Time Series Analysis WS8 1

*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, 26 Nov 2010 07:10:57 +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/Nov/26/t1290755734ev4702qweumnfoz.htm/, Retrieved Fri, 26 Nov 2010 08:15:44 +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/Nov/26/t1290755734ev4702qweumnfoz.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 «

43880 25222 43110 21333 44496 19778 44164 25943 40399 21698 36763 20077 37903 25673 35532 19094 35533 19306 32110 15443 33374 15179 35462 18288 33508 18264 36080 16406 34560 15678 38737 19657 38144 18821 37594 19493 36424 21078 36843 19296 37246 19985 38661 16972 40454 16951 44928 23126 48441 24890 48140 21042 45998 20842 47369 23904 49554 22578 47510 25452 44873 21928 45344 25227 42413 26210 36912 17436 43452 21258 42142 25638 44382 23516 43636 23891 44167 24617 44423 26174 42868 23339 43908 23660 42013 26500 38846 22469 35087 23163 33026 16170 34646 18267 37135 20561 37985 20372 43121 19017 43722 18242 43630 20937 42234 22065 39351 16731 39327 21943 35704 19254 30466 16397 28155 13644 29257 14375 29998 14814 32529 16061 34787 14784 33855 12824 34556 18282 31348 14936 30805 15701 28353 16394 24514 13085 21106 11431 21346 9334 23335 10921 24379 11725 26290 13077 30084 11794 29429 11047 30632 16797 27349 11482 27264 12657 27474 15277 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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation OPENVAC[t] = + 13329.2227586361 + 1.26119630769380OntvangenJobs[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) 13329.2227586361 1069.450689 12.4636 0 0 OntvangenJobs 1.26119630769380 0.064259 19.6268 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.867211275297138 R-squared 0.752055396002488 Adjusted R-squared 0.750103076285972 F-TEST (value) 385.211187307285 F-TEST (DF numerator) 1 F-TEST (DF denominator) 127 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3965.95767870293 Sum Squared Residuals 1997560179.27637 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 43880 45139.1160312889 -1259.11603128891 2 43110 40234.3235906678 2875.67640933216 3 44496 38273.163332204 6222.836667796 4 44164 46048.4385691363 -1884.43856913626 5 40399 40694.6602429761 -295.660242976089 6 36763 38650.2610282044 -1887.26102820444 7 37903 45707.9155660589 -7804.91556605893 8 35532 37410.5050577414 -1878.50505774144 9 35533 37677.8786749725 -2144.87867497253 10 32110 32805.8773383514 -695.877338351391 11 33374 32472.9215131202 901.078486879771 12 35462 36393.9808337402 -931.980833740243 13 33508 36363.7121223556 -2855.71212235559 14 36080 34020.4093826605 2059.59061733948 15 34560 33102.2584706594 1457.74152934057 16 38737 38120.5585789731 616.441421026949 17 38144 37066.198465741 1077.80153425896 18 37594 37913.7223845113 -319.722384511268 19 36424 39912.7185322059 -3488.71853220594 20 36843 37665.2667118956 -822.26671189559 21 37246 38534.2309678966 -1288.23096789662 22 38661 34734.2464928152 3926.75350718479 23 40454 34707.7613703536 5746.23862964636 24 44928 42495.6485703628 2432.35142963717 25 48441 44720.3988571347 3720.60114286531 26 48140 39867.315465129 8272.68453487104 27 45998 39615.0762035902 6382.9237964098 28 47369 43476.8592977486 3892.14070225140 29 49554 41804.5129937466 7749.48700625337 30 47510 45429.1911820586 2080.80881794140 31 44873 40984.7353937457 3888.26460625434 32 45344 45145.4220128275 198.577987172502 33 42413 46385.1779832905 -3972.1779832905 34 36912 35319.4415795851 1592.55842041487 35 43452 40139.7338675908 3312.26613240918 36 42142 45663.7736952896 -3521.77369528965 37 44382 42987.5151303634 1394.48486963659 38 43636 43460.4637457486 175.536254251414 39 44167 44376.0922651343 -209.092265134281 40 44423 46339.7749162135 -1916.77491621352 41 42868 42764.2833839016 103.716616098390 42 43908 43169.1273986713 738.872601328681 43 42013 46750.9249125217 -4737.9249125217 44 38846 41667.042596208 -2821.04259620801 45 35087 42542.3128337475 -7455.3128337475 46 33026 33722.7670540448 -696.767054044782 47 34646 36367.4957112787 -1721.49571127867 48 37135 39260.6800411282 -2125.68004112824 49 37985 39022.3139389741 -1037.31393897411 50 43121 37313.392942049 5807.60705795098 