*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: Sun, 19 Dec 2010 14:57:09 +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/19/t12927705422fufup2jnwxddj7.htm/, Retrieved Sun, 19 Dec 2010 15:55:42 +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/19/t12927705422fufup2jnwxddj7.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 «

9 24 14 11 12 24 26 9 25 11 7 8 25 23 9 17 6 17 8 30 25 9 18 12 10 8 19 23 9 18 8 12 9 22 19 9 16 10 12 7 22 29 10 20 10 11 4 25 25 10 16 11 11 11 23 21 10 18 16 12 7 17 22 10 17 11 13 7 21 25 10 23 13 14 12 19 24 10 30 12 16 10 19 18 10 23 8 11 10 15 22 10 18 12 10 8 16 15 10 15 11 11 8 23 22 10 12 4 15 4 27 28 10 21 9 9 9 22 20 10 15 8 11 8 14 12 10 20 8 17 7 22 24 10 31 14 17 11 23 20 10 27 15 11 9 23 21 10 34 16 18 11 21 20 10 21 9 14 13 19 21 10 31 14 10 8 18 23 10 19 11 11 8 20 28 10 16 8 15 9 23 24 10 20 9 15 6 25 24 10 21 9 13 9 19 24 10 22 9 16 9 24 23 10 17 9 13 6 22 23 10 24 10 9 6 25 29 10 25 16 18 16 26 24 10 26 11 18 5 29 18 10 25 8 12 7 32 25 10 17 9 17 9 25 21 10 32 16 9 6 29 26 10 33 11 9 6 28 22 10 13 16 12 5 17 22 10 32 12 18 12 28 22 10 25 12 12 7 29 23 10 29 14 18 10 26 30 10 22 9 14 9 25 23 10 18 10 15 8 14 17 10 17 9 16 5 25 23 10 20 10 10 8 26 23 10 15 12 11 8 20 25 10 20 14 14 10 18 24 10 33 14 9 6 32 24 10 29 10 12 8 25 23 10 23 14 17 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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation PersonalStandards[t] = + 21.4357024204095 -1.45276649903959Month[t] + 0.316958593741161ConcernOverMistakes[t] -0.333187590337108DoubtsAboutActions[t] + 0.191039573493092ParentalExpectations[t] + 0.0627374930000941ParentalCriticism[t] + 0.402168449432824Organization[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) 21.4357024204095 14.544837 1.4738 0.142612 0.071306 Month -1.45276649903959 1.43617 -1.0116 0.313358 0.156679 ConcernOverMistakes 0.316958593741161 0.054636 5.8012 0 0 DoubtsAboutActions -0.333187590337108 0.107323 -3.1045 0.002274 0.001137 ParentalExpectations 0.191039573493092 0.101966 1.8736 0.062911 0.031455 ParentalCriticism 0.0627374930000941 0.130755 0.4798 0.632053 0.316026 Organization 0.402168449432824 0.071728 5.6069 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.607615158935307 R-squared 0.369196181367979 Adjusted R-squared 0.344296030632504 F-TEST (value) 14.8270661206077 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 2.65010235978025e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.39721020256090 Sum Squared Residuals 1754.23764837835 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 24.6138488238001 -0.613848823800054 2 25 23.7087565742813 1.29124342571867 3 30 25.5537584098342 4.44624159016584 4 19 21.7299775482354 -2.72997754823537 5 22 21.8988707518388 0.101129248161214 6 22 24.4947878920103 -2.49478789201030 7 25 22.3219299177107 2.67807008228931 8 23 19.5513966056783 3.44860339432171 9 17 18.8616338924006 -1.86163389240061 10 21 21.6081581721366 -0.608158172136559 11 19 22.9460931429700 -3.94609314297004 12 19 23.3415843538843 -4.34158435388433 13 15 23.1091004893105 -8.10910048931047 14 16 17.0598634537332 -1.05986345373318 15 23 19.4483939823697 3.55160601763033 16 27 23.7560503520749 3.24394964792511 17 22 20.8928421726391 1.10715782736088 18 14 16.4262722590528 -2.42627225905275 19 22 23.9205865689109 -1.92058656891091 20 23 24.0502817323101 -1.05028173231011 21 23 21.5797157894824 1.42028421051756 22 21 24.5258219063525 -3.52582190635246 23 19 22.5011584615378 -3.50115846153778 24 18 23.7312975871567 -5.73129758715665 25 20 23.1292390539313 -3.12923905393126 26 23 22.3961480329603 0.603851967039729 27 25 23.1425823385875 1.85741766141248 28 19 23.2656742643428 -4.26567426434278 29 24 23.7535831291304 0.246416870869606 30 22 21.4074589609450 0.592541039054967 31 25 24.9418339294206 0.0581660705793739 32 26 23.5955558254138 2.40444417458621 33 29 22.4753292512425 6.5246707487575 34 32 24.9523501195841 7.04764988041592 35 25 21.5554928350520 3.44450716494796 36 29 24.2718717890288 4.72812821097121 37 28 24.6460945367242 3.35390546327581 38 17 17.1513659376946 -0.151365937694621 39 28 26.0917294720843 1.90827052791568 40 29 22.81526285937 6.18473714063001 41 26 27.5663511196490 -1.56635111964903 42 25 23.3715039821442 1.62849601785579 43 14 19.4857734007385 -5.48577340073851 44 25 21.9178401884242 3.08215981157578 45 26 21.5775034173523 4.42249658264768 46 20 20.3217117403310 -0.321711740331039 47 18 21.5365547854093 -3.53655478540926 48 32 24.4508686645785 7.54913133542148 49 25 24.8122099080089 0.187790091991051 50 25 21.6658314598133 3.33416854018673 51 23 20.6761500477436 2.32384995225638 52 21 22.0610214166261 -1.06102141662611 53 20 23.9704248115026 -3.97042481150262 54 15 16.2273390230278 -1.22733902302779 55 30 27.0004459445618 2.99955405543824 56 24 25.2747820523711 -1.27478205237109 57 26 24.2021735495521 1.79782645044788 58 23 19.4483939823697 3.55160601763033 59 22 21.2281709931188 0.771829006881173 60 14 15.7677534776693 -1.76775347766932 61 24 22.2089687653179 1.79103123468213 62 24 22.7442741950054 1.25572580499461 63 22 23.0420213929707 -1.04202139297071 64 24 20.0268502543054 3.97314974569459 65 19 18.4107445744335 0.589255425566478 66 31 26.5328702642221 4.46712973577795 67 22 26.3236311521052 -4.32363115210522 68 27 21.3625142355619 5.63748576443811 69 19 17.7702580280537 1.22974197194631 70 25 22.2396922993740 2.76030770062605 71 20 24.6967205525091 -4.69672055250909 72 21 21.3399553474551 -0.339955347455079 73 27 27.3047176538651 -0.304717653865059 74 23 24.4807218762822 -1.48072187628224 75 25 25.4465023504673 -0.446502350467311 76 20 22.1061214466963 -2.10612144669634 77 21 19.2780235331605 1.72197646683950 78 22 22.4571510668245 -0.457151066824549 79 23 23.0071803395339 -0.00718033953388612 80 25 23.8254598619908 1.17454013800924 81 25 23.5028963414381 1.49710365856187 82 17 23.67388151301 -6.67388151301 83 19 21.3990371014657 -2.39903710146571 84 25 23.9177594744181 1.0822405255819 85 19 22.2340110089722 -3.2340110089722 86 20 23.0469428181477 -3.04694281814765 87 25 22.3219299177107 2.67807008228932 88 23 20.8819312104019 2.11806878959806 89 27 24.5672909361337 2.43270906386632 90 17 20.7755495787316 -3.7755495787316 91 17 23.3128313618560 -6.31283136185604 92 19 19.9684697480727 -0.968469748072705 93 17 19.5972293995572 -2.59722939955719 94 22 21.8346381380014 0.165361861998561 95 21 23.5189207711728 -2.51892077117284 96 32 28.6229385772279 3.37706142277205 97 21 24.6961550923205 -3.69615509232055 98 21 24.4054976510909 -3.40549765109090 99 18 21.1087371690687 -3.10873716906870 100 18 21.1758655275826 -3.17586552758262 101 23 22.8047151531758 0.1952848468242 102 19 20.4445404817782 -1.44454048177819 103 19 23.3415843538843 -4.34158435388433 104 21 22.2884658145770 -1.28846581457704 105 20 23.9251540933176 -3.92515409331759 106 17 18.6150255237399 -1.6150255237399 107 18 20.0850890021707 -2.08508900217065 108 19 20.6597714936709 -1.65977149367094 109 22 22.1686194723098 -0.168619472309782 110 15 18.7461445369008 -3.74614453690075 111 14 18.7358362980932 -4.7358362980932 112 18 26.5789032103476 -8.57890321034757 113 24 21.3515047489764 2.64849525102359 114 35 23.4653775274175 11.5346224725825 115 29 19.2298425795621 9.77015742043792 116 21 21.7631189139737 -0.76311891397371 117 25 20.3110561545158 4.68894384548418 118 19 20.2772110491958 -1.27721104919578 119 22 23.2496498346081 -1.24964983460807 120 13 16.5896022137004 -3.58960221370041 121 26 22.8707060287732 3.12929397122682 122 17 16.8467267725246 0.153273227475435 123 25 20.2223672187276 4.77763278127244 124 20 20.5737892482138 -0.573789248213824 125 19 18.2881891791194 0.711810820880556 126 21 22.5815928414669 -1.58159284146685 127 22 20.8103041067532 1.18969589324682 128 24 22.6418607488068 1.35813925119322 129 21 22.9769873651409 -1.97698736514093 130 26 25.3605912469977 0.639408753002286 131 24 20.6287219668130 3.37127803318703 132 16 20.2205988808453 -4.22059888084532 133 23 22.1691476692572 0.830852330742773 134 18 20.5340546775684 -2.53405467756842 135 16 22.2765411580797 -6.27654115807966 136 26 24.1133944802862 1.88660551971376 137 19 18.9941222715462 0.00587772845380561 138 21 16.8913827683469 4.10861723165309 139 21 22.1399879062222 -1.13998790622216 140 22 18.6902768503474 3.30972314965263 141 23 19.6665208680271 3.33347913197293 142 29 24.7592185781225 4.24078142187747 143 21 19.7118015332462 1.28819846675377 144 21 19.8693613093612 1.13063869063880 145 23 22.0182202841013 0.981779715898743 146 27 22.8987382559258 4.10126174407416 147 25 25.1885762485626 -0.188576248562635 148 21 20.8324877398840 0.167512260116049 149 10 17.0659887783828 -7.06598877838282 150 20 22.5609237171829 -2.56092371718294 151 26 22.428674805424 3.57132519457600 152 24 23.6624525156503 0.337547484349669 153 29 31.4012790263770 -2.40127902637696 154 19 18.7594385593829 0.240561440617139 155 24 22.2618936786481 1.73810632135187 156 22 20.8928421726391 1.10715782736088 157 24 23.3736298288591 0.626370171140913 158 22 21.8903622378561 0.109637762143861 159 19 23.3415843538843 -4.34158435388433 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.169352997889064 0.338705995778128 0.830647002110936 11 0.480870239496937 0.961740478993874 0.519129760503063 12 0.410595130318285 0.82119026063657 0.589404869681715 13 0.835137675572248 0.329724648855504 0.164862324427752 14 0.759254805808751 0.481490388382497 0.240745194191249 15 0.74158908380988 0.516821832380241 0.258410916190121 16 0.662066008333031 0.675867983333937 0.337933991666969 17 0.602342585095619 0.795314829808763 0.397657414904381 18 0.586069164280158 0.827861671439685 0.413930835719842 19 0.509381121073128 0.981237757853744 0.490618878926872 20 0.506088462523943 0.987823074952115 0.493911537476057 21 0.502510726109251 0.994978547781497 0.497489273890749 22 0.433051718248298 0.866103436496596 0.566948281751702 23 0.373378301321643 0.746756602643286 0.626621698678357 24 0.392110091939847 0.784220183879693 0.607889908060153 25 0.361372653590981 0.722745307181962 0.638627346409019 26 0.299596916212072 0.599193832424143 0.700403083787928 27 0.258944126165215 0.51788825233043 0.741055873834785 28 0.250749534753605 0.50149906950721 0.749250465246395 29 0.208362925460923 0.416725850921846 0.791637074539077 30 0.163340892424365 0.326681784848731 0.836659107575635 31 0.134080869820156 0.268161739640311 0.865919130179844 32 0.169609659296452 0.339219318592905 0.830390340703548 33 0.287887300079652 0.575774600159304 0.712112699920348 