WS 10 MR

*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 11:32:14 +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/t1292326261r4lz47sx4z3uxdz.htm/, Retrieved Tue, 14 Dec 2010 12:31:01 +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/t1292326261r4lz47sx4z3uxdz.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 1 24 13 13 13 25 1 25 12 12 13 17 1 30 15 10 16 18 0 19 12 9 12 18 1 22 10 10 11 16 1 22 12 12 12 20 1 25 15 13 18 16 1 23 9 12 11 18 1 17 12 12 14 17 1 21 11 6 9 23 0 19 11 5 14 30 1 19 11 12 12 23 0 15 15 11 11 18 1 16 7 14 12 15 1 23 11 14 13 12 0 27 11 12 11 21 0 22 10 12 12 15 1 14 14 11 16 20 0 22 10 11 9 31 1 23 6 7 11 27 0 23 11 9 13 34 1 21 15 11 15 21 1 19 11 11 10 31 1 18 12 12 11 19 0 20 14 12 13 16 1 23 15 11 16 20 0 25 9 11 15 21 1 19 13 8 14 22 1 24 13 9 14 17 0 22 16 12 14 24 1 25 13 10 8 25 0 26 12 10 13 26 1 29 14 12 15 25 1 32 11 8 13 17 0 25 9 12 11 32 0 29 16 11 15 33 0 28 12 12 15 13 0 17 10 7 9 32 1 28 13 11 13 25 0 29 16 11 16 29 0 26 14 12 13 22 1 25 15 9 11 18 0 14 5 15 12 17 0 25 8 11 12 20 1 26 11 11 12 15 1 20 16 11 14 20 1 18 17 11 14 33 1 32 9 15 8 29 1 25 9 11 13 23 0 25 13 12 16 26 1 23 10 12 13 18 0 21 6 9 11 20 0 20 12 12 14 11 1 15 8 12 13 28 0 30 14 13 13 26 1 24 12 11 13 22 1 26 11 9 12 17 1 24 16 9 16 12 0 22 8 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 8 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation CoM[t] = + 13.6486392323600 -0.745977696548505GENDER[t] + 0.583058986338514PersSt[t] -0.087313326112899Popularity[t] -0.135563432124363FindFrie[t] -0.158138000123378`Liked `[t] + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 13.6486392323600 4.158206 3.2823 0.001281 0.00064 GENDER -0.745977696548505 0.864467 -0.8629 0.389552 0.194776 PersSt 0.583058986338514 0.099148 5.8807 0 0 Popularity -0.087313326112899 0.17293 -0.5049 0.614366 0.307183 FindFrie -0.135563432124363 0.237003 -0.572 0.568184 0.284092 `Liked ` -0.158138000123378 0.231885 -0.682 0.496312 0.248156 Multiple Linear Regression - Regression Statistics Multiple R 0.460249477153909 R-squared 0.211829581220446 Adjusted R-squared 0.185557233927794 F-TEST (value) 8.06283423634909 F-TEST (DF numerator) 5 F-TEST (DF denominator) 150 p-value 9.26157895819735e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.14761948252781 Sum Squared Residuals 3974.69795053498 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 21.9428853492475 2.05711465075250 2 25 22.7488210938232 2.25117890617675 3 17 25.1988889110557 -8.19888891105572 4 18 20.5612731688371 -2.56127316883714 5 18 21.761673651529 -3.76167365152899 6 16 21.1577821349311 -5.15778213493108 7 20 21.5606276827433 -1.56062768274330 8 16 22.1609190997317 -6.16091909973167 9 18 17.9262112029918 0.0737887970082426 10 17 21.9498310678218 -4.94983106782178 11 23 20.8745642232007 2.12543577679927 12 30 19.4959185020284 10.5040814979716 13 23 17.8541083810190 5.14589161898096 14 18 17.8248679832158 0.175132016784232 15 15 21.3988895830104 -6.39888958301039 16 12 25.0645060894084 -13.0645060894084 17 21 22.0783864837054 -1.07838648370539 18 15 15.8216950236280 -0.821695023628023 19 20 22.6883639161999 -2.68836391619988 20 31 23.1006762386922 7.89932376130781 21 27 22.8226844401807 4.17731555981929 22 34 19.9739326020081 14.0260673979919 23 21 19.9477579343996 1.05224206560044 24 31 18.9836841897004 12.0163158102996 25 19 20.4048772064534 -1.40487720645338 26 16 20.9819125745618 -4.98191257456175 27 20 23.5760262005881 -3.57602620058806 28 21 19.5472695780533 1.45273042194666 29 22 22.3270010776215 -0.327001077621547 30 17 21.2382305267812 -4.23823052678124 31 24 23.7233246325760 0.276675367424035 32 25 24.348984640959 0.651015359041007 33 26 24.5901543867048 1.40984561329525 34 25 27.4598010528032 -2.4598010528032 35 17 24.0730147689572 -7.0730147689572 36 32 25.2970688631518 6.70293113684818 37 33 24.9276997491405 8.07230025085946 38 13 20.3153227130048 -7.31532271300477 39 32 24.5462481588503 7.45375184114975 40 25 25.1389308630284 -0.138930863028443 41 29 23.9032311244845 5.09676887551553 42 22 23.2098474121044 -1.20984741210440 43 18 17.4437909271887 0.556209072811322 44 17 24.1377535270711 -7.13775352707109 45 20 23.7128948385224 -3.7128948385224 46 15 19.4616982896801 -4.46169828968007 47 20 18.2082669908901 1.79173300910986 48 33 27.4761736807753 5.52382631922466 49 29 23.1463245042863 5.85367549571369 50 23 22.9330714638887 0.06692853611128 51 26 21.757329773372 4.24267022662798 52 18 22.4094090983149 -4.40940909831494 53 20 20.4213658585558 -0.421365858555804 54 11 17.2674845348897 -6.26748453488971 55 28 26.0999036377142 1.90009636228584 56 26 22.3013255396091 3.69867446039090 57 22 23.9840217027711 -1.98402170277113 58 17 21.7487850990361 -4.74878509903609 59 12 21.9141625676854 -9.91416256768541 60 14 15.8925196976385 -1.89251969763850 61 17 23.5064444347211 -6.50644443472111 62 21 22.4043484994583 -1.40434849945826 63 19 22.5559637517554 -3.5559637517554 64 18 21.6357962349107 -3.63579623491074 65 10 20.0772354506273 -10.0772354506273 66 29 26.8185260561770 2.18147394382296 67 31 21.245095461044 9.75490453895602 68 19 24.7317414370593 -5.73174143705926 69 9 18.9885271974535 -9.98852719745347 70 20 25.0999692099003 -5.09996920990034 71 28 20.4531273124649 7.54687268753515 72 19 20.3292718223563 -1.32927182235629 73 30 23.9796778246142 6.02032217538584 74 29 22.5968227360603 6.40317726393971 75 26 23.7659256546205 2.23407434537952 76 23 19.8335261621307 3.16647383786932 77 13 20.4391597164682 -7.4391597164682 78 21 21.5418978633052 -0.541897863305159 79 19 21.9959161653455 -2.99591616534555 80 28 24.3349547472959 3.6650452527041 81 23 24.0895034210596 -1.08950342105963 82 18 18.8812411437589 -0.881241143758895 83 21 19.4829676518691 1.5170323481309 84 20 23.3527126104212 -3.35271261042115 85 23 19.3212918498026 3.67870815019736 86 21 20.6020784266782 0.397921573321803 87 21 24.2037974909950 -3.20379749099496 88 15 21.9442442815213 -6.94424428152128 89 28 23.3849731939263 4.61502680607371 90 19 18.5526772875887 0.447322712411326 91 26 17.5708719826436 8.42912801735643 92 10 19.2443812598956 -9.24438125989557 93 16 17.2606818982934 -1.26068189829341 94 22 21.0088310207177 0.991168979282265 95 19 20.7102865807169 -1.71028658071693 96 31 27.3211366506654 3.6788633493346 97 31 21.4436556135426 9.5563443864574 98 29 21.8506667177151 7.14933328228494 99 19 19.7266769403657 -0.72667694036575 100 22 18.5800948633408 3.41990513665925 101 23 21.6405769449974 1.35942305500264 102 15 18.5849378710938 -3.58493787109381 103 20 19.3430603415878 0.656939658412232 104 18 20.7750253388308 -2.77502533883082 105 23 22.0235513322012 0.976448667798765 106 25 17.2997451183948 7.70025488160516 107 21 19.9464527285896 1.05354727141042 108 24 19.6411056519925 4.35889434800752 109 25 21.4618863033846 3.53811369661535 110 17 17.6290256952648 -0.629025695264763 111 13 