Personal Standards (Yt)

*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, 30 Nov 2010 11:17:13 +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/30/t1291115783dqvdkbw3p9ha1ix.htm/, Retrieved Tue, 30 Nov 2010 12:16:37 +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/Nov/30/t1291115783dqvdkbw3p9ha1ix.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

24 24 25 25 30 17 19 18 22 18 22 16 25 20 23 16 17 18 21 17 19 23 19 30 15 23 16 18 23 15 27 12 22 21 14 15 22 20 23 31 23 27 21 34 19 21 18 31 20 19 23 16 25 20 19 21 24 22 22 17 25 24 26 25 29 26 32 25 25 17 29 32 28 33 17 13 28 32 29 25 26 29 25 22 14 18 25 17 26 20 20 15 18 20 32 33 25 29 25 23 23 26 21 18 20 20 15 11 30 28 24 26 26 22 24 17 22 12 14 14 24 17 24 21 24 19 24 18 19 10 31 29 22 31 27 19 19 9 25 20 20 28 21 19 27 30 23 29 25 26 20 23 21 13 22 21 23 19 25 28 25 23 17 18 19 21 25 20 19 23 20 21 26 21 23 15 27 28 17 19 17 26 19 10 17 16 22 22 21 19 32 31 21 31 21 29 18 19 18 22 23 23 19 15 20 20 21 18 20 23 17 25 18 21 19 24 22 25 15 17 14 13 18 28 24 21 35 25 29 9 21 16 25 19 20 17 22 25 13 20 26 29 17 14 25 22 20 15 19 19 21 20 22 15 24 20 21 18 26 33 24 22 16 16 23 17 18 16 16 21 26 26 19 18 21 18 21 17 22 22 23 30 29 30 21 24 21 21 23 21 27 29 25 3 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 9 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation PS[t] = + 14.5514432169931 + 0.328382757651301x[t] + 1.08162089861099M1[t] + 0.406425419305482M2[t] + 1.80572354132149M3[t] + 1.63550358771727M4[t] + 1.03025002187994M5[t] + 1.85898982437003M6[t] + 2.36391663137686M7[t] + 2.76323282770756M8[t] + 2.13843125245325M9[t] + 1.45968193131887M10[t] + 0.411295472818057M11[t] -0.0112734900892955t + 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) 14.5514432169931 1.773089 8.2068 0 0 x 0.328382757651301 0.055901 5.8744 0 0 M1 1.08162089861099 1.486541 0.7276 0.468026 0.234013 M2 0.406425419305482 1.49262 0.2723 0.785786 0.392893 M3 1.80572354132149 1.486453 1.2148 0.226422 0.113211 M4 1.63550358771727 1.525793 1.0719 0.285544 0.142772 M5 1.03025002187994 1.527359 0.6745 0.501048 0.250524 M6 1.85898982437003 1.532393 1.2131 0.227053 0.113527 M7 2.36391663137686 1.522166 1.553 0.122604 0.061302 M8 2.76323282770756 1.518104 1.8202 0.070793 0.035396 M9 2.13843125245325 1.514019 1.4124 0.159969 0.079984 M10 1.45968193131887 1.512799 0.9649 0.336207 0.168104 M11 0.411295472818057 1.519187 0.2707 0.786981 0.39349 t -0.0112734900892955 0.006674 -1.6891 0.09335 0.046675 Multiple Linear Regression - Regression Statistics Multiple R 0.483105972728421 R-squared 0.233391380885874 Adjusted R-squared 0.164660952965297 F-TEST (value) 3.39575044048285 F-TEST (DF numerator) 13 F-TEST (DF denominator) 145 p-value 0.000140547979544881 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.85416881771716 Sum Squared Residuals 2153.91950494218 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 23.5029768091459 0.497023190854101 2 25 23.1448905974025 1.85510940259752 3 30 21.9058531681188 8.0941468318812 4 19 22.0527424820766 -3.05274248207656 5 22 21.4362154261499 0.56378457385005 6 22 21.5969162232482 0.40308377675185 7 25 23.4041005707709 1.59589942922912 8 23 22.4786122464071 0.52138775359292 9 17 22.4993026963661 -5.49930269636609 10 21 21.4808971274911 -0.4808971274911 11 19 22.3915337248088 -3.39153372480879 12 19 24.2676440654606 -5.26764406546056 13 15 23.0393121704231 -8.03931217042313 14 16 20.7109294127718 -4.71092941277183 15 23 21.1138057717446 1.88619422825536 16 27 19.9471640550972 7.05283594490278 17 22 22.2860818180323 -0.286081818032306 18 14 21.1332515845253 -7.1332515845253 19 22 23.2688186896993 -1.26881868969933 20 23 27.2690717301051 -4.26907173010505 21 23 25.3194656341562 -2.31946563415624 22 21 26.9281221264917 -5.92812212649167 23 19 21.5994863284347 -2.59948632843465 24 18 24.4607449420403 -6.46074494204031 25 20 21.5904992587464 -1.59049925874639 26 23 19.9188820163977 