Multiple Regression

*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: Sat, 25 Dec 2010 09:35:42 +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/25/t12932696388y20fc6c0e98r8x.htm/, Retrieved Sat, 25 Dec 2010 10:34:00 +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/25/t12932696388y20fc6c0e98r8x.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 «

13 13 14 13 3 12 12 8 13 5 15 10 12 16 6 12 9 7 12 6 10 10 10 11 5 12 12 7 12 3 15 13 16 18 8 9 12 11 11 4 12 12 14 14 4 11 6 6 9 4 11 5 16 14 6 11 12 11 12 6 15 11 16 11 5 7 14 12 12 4 11 14 7 13 6 11 12 13 11 4 10 12 11 12 6 14 11 15 16 6 10 11 7 9 4 6 7 9 11 4 11 9 7 13 2 15 11 14 15 7 11 11 15 10 5 12 12 7 11 4 14 12 15 13 6 15 11 17 16 6 9 11 15 15 7 13 8 14 14 5 13 9 14 14 6 16 12 8 14 4 13 10 8 8 4 12 10 14 13 7 14 12 14 15 7 11 8 8 13 4 9 12 11 11 4 16 11 16 15 6 12 12 10 15 6 10 7 8 9 5 13 11 14 13 6 16 11 16 16 7 14 12 13 13 6 15 9 5 11 3 5 15 8 12 3 8 11 10 12 4 11 11 8 12 6 16 11 13 14 7 17 11 15 14 5 9 15 6 8 4 9 11 12 13 5 13 12 16 16 6 10 12 5 13 6 6 9 15 11 6 12 12 12 14 5 8 12 8 13 4 14 13 13 13 5 12 11 14 13 5 11 9 12 12 4 16 9 16 16 6 8 11 10 15 2 15 11 15 15 8 7 12 8 12 3 16 12 16 14 6 14 9 19 12 6 16 11 14 15 6 9 9 6 12 5 14 12 13 13 5 11 12 15 12 6 13 12 7 12 5 15 12 13 13 6 5 14 4 5 2 15 11 14 13 5 13 12 13 13 5 11 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 6 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation Knowingpeople[t] = + 0.704773125332253 + 0.388112646909159Popularity[t] -0.072086130850391Findingfriends[t] + 0.267672517283153Liked[t] + 0.6695223593835Celebrity[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) 0.704773125332253 1.797372 0.3921 0.695528 0.347764 Popularity 0.388112646909159 0.097694 3.9727 0.00011 5.5e-05 Findingfriends -0.072086130850391 0.121313 -0.5942 0.553257 0.276628 Liked 0.267672517283153 0.125002 2.1413 0.033851 0.016926 Celebrity 0.6695223593835 0.199827 3.3505 0.001019 0.00051 Multiple Linear Regression - Regression Statistics Multiple R 0.652918056368862 R-squared 0.426301988332492 Adjusted R-squared 0.411104690010174 F-TEST (value) 28.0511693125378 F-TEST (DF numerator) 4 F-TEST (DF denominator) 151 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.65644680094332 Sum Squared Residuals 1065.56315054255 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14 10.3014276369277 3.69857236307227 2 8 11.324445839636 -3.32444583963596 3 12 14.1054959532972 -2.10549595329718 4 7 11.9425540742875 -4.94255407428749 5 10 10.1570477729521 -0.157047772952123 6 7 9.71772860358581 -2.71772860358581 7 16 15.7636273140793 0.236372685920685 8 11 8.95524050495868 2.04475949504132 9 14 10.9225959975356 3.07740400246438 10 6 9.62863754931304 -3.62863754931304 11 16 12.3781309853462 3.62186901465381 12 11 11.3381830348271 -0.33818303482715 13 16 12.0255248766475 3.97447512335247 14 12 8.30251546672273 3.69748453327727 15 7 11.4616832904095 -4.46168329040952 16 13 9.731465798777 3.268534201223 17 11 10.950070387918 0.049929612082009 18 15 13.6452971755376 1.35470282446237 19 7 8.88009424815192 -1.88009424815192 20 9 8.15133321848316 0.848666781516844 21 7 9.14402450712748 -2.14402450712748 22 14 14.4352596645471 -0.435259664547138 23 15 10.2054017717277 4.79459822827226 24 7 10.1195784456862 -3.11957844568616 25 15 12.7701934928378 2.22980650716222 26 17 14.0334098224468 2.96659017755321 27 15 12.1065837830922 2.89341621690782 28 14 