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, 13 Dec 2010 11:25:01 +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/13/t12922393982gbuby474ro5lcu.htm/, Retrieved Mon, 13 Dec 2010 12:23:38 +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/13/t12922393982gbuby474ro5lcu.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 «

24 14 11 12 24 25 11 7 8 25 17 6 17 8 30 18 12 10 8 19 18 8 12 9 22 16 10 12 7 22 20 10 11 4 25 16 11 11 11 23 18 16 12 7 17 17 11 13 7 21 23 13 14 12 19 30 12 16 10 19 23 8 11 10 15 18 12 10 8 16 15 11 11 8 23 12 4 15 4 27 21 9 9 9 22 15 8 11 8 14 20 8 17 7 22 31 14 17 11 23 27 15 11 9 23 34 16 18 11 21 21 9 14 13 19 31 14 10 8 18 19 11 11 8 20 16 8 15 9 23 20 9 15 6 25 21 9 13 9 19 22 9 16 9 24 17 9 13 6 22 24 10 9 6 25 25 16 18 16 26 26 11 18 5 29 25 8 12 7 32 17 9 17 9 25 32 16 9 6 29 33 11 9 6 28 13 16 12 5 17 32 12 18 12 28 25 12 12 7 29 29 14 18 10 26 22 9 14 9 25 18 10 15 8 14 17 9 16 5 25 20 10 10 8 26 15 12 11 8 20 20 14 14 10 18 33 14 9 6 32 29 10 12 8 25 23 14 17 7 25 26 16 5 4 23 18 9 12 8 21 20 10 12 8 20 11 6 6 4 15 28 8 24 20 30 26 13 12 8 24 22 10 12 8 26 17 8 14 6 24 12 7 7 4 22 14 15 13 8 14 17 9 12 9 24 21 10 13 6 24 19 12 14 7 24 18 13 8 9 24 10 10 11 5 19 29 11 9 5 31 31 8 11 8 22 19 9 13 8 27 9 13 10 6 19 20 11 11 8 25 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 10 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation CM[t] = -3.87026014455679 + 0.791349774058288D[t] + 0.270704258738879PE[t] + 0.21984376460609PC[t] + 0.521408237815546PS[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) -3.87026014455679 2.544353 -1.5211 0.130281 0.06514 D 0.791349774058288 0.129368 6.117 0 0 PE 0.270704258738879 0.131737 2.0549 0.04158 0.02079 PC 0.21984376460609 0.166072 1.3238 0.187536 0.093768 PS 0.521408237815546 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) 25.9121750960920 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 3092.92839413998 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 25.3383064212335 -1.33830642123346 2 25 21.5234732434939 3.47652675650607 3 17 22.880808149669 -5.88080814966899 4 18 19.9984863668756 -1.99848636687556 5 18 19.1585642661729 -1.15856426617294 6 16 20.3015762850773 -4.3015762850773 7 20 20.9355654459668 -0.935565445966783 8 16 22.2230050966366 -6.22300509663661 9 18 22.4426337403493 -4.4426337403493 10 17 20.8422220800589 -3.84222208005892 11 23 22.7520282343137 0.247971765686269 12 30 22.0623994485210 7.93760055147898 13 23 15.4578461073313 7.5421538926687 14 18 18.4342616534289 -0.434261653428935 15 15 21.5634738028183 -6.56347380281834 16 12 18.3131003122037 -6.31310031220366 17 21 19.1378012640146 1.86219873598545 18 15 14.4967503403036 0.503249659696426 19 20 20.0723980306551 -0.0723980306551169 20 31 26.2212799712447 4.77872002875525 21 27 24.9487166636576 2.05128333634242 22 34 27.0318673024691 6.96813269753089 23 21 19.8064729026867 1.19352709731333 24 31 21.0597776771766 9.9402223228234 25 19 19.9992490893717 -0.999249089371705 26 16 20.4920852802051 -4.49208528020508 27 20 21.6667202360762 -1.66672023607619 28 21 18.6563935855234 2.34360641447657 29 22 22.0755475508178 -0.0755475508177945 30 17 19.5610870051518 -2.5610870051518 31 24 20.8338444577012 3.16615554229879 32 25 30.7381273145773 -5.73812731457728 33 26 25.9273217470655 0.0726782529345073 34 25 23.9329591151162 1.06704088488383 35 17 22.8676600473722 -5.86766004737222 36 32 27.6675760533131 4.33242394668689 37 33 23.1894189452061 9.81058105479388 38 13 22.0029462111371 -9.00294621113711 39 32 27.7361696355509 4.26383036444914 40 25 25.5341334979027 -0.534133497902686 41 29 27.8363651788242 