Meervoudige lineaire regressie

*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, 22 Dec 2010 19:11:38 +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/Dec/22/t1293045013xnb6ygtp7r7nz10.htm/, Retrieved Wed, 22 Dec 2010 20:10:16 +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/Dec/22/t1293045013xnb6ygtp7r7nz10.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 24 24 11 7 8 25 25 6 17 8 30 17 12 10 8 19 18 8 12 9 22 18 10 12 7 22 16 10 11 4 25 20 11 11 11 23 16 16 12 7 17 18 11 13 7 21 17 13 14 12 19 23 12 16 10 19 30 8 11 10 15 23 12 10 8 16 18 11 11 8 23 15 4 15 4 27 12 9 9 9 22 21 8 11 8 14 15 8 17 7 22 20 14 17 11 23 31 15 11 9 23 27 16 18 11 21 34 9 14 13 19 21 14 10 8 18 31 11 11 8 20 19 8 15 9 23 16 9 15 6 25 20 9 13 9 19 21 9 16 9 24 22 9 13 6 22 17 10 9 6 25 24 16 18 16 26 25 11 18 5 29 26 8 12 7 32 25 9 17 9 25 17 16 9 6 29 32 11 9 6 28 33 16 12 5 17 13 12 18 12 28 32 12 12 7 29 25 14 18 10 26 29 9 14 9 25 22 10 15 8 14 18 9 16 5 25 17 10 10 8 26 20 12 11 8 20 15 14 14 10 18 20 14 9 6 32 33 10 12 8 25 29 14 17 7 25 23 16 5 4 23 26 9 12 8 21 18 10 12 8 20 20 6 6 4 15 11 8 24 20 30 28 13 12 8 24 26 10 12 8 26 22 8 14 6 24 17 7 7 4 22 12 15 13 8 14 14 9 12 9 24 17 10 13 6 24 21 12 14 7 24 19 13 8 9 24 18 10 11 5 19 10 11 9 5 31 29 8 11 8 22 31 9 13 8 27 19 13 10 6 19 9 11 11 8 25 20 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 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation CM[t] = -3.87026014455676 + 0.791349774058288DA[t] + 0.270704258738877PC[t] + 0.219843764606092PE[t] + 0.521408237815545PS[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) -3.87026014455676 2.544353 -1.5211 0.130281 0.06514 DA 0.791349774058288 0.129368 6.117 0 0 PC 0.270704258738877 0.131737 2.0549 0.04158 0.02079 PE 0.219843764606092 0.166072 1.3238 0.187536 0.093768 PS 0.521408237815545 0.087249 5.9761 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.634260918916661 R-squared 0.402286913265007 Adjusted R-squared 0.386761898025137 F-TEST (value) 25.9121750960921 F-TEST (DF numerator) 4 F-TEST (DF denominator) 154 p-value 2.22044604925031e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.48151208983068 Sum Squared Residuals 3092.92839413997 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 25.3383064212331 -1.33830642123309 2 25 21.5234732434939 3.47652675650608 3 17 22.880808149669 -5.88080814966899 4 18 19.9984863668756 -1.99848636687557 5 18 19.1585642661729 -1.1585642661729 6 16 20.3015762850773 -4.3015762850773 7 20 20.9355654459668 -0.93556544596678 8 16 22.2230050966366 -6.22300509663662 9 18 22.4426337403493 -4.4426337403493 10 17 20.8422220800589 -3.84222208005892 11 23 22.7520282343137 0.247971765686259 12 30 22.062399448521 7.93760055147898 13 23 15.4578461073313 7.5421538926687 14 18 18.4342616534289 -0.434261653428938 15 15 21.5634738028183 -6.56347380281835 16 12 18.3131003122037 -6.31310031220365 17 21 19.1378012640146 1.86219873598544 18 15 14.4967503403036 0.503249659696428 19 20 20.0723980306551 -0.0723980306551079 20 31 26.2212799712448 4.77872002875525 21 27 24.9487166636576 2.05128333634241 22 34 27.0318673024691 6.96813269753088 23 21 19.8064729026867 1.19352709731332 24 31 21.0597776771766 9.9402223228234 25 19 19.9992490893717 -0.99924908937171 26 16 20.4920852802051 -4.49208528020508 27 20 21.6667202360762 -1.66672023607619 28 21 18.6563935855234 2.34360641447657 29 22 22.0755475508178 -0.0755475508177946 30 17 19.5610870051518 -2.56108700515179 31 24 