*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 21:05:07 +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/t1290546197ghhni3y847qcbvz.htm/, Retrieved Tue, 23 Nov 2010 22:03:21 +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/t1290546197ghhni3y847qcbvz.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 11 12 12 11 7 8 11 6 17 8 14 12 10 8 12 8 12 9 21 10 12 7 12 10 11 4 22 11 11 11 11 16 12 7 10 11 13 7 13 13 14 12 10 12 16 10 8 8 11 10 15 12 10 8 14 11 11 8 10 4 15 4 14 9 9 9 14 8 11 8 11 8 17 7 10 14 17 11 13 15 11 9 7 16 18 11 14 9 14 13 12 14 10 8 14 11 11 8 11 8 15 9 9 9 15 6 11 9 13 9 15 9 16 9 14 9 13 6 13 10 9 6 9 16 18 16 15 11 18 5 10 8 12 7 11 9 17 9 13 16 9 6 8 11 9 6 20 16 12 5 12 12 18 12 10 12 12 7 10 14 18 10 9 9 14 9 14 10 15 8 8 9 16 5 14 10 10 8 11 12 11 8 13 14 14 10 9 14 9 6 11 10 12 8 15 14 17 7 11 16 5 4 10 9 12 8 14 10 12 8 18 6 6 4 14 8 24 20 11 13 12 8 12 10 12 8 13 8 14 6 9 7 7 4 10 15 13 8 15 9 12 9 20 10 13 6 12 12 14 7 12 13 8 9 14 10 11 5 13 11 9 5 11 8 11 8 17 9 13 8 12 13 10 6 13 11 11 8 14 8 12 7 13 9 9 7 15 9 15 9 13 15 18 11 10 9 15 6 11 10 12 8 19 14 13 6 13 12 14 9 17 12 10 8 13 11 13 6 9 14 13 10 11 6 11 8 10 12 13 8 9 8 16 10 12 14 8 5 12 11 16 7 13 10 11 5 13 14 9 8 12 12 16 14 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 'RServer@AstonUniversity' @ vre.aston.ac.uk R Framework error message Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Multiple Linear Regression - Estimated Regression Equation Depression[t] = + 13.7909534342014 -0.0552145384139858Concerns[t] + 0.0174589172036399Expectations[t] -0.068568336220047Criticism[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) 13.7909534342014 1.359126 10.1469 0 0 Concerns -0.0552145384139858 0.090769 -0.6083 0.543865 0.271932 Expectations 0.0174589172036399 0.089364 0.1954 0.845356 0.422678 Criticism -0.068568336220047 0.112304 -0.6106 0.542368 0.271184 Multiple Linear Regression - Regression Statistics Multiple R 0.0755276090147059 R-squared 0.00570441972347828 Adjusted R-squared -0.0131746102817722 F-TEST (value) 0.302156399025365 F-TEST (DF numerator) 3 F-TEST (DF denominator) 158 p-value 0.82380333166505 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.18811928962261 Sum Squared Residuals 1605.92852756847 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 12 12.3871779510051 -0.387177951005099 2 11 12.7572592423127 -1.75725924231265 3 14 13.207921106419 0.792078893581017 4 12 12.7544214555096 -0.754421455509589 5 21 12.9416291073528 8.05837089264724 6 12 12.9683367029649 -0.968336702964887 7 22 13.1565827944214 8.84341720557861 8 11 12.6213899024671 -1.62138990246707 9 10 12.637049472481 -2.63704947248097 10 13 12.9305810817545 0.0694189182454588 11 10 12.49476924103 -2.49476924102997 12 8 12.7220382862913 -4.72203828629133 13 15 12.8556018539291 2.14439814607092 14 14 12.7544214555096 1.24557854449041 15 10 12.8270949111272 -2.82709491112721 16 14 13.5577056937199 0.442294306280137 17 14 12.8340378173279 1.16596218267214 18 11 12.9927385263692 -1.99273852636917 19 10 13.1660603658111 -3.16606036581106 20 13 12.560499790447 0.439500209553045 21 7 12.5376684212512 -5.53766842125122 22 14 12.4675296308226 1.53247036917738 23 12 12.6470590584659 -0.64705905846587 24 14 12.6439923786816 1.35600762131838 25 11 12.8270949111272 -1.82709491112721 26 9 12.9940058589637 -3.99400585896368 27 11 13.1444963292098 -2.14449632920984 28 15 12.9038734861424 2.09612651385758 29 14 12.9562502377533 1.04374976224666 30 13 13.1095784948026 -0.10957849480256 31 9 12.984528287574 -3.98452828757401 32 15 12.1246879497224 2.87531205027761 33 10 13.1550123402128 -3.15501234021283 34 11 13.0787657797929 -2.07876577979286 35 13 12.973709154957 0.0262908450430216 36 8 