WS 10 - MR: Concern over mistakes

*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, 14 Dec 2010 10:55:32 +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/14/t1292324072bloqux0ch52txml.htm/, Retrieved Tue, 14 Dec 2010 11:54:32 +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/14/t1292324072bloqux0ch52txml.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 «

0 25 11 7 8 25 23 0 17 6 17 8 30 25 0 18 8 12 9 22 19 0 16 10 12 7 22 29 0 20 10 11 4 25 25 0 16 11 11 11 23 21 0 18 16 12 7 17 22 0 17 11 13 7 21 25 0 30 12 16 10 19 18 0 23 8 11 10 15 22 0 18 12 10 8 16 15 0 21 9 9 9 22 20 0 31 14 17 11 23 20 0 27 15 11 9 23 21 0 21 9 14 13 19 21 0 16 8 15 9 23 24 0 20 9 15 6 25 24 0 17 9 13 6 22 23 0 25 16 18 16 26 24 0 26 11 18 5 29 18 0 25 8 12 7 32 25 0 17 9 17 9 25 21 0 32 12 18 12 28 22 0 22 9 14 9 25 23 0 17 9 16 5 25 23 0 20 14 14 10 18 24 0 29 10 12 8 25 23 0 23 14 17 7 25 21 0 20 10 12 8 20 28 0 11 6 6 4 15 16 0 26 13 12 8 24 29 0 22 10 12 8 26 27 0 14 15 13 8 14 16 0 19 12 14 7 24 28 0 20 11 11 8 25 25 0 28 8 12 7 20 22 0 19 9 9 7 21 23 0 30 9 15 9 27 26 0 29 15 18 11 23 23 0 26 9 15 6 25 25 0 23 10 12 8 20 21 0 21 12 14 9 22 24 0 28 11 13 6 25 22 0 23 14 13 10 25 27 0 18 6 11 8 17 26 0 20 8 16 10 25 24 0 21 10 11 5 26 24 0 28 12 16 14 27 22 0 10 5 8 6 19 24 0 22 10 15 6 22 20 0 31 10 21 12 32 26 0 29 13 18 12 21 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 7 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation CM[t] = -1.97558860391637 -0.584520417545623Gender[t] + 0.825198555334064D[t] + 0.240632907570932PE[t] + 0.182865509202120PC[t] + 0.556669097802935PS[t] -0.0951728207275587O[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) -1.97558860391637 3.057456 -0.6462 0.519154 0.259577 Gender -0.584520417545623 0.791394 -0.7386 0.461292 0.230646 D 0.825198555334064 0.132115 6.2461 0 0 PE 0.240632907570932 0.133733 1.7994 0.073946 0.036973 PC 0.182865509202120 0.168683 1.0841 0.280046 0.140023 PS 0.556669097802935 0.096795 5.751 0 0 O -0.0951728207275587 0.106862 -0.8906 0.374541 0.187271 Multiple Linear Regression - Regression Statistics Multiple R 0.639761924721091 R-squared 0.409295320322835 Adjusted R-squared 0.385978030335578 F-TEST (value) 17.5532971690331 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 2.22044604925031e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.48437540723029 Sum Squared Residuals 3056.66266453172 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 25 21.9767024997114 3.02329750028864 2 17 22.8500386463099 -5.85003864630991 3 18 19.5978208702674 -1.59782087026737 4 16 19.9307587552557 -3.93075875525567 5 20 21.1922278963974 -1.19222789639742 6 16 22.5648381034507 -6.5648381034507 7 18 22.7648143433383 -4.76481434333829 8 17 20.8206124032680 -3.82061240326797 9 30 22.4691777584082 7.53082224159177 10 23 15.3578513250953 7.64214867490467 11 18 19.2751604633523 -1.27516046335227 12 21 19.6059478821611 1.39405211783892 13 31 26.5794040356060 4.42059596439397 14 27 25.4999013063827 1.50009869361730 15 21 19.7753943426879 1.22460565731214 16 16 20.4005245871453 -4.40052458714531 17 20 21.7904648104789 -1.79046481047888 18 17 19.7343645226558 -2.73436452265577 19 25 30.6740776103543 -5.67407761035427 20 26 26.7776084502348 -0.777608450234776 21 25 24.2277439055271 0.772256094472872 22 17 23.1058456154098 -6.10584561540978 23 32 27.9455051892705 4.05449481072949 24 22 22.1936012512419 -0.193601251241868 25 17 21.9434050295753 -4.94340502957525 26 20 22.5106030317662 -2.51060303176620 27 29 22.3546684822319 6.64533151776805 28 23 26.8661073736759 -3.86610737367586 29 20 19.0954588895795 0.904541110420521 30 11 11.9781335457252 -0.978133545725176 31 26 23.7025581260659 2.29744187393415 32 22 22.5306462971246 -0.530646297124649 33 14 21.2641438357338 -7.26414383573383 34 19 23.2709326973991 -4.27093269739909 35 20 22.7488884885400 -2.74888848853996 36 28 17.8332331940746 10.1667668059254 37 19 18.3980293037712 0.601970696228773 38 30 23.262053892236 6.73794610776401 39 29 27.3597170363284 1.64028296367165 40 26 21.6952919897513 4.30470801024868 41 23 19.7616686346724 3.23833136532761 42 21 22.9040168031077 -1.90401680310770 43 28 23.1499417474603 4.85005825253974 44 23 25.8811353466331 -2.88113534663314 45 18 14.0743701087186 3.9256298912814 46 20 21.9373611995242 -1.93736119952423 47 21 22.0269353241300 -1.02693532413003 48 28 27.2733012947300 0.726698705270044 49 10 13.4652256493285 -3.46522564932849 50 22 21.3263473553144 0.673652644685626 51 31 28.8629919096167 2.13700809038331 52 29 24.9691928807116 4.03080711928841 53 22 19.0793089880926 2.92069101190743 54 23 22.5193056691982 0.480694330801768 55 20 21.4624955543769 -1.46249555437688 56 18 19.6603975421967 -1.66039754219667 57 25 21.1742630517879 3.8257369482121 58 21 16.7144932869646 4.28550671303536 59 24 19.5572018318759 4.44279816812408 60 25 25.4462963019337 -0.446296301933674 61 13 14.7787370694396 -1.77873706943965 62 28 18.4064085333079 9.59359146669207 63 25 28.0091946916564 -3.00919469165641 64 9 20.8666155494301 -11.8666155494301 65 16 18.0744585395891 -2.07445853958909 66 19 21.1135941852984 -2.11359418529838 67 29 21.8970823814334 7.10291761856663 68 14 19.2098584910333 -5.20985849103332 69 22 27.0660163292267 -5.06601632922667 70 15 15.9210517772642 -0.921051777264193 71 15 17.7263634054771 -2.72636340547711 72 20 22.0970465700095 -2.09704657000947 73 18 20.5066049531815 -2.50660495318152 74 33 25.7811532523451 7.21884674765491 75 22 23.8882914785782 -1.88829147857816 76 16 16.7097936881266 -0.709793688126585 77 16 15.354226927422 0.645773072578004 78 18 21.4100370051950 -3.41003700519496 79 18 23.153615825737 -5.15361582573698 80 22 24.8359669666564 -2.83596696665641 81 30 24.8596466809997 5.14035331900031 82 30 27.4145445459564 2.58545545404359 83 24 29.7480139830914 -5.74801398309136 84 21 25.5638598388168 -4.56385983881685 85 29 27.7176612631395 1.28233873686053 86 31 23.2961912568649 7.7038087431351 87 20 19.1648135810958 0.835186418904233 88 16 14.3140271763316 1.68597282366844 89 22 19.0534411782779 2.94655882172207 90 20 20.4731473363914 -0.473147336391438 91 28 27.6165495259896 0.383450474010433 92 38 26.8183371633487 11.1816628366513 93 22 19.3518911648210 2.64810883517896 94 20 25.7481072085238 -5.74810720852381 95 17 18.2547028707021 -1.25470287070208 96 22 24.3430594166699 -2.34305941666993 97 31 26.285379920609 4.71462007939099 98 24 24.7195838552745 -0.719583855274521 99 18 19.5992647733950 -1.59926477339498 100 23 22.0232841750937 0.976715824906306 101 15 21.3365483375711 -6.33654833757115 102 12 17.4468675105543 -5.44686751055433 103 15 14.8026589986181 0.197341001381876 104 20 19.3748698685344 0.625130131465627 105 34 26.7725754406936 7.2274245593064 106 31 20.6929927862602 10.3070072137398 107 19 19.095504119797 -0.0955041197969886 108 21 17.9332605185801 3.06673948141986 109 22 21.5336775510352 0.466322448964825 110 24 20.1114813992039 3.88851860079606 111 32 27.5748675846027 4.42513241539726 