1.16363482117583 42 22 22.0555472711556 -0.0555472711555819 43 18 17.1622669233757 0.837733076624338 44 17 21.717580730209 -4.71758073020898 45 20 22.0656444834678 -2.06564448346781 46 15 20.79059886343 -5.79059886342999 47 20 22.5822822413443 -2.58228224134429 48 33 27.6491012186432 5.35089878135683 49 29 22.0856447631300 6.91435523686998 50 23 26.3847213884515 -3.38472138845148 51 26 23.0166220622521 2.98337793774786 52 18 19.2086620378096 -1.20866203780955 53 20 19.4786035740523 0.521396425947703 54 11 11.2025626778838 -0.202562677883789 55 28 28.9965626842308 -0.996562684230797 56 26 23.9382858474893 2.06171415251066 57 22 22.6070530009456 -0.607053000945567 58 17 20.0832579654635 -3.08325796546348 59 12 15.9144743753898 -3.91447437538977 60 14 20.5776072761893 -6.57760727618934 61 17 20.9927305158623 -3.99273051586228 62 21 21.3952532548412 -0.395253254841176 63 19 23.4685008263027 -4.46850082630272 64 18 23.0753125771399 -5.07531257713991 65 10 18.0269597836796 -8.0269597836796 66 29 24.5337998940467 4.46620010595333 67 31 18.6680162428279 12.3319837571721 68 19 22.6078157234417 -3.6078157234417 69 9 20.3501486117217 -11.3501486117217 70 20 22.6062902784494 -2.60629027844943 71 28 17.6760602613296 10.3239397386704 72 19 18.1767054969868 0.823294503013172 73 30 23.3690680055255 6.63093199447445 74 29 27.2833340040419 1.71666599595809 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 22.0841193181377 -3.08411931813775 80 28 22.708011266715 5.29198873328499 81 23 25.9614356473142 -2.96143564731423 82 18 14.4782755056336 3.52172449436637 83 21 20.8105991430922 0.189400856907795 84 20 22.0254497791811 -2.02544977918114 85 23 20.3802461036961 2.61975389630388 86 21 21.13292661846 -0.132926618460010 87 21 21.6768174483884 -0.676817448388418 88 15 23.3961146075154 -8.39611460751544 89 28 27.1130404094697 0.886959590530259 90 19 17.6945350959996 1.30546490400043 91 26 21.6211864743166 4.37881352568343 92 10 13.4779419017776 -3.47794190177762 93 16 17.2340845646290 -1.23408456462904 94 22 20.8938452966878 1.10615470331216 95 19 19.3776453082829 -0.377645308282855 96 31 29.0512158149131 1.94878418508689 97 31 25.5093627383014 5.49063726169859 98 29 24.8776617449003 4.12233825509966 99 19 17.4245935597568 1.57540644024317 100 22 18.7064913571601 3.29350864283991 101 23 22.2946285929277 0.705371407072252 102 15 16.1434584848497 -1.14345848484971 103 20 21.0218711403783 -1.02187114037834 104 18 19.6691125691801 -1.66911256918008 105 23 22.8129859407587 0.187014059241253 106 25 20.1495424042817 4.85045759571834 107 21 16.0918352682208 4.90816473177922 108 24 18.8762373501295 5.12376264987048 109 25 25.1584632159514 -0.158463215951443 110 17 19.5972739519955 -2.59727395199554 111 13 14.5476108344364 -1.54761083443636 112 28 18.8152796436845 9.1847203563155 113 21 19.8289554947995 1.17104450520046 114 25 27.2094346653622 -2.20943466536215 115 9 20.5825928770218 -11.5825928770218 116 16 18.0284852286719 -2.02848522867188 117 19 20.2737669605913 -1.27376696059127 118 17 19.0181530426818 -2.01815304268177 119 25 24.7187756867393 0.281224313260737 120 20 14.6579035900219 5.3420964099781 121 29 21.1655064228851 7.8344935771149 122 14 18.4858848700579 -4.48588487005786 123 22 26.4519836706592 -4.4519836706592 124 15 15.8319909442903 -0.831990944290269 125 19 25.5680322772580 -6.56803227725802 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 -1.28582185192991 132 16 16.6016208487318 -0.60162084873183 133 17 19.3212429608835 -2.32124296088350 134 16 15.1615997156636 0.838400284336364 135 21 17.3929706227901 3.60702937720988 136 26 27.5864239222436 -1.58642392224364 137 18 20.8915571291994 -2.89155712919943 138 18 22.0732593833294 -4.07325938332938 139 17 18.6371560283574 -1.63715602835736 140 22 23.9946881948887 -1.99468819488870 141 30 23.6159583721215 6.38404162787847 142 30 27.0057775679376 2.99422243206241 143 24 29.0519871882406 -5.05198718824062 144 21 21.9437080946466 -0.943708094646615 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 13.6930151864447 2.30698481355535 150 22 18.8770000726257 3.12299992737434 151 20 20.1821431846379 -0.182143184637916 152 28 27.3951522046197 0.604847795380283 153 38 27.1791220524943 10.8208779475057 154 22 18.2675665504440 3.73243344955596 155 20 25.6204391923142 -5.62043919231424 156 17 17.9968622917052 -0.996862291705163 157 28 24.4589313628087 3.54106863719125 158 22 24.1472696772871 -2.14726967728707 159 31 26.3161574329763 4.68384256702374 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 0.0462833232433121 0.0925666464866241 0.953716676756688 11 0.136453455808620 0.272906911617241 0.86354654419138 12 0.67857177059138 0.64285645881724 0.32142822940862 13 0.643414076011461 0.713171847977077 0.356585923988539 14 0.567783558171662 0.864432883656676 0.432216441828338 15 0.569122557763125 0.86175488447375 0.430877442236875 16 0.513283482155147 0.973433035689707 0.486716517844853 17 0.436445285343431 0.872890570686862 0.563554714656569 18 0.392440587440326 0.784881174880652 0.607559412559674 19 0.33385110417708 0.66770220835416 0.66614889582292 20 0.389999767621082 0.779999535242163 0.610000232378918 21 0.365911887274289 0.731823774548578 0.634088112725711 22 0.385864828057293 0.771729656114586 0.614135171942707 23 0.332908279839804 0.665816559679609 0.667091720160196 24 0.563082579605269 0.873834840789462 0.436917420394731 25 0.497682619618304 0.99536523923661 0.502317380381696 26 0.473919166270782 0.947838332541563 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 0.302408817409685 0.604817634819371 0.697591182590314 32 0.366853591250794 0.733707182501588 0.633146408749206 33 0.339028600436958 0.678057200873916 0.660971399563042 34 0.361207893241441 0.722415786482883 0.638792106758559 35 0.368444546953223 0.736889093906445 0.631555453046777 36 0.361474490254023 0.722948980508045 0.638525509745977 37 0.577578200388808 0.844843599222383 0.422421799611192 38 0.78260517045761 0.434789659084782 0.217394829542391 39 0.784405290321043 0.431189419357913 0.215594709678957 40 0.74349492159423 0.513010156811539 0.256505078405769 41 0.702884392974117 0.594231214051766 0.297115607025883 42 0.655146396262043 0.689707207475915 0.344853603737957 43 0.611368554942786 0.777262890114429 0.388631445057214 44 0.597432376386062 0.805135247227876 0.402567623613938 45 0.56029152025291 0.879416959494179 0.439708479747090 46 0.599847311253942 0.800305377492116 0.400152688746058 47 0.568314842726951 0.863370314546097 0.431685157273049 48 0.571709334877340 0.85658133024532 0.42829066512266 49 0.63706095531445 0.725878089371101 0.362939044685550 50 0.61013593548098 0.77972812903804 0.38986406451902 51 0.577058853704684 0.845882292590631 0.422941146295316 52 0.529987311062677 0.940025377874647 0.470012688937323 53 0.481404968014638 0.962809936029277 0.518595031985362 54 0.432210934933713 0.864421869867425 0.567789065066287 55 0.385690530342628 0.771381060685257 0.614309469657372 56 0.347423760499948 0.694847520999896 0.652576239500052 57 0.304294931656246 0.608589863312491 0.695705068343754 58 0.278408906729775 0.55681781345955 0.721591093270225 59 0.268493664658881 0.536987329317763 0.731506335341119 60 0.309999065691784 0.619998131383569 0.690000934308216 61 0.302880462430169 0.605760924860338 0.69711953756983 62 0.264127601579887 