34 0.575269791428333 0.849460417143335 0.424730208571667 35 0.555604877645333 0.888790244709334 0.444395122354667 36 0.632957884188858 0.734084231622284 0.367042115811142 37 0.630926562279416 0.738146875441168 0.369073437720584 38 0.585209780968089 0.829580438063822 0.414790219031911 39 0.553306728581482 0.893386542837035 0.446693271418518 40 0.648790517896967 0.702418964206065 0.351209482103033 41 0.615610530514884 0.768778938970233 0.384389469485116 42 0.573418864138486 0.853162271723028 0.426581135861514 43 0.659178865536056 0.681642268927889 0.340821134463945 44 0.635731057675632 0.728537884648736 0.364268942324368 45 0.670468057207823 0.659063885584354 0.329531942792177 46 0.621243755092354 0.757512489815292 0.378756244907646 47 0.611622402995843 0.776755194008314 0.388377597004157 48 0.728115029078236 0.543769941843529 0.271884970921765 49 0.68782845334811 0.624343093303779 0.312171546651890 50 0.677367268203007 0.645265463593985 0.322632731796993 51 0.640848710965455 0.718302578069089 0.359151289034545 52 0.597711541147955 0.80457691770409 0.402288458852045 53 0.623943470899754 0.752113058200493 0.376056529100247 54 0.585893845344138 0.828212309311724 0.414106154655862 55 0.644319515383498 0.711360969233004 0.355680484616502 56 0.608768248252264 0.782463503495472 0.391231751747736 57 0.571734317690662 0.856531364618676 0.428265682309338 58 0.590844670374714 0.818310659250573 0.409155329625286 59 0.545440351615936 0.909119296768129 0.454559648384064 60 0.504925504798661 0.990148990402677 0.495074495201339 61 0.472737443133902 0.945474886267804 0.527262556866098 62 0.432343664657837 0.864687329315674 0.567656335342163 63 0.390678805222763 0.781357610445527 0.609321194777237 64 0.427550797002086 0.855101594004172 0.572449202997914 65 0.383073105978811 0.766146211957622 0.616926894021189 66 0.407598273420589 0.815196546841177 0.592401726579411 67 0.46298287167426 0.92596574334852 0.53701712832574 68 0.547227783066574 0.905544433866852 0.452772216933426 69 0.507718538992551 0.984562922014899 0.492281461007449 70 0.492416416996911 0.984832833993821 0.507583583003089 71 0.550571930671905 0.89885613865619 0.449428069328095 72 0.504137910434641 0.991724179130719 0.495862089565359 73 0.460385789644567 0.920771579289134 0.539614210355433 74 0.424150973918667 0.848301947837334 0.575849026081333 75 0.389469910042104 0.778939820084208 0.610530089957896 76 0.361721947925122 0.723443895850244 0.638278052074878 77 0.335043239751574 0.670086479503147 0.664956760248426 78 0.294183973737075 0.58836794747415 0.705816026262925 79 0.255826482104227 0.511652964208453 0.744173517895773 80 0.227107546891345 0.45421509378269 0.772892453108655 81 0.200329223237744 0.400658446475488 0.799670776762256 82 0.300218514256004 0.600437028512009 0.699781485743996 83 0.279434656146681 0.558869312293361 0.72056534385332 84 0.246600957950405 0.49320191590081 0.753399042049595 85 0.246381447043366 0.492762894086731 0.753618552956634 86 0.240044504877255 0.48008900975451 0.759955495122745 87 0.237572504924595 0.47514500984919 0.762427495075405 88 0.220027160683924 0.440054321367848 0.779972839316076 89 0.205118563996964 0.410237127993928 0.794881436003036 90 0.208093109050722 0.416186218101445 0.791906890949278 91 0.292520971755656 0.585041943511312 0.707479028244344 92 0.254273852137959 0.508547704275919 0.74572614786204 93 0.234038067234511 0.468076134469022 0.765961932765489 94 0.202023536916678 0.404047073833355 0.797976463083322 95 0.187040568380407 0.374081136760814 