12.2685755272298 1.73142447277016 29 14 12.8660117557629 1.13398824423705 30 8 12.4750465851723 -4.47504658517226 31 8 9.84884580244664 -1.84884580244664 32 14 12.8076628201037 1.19233717989626 33 14 13.9750608867876 0.0249391132124124 34 8 10.5551553567449 -2.55515535674487 35 11 8.95524050495868 2.04475949504132 36 16 14.1538499520728 1.8461500479272 37 10 12.5293132335858 -2.52931323358577 38 8 9.83796113093699 -1.83796113093699 39 14 12.454166976779 1.54583302322099 40 16 15.0910448287395 0.90895517126055 41 13 12.7701934928378 0.229806507162218 42 5 10.8306524195813 -5.83065241958131 43 8 6.78468168267052 1.21531831732948 44 10 8.90688650618306 1.09311349381694 45 8 11.4102691656775 -3.41026916567754 46 13 14.5556997941731 -1.55569979417314 47 15 13.6047677223153 1.3952322776847 48 6 7.93596456055805 -1.93596456055805 49 12 10.2321940297589 1.76780597024112 50 16 13.1850983977781 2.81490160222192 51 5 11.2177429052011 -6.21774290520115 52 15 9.34620567554937 5.65379432445063 53 12 11.5921183569191 0.407881643080883 54 8 9.10247289261583 -1.10247289261583 55 13 12.0285850026039 0.97141499739611 56 14 11.3965319704864 2.60346802951365 57 12 10.2153967086113 1.78460329138868 58 16 14.5656947310567 1.43430526894327 59 10 8.37085933926553 1.62914066073448 60 15 15.1047820239306 -0.104782023930638 61 8 7.77716536904001 0.222834630959986 62 16 13.8140913039393 2.18590869606075 63 19 12.7187793681058 6.2812206318942 64 14 14.1538499520728 -0.153849952072798 65 6 10.1086937741765 -4.10869377417651 66 13 12.1006711334543 0.899328866545718 67 15 11.3381830348271 3.66181696517285 68 7 11.444885969262 -4.44488596926197 69 13 13.1583061397469 -0.158306139746941 70 4 4.31353783315534 -0.313537833155342 71 14 12.5608699112138 1.43913008878617 72 13 11.7125584865451 1.28744151345488 73 11 11.2760918408603 -0.276091840860348 74 14 13.1090624063453 0.890937593654738 75 12 12.1381404607202 -0.138140460720245 76 15 11.9939681990195 3.00603180098054 77 14 10.9846871915024 3.01531280849758 78 13 11.6127903630375 1.38720963696247 79 8 11.6988212913539 -3.69882129135394 80 6 6.4518578454642 -0.451857845464202 81 7 8.44668772842351 -1.44668772842351 82 13 12.935037760657 0.0649622393430256 83 13 13.6452971755376 -0.645297175537633 84 11 10.4247202902353 0.575279709764726 85 5 10.105841250495 -5.10584125049497 86 12 11.6542095508859 0.345790449114081 87 8 8.75965411852592 -0.759654118525917 88 11 12.2202215284542 -1.22022152845422 89 14 15.4928946708398 -1.4928946708398 90 9 9.68311180000138 -0.683111800001383 91 10 13.6452971755376 -3.64529717553763 92 13 11.8251740706178 1.17482592938216 93 16 15.0189586978891 0.98104130211094 94 16 13.3024784014477 2.69752159855228 95 11 11.1288594532032 -0.128859453203201 96 8 9.34335315186784 -1.34335315186784 97 4 10.8019482656348 -6.80194826563478 98 7 7.55784685053248 -0.557846850532477 99 14 11.7600227506947 2.23997724930533 100 11 12.3820808459286 -1.38208084592862 101 17 15.0910448287395 1.90895517126055 102 15 14.7512861806059 0.248713819394094 103 17 13.9643838175528 3.03561618244723 104 5 9.7414607356606 -4.74146073566059 105 4 5.55213229606351 -1.55213229606351 106 10 14.8401696326038 -4.84016963260385 107 11 8.96523544184227 2.03476455815773 108 15 14.7166693770215 0.283330622978522 109 10 8.84479531221626 1.15520468778374 110 9 9.9982485814341 -0.998248581434088 111 12 11.3481779717107 0.651822028289261 112 15 12.9518350818045 