3.08111798360231 27 25 22.6204376789296 2.3795623210704 28 19 22.7673269928874 -3.76732699288738 29 24 22.4791826946121 1.52081730538794 30 22 21.6547352187564 0.345264781243643 31 25 24.447067839233 0.552932160767008 32 26 25.1634933031257 0.836506696874298 33 29 24.8558009954334 4.1441990045666 34 32 23.8373954265584 8.16260457344159 35 25 20.1506734167579 4.8493265832421 36 29 24.6538458186201 4.34615418137993 37 28 26.0525759847931 1.94742401520694 38 17 18.7984518623722 -1.79845186237224 39 28 26.4257488896737 1.57425111032633 40 29 23.9455761424210 5.05442385757896 41 26 24.6425801170996 1.35741988290038 42 25 23.1613671259413 1.83863287405868 43 14 22.3414894122536 -8.34148941225363 44 25 22.4011493608437 2.59885063915625 45 26 22.7502225684540 3.24977743154596 46 20 20.4182859689739 -0.418285968973859 47 18 21.0005398086403 -3.00053980864026 48 32 24.8469466951998 7.15305330480018 49 25 24.6037630731163 0.39623692688369 50 25 21.9469975578137 3.05300244218630 51 23 24.3201704626943 -1.32017046269432 52 21 21.5116149577904 -0.51161495779039 53 20 21.5518534171664 -1.55185341716637 54 15 19.4138749107055 -4.41387491070546 55 30 25.4900351076951 4.5099648923049 56 24 25.2213122986339 -1.22131229863391 57 26 23.2717062026851 2.7282937973149 58 24 20.9397696032049 3.06023039679508 59 22 18.2381958663583 3.76180413364169 60 14 18.4723924187536 -4.47239241875355 61 24 20.5278881002292 3.47211189977085 62 24 21.1549501614396 2.84504983856044 63 24 21.8862092780637 2.11379072193634 64 24 21.3763330767188 2.62366692328116 65 19 18.1327439595818 0.867256040418188 66 31 25.1894826673573 5.81051733264267 67 22 26.3399014995775 -4.33990149957747 68 27 22.7873511140033 4.21264888599674 69 19 18.8674484721466 0.13255152785336 70 25 21.7896359950873 3.21036400491273 71 20 23.3570381077076 -3.35703810770758 72 21 19.9790243259385 1.02097567406149 73 27 24.6615820686245 2.33841793137548 74 23 23.6467303415784 -0.646730341578419 75 25 24.0496067005512 0.950393299448774 76 20 22.8829649839038 -2.88296498390381 77 21 18.9826103514642 2.01738964853583 78 22 22.4271387250754 -0.427138725075379 79 23 22.2640265266903 0.735973473309696 80 25 25.6075140517934 -0.607514051793423 81 25 23.3295251981933 1.67047480180669 82 17 20.9975885987131 -3.99758859871312 83 19 20.9230769230769 -1.92307692307692 84 25 20.1721252025183 4.82787479748173 85 19 22.2276208839939 -3.22762088399387 86 20 20.8843863992965 -0.884386399296465 87 26 22.2724110312232 3.72758896877682 88 23 20.1206210416218 2.87937895837815 89 27 23.7730698351621 3.22693016483786 90 17 21.6350913287012 -4.63509132870123 91 17 24.4274239491779 -7.42742394917786 92 19 19.5613425329985 -0.561342532998458 93 17 20.8955640135627 -3.89556401356266 94 22 22.1758377482468 -0.175837748246784 95 21 20.1310295267028 0.868970473297223 96 32 23.6490536556110 8.35094634438896 97 21 24.7194010641327 -3.71940106413273 98 21 23.3761665794353 -2.37616657943533 99 18 21.4803636348490 -3.48036363484903 100 18 22.2840184641094 -4.28401846410941 101 23 21.9958741658341 1.00412583416591 102 19 20.1862784170245 -1.18627841702448 103 20 22.3218455221985 -2.32184552219851 104 21 22.0531227131373 -1.05312271313732 105 20 23.0589614360502 -3.05896143605022 106 17 23.0257041401291 -6.02570414012914 107 18 20.6525131609338 -2.65251316093383 108 19 21.2150924709804 -2.21509247098038 109 22 22.6138226371534 -0.613822637153377 110 15 19.3002916065482 -4.30029160654817 111 14 19.3747852078697 -5.37478520786968 112 18 24.1190331289457 -6.11903312894567 113 24 21.2038267694599 2.79617323054006 114 35 23.3348241124659 11.6651758875341 115 29 18.5743533069627 10.4256466930373 116 21 21.2610753167632 -0.261075316763173 117 25 21.6101485243735 3.38985147562653 118 20 20.2633601978472 -0.263360197847188 119 22 21.8307623104675 0.169237689532508 120 13 19.7662795593036 -6.76627955930363 121 26 23.7920717866870 2.20792821331296 122 17 18.1798614525227 -1.17986145252272 