0.528255203159775 0.735872398420113 63 0.260954800192687 0.521909600385374 0.739045199807313 64 0.295323528401571 0.590647056803141 0.70467647159843 65 0.378838368578730 0.757676737157461 0.62116163142127 66 0.373223113883682 0.746446227767364 0.626776886116318 67 0.692833117263778 0.614333765472443 0.307166882736222 68 0.678836116845937 0.642327766308126 0.321163883154063 69 0.860802760439989 0.278394479120022 0.139197239560011 70 0.84353945270771 0.31292109458458 0.15646054729229 71 0.939681608831361 0.120636782337278 0.0603183911686388 72 0.925094822071223 0.149810355857554 0.0749051779287768 73 0.943137465445567 0.113725069108867 0.0568625345544334 74 0.931796158256513 0.136407683486974 0.0682038417434868 75 0.932090999164874 0.135818001670252 0.067909000835126 76 0.926780576332529 0.146438847334943 0.0732194236674715 77 0.97445070489384 0.051098590212321 0.0255492951061605 78 0.968310495105328 0.0633790097893433 0.0316895048946717 79 0.963671684738382 0.072656630523236 0.036328315261618 80 0.967257622753572 0.0654847544928568 0.0327423772464284 81 0.962112924664314 0.075774150671372 0.037887075335686 82 0.959083407520895 0.0818331849582102 0.0409165924791051 83 0.948206301556903 0.103587396886193 0.0517936984430967 84 0.93779673222795 0.124406535544102 0.0622032677720508 85 0.928153851712837 0.143692296574326 0.0718461482871632 86 0.914374742126224 0.171250515747551 0.0856252578737754 87 0.89556827902722 0.208863441945561 0.104431720972780 88 0.940864099797194 0.118271800405612 0.0591359002028062 89 0.927705181177519 0.144589637644963 0.0722948188224815 90 0.91184444641274 0.176311107174520 0.0881555535872599 91 0.910504610510087 0.178990778979827 0.0894953894899133 92 0.902430229361421 0.195139541277158 0.0975697706385788 93 0.884265472298464 0.231469055403072 0.115734527701536 94 0.862375734296772 0.275248531406457 0.137624265703228 95 0.834848200846674 0.330303598306652 0.165151799153326 96 0.80848041782279 0.383039164354421 0.191519582177211 97 0.821519834174296 0.356960331651409 0.178480165825704 98 0.816900585951684 0.366198828096632 0.183099414048316 99 0.786465930556236 0.427068138887528 0.213534069443764 100 0.767618743754846 0.464762512490308 0.232381256245154 101 0.729659029972167 0.540681940055667 0.270340970027833 102 0.694571311266634 0.610857377466733 0.305428688733366 103 0.656507833363714 0.686984333272572 0.343492166636286 104 0.617437329409741 0.765125341180519 0.382562670590259 105 0.570656931449555 0.85868613710089 0.429343068550445 106 0.567469070023491 0.865061859953018 0.432530929976509 107 0.573804781061314 0.852390437877371 0.426195218938686 108 0.595237846149083 0.809524307701833 0.404762153850917 109 0.545689630075504 0.908620739848992 0.454310369924496 110 0.522797637479418 0.954404725041164 0.477202362520582 111 0.482248827408852 0.964497654817705 0.517751172591148 112 0.675340758243383 0.649318483513234 0.324659241756617 113 0.664486089421435 0.67102782115713 0.335513910578565 114 0.623160547787974 0.753678904424053 0.376839452212026 115 0.815609371193271 0.368781257613458 0.184390628806729 116 0.798092730415991 0.403814539168018 0.201907269584009 117 0.775528219051172 0.448943561897656 0.224471780948828 118 0.745611902436624 0.508776195126752 0.254388097563376 119 0.699032167836682 0.601935664326636 0.300967832163318 120 0.732820522987983 0.534358954024033 0.267179477012017 121 0.790298781620696 0.419402436758609 0.209701218379304 122 0.786815173206343 0.426369653587313 0.213184826793657 123 0.786111168750038 0.427777662499924 0.213888831249962 124 0.742034337143441 0.515931325713117 0.257965662856559 125 0.789696818677349 0.420606362645302 0.210303181322651 