multiple regression - belonging

*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 08:31:57 +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/Dec/14/t1292315427bo5zzm4gi7xs63h.htm/, Retrieved Tue, 14 Dec 2010 09:30:37 +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/t1292315427bo5zzm4gi7xs63h.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 15 9 42 12 12 18 9 51 15 15 11 9 42 14 12 16 8 46 10 10 12 14 41 10 12 17 14 49 9 15 15 15 47 18 9 19 11 33 11 11 18 8 47 12 11 10 14 42 11 11 14 9 32 15 15 18 6 53 17 7 18 14 41 14 11 14 8 41 24 11 14 11 33 7 10 12 16 37 18 14 16 11 43 11 6 13 13 33 14 11 16 7 49 18 15 14 9 42 12 11 9 15 43 11 12 9 16 37 5 14 17 10 43 12 15 13 14 42 11 9 15 12 43 10 13 17 6 46 11 13 16 4 33 15 16 12 12 42 16 13 11 14 40 14 12 16 13 44 8 14 17 9 42 13 11 17 14 52 18 9 16 14 44 17 16 13 10 45 10 12 12 14 46 13 10 12 8 36 11 13 16 8 45 12 16 14 10 49 12 14 12 9 43 12 15 12 9 43 9 5 14 11 37 18 8 8 15 32 7 11 15 9 45 14 16 14 9 45 16 17 11 10 45 12 9 13 8 45 17 9 14 8 31 12 13 15 14 33 9 10 16 10 44 12 6 10 11 49 9 12 11 9 44 13 8 12 12 41 10 14 14 13 44 10 12 15 14 38 11 11 16 15 33 13 16 9 11 47 13 8 11 9 37 13 15 15 8 48 6 7 15 7 40 7 16 13 10 50 13 14 17 10 54 21 16 17 10 43 11 9 15 9 54 9 14 13 13 44 18 11 15 11 47 9 13 13 8 33 9 15 15 10 45 15 5 10 14 33 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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation belonging[t] = + 30.412552707353 + 0.616533594321869popularity[t] + 0.510913274781838hapiness[t] -0.430298147948814doubsaboutactions[t] + 0.226540094212896parentalexpectations[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) 30.412552707353 5.931119 5.1276 1e-06 0 popularity 0.616533594321869 0.19293 3.1956 0.00173 0.000865 hapiness 0.510913274781838 0.260515 1.9612 0.051873 0.025936 doubsaboutactions -0.430298147948814 0.223642 -1.924 0.056407 0.028203 parentalexpectations 0.226540094212896 0.16801 1.3484 0.179748 0.089874 Multiple Linear Regression - Regression Statistics Multiple R 0.407575041565467 R-squared 0.166117414507092 Adjusted R-squared 0.14194690478266 F-TEST (value) 6.87273112569805 F-TEST (DF numerator) 4 F-TEST (DF denominator) 138 p-value 4.48569440201219e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.81522948809898 Sum Squared Residuals 6409.73471061264 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 42 44.9369863542805 -2.93698635428054 2 51 46.5328128669426 4.46718713305736 3 42 44.5794806322225 -2.57948063222247 4 46 44.8085839942633 1.19141600573670 5 41 38.9500748187993 2.04992518120068 6 49 42.5111682871394 6.48883171286065 7 47 44.9475052205085 2.05249477949147 8 33 43.4273686860097 -10.4273686860097 9 47 45.6669571379309 1.33304286206911 10 42 38.7713219577704 3.22867804222959 11 32 43.8726261734934 -11.8726261734934 12 53 50.1263882821805 2.87361171781952 13 41 41.0721140613763 -0.0721140613763252 14 41 46.3417851693583 -5.34178516935829 15 33 41.1997091238926 -8.19970912389262 16 37 39.9017992766049 -2.90179927660486 17 43 44.9772968332735 -1.97729683327349 18 33 38.3313122410941 -5.33131224109408 19 49 46.4346693015934 2.56533069840660 20 42 45.6591402681422 -3.6591402681422 21 43 37.8301105350398 5.16988946496025 22 37 36.6571054161354 0.342894583864567 