*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: Fri, 24 Dec 2010 15:12:46 +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/24/t1293203437ryi04l4hmoqwf4c.htm/, Retrieved Fri, 24 Dec 2010 16:10:49 +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/24/t1293203437ryi04l4hmoqwf4c.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 «

15 10 12 16 6 2 0 0 12 9 7 12 6 1 1 2 9 12 11 11 4 1 2 1 10 12 11 12 6 0 0 0 13 9 14 14 6 0 0 0 16 11 16 16 7 1 0 0 14 12 13 13 6 0 0 0 16 11 13 14 7 1 1 0 10 12 5 13 6 0 0 0 8 12 8 13 4 2 0 1 12 11 14 13 5 1 0 0 15 11 15 15 8 0 0 0 14 12 8 14 4 0 1 0 14 6 13 12 6 1 1 2 12 13 12 12 6 1 2 1 12 11 11 12 5 0 0 0 10 12 8 11 4 0 0 0 4 10 4 10 2 0 0 0 14 11 15 15 8 0 1 0 15 12 12 16 7 0 0 0 16 12 14 14 6 0 0 0 12 12 9 13 4 0 1 0 12 11 16 13 4 0 0 0 12 12 10 13 4 0 0 1 12 12 8 13 5 1 0 1 12 12 14 14 4 0 0 0 11 6 6 9 4 3 2 1 11 5 16 14 6 1 0 0 11 12 11 12 6 1 1 0 11 14 7 13 6 1 1 0 11 12 13 11 4 3 1 1 11 9 7 13 2 0 0 0 15 11 14 15 7 0 0 0 15 11 17 16 6 0 0 0 9 11 15 15 7 0 0 0 16 12 8 14 4 0 0 0 13 10 8 8 4 0 2 1 9 12 11 11 4 1 0 0 16 11 16 15 6 0 0 0 12 12 10 15 6 0 0 0 15 9 5 11 3 0 0 2 5 15 8 12 3 0 0 0 11 11 8 12 6 2 2 0 17 11 15 14 5 2 2 0 9 15 6 8 4 0 1 1 13 12 16 16 6 0 0 0 16 9 16 16 6 0 0 0 16 12 16 14 6 0 0 0 14 9 19 12 6 2 0 2 16 11 14 15 6 1 0 0 11 12 15 1 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 12 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Popularity[t] = -0.340957140032500 + 0.117850045256176FindingFriends[t] + 0.240882362067202KnowingPeople[t] + 0.372073239661235Liked[t] + 0.610915345027388Celebrity[t] -0.0436536294476873B[t] + 0.171832293382581`2B`[t] + 0.50219147193765`3B`[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) -0.340957140032500 1.464149 -0.2329 0.816184 0.408092 FindingFriends 0.117850045256176 0.096374 1.2228 0.223335 0.111668 KnowingPeople 0.240882362067202 0.061604 3.9102 0.00014 7e-05 Liked 0.372073239661235 0.096858 3.8414 0.000181 9e-05 Celebrity 0.610915345027388 0.156335 3.9077 0.000141 7.1e-05 B -0.0436536294476873 0.223131 -0.1956 0.845159 0.42258 `2B` 0.171832293382581 0.268543 0.6399 0.523248 0.261624 `3B` 0.50219147193765 0.3164 1.5872 0.1146 0.0573 Multiple Linear Regression - Regression Statistics Multiple R 0.71619317008086 R-squared 0.512932656870471 Adjusted R-squared 0.489895687938669 F-TEST (value) 22.265631315862 F-TEST (DF numerator) 7 F-TEST (DF denominator) 148 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.09738583856901 Sum Squared Residuals 651.056048662812 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 15 13.2594883031844 1.74051169681562 2 12 11.6688023556528 0.331197644347162 3 9 11.0616188314191 -2.06161883141909 4 10 11.8533203318800 -1.85332033187998 5 13 12.9665637616355 0.0334362383644692 6 16 14.9954367711845 1.00456322881554 7 14 12.7071582956756 1.29284170432438 8 16 13.7004754990430 2.29952450095704 9 10 10.780099399138 -0.780099399138003 10 8 10.6958000083271 -2.69580000832711 11 12 12.1756216380116 -0.175621638011571 12 15 15.0370501439311 -0.0370501439310947 13 14 10.8248213283286 3.17517867167135 14 14 12.7605463922875 1.23945360771248 15 12 13.0142551684585 -1.01425516845848 16 12 11.1245549415964 0.875445058403584 17 10 9.53676931596236 0.463230684037638 18 4 6.74363584746519 -2.74363584746519 19 14 15.2088824373137 -1.20888243731368 20 15 14.1934109976195 0.806589002380489 21 16 13.3201138974041 2.67988610259594 22 12 10.6936304507346 