20.8338444577012 3.16615554229879 32 25 30.7381273145773 -5.7381273145773 33 26 25.9273217470655 0.0726782529345164 34 25 23.9329591151162 1.06704088488382 35 17 22.8676600473722 -5.86766004737222 36 32 27.6675760533131 4.33242394668688 37 33 23.1894189452061 9.81058105479386 38 13 22.0029462111371 -9.00294621113711 39 32 27.7361696355509 4.26383036444913 40 25 25.5341334979027 -0.534133497902692 41 29 27.8363651788242 1.16363482117583 42 22 22.0555472711556 -0.0555472711555851 43 18 17.1622669233757 0.837733076624342 44 17 21.717580730209 -4.71758073020897 45 20 22.0656444834678 -2.06564448346782 46 15 20.79059886343 -5.79059886343 47 20 22.5822822413443 -2.5822822413443 48 33 27.6491012186432 5.35089878135682 49 29 22.08564476313 6.91435523686997 50 23 26.3847213884515 -3.38472138845147 51 26 23.0166220622522 2.98337793774785 52 18 19.2086620378096 -1.20866203780956 53 20 19.4786035740523 0.521396425947702 54 11 11.2025626778838 -0.202562677883786 55 28 28.9965626842308 -0.996562684230813 56 26 23.9382858474893 2.06171415251066 57 22 22.6070530009456 -0.607053000945571 58 17 20.0832579654635 -3.08325796546347 59 12 15.9144743753898 -3.91447437538977 60 14 20.5776072761893 -6.57760727618935 61 17 20.9927305158623 -3.99273051586228 62 21 21.3952532548412 -0.395253254841174 63 19 23.4685008263027 -4.46850082630272 64 18 23.0753125771399 -5.07531257713993 65 10 18.0269597836796 -8.0269597836796 66 29 24.5337998940467 4.46620010595332 67 31 18.6680162428279 12.3319837571721 68 19 22.6078157234417 -3.60781572344171 69 9 20.3501486117217 -11.3501486117217 70 20 22.6062902784494 -2.60629027844944 71 28 17.6760602613296 10.3239397386704 72 19 18.1767054969868 0.823294503013169 73 30 23.3690680055256 6.63093199447445 74 29 27.2833340040419 1.71666599595808 75 26 21.6667202360762 4.33327976392381 76 23 19.4786035740523 3.5213964259477 77 13 22.9964276376277 -9.9964276376277 78 21 22.8653718798838 -1.86537187988381 79 19 22.0841193181378 -3.08411931813776 80 28 22.708011266715 5.29198873328499 81 23 25.9614356473142 -2.96143564731424 82 18 14.4782755056336 3.52172449436637 83 21 20.8105991430922 0.189400856907793 84 20 22.0254497791811 -2.02544977918114 85 23 20.3802461036961 2.61975389630388 86 21 21.13292661846 -0.132926618460004 87 21 21.6768174483884 -0.676817448388418 88 15 23.3961146075155 -8.39611460751546 89 28 27.1130404094698 0.886959590530243 90 19 17.6945350959996 1.30546490400043 91 26 21.6211864743166 4.37881352568343 92 10 13.4779419017776 -3.47794190177762 93 16 17.234084564629 -1.23408456462904 94 22 20.8938452966878 1.10615470331216 95 19 19.3776453082829 -0.377645308282863 96 31 29.0512158149131 1.94878418508689 97 31 25.5093627383014 5.49063726169858 98 29 24.8776617449003 4.12233825509966 99 19 17.4245935597568 1.57540644024317 100 22 18.7064913571601 3.29350864283992 101 23 22.2946285929278 0.705371407072249 102 15 16.1434584848497 -1.1434584848497 103 20 21.0218711403783 -1.02187114037834 104 18 19.6691125691801 -1.66911256918008 105 23 22.8129859407588 0.187014059241242 106 25 20.1495424042817 4.85045759571834 107 21 16.0918352682208 4.90816473177922 108 24 18.8762373501295 5.12376264987047 109 25 25.1584632159514 -0.158463215951451 110 17 19.5972739519955 -2.59727395199554 111 13 14.5476108344364 -1.54761083443636 112 28 18.8152796436845 9.1847203563155 113 21 19.8289554947995 1.17104450520045 114 25 27.2094346653622 -2.20943466536216 115 9 20.5825928770218 -11.5825928770218 116 16 18.0284852286719 -2.02848522867187 117 19 20.2737669605913 -1.27376696059126 118 17 19.0181530426818 -2.01815304268177 119 25 24.7187756867393 0.281224313260733 120 20 14.6579035900219 5.34209640997811 121 29 21.1655064228851 7.8344935771149 122 14 18.4858848700579 -4.48588487005786 123 22 26.4519836706592 -4.45198367065921 124 15 15.8319909442903 -0.831990944290274 125 19 25.568032277258 -6.56803227725803 126 20 22.1448828796205 -2.14488287962052 127 15 17.5179369256647 -2.51793692566469 128 20 22.0848820406339 -2.08488204063389 129 18 20.7612640939517 -2.76126409395169 130 33 25.5017478384398 7.49825216156016 131 22 23.2858218519299 -1.28582185192992 132 16 16.6016208487318 -0.601620848731829 133 17 19.3212429608835 -2.32124296088349 134 16 15.1615997156636 0.83840028433637 135 21 17.3929706227901 3.60702937720988 136 26 27.5864239222436 -1.58642392224364 137 18 20.8915571291994 -2.89155712919943 138 18 22.0732593833294 -4.07325938332939 139 17 18.6371560283574 -1.63715602835736 140 22 23.9946881948887 -1.99468819488872 141 30 23.6159583721215 6.38404162787845 142 30 27.0057775679376 2.9942224320624 143 24 29.0519871882406 -5.05198718824063 144 21 21.9437080946466 -0.943708094646622 145 21 25.4299301971865 -4.42993019718646 146 29 27.1661680951598 1.83383190484022 147 31 22.8676600473722 8.13233995262778 148 20 18.7181140144646 1.28188598553541 149 16 13.6930151864446 2.30698481355535 150 22 18.8770000726257 3.12299992737434 151 20 20.1821431846379 -0.182143184637921 152 28 27.3951522046197 0.604847795380281 153 38 27.1791220524943 10.8208779475057 154 22 18.267566550444 3.73243344955596 155 20 25.6204391923142 -5.62043919231425 156 17 17.9968622917052 -0.996862291705158 157 28 24.4589313628088 3.54106863719124 158 22 24.1472696772871 -2.14726967728707 159 31 26.3161574329763 4.68384256702373 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.211640447971904 0.423280895943808 0.788359552028096 9 0.103632597637002 0.207265195274004 0.896367402362998 10 0.0462833232433122 0.0925666464866244 0.953716676756688 11 0.13645345580862 0.27290691161724 0.86354654419138 12 0.67857177059138 0.64285645881724 0.32142822940862 13 0.643414076011461 0.713171847977077 0.356585923988539 14 0.567783558171661 0.864432883656677 0.432216441828339 15 0.569122557763125 0.86175488447375 0.430877442236875 16 0.513283482155145 0.97343303568971 0.486716517844855 17 0.43644528534343 0.872890570686861 0.56355471465657 18 0.392440587440326 0.784881174880652 0.607559412559674 19 0.33385110417708 0.66770220835416 0.66614889582292 20 0.389999767621081 0.779999535242162 0.610000232378919 21 0.365911887274288 0.731823774548576 0.634088112725712 22 0.385864828057294 0.771729656114588 0.614135171942706 23 0.332908279839805 0.66581655967961 0.667091720160195 24 0.563082579605268 0.873834840789464 0.436917420394732 25 0.497682619618305 0.99536523923661 0.502317380381695 26 0.473919166270782 0.947838332541564 0.526080833729218 27 0.415380302546625 0.83076060509325 0.584619697453375 28 0.363898694803445 0.72779738960689 0.636101305196555 29 0.307021599800677 0.614043199601354 0.692978400199323 30 0.257865594089581 0.515731188179162 0.742134405910419 31 0.302408817409684 0.604817634819369 0.697591182590316 32 0.366853591250795 0.733707182501589 0.633146408749205 33 0.339028600436958 0.678057200873915 0.660971399563042 34 0.361207893241441 0.722415786482883 0.638792106758559 35 0.368444546953223 0.736889093906446 0.631555453046777 36 0.361474490254024 0.722948980508047 