23 43 46.1450483502170 -3.14504835021703 24 42 42.7701961594034 -0.770196159403397 25 43 40.7268773447206 2.27312265527941 26 46 47.0231672534775 -1.02316725347753 27 33 48.2790106514449 -15.2790106514449 28 42 44.8691132459055 -2.86911324590554 29 40 41.1949227038347 -1.19492270383467 30 44 42.2040130660934 1.79598693390657 31 42 46.8018865923787 -4.80188659237874 32 52 43.9334955407335 8.06650445926646 33 44 41.9629749830951 2.03702501690493 34 45 44.8813822513076 0.118617748692373 35 46 40.8627622900817 5.13723770991826 36 36 41.7584038007051 -5.7584038007051 37 45 45.8781977770110 -0.878197777010954 38 49 45.8453757145153 3.15462428548474 39 43 44.0207801242567 -1.02078012425666 40 43 43.9576934359398 -0.957693435939837 41 37 39.9924485943033 -2.99244859430326 42 32 34.5634361004407 -2.56343610044072 43 45 44.1569993540624 0.843000645937645 44 45 47.1818342393157 -2.18183423931565 45 45 44.9291694844916 0.0708305155083902 46 45 43.0120240464424 1.98797595355756 47 31 42.3902368501598 -11.3902368501598 48 33 42.1058753318975 -9.10587533189754 49 44 43.1680006981477 0.83199930185228 50 49 36.5264682415817 12.4735317584183 51 44 42.503339755044 1.49666024495603 52 41 38.5776039260532 2.42239607394679 53 44 42.8683338935993 1.13166610640072 54 38 41.9424219260015 -3.94242192600147 55 33 41.8595836469384 -8.85958364693841 56 47 43.0870512868701 3.91294871312985 57 37 40.0372053777565 -3.0372053777565 58 48 45.2411111255955 2.75888887440452 59 40 40.9656806131822 -0.965680613182238 60 50 45.5610025339463 4.43899746605369 61 54 48.1839091981331 5.8160908018669 62 43 47.1515754446479 -4.15157544464788 63 54 41.7912316943541 12.2087683056459 64 44 44.1697413725206 -0.169741372520612 65 47 42.1637025871002 4.83629741289975 66 33 43.6658376700268 -10.6658376700268 67 45 46.4193756776139 -1.41937567761391 68 33 34.6190402034134 -1.6190402034134 69 44 45.0829171528135 -1.08291715281352 70 47 44.4488551199754 2.55114488002456 71 45 41.1449123184207 3.85508768157934 72 43 42.4480757676692 0.551924232330809 73 43 37.221059526062 5.77894047393797 74 33 43.6833602773896 -10.6833602773896 75 46 43.2333163698479 2.76668363015209 76 47 43.5129031303589 3.48709686964110 77 47 42.0383248456606 4.96167515433936 78 0 41.522157968918 -41.522157968918 79 43 43.3867239225719 -0.386723922571923 80 46 43.4195518162210 2.58044818377904 81 36 38.1700994808881 -2.17009948088806 82 42 39.3400624877549 2.65993751224505 83 44 42.7451851355430 1.25481486445695 84 47 47.0131272314588 -0.0131272314588052 85 41 40.2712280573135 0.728771942686462 86 47 44.0816494914968 2.91835050850321 87 46 44.5395102688272 1.46048973117281 88 47 46.8672022640789 0.132797735921066 89 46 46.7690586987297 -0.769058698729703 90 46 45.1810490558561 0.81895094414394 91 36 44.776563398115 -8.77656339811497 92 30 39.8667423995724 -9.86674239957245 93 48 43.0799029859706 4.92009701402945 94 45 41.5524284258925 3.44757157410751 95 49 45.1863084889702 3.81369151102983 96 55 46.8974610587467 8.10253894125329 97 11 42.0305196381786 -31.0305196381786 98 52 45.5512909652188 6.4487090347812 99 33 36.2801765566226 -3.28017655662258 100 47 48.1961782035352 -1.19617820353519 101 33 38.7213115723564 -5.72131157235639 102 44 44.0010343646638 -0.00103436466376364 103 