1.30636954926538 23 12 12.0901246465663 -0.0901246465662739 24 12 11.2648719913569 0.735128008643113 25 12 11.3503689828022 0.649631017197816 26 12 12.0982832073493 -0.0982832073492803 27 11 8.31865301132818 2.68134698867182 28 11 12.9332746752975 -1.93327467529754 29 11 11.9814989958149 -0.981498995814874 30 11 11.6257428777197 -0.625742877719652 31 11 11.2842440032755 -0.284244003275542 32 11 8.46465260739433 2.53534739260567 33 15 14.1852524368365 0.814747563163496 34 15 14.6690574176720 0.330942582328042 35 9 14.4261347989037 -5.42613479890371 36 16 10.6529890349461 5.34701096505393 37 13 9.03070556516912 3.96929443483088 38 9 10.2157627727163 -1.21576277271628 39 16 14.0561018159435 1.94389818405648 40 12 12.7286576887965 -0.728657688796484 41 15 8.85403969284014 6.14596030715986 42 5 9.65147734636474 -4.65147734636474 43 11 11.2691805282920 -0.269180528291986 44 17 13.0885881970575 3.91141180294252 45 9 8.96635877393301 0.0336412260669887 46 13 14.5460251008609 -1.54602510086093 47 16 14.1924749650924 1.80752503490760 48 16 13.8018786215385 2.19812137846154 49 14 14.343904777629 -0.343904777628995 50 16 13.5306834623614 2.46931653763857 51 11 12.8168497801488 -1.81684978014879 52 11 11.8687014209189 -0.868701420918887 53 11 13.7292333448507 -2.72923334485071 54 12 12.2305758430961 -0.230575843096066 55 12 13.8192931556826 -1.81929315568257 56 12 12.0829021183104 -0.0829021183103742 57 14 13.7055279694031 0.294472030596851 58 10 10.9193976374449 -0.919397637444866 59 9 9.39051061781011 -0.390510617810114 60 12 12.2715659514931 -0.271565951493069 61 10 10.0318748724346 -0.031874872434624 62 14 12.9828808832015 1.01711911679846 63 8 9.94996681078992 -1.94996681078992 64 16 14.5003312147122 1.49966878528781 65 14 15.7231004033153 -1.72310040331527 66 14 10.7545219586362 3.24547804136377 67 12 11.2444452435536 0.755554756446359 68 14 13.3994925847674 0.600507415232604 69 7 11.1327091568048 -4.13270915680476 70 19 13.9330694991325 5.0669305008675 71 15 12.8424296866717 2.15757031332825 72 8 11.2639043799735 -3.26390437997346 73 10 14.2866196349010 -4.28661963490102 74 13 12.9593412333796 0.0406587666203699 75 13 11.2331446679168 1.76685533208317 76 10 10.3937492946118 -0.393749294611803 77 12 9.057044848529 2.94295515147099 78 15 17.3038760808146 -2.30387608081458 79 7 11.0644184649571 -4.06441846495707 80 14 14.1872926935376 -0.187292693537553 81 10 8.43389042931651 1.56610957068349 82 6 9.70389833189643 -3.70389833189643 83 11 11.2566306516474 -0.25663065164738 84 12 9.29588695389516 2.70411304610484 85 14 14.1933059636853 -0.193305963685324 86 12 13.3232559122579 -1.32325591225786 87 14 14.3031024820927 -0.30310248209268 88 11 10.0658729421299 0.934127057870083 89 10 9.27282579787637 0.727174202123635 90 13 13.3323820844243 -0.332382084424296 91 8 10.2727572345018 -2.27275723450183 92 9 11.7375105433249 -2.73751054332485 93 6 12.0912264047190 -6.09122640471903 94 12 13.1881631426699 -1.18816314266988 95 14 12.2140929959044 1.78590700409559 96 11 10.5188218681239 0.481178131876121 97 8 10.6256841059207 -2.62568410592072 98 7 9.29792721059621 -2.29792721059621 99 9 10.5302990994509 -1.53029909945087 100 14 12.1807679851354 1.81923201486456 101 13 10.2788755385838 2.72112446141622 102 15 12.7071582956756 2.29284170432438 103 5 5.35466983018372 -0.354669830183719 104 15 12.2601466724988 2.73985332750122 105 13 12.2680752440308 0.731924755969187 106 12 11.6248427696235 0.375157230376472 