112 33 23.2728969930397 9.72710300696028 113 13 21.8145629073884 -8.81456290738843 114 25 25.4643560573641 -0.464356057364075 115 29 26.7709301025624 2.22906989743756 116 18 16.9397236359322 1.06027636406781 117 20 21.8455513473474 -1.84555134734740 118 15 20.2062211373137 -5.20622113731373 119 33 27.7848234087985 5.21517659120147 120 26 23.0969359905523 2.90306400944772 121 18 18.6231002974130 -0.623100297412962 122 28 28.2705959064922 -0.270595906492178 123 17 19.7737894736804 -2.77378947368044 124 12 15.2140544269744 -3.21405442697439 125 17 20.3808002792963 -3.38080027929633 126 21 20.9932080353225 0.00679196467747714 127 18 22.8142356910764 -4.81423569107642 128 10 17.6409040426914 -7.64090404269142 129 29 23.9986562114259 5.00134378857407 130 31 18.1139379323109 12.8860620676891 131 19 22.4892662539842 -3.48926625398418 132 9 19.8683866688697 -10.8683866688697 133 13 22.5288221425224 -9.52882214252242 134 19 21.2549042402414 -2.25490424024137 135 21 20.4163363168353 0.583663683164666 136 23 19.8391082584047 3.16089174159535 137 21 20.4964944313598 0.503505568640237 138 15 22.6646684433386 -7.66466844333857 139 19 17.3242754145158 1.67572458548416 140 26 21.0036824980134 4.99631750198659 141 16 16.8714985872778 -0.871498587277751 142 19 18.4626799460636 0.537320053936405 143 31 24.9684486883678 6.03155131163216 144 19 17.0557459569847 1.94425404301529 145 15 15.7791524349174 -0.779152434917398 146 23 21.8416579834759 1.15834201652414 147 17 19.3288659310441 -2.32886593104411 148 21 19.6752981232915 1.32470187670850 149 17 19.1050626727989 -2.10506267279891 150 25 24.2105264038011 0.789473596198866 151 20 15.1730519865685 4.82694801343146 152 19 25.3463762502684 -6.34637625026839 153 20 21.5718347666633 -1.57183476666331 154 17 18.7568634163864 -1.75686341638642 155 21 16.7601261844599 4.23987381554009 156 26 27.1883799281907 -1.18837992819071 157 17 17.9807672512810 -0.980767251281018 158 21 21.8225305639563 -0.822530563956327 159 28 24.1784674599212 3.82153254007884 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.916865412283638 0.166269175432723 0.0831345877163616 11 0.923819281273692 0.152361437452615 0.0761807187263076 12 0.86696345560563 0.266073088788741 0.133036544394370 13 0.882994334228045 0.234011331543909 0.117005665771955 14 0.835429749502 0.329140500995999 0.164570250498000 15 0.776613219837136 0.446773560325729 0.223386780162864 16 0.735292586829922 0.529414826340155 0.264707413170078 17 0.660466739586066 0.679066520827868 0.339533260413934 18 0.578034704602716 0.843930590794568 0.421965295397284 19 0.558739042937225 0.88252191412555 0.441260957062775 20 0.47787448801398 0.95574897602796 0.52212551198602 21 0.468381891160474 0.936763782320948 0.531618108839526 22 0.489505315835564 0.979010631671127 0.510494684164436 23 0.541398066095625 0.91720386780875 0.458601933904375 24 0.469634806118568 0.939269612237136 0.530365193881432 25 0.427957680529828 0.855915361059656 0.572042319470172 26 0.363098475400166 0.726196950800332 0.636901524599834 27 0.484124496146307 0.968248992292614 0.515875503853693 28 0.433843716465696 0.867687432931392 0.566156283534304 29 0.401474964858175 0.80294992971635 0.598525035141825 30 0.368735458706193 0.737470917412385 0.631264541293807 31 0.356054323384974 0.712108646769949 0.643945676615026 32 0.298983460308220 0.597966920616439 0.70101653969178 33 0.365342992686561 0.730685985373121 0.634657007313439 34 0.330439173820368 0.660878347640736 0.669560826179632 35 0.294151186100221 