42 39.6222125160939 2.37778748390614 104 55 42.2267834442637 12.7732165557363 105 42 43.7039191656366 -1.70391916563656 106 46 44.7612639429821 1.23873605701787 107 46 46.6862204196666 -0.68622041966665 108 47 46.6003516908729 0.399648309127147 109 33 42.8758164789434 -9.87581647894343 110 53 49.464296438058 3.53570356194200 111 42 42.9914768205022 -0.991476820502178 112 44 43.4598564640608 0.540143535939195 113 55 45.9185082560041 9.08149174399586 114 40 35.7311876173843 4.26881238261573 115 46 46.3562889892971 -0.356288989297095 116 53 45.5109863173790 7.48901368262104 117 44 45.3194972690451 -1.31949726904513 118 35 39.9618555151909 -4.96185551519093 119 40 39.0034499383886 0.996550061611378 120 44 44.8112801595495 -0.811280159549488 121 46 46.1017074214931 -0.101707421493107 122 45 42.0032854620883 2.99671453791174 123 53 44.6298311332344 8.37016886676562 124 45 44.7284418804864 0.271558119513565 125 48 42.0655648529044 5.93443514709564 126 46 45.5990840295561 0.400915970443874 127 55 41.1374239019232 13.8625760980768 128 47 49.6001813834191 -2.60018138341915 129 43 41.8162427182145 1.18375728178551 130 38 38.5850923425507 -0.585092342550694 131 40 40.9131069599403 -0.913106959940305 132 47 41.5774336185995 5.4225663814005 133 47 41.4315028200663 5.56849717993371 134 42 41.615509283056 0.384490716944030 135 53 43.3717587518836 9.62824124811636 136 43 44.9772968332735 -1.97729683327349 137 44 44.4160330574797 -0.416033057479743 138 42 42.689575201417 -0.68957520141703 139 51 44.043567995887 6.95643200411302 140 54 42.2443118827799 11.7556881172201 141 41 43.0598229419331 -2.05982294193311 142 51 43.686402389427 7.31359761057296 143 51 43.9554644525565 7.04453554744353 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.597440620714478 0.805118758571044 0.402559379285522 9 0.475728075470647 0.951456150941293 0.524271924529353 10 0.362864486345942 0.725728972691883 0.637135513654058 11 0.353397989648564 0.706795979297127 0.646602010351436 12 0.28705494551777 0.57410989103554 0.71294505448223 13 0.262535586235171 0.525071172470342 0.737464413764829 14 0.205008434192043 0.410016868384085 0.794991565807957 15 0.232827008341727 0.465654016683454 0.767172991658273 16 0.169006793876959 0.338013587753917 0.830993206123041 17 0.137693072652727 0.275386145305455 0.862306927347273 18 0.0966812150311128 0.193362430062226 0.903318784968887 19 0.100276166445054 0.200552332890109 0.899723833554946 20 0.07739960400775 0.1547992080155 0.92260039599225 21 0.0833503092307999 0.166700618461600 0.9166496907692 22 0.056293215013495 0.11258643002699 0.943706784986505 23 0.0432324141286542 0.0864648282573083 0.956767585871346 24 0.0308293951175297 0.0616587902350594 0.96917060488247 25 0.0246656143087032 0.0493312286174063 0.975334385691297 26 0.0159987688551355 0.0319975377102709 0.984001231144864 27 0.0451527092970399 0.0903054185940799 0.95484729070296 28 0.0341103289641478 0.0682206579282956 0.965889671035852 29 0.0230987699602323 0.0461975399204646 0.976901230039768 30 0.0153109332107159 0.0306218664214318 0.984689066789284 31 0.0118023922170776 0.0236047844341553 0.988197607782922 32 0.0130085883731660 0.0260171767463321 0.986991411626834 33 0.00852149255993075 0.0170429851198615 0.99147850744007 34 0.0055707203137654 