2.04816491819547 113 7 11.6058555521103 -4.6058555521103 114 13 13.3055385274041 -0.305538527404088 115 12 14.6308460509799 -2.6308460509799 116 14 13.8861774347896 0.113822565210355 117 14 13.8140913039393 0.185908696060746 118 8 12.4088731039598 -4.40887310395976 119 15 13.0378660101209 1.96213398987907 120 12 11.235562387638 0.76443761236198 121 12 10.6549234802525 1.34507651974754 122 16 11.9050847470215 4.09491525297848 123 9 8.90688650618306 0.0931134938169358 124 15 12.5776672323614 2.42233276763862 125 15 13.8140913039393 1.18590869606075 126 6 11.5921183569191 -5.59211835691912 127 14 15.6884810572726 -1.68848105727256 128 15 11.9939681990195 3.00603180098054 129 10 11.4923502334115 -1.49235023341152 130 6 5.42931417283237 0.570685827167625 131 14 15.6884810572726 -1.68848105727256 132 12 13.2303922705973 -1.23039227059733 133 8 10.6817157382836 -2.6817157382836 134 11 12.8453397496445 -1.84533974964454 135 13 13.4259786570301 -0.425978657030094 136 9 10.6549234802525 -1.65492348025246 137 15 13.1099521409713 1.89004785902867 138 13 7.77716536904001 5.22283463095999 139 15 15.2461017619499 -0.246101761949885 140 14 11.7362906186199 2.2637093813801 141 16 10.7270096111029 5.27299038889714 142 14 12.6497533632118 1.35024663678822 143 14 12.6222789728294 1.3777210271706 144 10 7.37293753333454 2.62706246666546 145 10 10.6549234802525 -0.654923480252464 146 4 11.1456567743508 -7.14565677435075 147 8 10.0396677692825 -2.03966776928248 148 15 11.5368295472163 3.46317045278372 149 16 13.4980647878805 2.50193521211951 150 12 15.4208085399894 -3.42080853998941 151 12 13.1236893361625 -1.12368933616251 152 15 15.0189586978891 -0.0189586978890594 153 9 9.29499915309222 -0.294999153092224 154 12 13.4497107891049 -1.44971078910487 155 14 12.574607106405 1.42539289359498 156 11 9.65563740961901 1.34436259038099 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.714599638652761 0.570800722694478 0.285400361347239 9 0.568070147247839 0.863859705504322 0.431929852752161 10 0.509771806274835 0.98045638745033 0.490228193725165 11 0.385067044660113 0.770134089320227 0.614932955339887 12 0.366632293127943 0.733264586255887 0.633367706872057 13 0.941647589996298 0.116704820007403 0.0583524100037016 14 0.928216337327801 0.143567325344398 0.071783662672199 15 0.94941577511611 0.101168449767779 0.0505842248838893 16 0.95082138318435 0.0983572336312982 0.0491786168156491 17 0.928821690316999 0.142356619366002 0.0711783096830009 18 0.901125452954643 0.197749094090714 0.0988745470453571 19 0.871271474037379 0.257457051925242 0.128728525962621 20 0.82887379279171 0.342252414416579 0.171126207208289 21 0.873528837805618 0.252942324388765 0.126471162194382 22 0.832831761666721 0.334336476666559 0.167168238333279 23 0.911428657002901 0.177142685994197 0.0885713429970986 24 0.917329789424321 0.165340421151358 0.0826702105756792 25 0.909597354285369 0.180805291429262 0.0904026457146308 26 0.906830296475766 0.186339407048469 0.0931697035242343 27 0.89425786540748 0.211484269185039 0.105742134592519 28 0.872712218277176 0.254575563445649 0.127287781722824 29 0.841191661954342 0.317616676091315 0.158808338045657 30 0.884782250960574 0.230435498078852 0.115217749039426 31 0.858300475668252 0.283399048663497 0.141699524331748 32 0.826425813146499 0.347148373707002 0.173574186853501 33 0.787037121706629 0.425925756586742 0.212962878293371 34 0.78541693584063 0.429166128318741 0.214583064159371 