16.5354744343378 -3.53547443433784 112 28 19.2096619179511 8.7903380820489 113 21 22.2530754335976 -1.25307543359763 114 25 28.8344860012843 -3.83448600128434 115 9 24.3447030604685 -15.3447030604685 116 16 20.0447572760186 -4.04475727601858 117 19 22.2414297892483 -3.24142978924827 118 17 19.4464254878734 -2.44642548787344 119 25 21.4128571790070 3.58714282099297 120 20 15.8711880377830 4.12881196221698 121 29 23.3318800801618 5.66811991983824 122 14 18.2034239831371 -4.20342398313708 123 22 23.3917758305226 -1.39177583052259 124 15 19.4525114037700 -4.45251140377004 125 19 19.4890535677657 -0.489053567765694 126 20 20.2584471483458 -0.258447148345814 127 15 20.1759768299860 -5.17597682998598 128 20 22.1657621074847 -2.16576210748473 129 18 21.6339918995047 -3.63399189950467 130 33 26.7418601152213 6.25813988477869 131 22 21.342094802663 0.657905197336996 132 16 18.1208913671108 -2.12089136711079 133 17 22.0288934695504 -5.02889346955039 134 16 18.1282554309696 -2.12825543096963 135 21 17.8271899348631 3.17281006513695 136 26 24.0778577767103 1.92214222328973 137 18 19.0532659555674 -1.05326595556735 138 18 21.0112897791571 -3.01128977915707 139 17 20.2350935619806 -3.23509356198065 140 22 21.1126329989331 0.887367001066946 141 30 22.4642442498191 7.53575575018091 142 30 24.8356057129410 5.16439428705897 143 24 20.4262088663089 3.57379113369113 144 21 22.1439313180332 -1.14393131803316 145 21 21.5827031211462 -0.58270312114622 146 29 24.6999799831502 4.30002001684978 147 31 23.6859140947000 7.31408590530003 148 20 20.6142232006236 -0.614223200623649 149 16 13.7184217524078 2.28157824759218 150 22 19.1679968574323 2.83200314256767 151 20 24.1261078827217 -4.12610788272173 152 28 21.342094802663 6.657905197337 153 38 25.6366984497637 12.3633015502363 154 22 19.0306913875683 2.96930861243166 155 20 22.2848368875067 -2.28483688750668 156 17 19.2278926077931 -2.22789260779315 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.449149843603004 0.898299687206009 0.550850156396996 10 0.310175664966469 0.620351329932939 0.68982433503353 11 0.364590846620064 0.729181693240127 0.635409153379936 12 0.69739353688798 0.605212926224039 0.302606463112020 13 0.59582995960866 0.80834008078268 0.40417004039134 14 0.523893485072347 0.952213029855307 0.476106514927653 15 0.50422347907114 0.99155304185772 0.49577652092886 16 0.477048619221325 0.95409723844265 0.522951380778675 17 0.445533958048086 0.891067916096171 0.554466041951914 18 0.563408872257626 0.873182255484747 0.436591127742374 19 0.483877293064469 0.967754586128938 0.516122706935531 20 0.677518591517262 0.644962816965477 0.322481408482738 21 0.69063373660551 0.61873252678898 0.30936626339449 22 0.93177439288514 0.136451214229719 0.0682256071148595 23 0.90577393008262 0.188452139834759 0.0942260699173795 24 0.960477656544275 0.0790446869114502 0.0395223434557251 25 0.944422830464106 0.111154339071789 0.0555771695358943 26 0.942666121880165 0.114667756239670 0.0573338781198348 27 0.924552077747891 0.150895844504218 0.0754479222521089 28 0.903208823992572 0.193582352014856 0.096791176007428 29 0.873480297558236 0.253039404883528 0.126519702441764 30 0.847149058868341 0.305701882263318 0.152850941131659 31 0.815104956191173 0.369790087617655 0.184895043808827 32 0.804407288339321 0.391185423321357 0.195592711660679 33 0.798450527884033 0.403098944231934 0.201549472115967 34 0.761720400733752 0.476559198532496 0.238279599266248 35 