107 6 7.7895202723255 -1.78952027232549 108 7 9.6679601935564 -2.66796019355640 109 13 8.5752801243946 4.4247198756054 110 16 14.9243464457988 1.07565355420121 111 10 13.3334547297419 -3.33345472974191 112 16 15.1569404458883 0.84305955411168 113 15 13.1941052913649 1.80589470863513 114 8 8.43074841446271 -0.430748414462713 115 11 12.6098716110132 -1.6098716110132 116 13 13.2430819236266 -0.243081923626609 117 16 15.2363191332517 0.763680866748342 118 11 8.71165327354349 2.28834672645651 119 14 14.4404116637687 -0.440411663768671 120 9 10.2414724804339 -1.24147248043391 121 8 10.2881383235407 -2.28813832354073 122 8 11.1352322528836 -3.13523225288359 123 11 11.9044264788345 -0.904426478834538 124 12 13.3284381838127 -1.32843818381271 125 11 11.0872496054817 -0.0872496054816573 126 14 14.6275200122560 -0.627520012255971 127 11 12.7034912388105 -1.70349123881052 128 14 12.3289667519324 1.67103324806757 129 13 14.7677542830899 -1.76775428308994 130 12 10.7821396558391 1.21786034416095 131 4 5.97909173317461 -1.97909173317461 132 15 12.9351423947771 2.06485760522290 133 10 11.3971355142685 -1.39713551426854 134 13 13.8895925253750 -0.889592525374987 135 15 14.2117931431470 0.788206856852951 136 12 13.2757008911194 -1.27570089111944 137 13 13.3201138974041 -0.320113897404057 138 8 7.92246775127824 0.0775322487217605 139 10 10.5697598234316 -0.569759823431602 140 15 13.6840285762823 1.31597142371771 141 16 14.4322531029857 1.56774689701434 142 16 14.9160580838211 1.08394191617888 143 14 12.9747223224185 1.02527767758146 144 14 13.0884875086980 0.911512491302045 145 12 10.6663255217093 1.33367447829073 146 15 13.1331087495291 1.86689125047093 147 13 12.8681685072245 0.131831492775490 148 16 13.2022638521479 2.79773614785212 149 14 13.5609962594713 0.439003740528741 150 8 10.0318748724346 -2.03187487243462 151 16 13.7328285528538 2.26717144714616 152 16 15.9164612026538 0.0835387973461524 153 12 13.1889230198100 -1.18892301981002 154 11 12.2919572751686 -1.29195727516855 155 16 15.9164612026538 0.0835387973461524 156 9 10.0318748724346 -1.03187487243462 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.284051307091087 0.568102614182174 0.715948692908913 12 0.245727430543219 0.491454861086438 0.754272569456781 13 0.293531730457060 0.587063460914119 0.70646826954294 14 0.200301873794721 0.400603747589441 0.79969812620528 15 0.122471036879390 0.244942073758780 0.87752896312061 16 0.100241936937113 0.200483873874225 0.899758063062887 17 0.0787920615111758 0.157584123022352 0.921207938488824 18 0.122404801195032 0.244809602390064 0.877595198804968 19 0.217726660115610 0.435453320231219 0.78227333988439 20 0.157705740600970 0.315411481201941 0.84229425939903 21 0.180729143909594 0.361458287819187 0.819270856090406 22 0.132183218133252 0.264366436266503 0.867816781866748 23 0.100398762660240 0.200797525320481 0.89960123733976 24 0.0693045915398021 0.138609183079604 0.930695408460198 25 0.0524550747861004 0.104910149572201 0.9475449252139 26 0.0399844851410997 0.0799689702821994 0.9600155148589 27 0.0598272896785518 0.119654579357104 0.940172710321448 28 0.117873532987169 0.235747065974338 0.882126467012831 29 0.0924615780623827 0.184923156124765 0.907538421937617 30 0.0710435295919271 0.142087059183854 0.928956470408073 31 0.051160209961623 0.102320419923246 0.948839790038377 32 0.0445448488494241 0.0890896976988482 0.955455151150576 33 0.0314290206032636 0.0628580412065272 0.968570979396736 34 