0.588302372200443 0.705848813899779 36 0.555570002036792 0.888859995926415 0.444429997963208 37 0.497182770415163 0.994365540830325 0.502817229584837 38 0.577528381033656 0.844943237932687 0.422471618966344 39 0.54903122869466 0.901937542610681 0.450968771305340 40 0.564359338843561 0.871281322312878 0.435640661156439 41 0.534686596108021 0.930626807783958 0.465313403891979 42 0.485954873515682 0.971909747031365 0.514045126484318 43 0.511615745988337 0.976768508023325 0.488384254011663 44 0.472236970597281 0.944473941194563 0.527763029402719 45 0.441404607471685 0.88280921494337 0.558595392528315 46 0.4053380788824 0.8106761577648 0.5946619211176 47 0.356139540149527 0.712279080299054 0.643860459850473 48 0.308217862193063 0.616435724386127 0.691782137806937 49 0.312299654509936 0.624599309019872 0.687700345490064 50 0.270914747584070 0.541829495168139 0.72908525241593 51 0.237577439677334 0.475154879354669 0.762422560322666 52 0.228819613553470 0.457639227106941 0.77118038644653 53 0.204134648833000 0.408269297666000 0.795865351167 54 0.169833316336179 0.339666632672359 0.83016668366382 55 0.147042097747925 0.294084195495851 0.852957902252075 56 0.127003085250397 0.254006170500795 0.872996914749603 57 0.125038357112197 0.250076714224394 0.874961642887803 58 0.116151857702009 0.232303715404018 0.883848142297991 59 0.106920825331619 0.213841650663238 0.89307917466838 60 0.0858517106149708 0.171703421229942 0.91414828938503 61 0.0725398186680013 0.145079637336003 0.927460181331999 62 0.144173466565904 0.288346933131808 0.855826533434096 63 0.13645846681602 0.27291693363204 0.86354153318398 64 0.347007211374299 0.694014422748598 0.652992788625701 65 0.31400234264971 0.62800468529942 0.68599765735029 66 0.286279203769625 0.572558407539251 0.713720796230375 67 0.378524880368781 0.757049760737562 0.621475119631219 68 0.400206799531263 0.800413599062525 0.599793200468737 69 0.408043088416295 0.81608617683259 0.591956911583705 70 0.364149782074936 0.728299564149872 0.635850217925064 71 0.336658290783443 0.673316581566887 0.663341709216557 72 0.303254106661520 0.606508213323041 0.69674589333848 73 0.278362229696094 0.556724459392188 0.721637770303906 74 0.347594491656763 0.695188983313526 0.652405508343237 75 0.313094361740644 0.626188723481287 0.686905638259356 76 0.274821819217423 0.549643638434846 0.725178180782577 77 0.237115342424741 0.474230684849482 0.762884657575259 78 0.223577971318985 0.447155942637969 0.776422028681016 79 0.237658798025799 0.475317596051598 0.762341201974201 80 0.218858830549254 0.437717661098508 0.781141169450746 81 0.227494527841219 0.454989055682439 0.77250547215878 82 0.203831697898577 0.407663395797154 0.796168302101423 83 0.237831217654596 0.475662435309192 0.762168782345404 84 0.251318054119413 0.502636108238827 0.748681945880587 85 0.217917578341276 0.435835156682552 0.782082421658724 86 0.271201937730116 0.542403875460232 0.728798062269884 87 0.233972948299980 0.467945896599961 0.76602705170002 88 0.201879417070249 0.403758834140498 0.798120582929751 89 0.180102488733972 0.360204977467943 0.819897511266028 90 0.152433222793873 0.304866445587747 0.847566777206127 91 0.127448165010070 0.254896330020140 0.87255183498993 92 0.300046921133984 0.600093842267968 0.699953078866016 93 0.275286198252167 0.550572396504333 0.724713801747833 94 0.297993884032354 0.595987768064708 0.702006115967646 95 0.260771438328869 0.521542876657737 0.739228561671131 96 0.244750645936698 0.489501291873396 0.755249354063302 97 