123 25 22.1949481456598 2.80505185434016 124 20 19.7147753984072 0.285224601592786 125 19 20.4117793730858 -1.41177937308579 126 21 21.5576284431379 -0.557628443137896 127 22 20.4093679717989 1.59063202820108 128 24 22.4393244662968 1.56067553370317 129 21 21.1464838856506 -0.146483885650622 130 26 25.3822024391965 0.61779756080354 131 24 20.7103321564420 3.28966784355796 132 16 18.3174666476269 -2.31746664762688 133 23 19.7161968137999 3.28380318620012 134 18 18.7013450867538 -0.701345086753777 135 16 21.731283506937 -5.73128350693699 136 26 23.1917038515000 2.80829614850002 137 19 19.9481147343629 -0.948114734362946 138 21 20.7655810467637 0.234418953236252 139 21 20.9308516060300 0.0691483939700265 140 22 22.9608081005279 -0.96080810052789 141 23 24.9517950963947 -1.95179509639469 142 29 24.261772285171 4.73822771482899 143 21 21.2318157906731 -0.231815790673101 144 21 19.8240985548118 1.17590144518816 145 23 20.8944459633335 2.10555403666646 146 27 22.8350390551491 4.16496094485085 147 25 24.8798292023785 0.120170797621541 148 21 21.0861254245206 -0.086125424520628 149 10 19.1560673379888 -9.1560673379888 150 20 21.9438301962974 -1.94383019629741 151 26 21.7807179979123 4.21928200208767 152 24 24.7958227653642 -0.795822765364149 153 29 27.4435752765336 1.55642472346645 154 19 21.4994283428891 -2.49942834288906 155 24 19.7830028789963 4.21699712100365 156 19 18.3752856431351 0.624714356864907 157 24 23.0578433858211 0.942156614178902 158 22 20.4010778705185 1.59892212948151 159 17 24.7445473213069 -7.74454732130691 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.93874717849241 0.122505643015179 0.0612528215075893 18 0.912024638561513 0.175950722876974 0.0879753614384872 19 0.851669064270418 0.296661871459163 0.148330935729582 20 0.795824742323816 0.408350515352368 0.204175257676184 21 0.820051155885091 0.359897688229817 0.179948844114909 22 0.771324099258882 0.457351801482237 0.228675900741118 23 0.720179929029538 0.559640141940924 0.279820070970462 24 0.674673485662807 0.650653028674387 0.325326514337193 25 0.662532984301595 0.67493403139681 0.337467015698405 26 0.673968393098605 0.65206321380279 0.326031606901395 27 0.599061613273298 0.801876773453404 0.400938386726702 28 0.558445712908388 0.883108574183223 0.441554287091612 29 0.520247162580927 0.959505674838146 0.479752837419073 30 0.529093059151996 0.941813881696008 0.470906940848004 31 0.466376087612321 0.932752175224642 0.533623912387679 32 0.431558318984623 0.863116637969246 0.568441681015377 33 0.589968069285319 0.820063861429363 0.410031930714681 34 0.798624783665516 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0.123553725566247 52 0.860819944958613 0.278360110082775 0.139180055041387 53 0.848134442886428 0.303731114227145 0.151865557113572 54 0.860903957930008 0.278192084139985 0.139096042069992 55 0.864475481886133 0.271049036227734 0.135524518113867 56 0.84183425378702 0.31633149242596 0.15816574621298 57 0.815681165500488 0.368637668999023 0.184318834499512 58 0.78936770192333 0.421264596153339 0.210632298076670 59 0.772639269603574 0.454721460792852 0.227360730396426 60 0.797538854119588 0.404922291760824 0.202461145880412 61 0.780063589094086 0.439872821811828 0.219936410905914 62 0.750359834930401 0.499280330139198 0.249640165069599 63 0.728833844512606 0.542332310974788 0.271166155487394 64 0.699358969012784 0.601282061974432 0.300641030987216 65 0.656864712105634 0.686270575788732 0.343135287894366 66 0.68507065543135 0.6298586891373 0.31492934456865 67 0.718721433593516 0.562557132812967 0.281278566406484 68 0.712043591767296 0.575912816465409 0.287956408232704 69 0.672563590649973 0.654872818700054 0.327436409350027 70 0.65431021265736 0.691379574685279 0.345689787342640 71 0.662269182397974 0.675461635204052 0.337730817602026 72 0.616968126261803 0.766063747476395 0.383031873738198 73 0.577264991502798 0.845470016994405 0.422735008497202 74 0.543946557681907 0.912106884636185 