0.0221636447624367 0.0443272895248734 0.977836355237563 35 0.182673891948234 0.365347783896468 0.817326108051766 36 0.370520364808077 0.741040729616153 0.629479635191923 37 0.517377824332025 0.96524435133595 0.482622175667975 38 0.463128992742579 0.926257985485158 0.536871007257421 39 0.448216663904003 0.896433327808006 0.551783336095997 40 0.410821746628199 0.821643493256398 0.589178253371801 41 0.67543707611811 0.64912584776378 0.32456292388189 42 0.83048369887589 0.33903260224822 0.16951630112411 43 0.794627385763124 0.410745228473751 0.205372614236876 44 0.83868794382951 0.322624112340980 0.161312056170490 45 0.81475541247398 0.37048917505204 0.18524458752602 46 0.807766408362064 0.384467183275872 0.192233591637936 47 0.782548125491309 0.434903749017383 0.217451874508691 48 0.80099088089677 0.398018238206462 0.199009119103231 49 0.763095850256352 0.473808299487296 0.236904149743648 50 0.780973205457225 0.438053589085549 0.219026794542775 51 0.757082851342872 0.485834297314255 0.242917148657128 52 0.732128180570304 0.535743638859391 0.267871819429696 53 0.840312405860343 0.319375188279315 0.159687594139657 54 0.807639069993114 0.384721860013771 0.192360930006886 55 0.804379849877538 0.391240300244924 0.195620150122462 56 0.7712752540834 0.457449491833201 0.228724745916601 57 0.732268950888216 0.535462098223569 0.267731049111784 58 0.692192701073237 0.615614597853526 0.307807298926763 59 0.661194964219663 0.677610071560674 0.338805035780337 60 0.643311342893094 0.713377314213813 0.356688657106906 61 0.596418157142436 0.807163685715129 0.403581842857564 62 0.556013333143399 0.887973333713203 0.443986666856601 63 0.542967889044806 0.914064221910389 0.457032110955194 64 0.529285137670853 0.941429724658293 0.470714862329147 65 0.532017396777 0.935965206446 0.467982603223 66 0.596813315049907 0.806373369900186 0.403186684950093 67 0.553289451310487 0.893421097379027 0.446710548689513 68 0.511645774274071 0.976708451451858 0.488354225725929 69 0.683911400116417 0.632177199767166 0.316088599883583 70 0.84808273135509 0.303834537289819 0.151917268644909 71 0.84459872611896 0.310802547762079 0.155401273881040 72 0.880829260934446 0.238341478131109 0.119170739065554 73 0.945459682436079 0.109080635127842 0.0545403175639212 74 0.931209910402904 0.137580179194192 0.0687900895970959 75 0.923540532707272 0.152918934585455 0.0764594672927276 76 0.905011951293937 0.189976097412127 0.0949880487060633 77 0.924134938512681 0.151730122974638 0.0758650614873191 78 0.931767812511598 0.136464374976804 0.068232187488402 79 0.9712456585068 0.0575086829863991 0.0287543414931995 80 0.962527467132067 0.0749450657358662 0.0374725328679331 81 0.959397438899141 0.0812051222017173 0.0406025611008586 82 0.979705144616338 0.0405897107673232 0.0202948553836616 83 0.97366612300419 0.0526677539916197 0.0263338769958098 84 0.979118139563039 0.0417637208739227 0.0208818604369614 85 0.97228802238923 0.0554239552215376 0.0277119776107688 86 0.967070853758719 0.0658582924825616 0.0329291462412808 87 0.95781481036991 0.0843703792601777 0.0421851896300888 88 0.951104066106044 0.0977918677879118 0.0488959338939559 89 0.951685559556256 0.0966288808874874 0.0483144404437437 90 0.93812715395344 0.123745692093122 0.0618728460465608 91 0.941002632309504 0.117994735380991 0.0589973676904957 92 0.952735318298962 0.0945293634020768 0.0472646817010384 93 0.996895006349853 0.00620998730029496 0.00310499365014748 94 0.995881007258283 0.00823798548343327 