0.638525509745976 37 0.577578200388808 0.844843599222383 0.422421799611192 38 0.782605170457609 0.434789659084783 0.217394829542391 39 0.784405290321042 0.431189419357915 0.215594709678958 40 0.74349492159423 0.513010156811539 0.25650507840577 41 0.702884392974118 0.594231214051765 0.297115607025882 42 0.655146396262042 0.689707207475916 0.344853603737958 43 0.611368554942783 0.777262890114433 0.388631445057217 44 0.597432376386062 0.805135247227876 0.402567623613938 45 0.560291520252913 0.879416959494173 0.439708479747087 46 0.599847311253943 0.800305377492114 0.400152688746057 47 0.56831484272695 0.8633703145461 0.43168515727305 48 0.571709334877341 0.856581330245317 0.428290665122659 49 0.63706095531445 0.725878089371101 0.362939044685551 50 0.61013593548098 0.77972812903804 0.38986406451902 51 0.577058853704684 0.845882292590631 0.422941146295316 52 0.529987311062677 0.940025377874647 0.470012688937323 53 0.481404968014638 0.962809936029275 0.518595031985362 54 0.432210934933712 0.864421869867423 0.567789065066288 55 0.385690530342628 0.771381060685257 0.614309469657372 56 0.347423760499948 0.694847520999895 0.652576239500052 57 0.304294931656246 0.608589863312492 0.695705068343754 58 0.278408906729776 0.556817813459553 0.721591093270224 59 0.268493664658882 0.536987329317763 0.731506335341118 60 0.309999065691785 0.61999813138357 0.690000934308215 61 0.302880462430169 0.605760924860339 0.69711953756983 62 0.264127601579889 0.528255203159777 0.735872398420111 63 0.260954800192686 0.521909600385371 0.739045199807314 64 0.295323528401571 0.590647056803142 0.704676471598429 65 0.378838368578731 0.757676737157462 0.621161631421269 66 0.373223113883677 0.746446227767355 0.626776886116323 67 0.692833117263778 0.614333765472443 0.307166882736222 68 0.678836116845935 0.64232776630813 0.321163883154065 69 0.860802760439991 0.278394479120017 0.139197239560009 70 0.843539452707712 0.312921094584577 0.156460547292288 71 0.93968160883136 0.120636782337279 0.0603183911686395 72 0.925094822071224 0.149810355857553 0.0749051779287764 73 0.943137465445567 0.113725069108866 0.056862534554433 74 0.931796158256514 0.136407683486972 0.0682038417434858 75 0.932090999164874 0.135818001670252 0.0679090008351258 76 0.926780576332528 0.146438847334944 0.073219423667472 77 0.97445070489384 0.0510985902123209 0.0255492951061604 78 0.968310495105328 0.0633790097893434 0.0316895048946717 79 0.963671684738382 0.072656630523236 0.036328315261618 80 0.967257622753572 0.0654847544928569 0.0327423772464285 81 0.962112924664314 0.075774150671372 0.037887075335686 82 0.959083407520895 0.0818331849582096 0.0409165924791048 83 0.948206301556903 0.103587396886194 0.051793698443097 84 0.93779673222795 0.124406535544103 0.0622032677720513 85 0.928153851712837 0.143692296574325 0.0718461482871627 86 0.914374742126224 0.171250515747551 0.0856252578737755 87 0.89556827902722 0.20886344194556 0.10443172097278 88 0.940864099797194 0.118271800405613 0.0591359002028063 89 0.927705181177519 0.144589637644963 0.0722948188224814 90 0.91184444641274 0.176311107174519 0.0881555535872597 91 0.910504610510087 0.178990778979827 0.0894953894899133 92 0.902430229361421 0.195139541277158 0.0975697706385788 93 0.884265472298464 0.231469055403073 0.115734527701536 94 0.862375734296771 0.275248531406458 0.137624265703229 95 0.834848200846674 0.330303598306652 0.165151799153326 96 0.808480417822789 0.383039164354423 0.191519582177211 97 0.821519834174295 0.35696033165141 