0.0111414406275308 0.994429279686235 35 0.00481862253266961 0.00963724506533922 0.99518137746733 36 0.00325469351434969 0.00650938702869937 0.99674530648565 37 0.00212529412368423 0.00425058824736846 0.997874705876316 38 0.00154901634082213 0.00309803268164426 0.998450983659178 39 0.000988871411542903 0.00197774282308581 0.999011128588457 40 0.000604641312048233 0.00120928262409647 0.999395358687952 41 0.000374525413936076 0.000749050827872152 0.999625474586064 42 0.000216379258019646 0.000432758516039293 0.99978362074198 43 0.000153166864095342 0.000306333728190684 0.999846833135905 44 8.96631314683946e-05 0.000179326262936789 0.999910336868532 45 5.01279095161707e-05 0.000100255819032341 0.999949872090484 46 6.1385710442343e-05 0.000122771420884686 0.999938614289558 47 0.000106408672410746 0.000212817344821492 0.99989359132759 48 0.000362386625719256 0.000724773251438511 0.99963761337428 49 0.000245619524845623 0.000491239049691245 0.999754380475154 50 0.00306958380063952 0.00613916760127905 0.99693041619936 51 0.00225122436172797 0.00450244872345594 0.997748775638272 52 0.00160614781214924 0.00321229562429847 0.99839385218785 53 0.00104039883206646 0.00208079766413292 0.998959601167934 54 0.000834140842124923 0.00166828168424985 0.999165859157875 55 0.00146312234683071 0.00292624469366143 0.99853687765317 56 0.00112218210364044 0.00224436420728087 0.99887781789636 57 0.000761853790977201 0.00152370758195440 0.999238146209023 58 0.000603312780229307 0.00120662556045861 0.99939668721977 59 0.000399330026100266 0.000798660052200533 0.9996006699739 60 0.000331364864212417 0.000662729728424833 0.999668635135788 61 0.000345808211289995 0.00069161642257999 0.99965419178871 62 0.000253078934663712 0.000506157869327424 0.999746921065336 63 0.00118399445194412 0.00236798890388824 0.998816005548056 64 0.000769500803247529 0.00153900160649506 0.999230499196752 65 0.000658717049196801 0.00131743409839360 0.999341282950803 66 0.00123965506416688 0.00247931012833377 0.998760344935833 67 0.000825939669807051 0.00165187933961410 0.999174060330193 68 0.000553175605460668 0.00110635121092134 0.99944682439454 69 0.000356027226452397 0.000712054452904793 0.999643972773548 70 0.000247977325311045 0.000495954650622089 0.999752022674689 71 0.00017787854968241 0.00035575709936482 0.999822121450318 72 0.000110831621502511 0.000221663243005022 0.999889168378498 73 9.55563696450313e-05 0.000191112739290063 0.999904443630355 74 0.000193419371844867 0.000386838743689734 0.999806580628155 75 0.000133421555773419 0.000266843111546839 0.999866578444227 76 9.3171584665127e-05 0.000186343169330254 0.999906828415335 77 8.30506922662771e-05 0.000166101384532554 0.999916949307734 78 0.892829438936245 0.214341122127509 0.107170561063755 79 0.868065884836799 0.263868230326403 0.131934115163201 80 0.843299472589571 0.313401054820857 0.156700527410429 81 0.82592270301237 0.348154593975259 0.174077296987629 82 0.796929709209897 0.406140581580206 0.203070290790103 83 0.760838971006644 0.478322057986711 0.239161028993356 84 0.721637713164158 0.556724573671684 0.278362286835842 85 0.67847398170123 0.643052036597541 0.321526018298770 86 0.655991971532385 0.68801605693523 0.344008028467615 87 0.63307041244207 0.733859175115861 0.366929587557930 