0.227640178217521 0.455280356435042 0.772359821782479 98 0.196790951735935 0.39358190347187 0.803209048264065 99 0.168471224202114 0.336942448404228 0.831528775797886 100 0.140921905951150 0.281843811902299 0.85907809404885 101 0.168409862052628 0.336819724105256 0.831590137947372 102 0.157373873897125 0.31474774779425 0.842626126102875 103 0.135212777107084 0.270425554214168 0.864787222892916 104 0.113497630366606 0.226995260733212 0.886502369633394 105 0.154900645347182 0.309801290694364 0.845099354652818 106 0.310664365378879 0.621328730757758 0.689335634621121 107 0.269320963361609 0.538641926723218 0.730679036638391 108 0.248921233440605 0.49784246688121 0.751078766559395 109 0.210317575919245 0.420635151838489 0.789682424080755 110 0.198658051001164 0.397316102002329 0.801341948998836 111 0.187148630554629 0.374297261109259 0.81285136944537 112 0.292130727073060 0.584261454146119 0.70786927292694 113 0.418817577535921 0.837635155071842 0.581182422464079 114 0.36958345762303 0.73916691524606 0.63041654237697 115 0.345962430735081 0.691924861470162 0.654037569264919 116 0.298488332676857 0.596976665353714 0.701511667323143 117 0.264832274493222 0.529664548986445 0.735167725506778 118 0.271701325609062 0.543402651218124 0.728298674390938 119 0.290451154962427 0.580902309924853 0.709548845037573 120 0.285912134698727 0.571824269397453 0.714087865301273 121 0.241597250663634 0.483194501327269 0.758402749336366 122 0.221226472130995 0.442452944261989 0.778773527869005 123 0.193596031280021 0.387192062560042 0.806403968719979 124 0.167333113892619 0.334666227785239 0.83266688610738 125 0.158559206246466 0.317118412492933 0.841440793753534 126 0.125714430809553 0.251428861619106 0.874285569190447 127 0.128704205806982 0.257408411613963 0.871295794193018 128 0.179498513294582 0.358997026589164 0.820501486705418 129 0.30583707665818 0.61167415331636 0.69416292334182 130 0.747788538686879 0.504422922626242 0.252211461313121 131 0.699191491650317 0.601617016699365 0.300808508349683 132 0.893640015686247 0.212719968627507 0.106359984313753 133 0.963911901665727 0.0721761966685456 0.0360880983342728 134 0.946261847524804 0.107476304950391 0.0537381524751956 135 0.922091200689842 0.155817598620316 0.0779087993101578 136 0.943832887997952 0.112334224004096 0.0561671120020478 137 0.915888270929476 0.168223458141048 0.0841117290705242 138 0.942855927069664 0.114288145860671 0.0571440729303357 139 0.912423477250327 0.175153045499346 0.087576522749673 140 0.908161731887006 0.183676536225988 0.0918382681129941 141 0.862098626407462 0.275802747185076 0.137901373592538 142 0.800988453832128 0.398023092335744 0.199011546167872 143 0.899130198770117 0.201739602459767 0.100869801229883 144 0.84247018730781 0.315059625384381 0.157529812692191 145 0.780345607236105 0.439308785527789 0.219654392763895 146 0.710870832385727 0.578258335228545 0.289129167614273 147 0.630616538028545 0.73876692394291 0.369383461971455 148 0.493272067666649 0.986544135333298 0.506727932333351 149 0.474838263140947 0.949676526281894 0.525161736859053 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 1 0.00714285714285714 OK

Charts produced by software:

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Parameters (Session):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = no ;

Parameters (R input):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = no ;

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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