126 0.767002919916458 0.465994160167084 0.232997080083542 127 0.759016093732014 0.481967812535972 0.240983906267986 128 0.730895379905704 0.538209240188593 0.269104620094296 129 0.70790103818067 0.584197923638659 0.292098961819329 130 0.77456522819741 0.45086954360518 0.22543477180259 131 0.725641863815222 0.548716272369556 0.274358136184778 132 0.670085220201407 0.659829559597185 0.329914779798593 133 0.669418488223932 0.661163023552137 0.330581511776068 134 0.612810780987793 0.774378438024414 0.387189219012207 135 0.577033145406415 0.84593370918717 0.422966854593585 136 0.551701049992759 0.896597900014483 0.448298950007241 137 0.559075093613188 0.881849812773623 0.440924906386812 138 0.579930742398671 0.840138515202658 0.420069257601329 139 0.528308519482285 0.94338296103543 0.471691480517715 140 0.452096764119216 0.904193528238431 0.547903235880784 141 0.564241474836814 0.871517050326371 0.435758525163186 142 0.505689549919468 0.988620900161064 0.494310450080532 143 0.457157618031363 0.914315236062726 0.542842381968637 144 0.372092524386501 0.744185048773001 0.6279074756135 145 0.440998172515025 0.88199634503005 0.559001827484975 146 0.344222129691138 0.688444259382276 0.655777870308862 147 0.386815216333081 0.773630432666162 0.613184783666919 148 0.282387872872698 0.564775745745395 0.717612127127302 149 0.197245113561711 0.394490227123422 0.802754886438289 150 0.155347275613374 0.310694551226747 0.844652724386626 151 0.116295363728262 0.232590727456524 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:

http://www.freestatistics.org/blog/date/2010/Dec/13/t12922393982gbuby474ro5lcu/101ajb1292239489.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t12922393982gbuby474ro5lcu/101ajb1292239489.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t12922393982gbuby474ro5lcu/1504k1292239489.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t12922393982gbuby474ro5lcu/1504k1292239489.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t12922393982gbuby474ro5lcu/2504k1292239489.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t12922393982gbuby474ro5lcu/2504k1292239489.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t12922393982gbuby474ro5lcu/3504k1292239489.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t12922393982gbuby474ro5lcu/3504k1292239489.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t12922393982gbuby474ro5lcu/4ga3n1292239489.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t12922393982gbuby474ro5lcu/4ga3n1292239489.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t12922393982gbuby474ro5lcu/5ga3n1292239489.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t12922393982gbuby474ro5lcu/5ga3n1292239489.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t12922393982gbuby474ro5lcu/6ga3n1292239489.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t12922393982gbuby474ro5lcu/6ga3n1292239489.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t12922393982gbuby474ro5lcu/7r12q1292239489.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t12922393982gbuby474ro5lcu/7r12q1292239489.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t12922393982gbuby474ro5lcu/81ajb1292239489.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t12922393982gbuby474ro5lcu/81ajb1292239489.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t12922393982gbuby474ro5lcu/91ajb1292239489.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t12922393982gbuby474ro5lcu/91ajb1292239489.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') }

Copyright

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

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by