12.6532410570901 -4.6532410570901 37 20 12.92931374916 7.07068625083997 38 12 12.7741861449211 -0.774186144921066 39 10 12.6198194482585 -2.61981944825852 40 10 12.8579076261369 -2.85790762613692 41 9 12.6465270438706 -3.64652704387064 42 14 12.9213324033461 1.07866759665394 43 8 12.9521451183558 -4.95214511835576 44 14 13.2305235826335 0.769476417366473 45 11 12.8648505323376 -1.86485053233756 46 13 12.7718803727132 0.228119627286771 47 9 12.5766913750561 -3.57669137505608 48 11 12.7636701339181 -1.76367013391807 49 15 12.8997683667448 2.10023163325516 50 11 12.8347731353271 -1.83477313532714 51 10 12.7205420607156 -2.72054206071563 52 14 12.9549829051588 1.04501709484117 53 18 12.8997683667448 5.10023163325516 54 14 13.2901463620591 0.709853637940868 55 11 12.3968844153759 -1.39688441537593 56 12 12.7341247515029 -0.734124751502883 57 13 12.8997683667448 0.10023163325516 58 9 13.1822519504202 -4.18225195042019 59 10 13.2523907408488 -3.25239074084879 60 15 12.6411545918785 2.35884540812145 61 20 12.8864145689388 7.11358543106122 62 12 13.0543639563886 -1.05436395638857 63 12 12.8928254605442 -0.892825460544195 64 14 12.5957207464683 1.40427925353172 65 13 13.0880144582013 -0.0880144582013413 66 11 12.9978820853801 -1.99788208538008 67 17 12.9927385263692 4.00726147363083 68 12 12.9724418223625 -0.972441822362466 69 13 12.8363435895357 0.163656410464303 70 14 12.8270949111272 1.17290508887279 71 13 13.0787657797929 -0.0787657797928587 72 15 12.971174489768 2.02882551023205 73 13 12.9387913205497 0.0612086794503014 74 10 12.5227441692366 -2.52274416923661 75 11 13.1444963292098 -2.14449632920984 76 19 12.8997683667448 6.10023163325516 77 13 12.8335058027326 0.166494197267369 78 17 12.7556887881041 4.2443112118959 79 13 12.7544214555096 0.245578544490411 80 9 12.9991494179746 -3.99914941797459 81 11 12.5592324578524 -1.55923245785244 82 10 13.1031676031971 -3.10316760319714 83 9 12.8067982071205 -3.80679820712051 84 12 12.9428964399473 -0.942896439947277 85 12 12.8147795529345 -0.814779552934478 86 13 12.9829578333655 0.0170421666345391 87 13 13.0880144582013 -0.0880144582013413 88 12 12.626533461478 -0.626533461477977 89 15 12.4477649414111 2.55223505858885 90 22 12.9683367029649 9.03166329703511 91 13 12.7138280474962 0.286171952503823 92 15 13.2431420624403 1.7568579375597 93 13 12.9978820853801 0.00211791461992434 94 15 13.0892817907959 1.91071820920415 95 10 12.8003873155151 -2.80038731551509 96 11 12.7826252766974 -1.78262527669741 97 16 12.5348306344482 3.46516936555184 98 11 12.5646049098445 -1.56460490984453 99 11 13.0235512413789 -2.02355124137887 100 10 12.9172272839485 -2.91722728394848 101 10 12.8150084459157 -2.81500844591567 102 16 13.2025486544269 2.79745134557311 103 12 12.9400586531442 -0.940058653144211 104 11 12.9254375227436 -1.92543752274364 105 16 12.5243146234452 3.47568537655484 106 19 12.8671563045454 6.1328436954546 107 11 13.0438479453856 -2.04384794538558 108 16 12.8353051499224 3.16469485007763 109 15 12.5255819560397 2.47441804396032 110 24 12.816046885529 11.183953114471 111 14 13.0787657797929 0.921234220207141 112 15 12.8057597675072 2.19424023249282 113 11 12.7521156833018 -1.75211568330175 114 15 12.9644604765485 2.0355395234515 115 12 12.8450858429261 -0.845085842926083 116 10 13.2333613694366 -3.23336136943659 117 14 13.207921106419 0.792078893581017 118 13 12.92931374916 0.0706862508399713 119 9 12.6627186284798 -3.66271862847977 120 15 13.0489915043965 1.95100849560352 121 15 13.0315325871928 1.96846741280716 122 14 12.9131221645509 1.0868778354491 123 11 12.508123038836 -1.50812303883604 124 8 13.0425806127911 -5.04258061279107 125 11 12.3463556500105 -1.34635565001047 126 11 12.9318484143491 -1.93184841434905 127 8 13.2495529540457 -5.24955295404572 128 10 12.8270949111272 -2.82709491112721 129 11 12.8661178649321 -1.86611786493207 130 13 12.6614512958853 0.338548704114743 131 11 12.6563077368744 -1.65630773687435 132 20 12.9549829051588 7.04501709484117 133 10 13.1432289966153 -3.14322899661533 134 15 13.2320940368421 1.76790596315792 135 12 12.8997683667448 -0.89976836674484 136 14 12.7366594166919 1.26334058330809 137 23 12.871261423943 10.128738576057 138 14 12.7382298709005 1.26177012909954 139 16 12.9416291073528 3.05837089264724 140 11 12.3912830704026 -1.39128307040265 141 12 12.5579651252579 -0.55796512525793 142 10 12.7045793690877 -2.70457936908769 143 14 12.065597184892 1.93440281510799 144 12 12.7421060973169 -0.742106097316853 145 12 12.6157143288609 -0.615714328860941 146 11 12.6881588914974 -1.68815889149738 147 12 12.973709154957 -0.973709154956978 148 13 13.0060923241752 -0.00609232417523302 149 11 12.8864145689388 -1.88641456893878 150 19 12.90797860554 6.09202139446 151 12 12.9793847285631 -0.97938472856311 152 17 12.6383168050755 4.36168319492451 153 9 13.0702524193837 -4.07025241938366 154 12 13.1270374120062 -1.1270374120062 155 19 12.6413834848597 6.35861651514026 156 18 13.1095784948026 4.89042150519744 157 15 12.6614512958853 2.33854870411474 158 14 12.6493648306737 1.35063516932629 159 11 12.142146866926 -1.14214686692603 160 14 12.5111897186203 1.48881028137971 161 11 12.5702804834507 -1.57028048345067 162 6 12.7898713045121 -6.7898713045121 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.974651261751625 0.05069747649675 0.025348738248375 8 0.948512880370103 0.102974239259795 0.0514871196298975 9 0.914716669781115 0.17056666043777 0.085283330218885 10 0.866160923918828 0.267678152162345 0.133839076081172 11 0.801930666455501 0.396138667088997 0.198069333544499 12 0.775999731111513 0.448000537776973 0.224000268888487 13 0.697630017491962 0.604739965016076 0.302369982508038 14 0.613011391718285 0.77397721656343 0.386988608281715 15 0.639553215927928 0.720893568144145 0.360446784072072 16 0.708178632377929 0.583642735244143 0.291821367622071 17 0.638699283547206 0.722601432905588 0.361300716452794 18 0.654803820608683 0.690392358782634 0.345196179391317 19 0.630945023056161 0.738109953887677 0.369054976943839 20 0.663036646197019 0.673926707605963 0.336963353802981 21 0.705701993636609 0.588596012726782 0.294298006363391 22 0.758511696025504 0.482976607948991 0.241488303974496 23 0.701553181029229 0.596893637941542 0.298446818970771 24 0.659972213609201 0.680055572781598 0.340027786390799 25 0.618306856403602 0.763386287192796 0.381693143596398 26 0.647594127455893 0.704811745088213 0.352405872544107 27 0.615908789184118 0.768182421631763 0.384091210815882 28 0.583443863140021 0.833112273719958 0.416556136859979 29 0.534373846420396 0.931252307159208 0.465626153579604 30 0.473939746463522 0.947879492927044 0.526060253536478 31 0.524948459359564 0.950103081280872 0.475051540640436 32 0.561016933183695 0.87796613363261 0.438983066816305 33 0.5350428171862 0.9299143656276 0.4649571828138 34 0.49974555355878 0.99949110711756 0.50025444644122 35 0.442504886931949 0.885009773863898 0.557495113068051 36 0.445156332257689 0.890312664515379 0.55484366774231 37 0.687694108057168 0.624611783885664 0.312305891942832 38 0.643064473216826 0.713871053566349 0.356935526783174 39 0.613168273132622 0.773663453734755 0.386831726867378 40 0.589939876238829 0.820120247522343 0.410060123761171 41 0.573568459220402 0.852863081559195 0.426431540779598 42 0.527408352886791 0.945183294226418 0.472591647113209 43 0.579627461897454 0.840745076205093 0.420372538102547 44 0.539551253708181 0.920897492583638 0.460448746291819 45 0.506124267092546 0.987751465814907 0.493875732907454 46 0.457059241032007 