0.178480165825705 98 0.816900585951684 0.366198828096632 0.183099414048316 99 0.786465930556235 0.42706813888753 0.213534069443765 100 0.767618743754847 0.464762512490307 0.232381256245153 101 0.729659029972167 0.540681940055665 0.270340970027833 102 0.694571311266634 0.610857377466733 0.305428688733367 103 0.656507833363714 0.686984333272573 0.343492166636286 104 0.61743732940974 0.765125341180519 0.382562670590259 105 0.570656931449554 0.858686137100891 0.429343068550446 106 0.567469070023492 0.865061859953016 0.432530929976508 107 0.573804781061315 0.85239043787737 0.426195218938685 108 0.595237846149084 0.809524307701832 0.404762153850916 109 0.545689630075504 0.908620739848991 0.454310369924496 110 0.522797637479419 0.954404725041163 0.477202362520581 111 0.482248827408853 0.964497654817707 0.517751172591147 112 0.675340758243383 0.649318483513234 0.324659241756617 113 0.664486089421435 0.67102782115713 0.335513910578565 114 0.623160547787972 0.753678904424055 0.376839452212027 115 0.815609371193272 0.368781257613456 0.184390628806728 116 0.79809273041599 0.40381453916802 0.20190726958401 117 0.775528219051172 0.448943561897656 0.224471780948828 118 0.745611902436625 0.50877619512675 0.254388097563375 119 0.699032167836682 0.601935664326636 0.300967832163318 120 0.732820522987982 0.534358954024037 0.267179477012018 121 0.790298781620695 0.419402436758609 0.209701218379305 122 0.786815173206344 0.426369653587312 0.213184826793656 123 0.786111168750038 0.427777662499924 0.213888831249962 124 0.74203433714344 0.515931325713121 0.257965662856561 125 0.789696818677348 0.420606362645304 0.210303181322652 126 0.767002919916458 0.465994160167084 0.232997080083542 127 0.759016093732014 0.481967812535972 0.240983906267986 128 0.730895379905703 0.538209240188594 0.269104620094297 129 0.707901038180671 0.584197923638658 0.292098961819329 130 0.77456522819741 0.450869543605181 0.22543477180259 131 0.725641863815221 0.548716272369557 0.274358136184779 132 0.670085220201407 0.659829559597186 0.329914779798593 133 0.669418488223931 0.661163023552137 0.330581511776069 134 0.612810780987793 0.774378438024415 0.387189219012208 135 0.577033145406415 0.845933709187169 0.422966854593584 136 0.551701049992759 0.896597900014483 0.448298950007241 137 0.559075093613189 0.881849812773622 0.440924906386811 138 0.579930742398671 0.840138515202658 0.420069257601329 139 0.528308519482286 0.943382961035429 0.471691480517714 140 0.452096764119216 0.904193528238431 0.547903235880784 141 0.564241474836814 0.871517050326372 0.435758525163186 142 0.505689549919466 0.988620900161068 0.494310450080534 143 0.457157618031363 0.914315236062726 0.542842381968637 144 0.372092524386499 0.744185048772999 0.6279074756135 145 0.440998172515025 0.88199634503005 0.559001827484975 146 0.344222129691138 0.688444259382275 0.655777870308862 147 0.386815216333081 0.773630432666162 0.613184783666919 148 0.282387872872698 0.564775745745395 0.717612127127302 149 0.197245113561711 0.394490227123422 0.802754886438289 150 0.155347275613373 0.310694551226746 0.844652724386627 151 0.116295363728262 0.232590727456525 0.883704636271738 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 7 0.0486111111111111 OK

Charts produced by software:

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Parameters (Session):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 5 ; 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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