0.747360544510943 0.505278910978114 0.252639455489057 36 0.843541850512588 0.312916298974824 0.156458149487412 37 0.916622689559555 0.166754620880891 0.0833773104404453 38 0.934602284685727 0.130795430628545 0.0653977153142727 39 0.951695682292024 0.0966086354159522 0.0483043177079761 40 0.936530197802065 0.126939604395871 0.0634698021979354 41 0.93811787036936 0.123764259261281 0.0618821296306405 42 0.922050873170317 0.155898253659365 0.0779491268296826 43 0.90205522148358 0.195889557032839 0.0979447785164195 44 0.90604346365224 0.187913072695520 0.0939565363477602 45 0.891181788269272 0.217636423461457 0.108818211730729 46 0.898246539237701 0.203506921524597 0.101753460762299 47 0.875452115501979 0.249095768996042 0.124547884498021 48 0.89441943828501 0.211161123429978 0.105580561714989 49 0.899956216236305 0.200087567527391 0.100043783763695 50 0.87592390089626 0.248152198207481 0.124076099103741 51 0.864394641946146 0.271210716107707 0.135605358053854 52 0.85109968628666 0.297800627426679 0.148900313713340 53 0.820426190854944 0.359147618290113 0.179573809145057 54 0.837629793738342 0.324740412523316 0.162370206261658 55 0.81035357736533 0.379292845269341 0.189646422634671 56 0.791008288167243 0.417983423665515 0.208991711832757 57 0.759031546694227 0.481936906611545 0.240968453305773 58 0.759603463272288 0.480793073455425 0.240396536727712 59 0.832923145574848 0.334153708850305 0.167076854425152 60 0.808552614920142 0.382894770159716 0.191447385079858 61 0.820724021181165 0.358551957637669 0.179275978818834 62 0.79057423814451 0.41885152371098 0.20942576185549 63 0.773637660815885 0.452724678368230 0.226362339184115 64 0.758885007718297 0.482229984563405 0.241114992281702 65 0.84551944736446 0.308961105271082 0.154480552635541 66 0.820777072751557 0.358445854496885 0.179222927248443 67 0.889805091768424 0.220389816463152 0.110194908231576 68 0.896236540653996 0.207526918692007 0.103763459346003 69 0.94638684316408 0.107226313671839 0.0536131568359194 70 0.949563179704243 0.100873640591513 0.0504368202957566 71 0.961045679247015 0.0779086415059708 0.0389543207529854 72 0.950917495062785 0.0981650098744298 0.0490825049372149 73 0.956170597084793 0.0876588058304136 0.0438294029152068 74 0.963736743401594 0.0725265131968117 0.0362632565984058 75 0.955408828246482 0.0891823435070361 0.0445911717535181 76 0.947725502602412 0.104548994795177 0.0522744973975885 77 0.961992006461092 0.0760159870778155 0.0380079935389078 78 0.951182861333833 0.0976342773323345 0.0488171386661673 79 0.943909218252887 0.112181563494226 0.0560907817471131 80 0.937095850910504 0.125808298178992 0.0629041490894958 81 0.924943359711019 0.150113280577962 0.0750566402889811 82 0.907240198126503 0.185519603746993 0.0927598018734967 83 0.887451474220757 0.225097051558486 0.112548525779243 84 0.875543564331595 0.248912871336810 0.124456435668405 85 0.861248956385484 0.277502087229032 0.138751043614516 86 0.834957265245764 0.330085469508471 0.165042734754236 87 0.822991981746708 0.354016036506584 0.177008018253292 88 0.84889477679186 0.302210446416280 0.151105223208140 89 0.84537205300792 0.309255893984159 0.154627946992079 90 0.816138108269137 0.367723783461727 0.183861891730863 91 0.871329423681885 0.25734115263623 0.128670576318115 92 0.92550928142583 0.148981437148341 0.0744907185741704 93 0.908159865930719 0.183680268138563 0.0918401340692813 94 0.88718300895334 0.225633982093321 0.112816991046660 95 