0.914118482064014 0.542940758967993 47 0.447588225737859 0.895176451475719 0.552411774262141 48 0.406050973341013 0.812101946682026 0.593949026658987 49 0.382103353027946 0.764206706055891 0.617896646972054 50 0.344884821842885 0.68976964368577 0.655115178157115 51 0.321154315910468 0.642308631820936 0.678845684089532 52 0.281999487492258 0.563998974984516 0.718000512507742 53 0.359555892339864 0.719111784679728 0.640444107660136 54 0.318123123730061 0.636246247460123 0.681876876269939 55 0.283754634133543 0.567509268267086 0.716245365866457 56 0.245925983450224 0.491851966900448 0.754074016549776 57 0.209236970005526 0.418473940011051 0.790763029994474 58 0.236597005383572 0.473194010767143 0.763402994616428 59 0.251247193275952 0.502494386551905 0.748752806724048 60 0.25538666491623 0.510773329832461 0.74461333508377 61 0.429681309438431 0.859362618876862 0.570318690561569 62 0.387614517644756 0.775229035289513 0.612385482355244 63 0.347039735021967 0.694079470043933 0.652960264978033 64 0.312759370941594 0.625518741883189 0.687240629058406 65 0.27290638645681 0.545812772913621 0.72709361354319 66 0.249045719068763 0.498091438137526 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0.122740270183044 0.245480540366087 0.877259729816956 85 0.10360771262827 0.20721542525654 0.89639228737173 86 0.087127539728944 0.174255079457888 0.912872460271056 87 0.0708566090509772 0.141713218101954 0.929143390949023 88 0.057439736661121 0.114879473322242 0.94256026333888 89 0.0533561430794602 0.10671228615892 0.94664385692054 90 0.212282062553519 0.424564125107038 0.787717937446481 91 0.184767537068918 0.369535074137837 0.815232462931082 92 0.168505494497614 0.337010988995228 0.831494505502386 93 0.14129425417453 0.28258850834906 0.85870574582547 94 0.126370244160916 0.252740488321831 0.873629755839084 95 0.122449852207645 0.24489970441529 0.877550147792355 96 0.108937090243947 0.217874180487894 0.891062909756053 97 0.113813159174538 0.227626318349075 0.886186840825462 98 0.100530994181124 0.201061988362248 0.899469005818876 99 0.0894257299378796 0.178851459875759 0.91057427006212 100 0.0878364394618957 0.175672878923791 0.912163560538104 101 0.0853174199999694 0.170634839999939 0.914682580000031 102 0.0803720789872222 0.160744157974444 0.919627921012778 103 0.0674477393981239 0.134895478796248 0.932552260601876 104 0.058728027449451 0.117456054898902 0.94127197255055 105 0.0603488242404242 0.120697648480848 0.939651175759576 106 0.101161251318755 0.202322502637511 0.898838748681245 107 0.0889855662684295 0.177971132536859 0.91101443373157 108 0.0880300474406345 0.176060094881269 0.911969952559366 109 0.0788551076168684 0.157710215233737 0.921144892383132 110 0.445897097907275 0.89179419581455 0.554102902092726 111 0.4016978694963 0.8033957389926 0.5983021305037 112 0.3744408754422 0.7488817508844 0.6255591245578 113 0.337943160611457 0.675886321222915 0.662056839388543 114 0.307310924970682 0.614621849941364 0.692689075029318 115 0.269477336637555 0.53895467327511 0.730522663362445 116 0.273442921051707 0.546885842103415 0.726557078948292 117 0.233955178508218 0.467910357016435 0.766044821491782 118 0.197015163509287 0.394030327018574 0.802984836490713 119 0.218079659077871 0.436159318155743 0.781920340922129 120 0.196719337871606 0.393438675743213 0.803280662128394 121 0.181721595793763 0.363443191587526 0.818278404206237 122 0.152483549007171 0.304967098014342 0.847516450992829 123 0.13015476226554 0.260309524531079 0.86984523773446 124 0.148745804090228 0.297491608180456 0.851254195909772 125 0.124718516862101 0.249437033724203 0.875281483137899 126 0.115763317028594 0.231526634057189 0.884236682971406 127 0.165920038267034 0.331840076534069 0.834079961732966 128 0.158733834613207 0.317467669226413 