51 43722 36335.9658035863 7386.03419641367 52 43630 39734.8898528211 3895.11014717889 53 42234 41157.5192878997 1076.48071210029 54 39351 34430.298182661 4920.701817339 55 39327 41003.6533383611 -1676.65333836107 56 35704 37612.2964669725 -1908.29646697245 57 30466 34009.0586158913 -3543.05861589127 58 28155 30536.9851808103 -2381.98518081025 59 29257 31458.9196817344 -2201.91968173442 60 29998 32012.584860812 -2014.58486081199 61 32529 33585.2966565062 -1056.29665650616 62 34787 31974.7489715812 2812.25102841882 63 33855 29502.8042085013 4352.19579149866 64 34556 36386.4136558941 -1830.41365589408 65 31348 32166.4508103506 -818.450810350636 66 30805 33131.2659857364 -2326.26598573639 67 28353 34005.2750269682 -5652.27502696819 68 24514 29831.9764448094 -5317.97644480942 69 21106 27745.9577518839 -6639.95775188388 70 21346 25101.22909465 -3755.22909464999 71 23335 27102.7476349600 -3767.74763496004 72 24379 28116.7494663459 -3737.74946634586 73 26290 29821.8868743479 -3531.88687434787 74 30084 28203.7720115767 1880.22798842327 75 29429 27261.6583697295 2167.34163027054 76 30632 34513.5371389688 -3881.53713896879 77 27349 27810.2787635763 -461.278763576262 78 27264 29292.1844251165 -2028.18442511647 79 27474 32596.5187512742 -5122.51875127422 80 24482 28949.1390294238 -4467.13902942376 81 21453 28458.5336657309 -7005.53366573087 82 18788 23916.9657617255 -5128.96576172551 83 19282 24589.1833937263 -5307.1833937263 84 19713 25861.7304681893 -6148.73046818935 85 21917 27792.6220152685 -5875.62201526855 86 23812 25378.6922823426 -1566.69228234262 87 23785 24965.0198934191 -1180.01989341906 88 24696 27228.8672657294 -2532.86726572942 89 24562 26023.1635955742 -1461.16359557415 90 23580 25864.2528608047 -2284.25286080473 91 24939 27428.1362823450 -2489.13628234504 92 23899 28391.6902614231 -4492.6902614231 93 21454 26940.0533112675 -5486.05331126754 94 19761 23519.6889248020 -3758.68892480197 95 19815 24179.2945937258 -4364.29459372582 96 20780 27909.9132718841 -7129.91327188407 97 23462 26507.4629777286 -3045.46297772857 98 25005 23667.2488928021 1337.75110719786 99 24725 22916.8370897243 1808.16291027567 100 26198 25337.0728041887 860.927195811273 101 27543 26460.7987143439 1082.2012856561 102 26471 27025.8146601907 -554.814660190721 103 26558 27880.9057568071 -1322.90575680712 104 25317 27732.0845924992 -2415.08459249925 105 22896 26455.7539291131 -3559.75392911312 106 22248 20893.8782121835 1354.12178781652 107 23406 23867.7791057255 -461.779105725454 108 25073 26658.8065346518 -1585.80653465183 109 27691 25512.3790909582 2178.62090904184 110 30599 25063.3932054192 5535.60679458083 111 31948 24823.7659069574 7124.23409304265 112 32946 26561.6944189594 6384.3055810406 113 34012 28952.9226183468 5059.07738165316 114 32936 25944.9694244971 6991.03057550286 115 32974 31022.5457592724 1951.45424072764 116 30951 29033.6391820392 1917.36081796075 117 29812 28882.295625116 929.70437488401 118 29010 23499.5097838789 5510.49021612114 119 31068 27115.3595980370 3952.64040196302 120 32447 29259.3933211164 3187.60667888357 121 34844 30552.1195365026 4291.88046349742 122 35676 27208.6881248063 8467.31187519368 123 35387 24527.3847746493 10859.6152253507 124 36488 27878.3833641917 8609.61663580827 125 35652 30605.0897814257 5046.91021857428 126 33488 27016.9862860369 6471.01371396314 127 32914 32382.1153789663 531.884621033724 128 29781 30486.5373285025 -705.537328502499 129 27951 28754.9147980389 -803.914798038916 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.115330292386643 0.230660584773286 0.884669707613357 6 0.303117147241413 0.606234294482827 0.696882852758587 7 0.423787566596275 0.84757513319255 0.576212433403725 8 0.465607925770422 0.931215851540844 0.534392074229578 9 0.4328810733839 0.8657621467678 0.5671189266161 10 0.384772344554447 0.769544689108894 0.615227655445553 11 0.288832377243652 0.577664754487304 0.711167622756348 12 0.213477518591308 0.426955037182617 0.786522481408692 13 0.185499223813558 0.370998447627116 0.814500776186442 14 0.13815602142941 0.27631204285882 0.86184397857059 15 0.094193389010525 0.18838677802105 0.905806610989475 16 0.0639730070113265 0.127946014022653 