0.867018442757499 0.265963114485003 0.132981557242501 96 0.850786774689867 0.298426450620265 0.149213225310133 97 0.908383231224314 0.183233537551372 0.091616768775686 98 0.914007462459829 0.171985075080343 0.0859925375401715 99 0.89491195093965 0.2101760981207 0.10508804906035 100 0.880880191126805 0.238239617746389 0.119119808873195 101 0.855902752778525 0.28819449444295 0.144097247221475 102 0.83812340075783 0.323753198484339 0.161876599242170 103 0.805407241248054 0.389185517503893 0.194592758751946 104 0.782594023532291 0.434811952935417 0.217405976467709 105 0.755268946145143 0.489462107709715 0.244731053854857 106 0.818334063050485 0.36333187389903 0.181665936949515 107 0.785268628021567 0.429462743956865 0.214731371978433 108 0.769935395306455 0.460129209387089 0.230064604693545 109 0.742489085632706 0.515021828734589 0.257510914367294 110 0.704288750185034 0.591422499629933 0.295711249814966 111 0.692937966584408 0.614124066831185 0.307062033415592 112 0.761707429800842 0.476585140398315 0.238292570199158 113 0.720804670716655 0.55839065856669 0.279195329283345 114 0.701553713324773 0.596892573350454 0.298446286675227 115 0.960917619586651 0.0781647608266971 0.0390823804133485 116 0.957170292495802 0.0856594150083952 0.0428297075041976 117 0.955122557232714 0.0897548855345717 0.0448774427672859 118 0.942262128113584 0.115475743772832 0.057737871886416 119 0.929900440659942 0.140199118680115 0.0700995593400577 120 0.940969109165244 0.118061781669511 0.0590308908347557 121 0.93635177541822 0.127296449163562 0.0636482245817809 122 0.925374128816836 0.149251742366327 0.0746258711831637 123 0.912074081433844 0.175851837132312 0.0879259185661562 124 0.907125762683583 0.185748474632833 0.0928742373164166 125 0.877032982975456 0.245934034049088 0.122967017024544 126 0.841138047213152 0.317723905573697 0.158861952786848 127 0.858440369188894 0.283119261622212 0.141559630811106 128 0.848465742840752 0.303068514318496 0.151534257159248 129 0.861680296082617 0.276639407834765 0.138319703917383 130 0.84091248429131 0.31817503141738 0.15908751570869 131 0.801222261869934 0.397555476260133 0.198777738130066 132 0.748928197776579 0.502143604446842 0.251071802223421 133 0.865097170276716 0.269805659446568 0.134902829723284 134 0.829691395012636 0.340617209974728 0.170308604987364 135 0.823288063498986 0.353423873002029 0.176711936501014 136 0.76521040763914 0.46957918472172 0.23478959236086 137 0.708820143726534 0.582359712546933 0.291179856273466 138 0.759584393467222 0.480831213065556 0.240415606532778 139 0.686322647804708 0.627354704390584 0.313677352195292 140 0.675605966398197 0.648788067203605 0.324394033601802 141 0.733831155396905 0.532337689206189 0.266168844603095 142 0.644604198060763 0.710791603878475 0.355395801939238 143 0.607584542229154 0.784830915541693 0.392415457770846 144 0.502692480073742 0.994615039852516 0.497307519926258 145 0.462013750911528 0.924027501823056 0.537986249088472 146 0.376875889746633 0.753751779493266 0.623124110253367 147 0.311058583670905 0.62211716734181 0.688941416329095 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 12 0.0863309352517986 OK

Charts produced by software:

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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') }

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Software written by Ed van Stee & Patrick Wessa

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