0.841266165386793 129 0.142407067252172 0.284814134504343 0.857592932747828 130 0.112702229725513 0.225404459451027 0.887297770274487 131 0.0939812961633866 0.187962592326773 0.906018703836613 132 0.196076952307092 0.392153904614184 0.803923047692908 133 0.204967156408419 0.409934312816839 0.79503284359158 134 0.171112097359414 0.342224194718828 0.828887902640586 135 0.139012858713566 0.278025717427133 0.860987141286434 136 0.110951380699197 0.221902761398394 0.889048619300803 137 0.488183280057995 0.97636656011599 0.511816719942005 138 0.429965463049503 0.859930926099007 0.570034536950497 139 0.435559125498837 0.871118250997674 0.564440874501163 140 0.372349974280828 0.744699948561656 0.627650025719172 141 0.307494094434442 0.614988188868884 0.692505905565558 142 0.29785302549804 0.59570605099608 0.70214697450196 143 0.240347696445575 0.480695392891149 0.759652303554425 144 0.18524648904097 0.37049297808194 0.81475351095903 145 0.147347348894566 0.294694697789133 0.852652651105434 146 0.123494176029723 0.246988352059445 0.876505823970277 147 0.0953965365282338 0.190793073056468 0.904603463471766 148 0.0639322637634996 0.127864527526999 0.9360677362365 149 0.0456857684368893 0.0913715368737786 0.95431423156311 150 0.10891074214513 0.217821484290259 0.89108925785487 151 0.0704802080659097 0.140960416131819 0.92951979193409 152 0.0511236432225465 0.102247286445093 0.948876356777454 153 0.42019806537384 0.84039613074768 0.57980193462616 154 0.84053406699164 0.318931866016719 0.159465933008359 155 0.729182094352706 0.541635811294588 0.270817905647294 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 0.0134228187919463 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290546197ghhni3y847qcbvz/10590u1290546294.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290546197ghhni3y847qcbvz/10590u1290546294.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290546197ghhni3y847qcbvz/1zq301290546294.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290546197ghhni3y847qcbvz/1zq301290546294.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290546197ghhni3y847qcbvz/2rz2l1290546294.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290546197ghhni3y847qcbvz/2rz2l1290546294.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290546197ghhni3y847qcbvz/3rz2l1290546294.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290546197ghhni3y847qcbvz/3rz2l1290546294.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290546197ghhni3y847qcbvz/4rz2l1290546294.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290546197ghhni3y847qcbvz/4rz2l1290546294.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290546197ghhni3y847qcbvz/5k91o1290546294.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290546197ghhni3y847qcbvz/5k91o1290546294.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290546197ghhni3y847qcbvz/6k91o1290546294.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290546197ghhni3y847qcbvz/6k91o1290546294.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290546197ghhni3y847qcbvz/7d0191290546294.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290546197ghhni3y847qcbvz/7d0191290546294.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290546197ghhni3y847qcbvz/8d0191290546294.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290546197ghhni3y847qcbvz/8d0191290546294.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290546197ghhni3y847qcbvz/9590u1290546294.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290546197ghhni3y847qcbvz/9590u1290546294.ps (open in new window)

Parameters (Session):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 4 ; 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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