35 0.756758199654267 0.486483600691465 0.243241800345733 36 0.736498049120193 0.527003901759614 0.263501950879807 37 0.752920380192186 0.494159239615628 0.247079619807814 38 0.722120484809505 0.555759030380989 0.277879515190495 39 0.688391051527889 0.623217896944222 0.311608948472111 40 0.642573398109862 0.714853203780276 0.357426601890138 41 0.590703536945759 0.818592926108482 0.409296463054241 42 0.710365420724896 0.579269158550207 0.289634579275104 43 0.676434081242657 0.647131837514687 0.323565918757343 44 0.631569810087595 0.736860379824809 0.368430189912405 45 0.674965799575464 0.650068400849072 0.325034200424536 46 0.639510128582825 0.72097974283435 0.360489871417175 47 0.621191313947151 0.757617372105698 0.378808686052849 48 0.59133150146413 0.81733699707174 0.40866849853587 49 0.555756140885035 0.88848771822993 0.444243859114965 50 0.546843579265252 0.906312841469496 0.453156420734748 51 0.774904805393079 0.450190389213842 0.225095194606921 52 0.873564179763813 0.252871640472373 0.126435820236187 53 0.846561544471457 0.306876911057086 0.153438455528543 54 0.828864022009331 0.342271955981339 0.171135977990669 55 0.802880627767809 0.394238744464383 0.197119372232191 56 0.799675225706146 0.400649548587708 0.200324774293854 57 0.778769428326684 0.442461143346632 0.221230571673316 58 0.748702011756043 0.502595976487913 0.251297988243957 59 0.719906203478883 0.560187593042234 0.280093796521117 60 0.679069580174137 0.641860839651726 0.320930419825863 61 0.638189502468016 0.723620995063969 0.361810497531984 62 0.626439937065708 0.747120125868584 0.373560062934292 63 0.808952570739575 0.382094858520849 0.191047429260424 64 0.775293058673434 0.449413882653132 0.224706941326566 65 0.827291659961093 0.345416680077814 0.172708340038907 66 0.798699744489124 0.402600511021751 0.201300255510876 67 0.828125442471672 0.343749115056656 0.171874557528328 68 0.878452565293773 0.243094869412454 0.121547434706227 69 0.853384666623338 0.293230666753324 0.146615333376662 70 0.828423785176955 0.343152429646089 0.171576214823045 71 0.80557230403794 0.388855391924119 0.19442769596206 72 0.778355943397676 0.443288113204648 0.221644056602324 73 0.744245755403748 0.511508489192503 0.255754244596252 74 0.720647559247222 0.558704881505555 0.279352440752778 75 0.680779323145896 0.638441353708208 0.319220676854104 76 0.6928900633374 0.614219873325202 0.307109936662601 77 0.701799576001744 0.596400847996512 0.298200423998256 78 0.671060175775012 0.657879648449976 0.328939824224988 79 0.724341641552076 0.551316716895848 0.275658358447924 80 0.685087096368306 0.629825807263388 0.314912903631694 81 0.656339687672424 0.687320624655151 0.343660312327576 82 0.612267911462483 0.775464177075033 0.387732088537517 83 0.571996011304638 0.856007977390724 0.428003988695362 84 0.528928099640376 0.942143800719249 0.471071900359624 85 0.705305642585896 0.589388714828209 0.294694357414104 86 0.664393761325459 0.671212477349083 0.335606238674541 87 0.626446335556479 0.747107328887043 0.373553664443521 88 0.589981457159006 0.820037085681989 0.410018542840994 89 0.560844093349959 0.878311813300083 0.439155906650041 90 0.518698496131556 0.962603007736888 0.481301503868444 91 0.562102433942788 0.875795132114424 0.437897566057212 92 0.550930136552974 0.898139726894052 0.449069863447026 93 0.512100418370669 0.975799163258661 0.487899581629331 94 0.505542805219136 0.988914389561728 0.494457194780864 95 