0.00411899274171663 95 0.994941390506184 0.0101172189876329 0.00505860949381644 96 0.993079541870508 0.0138409162589837 0.00692045812949183 97 0.993987535336127 0.0120249293277468 0.00601246466387342 98 0.994844267596645 0.0103114648067103 0.00515573240335515 99 0.993127132629945 0.0137457347401099 0.00687286737005497 100 0.991694414921074 0.0166111701578523 0.00830558507892614 101 0.994473981481246 0.0110520370375088 0.00552601851875441 102 0.994406558393622 0.0111868832127562 0.00559344160637809 103 0.992218014546987 0.0155639709060270 0.00778198545301349 104 0.994019349086544 0.0119613018269119 0.00598065091345593 105 0.991441415159986 0.0171171696800276 0.00855858484001379 106 0.988497672019068 0.0230046559618644 0.0115023279809322 107 0.987400062007217 0.0251998759855668 0.0125999379927834 108 0.991634893610155 0.0167302127796901 0.00836510638984506 109 0.999074212556893 0.00185157488621441 0.000925787443107207 110 0.998673665883945 0.00265266823211051 0.00132633411605526 111 0.99967486858687 0.000650262826258955 0.000325131413129477 112 0.9994564864295 0.00108702714100130 0.000543513570500648 113 0.999343629893177 0.00131274021364511 0.000656370106822554 114 0.998975461555967 0.0020490768880651 0.00102453844403255 115 0.998627048971347 0.00274590205730567 0.00137295102865283 116 0.997757061148465 0.00448587770306973 0.00224293885153487 117 0.996427913871057 0.00714417225788633 0.00357208612894317 118 0.999233399109725 0.00153320178054984 0.000766600890274918 119 0.998789316895924 0.0024213662081517 0.00121068310407585 120 0.998092158470971 0.00381568305805747 0.00190784152902874 121 0.99799259589696 0.00401480820608018 0.00200740410304009 122 0.99797816099537 0.00404367800925835 0.00202183900462917 123 0.997082162127155 0.00583567574569092 0.00291783787284546 124 0.997711406169992 0.0045771876600169 0.00228859383000845 125 0.996134091941121 0.00773181611775705 0.00386590805887853 126 0.994426372579375 0.0111472548412498 0.0055736274206249 127 0.992194127843947 0.0156117443121068 0.00780587215605341 128 0.988491859747252 0.0230162805054967 0.0115081402527483 129 0.994688008304049 0.0106239833919030 0.00531199169595151 130 0.996552633525974 0.00689473294805252 0.00344736647402626 131 0.994617201764243 0.0107655964715141 0.00538279823575704 132 0.993957923003745 0.0120841539925108 0.00604207699625539 133 0.990806264327314 0.0183874713453729 0.00919373567268646 134 0.98402298987255 0.0319540202548992 0.0159770101274496 135 0.9721622218108 0.0556755563783988 0.0278377781891994 136 0.968542830349594 0.0629143393008114 0.0314571696504057 137 0.95735278762381 0.0852944247523812 0.0426472123761906 138 0.934835131228441 0.130329737543119 0.0651648687715593 139 0.921478877362845 0.157042245274311 0.0785211226371553 140 0.871929862311808 0.256140275376384 0.128070137688192 141 0.877114855021455 0.245770289957089 0.122885144978545 142 0.802854127032057 0.394291745935885 0.197145872967943 143 0.735516790175482 0.528966419649036 0.264483209824518 144 0.713612848629826 0.572774302740348 0.286387151370174 145 0.580909927333318 0.838180145333365 0.419090072666682 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 20 0.148148148148148 NOK 5% type I error level 45 0.333333333333333 NOK 10% type I error level 61 0.451851851851852 NOK

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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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