88 0.584799647910457 0.830400704179087 0.415200352089543 89 0.542441755020813 0.915116489958374 0.457558244979187 90 0.51847896343144 0.96304207313712 0.48152103656856 91 0.584429503631593 0.831140992736815 0.415570496368407 92 0.65528967681803 0.689420646363939 0.344710323181969 93 0.640665923995563 0.718668152008873 0.359334076004437 94 0.611795896457293 0.776408207085415 0.388204103542707 95 0.570608003609361 0.858783992781278 0.429391996390639 96 0.580474612049945 0.83905077590011 0.419525387950055 97 0.998901652824894 0.00219669435021304 0.00109834717510652 98 0.99853839299037 0.00292321401925804 0.00146160700962902 99 0.998933283245663 0.00213343350867461 0.00106671675433731 100 0.998776389496303 0.00244722100739492 0.00122361050369746 101 0.99918152634753 0.00163694730494003 0.000818473652470016 102 0.998649814421303 0.0027003711573945 0.00135018557869725 103 0.998014610303334 0.00397077939333199 0.00198538969666600 104 0.99893166949303 0.00213666101393892 0.00106833050696946 105 0.998902675280419 0.0021946494391619 0.00109732471958095 106 0.998177525319184 0.00364494936163095 0.00182247468081548 107 0.997295827399732 0.00540834520053618 0.00270417260026809 108 0.99582980452548 0.00834039094904015 0.00417019547452008 109 0.998088934175428 0.00382213164914441 0.00191106582457220 110 0.996968215583728 0.00606356883254367 0.00303178441627184 111 0.995594759713668 0.00881048057266382 0.00440524028633191 112 0.993799862060218 0.012400275879563 0.0062001379397815 113 0.9937656149891 0.0124687700217979 0.00623438501089893 114 0.990691388748725 0.0186172225025497 0.00930861125127484 115 0.986148777466078 0.0277024450678433 0.0138512225339217 116 0.982739686935138 0.0345206261297233 0.0172603130648616 117 0.985860501391398 0.0282789972172035 0.0141394986086017 118 0.98633746120822 0.027325077583561 0.0136625387917805 119 0.98929796855311 0.0214040628937810 0.0107020314468905 120 0.982339238252573 0.0353215234948535 0.0176607617474268 121 0.9792848587304 0.0414302825391996 0.0207151412695998 122 0.969265419403 0.0614691611939989 0.0307345805969994 123 0.966307441955381 0.0673851160892385 0.0336925580446193 124 0.948882221427397 0.102235557145206 0.051117778572603 125 0.924860196261282 0.150279607477437 0.0751398037387184 126 0.890747254653248 0.218505490693504 0.109252745346752 127 0.912432463554567 0.175135072890867 0.0875675364454334 128 0.907029226512845 0.185941546974310 0.0929707734871552 129 0.900250677797774 0.199498644404451 0.0997493222022257 130 0.865157092536118 0.269685814927764 0.134842907463882 131 0.93766797189188 0.124664056216240 0.0623320281081202 132 0.888947850802238 0.222104298395525 0.111052149197762 133 0.813060503810084 0.373878992379831 0.186939496189916 134 0.687672393367932 0.624655213264136 0.312327606632068 135 0.532105840866852 0.935788318266296 0.467894159133148 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 58 0.453125 NOK 5% type I error level 76 0.59375 NOK 10% type I error level 82 0.640625 NOK

Charts produced by software:

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Parameters (Session):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 4 ; 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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