0.458509146135325 0.91701829227065 0.541490853864675 96 0.43127662168779 0.862553243375579 0.56872337831221 97 0.646445968107389 0.707108063785223 0.353554031892611 98 0.606658600504486 0.786682798991027 0.393341399495514 99 0.603019817138753 0.793960365722495 0.396980182861247 100 0.569972901575805 0.86005419684839 0.430027098424195 101 0.555933618022022 0.888132763955956 0.444066381977978 102 0.508238987028197 0.983522025943606 0.491761012971803 103 0.569875927572311 0.860248144855377 0.430124072427689 104 0.74100631312975 0.5179873737405 0.25899368687025 105 0.733351565939 0.533296868121999 0.266648434060999 106 0.782367845216274 0.435264309567451 0.217632154783726 107 0.757014804866246 0.485970390267508 0.242985195133754 108 0.738021861592309 0.523956276815382 0.261978138407691 109 0.700605260021353 0.598789479957294 0.299394739978647 110 0.655885281798186 0.688229436403628 0.344114718201814 111 0.61252569399444 0.77494861201112 0.38747430600556 112 0.652252231315671 0.695495537368659 0.347747768684329 113 0.729804922234937 0.540390155530125 0.270195077765063 114 0.68355624665615 0.6328875066877 0.31644375334385 115 0.658092558715608 0.683814882568783 0.341907441284392 116 0.606610419075904 0.786779161848192 0.393389580924096 117 0.554518840296746 0.89096231940651 0.445481159703254 118 0.58119025396328 0.83761949207344 0.41880974603672 119 0.554784931237087 0.890430137525825 0.445215068762913 120 0.513959123674959 0.972081752650082 0.486040876325041 121 0.460371070794692 0.920742141589384 0.539628929205308 122 0.4819885777203 0.9639771554406 0.5180114222797 123 0.423288917250249 0.846577834500498 0.576711082749751 124 0.416346996903757 0.832693993807514 0.583653003096243 125 0.364099102167396 0.728198204334792 0.635900897832604 126 0.585609564500766 0.828780870998468 0.414390435499234 127 0.529286016017757 0.941427967964486 0.470713983982243 128 0.563502224570379 0.872995550859243 0.436497775429621 129 0.507558191427364 0.984883617145273 0.492441808572636 130 0.453593482331142 0.907186964662284 0.546406517668858 131 0.39402786913921 0.78805573827842 0.60597213086079 132 0.349397462841879 0.698794925683758 0.650602537158121 133 0.358603141547415 0.71720628309483 0.641396858452585 134 0.309986936035581 0.619973872071162 0.690013063964419 135 0.249954953442299 0.499909906884599 0.7500450465577 136 0.268496855157471 0.536993710314942 0.731503144842529 137 0.236555137105923 0.473110274211847 0.763444862894077 138 0.292327283967103 0.584654567934207 0.707672716032897 139 0.255624137691129 0.511248275382258 0.744375862308871 140 0.252868421517583 0.505736843035165 0.747131578482417 141 0.36747130160986 0.734942603219719 0.63252869839014 142 0.313435179715116 0.626870359430232 0.686564820284884 143 0.232576442225033 0.465152884450066 0.767423557774967 144 0.211608189961462 0.423216379922923 0.788391810038538 145 0.16456335941678 0.329126718833561 0.83543664058322 146 0.773120669036112 0.453758661927777 0.226879330963888 147 0.659877966546134 0.680244066907732 0.340122033453866 148 0.714984503386655 0.57003099322669 0.285015496613345 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 0.00709219858156028 OK

Charts produced by software:

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Parameters (Session):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 3 ; 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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