0.812959431619593 96 0.189270972264918 0.378541944529835 0.810729027735082 97 0.19317404736875 0.3863480947375 0.80682595263125 98 0.192909582407796 0.385819164815593 0.807090417592204 99 0.182085413291798 0.364170826583596 0.817914586708202 100 0.174096208785123 0.348192417570246 0.825903791214877 101 0.144856232005895 0.289712464011791 0.855143767994105 102 0.121059128440395 0.242118256880789 0.878940871559605 103 0.136798845006187 0.273597690012373 0.863201154993813 104 0.11427472413145 0.2285494482629 0.88572527586855 105 0.12843276615767 0.25686553231534 0.87156723384233 106 0.106880101660964 0.213760203321927 0.893119898339036 107 0.0929652530669494 0.185930506133899 0.90703474693305 108 0.0822988574733561 0.164597714946712 0.917701142526644 109 0.0660287423387991 0.132057484677598 0.9339712576612 110 0.0648259651592568 0.129651930318514 0.935174034840743 111 0.0762401632169728 0.152480326433946 0.923759836783027 112 0.291425975158849 0.582851950317698 0.708574024841151 113 0.272191685783222 0.544383371566445 0.727808314216778 114 0.755343089716033 0.489313820567934 0.244656910283967 115 0.945030565626986 0.109938868746027 0.0549694343730137 116 0.929027737756778 0.141944524486444 0.070972262243222 117 0.969272003799333 0.0614559924013347 0.0307279962006674 118 0.961461134311924 0.0770777313761515 0.0385388656880757 119 0.953317153466692 0.0933656930666166 0.0466828465333083 120 0.956233358018822 0.0875332839623554 0.0437666419811777 121 0.950768833995892 0.098462332008215 0.0492311660041075 122 0.9338012922891 0.132397415421800 0.0661987077108998 123 0.942068890600264 0.115862218799472 0.0579311093997359 124 0.921698057694183 0.156603884611635 0.0783019423058174 125 0.911743676933129 0.176512646133743 0.0882563230668713 126 0.885367809250454 0.229264381499092 0.114632190749546 127 0.881250429249946 0.237499141500107 0.118749570750053 128 0.851175643328857 0.297648713342286 0.148824356671143 129 0.816779781425961 0.366440437148078 0.183220218574039 130 0.779709759680044 0.440580480639913 0.220290240319956 131 0.765242061131922 0.469515877736157 0.234757938868079 132 0.767903542024973 0.464192915950054 0.232096457975027 133 0.738063288933429 0.523873422133142 0.261936711066571 134 0.681105093017495 0.637789813965009 0.318894906982505 135 0.835627135858693 0.328745728282614 0.164372864141307 136 0.806822985482011 0.386354029035977 0.193177014517989 137 0.74663557145349 0.50672885709302 0.25336442854651 138 0.805794967614156 0.388410064771687 0.194205032385843 139 0.750781628857222 0.498436742285557 0.249218371142778 140 0.687831409866246 0.624337180267507 0.312168590133754 141 0.632107958626873 0.735784082746255 0.367892041373127 142 0.6481225557038 0.7037548885924 0.3518774442962 143 0.631588080103792 0.736823839792415 0.368411919896208 144 0.565616016221708 0.868767967556585 0.434383983778292 145 0.457422263012321 0.914844526024643 0.542577736987679 146 0.436219210125734 0.872438420251469 0.563780789874265 147 0.391123885811319 0.782247771622638 0.608876114188681 148 0.271647139970196 0.543294279940392 0.728352860029804 149 0.759771854240023 0.480456291519953 0.240228145759977 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 5 0.0357142857142857 OK

Charts produced by software:

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Parameters (Session):

par1 = 6 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 6 ; 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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