756456 0.536208912487088 0.268104456243544 89 0.692541415399291 0.614917169201417 0.307458584600709 90 0.658080232698974 0.683839534602051 0.341919767301026 91 0.611216601703969 0.777566796592063 0.388783398296031 92 0.563025791207577 0.873948417584846 0.436974208792423 93 0.543125858566632 0.913748282866736 0.456874141433368 94 0.570578653385897 0.858842693228206 0.429421346614103 95 0.55415342968406 0.89169314063188 0.44584657031594 96 0.668888071025569 0.662223857948863 0.331111928974431 97 0.623484603474648 0.753030793050703 0.376515396525352 98 0.650108183380217 0.699783633239566 0.349891816619783 99 0.611916375657139 0.776167248685722 0.388083624342861 100 0.589863192679175 0.82027361464165 0.410136807320825 101 0.580165338974937 0.839669322050125 0.419834661025063 102 0.543522427806866 0.912955144386269 0.456477572193134 103 0.513168586272288 0.973662827455425 0.486831413727712 104 0.505439863486221 0.989120273027559 0.494560136513779 105 0.521629121815257 0.956741756369486 0.478370878184743 106 0.468710608462015 0.93742121692403 0.531289391537985 107 0.583295604274685 0.83340879145063 0.416704395725315 108 0.596003117123803 0.807993765752393 0.403996882876197 109 0.590062730522675 0.81987453895465 0.409937269477325 110 0.54152063919027 0.91695872161946 0.45847936080973 111 0.486994254918051 0.973988509836102 0.513005745081949 112 0.436235224193384 0.872470448386768 0.563764775806616 113 0.404028008231801 0.808056016463602 0.595971991768199 114 0.390308006499449 0.780616012998899 0.60969199350055 115 0.376413005229204 0.752826010458407 0.623586994770796 116 0.32143986217074 0.64287972434148 0.67856013782926 117 0.306419800605839 0.612839601211678 0.693580199394161 118 0.308864599873435 0.61772919974687 0.691135400126565 119 0.257265157839981 0.514530315679963 0.742734842160019 120 0.225593073174112 0.451186146348224 0.774406926825888 121 0.190473049553368 0.380946099106736 0.809526950446632 122 0.172008143860331 0.344016287720662 0.82799185613967 123 0.159803269507459 0.319606539014917 0.840196730492542 124 0.225421621099517 0.450843242199034 0.774578378900483 125 0.184350941175964 0.368701882351929 0.815649058824036 126 0.146250684621607 0.292501369243215 0.853749315378393 127 0.113316969390673 0.226633938781346 0.886683030609327 128 0.0878389660618943 0.175677932123789 0.912161033938106 129 0.0639122978478706 0.127824595695741 0.93608770215213 130 0.0539577693431655 0.107915538686331 0.946042230656834 131 0.0408230717478488 0.0816461434956976 0.959176928252151 132 0.214415156305962 0.428830312611924 0.785584843694038 133 0.164644852556013 0.329289705112026 0.835355147443987 134 0.119490764675610 0.238981529351219 0.88050923532439 135 0.186636256827903 0.373272513655807 0.813363743172097 136 0.200995474323622 0.401990948647243 0.799004525676378 137 0.23470842459043 0.46941684918086 0.76529157540957 138 0.59748751336796 0.805024973264081 0.402512486632040 139 0.495391820272549 0.990783640545098 0.504608179727451 140 0.440047336197441 0.880094672394882 0.559952663802559 141 0.356346888942106 0.712693777884213 0.643653111057894 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 5 0.037593984962406 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290472699ib9nrjd85lbyagf/10110v1290470269.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290472699ib9nrjd85lbyagf/10110v1290470269.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290472699ib9nrjd85lbyagf/1c03j1290470269.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290472699ib9nrjd85lbyagf/1c03j1290470269.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290472699ib9nrjd85lbyagf/2c03j1290470269.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290472699ib9nrjd85lbyagf/2c03j1290470269.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290472699ib9nrjd85lbyagf/3nr3m1290470269.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290472699ib9nrjd85lbyagf/3nr3m1290470269.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290472699ib9nrjd85lbyagf/4nr3m1290470269.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290472699ib9nrjd85lbyagf/4nr3m1290470269.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290472699ib9nrjd85lbyagf/5nr3m1290470269.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290472699ib9nrjd85lbyagf/5nr3m1290470269.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290472699ib9nrjd85lbyagf/6fi271290470269.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290472699ib9nrjd85lbyagf/6fi271290470269.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290472699ib9nrjd85lbyagf/78rjs1290470269.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290472699ib9nrjd85lbyagf/78rjs1290470269.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290472699ib9nrjd85lbyagf/88rjs1290470269.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290472699ib9nrjd85lbyagf/88rjs1290470269.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290472699ib9nrjd85lbyagf/98rjs1290470269.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290472699ib9nrjd85lbyagf/98rjs1290470269.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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