0.936026992988674 17 0.0427782174884846 0.0855564349769693 0.957221782511515 18 0.0264592023620766 0.0529184047241531 0.973540797637923 19 0.0220044270538301 0.0440088541076603 0.97799557294617 20 0.013377920355186 0.026755840710372 0.986622079644814 21 0.0080381710693775 0.0160763421387550 0.991961828930622 22 0.00822919013410653 0.0164583802682131 0.991770809865893 23 0.0146094017543531 0.0292188035087063 0.985390598245647 24 0.0177033496242719 0.0354066992485439 0.982296650375728 25 0.0322662048622570 0.0645324097245141 0.967733795137743 26 0.132270090133650 0.264540180267299 0.86772990986635 27 0.199858509420388 0.399717018840776 0.800141490579612 28 0.205526403188131 0.411052806376262 0.794473596811869 29 0.347900489215 0.69580097843 0.652099510785 30 0.305433961498129 0.610867922996259 0.694566038501871 31 0.29226334946086 0.58452669892172 0.70773665053914 32 0.244175719501356 0.488351439002712 0.755824280498644 33 0.250245669124572 0.500491338249144 0.749754330875428 34 0.207961647767542 0.415923295535084 0.792038352232458 35 0.190278199084450 0.380556398168900 0.80972180091555 36 0.181983632272979 0.363967264545958 0.81801636772702 37 0.151110626278011 0.302221252556022 0.848889373721989 38 0.120679765017098 0.241359530034197 0.879320234982901 39 0.0949452586525375 0.189890517305075 0.905054741347463 40 0.0762460263061484 0.152492052612297 0.923753973693852 41 0.0585091342265235 0.117018268453047 0.941490865773477 42 0.045081425383557 0.090162850767114 0.954918574616443 43 0.0468904982592064 0.0937809965184127 0.953109501740794 44 0.041651404796983 0.083302809593966 0.958348595203017 45 0.0873886735809008 0.174777347161802 0.9126113264191 46 0.0740079343292163 0.148015868658433 0.925992065670784 47 0.0642403390414406 0.128480678082881 0.93575966095856 48 0.0548572347568346 0.109714469513669 0.945142765243165 49 0.0430729648524274 0.0861459297048548 0.956927035147573 50 0.0554755505369105 0.110951101073821 0.94452444946309 51 0.0946525556964298 0.189305111392860 0.90534744430357 52 0.09749649717016 0.19499299434032 0.90250350282984 53 0.0819424348707711 0.163884869741542 0.918057565129229 54 0.089193692334713 0.178387384669426 0.910806307665287 55 0.0744487475993334 0.148897495198667 0.925551252400667 56 0.0650781995772696 0.130156399154539 0.93492180042273 57 0.0723657482803943 0.144731496560789 0.927634251719606 58 0.072375962714206 0.144751925428412 0.927624037285794 59 0.0669592312373004 0.133918462474601 0.9330407687627 60 0.0589734402414486 0.117946880482897 0.941026559758551 61 0.0476425629301912 0.0952851258603825 0.952357437069809 62 0.041940401485372 0.083880802970744 0.958059598514628 63 0.0418354942853893 0.0836709885707786 0.95816450571461 64 0.0345120155968836 0.0690240311937671 0.965487984403116 65 0.027413316098836 0.054826632197672 0.972586683901164 66 0.0233794701674330 0.0467589403348659 0.976620529832567 67 0.0312294274785043 0.0624588549570086 0.968770572521496 68 0.0410335534300605 0.082067106860121 0.95896644656994 69 0.0672037702099142 0.134407540419828 0.932796229790086 70 0.065927105913256 0.131854211826512 0.934072894086744 71 0.0625606735917909 0.125121347183582 0.937439326408209 72 0.0580983861983578 0.116196772396716 0.941901613801642 73 0.0519756542112147 0.103951308422429 0.948024345788785 74 0.0436462743752555 0.087292548750511 0.956353725624745 75 0.0369389253829375 0.0738778507658749 0.963061074617062 76 0.0337721609023301 0.0675443218046603 0.96622783909767 77 0.0252792036014579 0.0505584072029158 0.974720796398542 78 0.0196851433295314 0.0393702866590628 0.980314856670469 79 0.0228395244376111 0.0456790488752223 0.977160475562389 80 0.0238681168395113 0.0477362336790226 0.976131883160489 81 0.0416059084155527 0.0832118168311054 0.958394091584447 82 0.0457095058561561 0.0914190117123122 0.954290494143844 83 0.0531519359315767 0.106303871863153 0.946848064068423 84 0.0735129502067603 0.147025900413521 0.92648704979324 85 0.0985439762322073 0.197087952464415 0.901456023767793 86 0.0834393398139995 0.166878679627999 0.916560660186 87 0.0694423779632774 0.138884755926555 0.930557622036723 88 0.0620857870776213 0.124171574155243 0.937914212922379 89 0.0518465742717637 0.103693148543527 0.948153425728236 90 0.0459054287054982 0.0918108574109964 0.954094571294502 91 0.0414867286578835 0.082973457315767 0.958513271342117 92 0.0509481689743432 0.101896337948686 0.949051831025657 93 0.0786188936006857 0.157237787201371 0.921381106399314 94 0.0927703931447165 0.185540786289433 0.907229606855284 95 0.129996943414969 0.259993886829939 0.87000305658503 96 0.303142957942189 0.606285915884378 0.696857042057811 97 0.354647188395803 0.709294376791606 0.645352811604197 98 0.334222012847786 0.668444025695572 0.665777987152214 99 0.315647236786500 0.631294473573001 0.6843527632135 100 0.292870673706582 0.585741347413165 0.707129326293418 101 0.264470798814100 0.528941597628201 0.7355292011859 102 0.256647234229186 0.513294468458371 0.743352765770814 103 0.264844248293636 0.529688496587272 0.735155751706364 104 0.322668347845733 0.645336695691467 0.677331652154267 105 0.503190422766020 0.99361915446796 0.49680957723398 106 0.584621534477447 0.830756931045106 0.415378465522553 107 0.765076519766587 0.469846960466827 0.234923480233413 108 0.90982598570098 0.180348028598041 0.0901740142990204 109 0.941596842448789 0.116806315102423 0.0584031575512114 110 0.937396482689734 0.125207034620533 0.0626035173102663 111 0.9287146291341 0.142570741731798 0.0712853708658992 112 0.911944490008376 0.176111019983249 0.0880555099916245 113 0.890470485249384 0.219059029501231 0.109529514750616 114 0.865271656055242 0.269456687889515 0.134728343944757 115 0.811843641754413 0.376312716491174 0.188156358245587 116 0.762329977108688 0.475340045782624 0.237670022891312 117 0.74417703323807 0.51164593352386 0.25582296676193 118 0.808625522079809 0.382748955840383 0.191374477920191 119 0.791208810212062 0.417582379575877 0.208791189787938 120 0.708914634420895 0.58217073115821 0.291085365579105 121 0.642179944804808 0.715640110390384 0.357820055195192 122 0.571260227655156 0.857479544689688 0.428739772344844 123 0.474821738054438 0.949643476108875 0.525178261945562 124 0.509439905263394 0.981120189473212 0.490560094736606 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 10 0.0833333333333333 NOK 10% type I error level 32 0.266666666666667 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/26/t1290755734ev4702qweumnfoz/10tuzm1290755448.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290755734ev4702qweumnfoz/10tuzm1290755448.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290755734ev4702qweumnfoz/1mtks1290755448.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290755734ev4702qweumnfoz/1mtks1290755448.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290755734ev4702qweumnfoz/2xl2d1290755448.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290755734ev4702qweumnfoz/2xl2d1290755448.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290755734ev4702qweumnfoz/3xl2d1290755448.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290755734ev4702qweumnfoz/3xl2d1290755448.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290755734ev4702qweumnfoz/4xl2d1290755448.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290755734ev4702qweumnfoz/4xl2d1290755448.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290755734ev4702qweumnfoz/58cjy1290755448.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290755734ev4702qweumnfoz/58cjy1290755448.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290755734ev4702qweumnfoz/68cjy1290755448.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290755734ev4702qweumnfoz/68cjy1290755448.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290755734ev4702qweumnfoz/7il0j1290755448.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290755734ev4702qweumnfoz/7il0j1290755448.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290755734ev4702qweumnfoz/8il0j1290755448.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290755734ev4702qweumnfoz/8il0j1290755448.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290755734ev4702qweumnfoz/9tuzm1290755448.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290755734ev4702qweumnfoz/9tuzm1290755448.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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