0.456053442318093 75 0.526362029438142 0.947275941123717 0.473637970561858 76 0.526056768040518 0.947886463918964 0.473943231959482 77 0.493360008721391 0.986720017442781 0.506639991278609 78 0.446338033265781 0.892676066531562 0.553661966734219 79 0.398254132889778 0.796508265779557 0.601745867110222 80 0.358086150796796 0.716172301593592 0.641913849203204 81 0.323565523840246 0.647131047680491 0.676434476159754 82 0.339749319372317 0.679498638744634 0.660250680627683 83 0.308213231992832 0.616426463985664 0.691786768007168 84 0.327052022762512 0.654104045525024 0.672947977237488 85 0.318205248014795 0.63641049602959 0.681794751985205 86 0.281884249592745 0.56376849918549 0.718115750407255 87 0.31564661802409 0.63129323604818 0.68435338197591 88 0.313640843664746 0.627281687329491 0.686359156335254 89 0.314196946701007 0.628393893402013 0.685803053298993 90 0.337475452417463 0.674950904834925 0.662524547582537 91 0.514096219446481 0.971807561107037 0.485903780553519 92 0.469652882115221 0.939305764230441 0.530347117884779 93 0.462025033993136 0.924050067986271 0.537974966006864 94 0.416231540505635 0.83246308101127 0.583768459494365 95 0.369872036382246 0.739744072764492 0.630127963617754 96 0.593389216736769 0.813221566526463 0.406610783263231 97 0.596430929510316 0.807138140979369 0.403569070489684 98 0.563577367694925 0.87284526461015 0.436422632305075 99 0.557436836681115 0.885126326637771 0.442563163318885 100 0.552833045513074 0.894333908973853 0.447166954486926 101 0.52700373070844 0.94599253858312 0.47299626929156 102 0.488194601162265 0.97638920232453 0.511805398837735 103 0.509554889951283 0.980890220097434 0.490445110048717 104 0.458604239687327 0.917208479374653 0.541395760312673 105 0.439276812079479 0.878553624158957 0.560723187920521 106 0.522643788168953 0.954712423662095 0.477356211831047 107 0.524116327792422 0.951767344415156 0.475883672207578 108 0.484088742390103 0.968177484780206 0.515911257609897 109 0.461803049888086 0.923606099776172 0.538196950111914 110 0.513953570720015 0.97209285855997 0.486046429279985 111 0.523009715689854 0.953980568620293 0.476990284310146 112 0.715902570966377 0.568194858067245 0.284097429033623 113 0.707786934430235 0.58442613113953 0.292213065569765 114 0.937065154207579 0.125869691584843 0.0629348457924215 115 0.986121743364264 0.027756513271472 0.013878256635736 116 0.979393154651758 0.0412136906964839 0.0206068453482420 117 0.979505853123624 0.0409882937527519 0.0204941468763760 118 0.970037672683585 0.0599246546328292 0.0299623273164146 119 0.964739683140257 0.070520633719485 0.0352603168597425 120 0.991142244811425 0.0177155103771499 0.00885775518857494 121 0.989844179900676 0.0203116401986479 0.0101558200993240 122 0.988320173383937 0.0233596532321261 0.0116798266160631 123 0.995344279280725 0.00931144143854968 0.00465572071927484 124 0.992162920810037 0.0156741583799254 0.0078370791899627 125 0.988709673103367 0.0225806537932662 0.0112903268966331 126 0.981881389369675 0.0362372212606498 0.0181186106303249 127 0.972201869633234 0.0555962607335321 0.0277981303667660 128 0.962163877146241 0.0756722457075179 0.0378361228537590 129 0.952022656204235 0.0959546875915294 0.0479773437957647 130 0.950152894430446 0.0996942111391073 0.0498471055695537 131 0.925668873635266 0.148662252729467 0.0743311263647336 132 0.92522383915043 0.149552321699139 0.0747761608495694 133 0.90338474241641 0.193230515167178 0.0966152575835892 134 0.869139249914396 0.261721500171207 0.130860750085604 135 0.822789421516752 0.354421156966497 0.177210578483248 136 0.750707428480774 0.498585143038453 0.249292571519227 137 0.792057547005877 0.415884905988245 0.207942452994123 138 0.72048748482212 0.559025030355761 0.279512515177880 139 0.689799759049551 0.620400481900897 0.310200240950449 140 0.561604075569739 0.876791848860522 0.438395924430261 141 0.481881591319332 0.963763182638665 0.518118408680668 142 0.475159026424130 0.950318052848261 0.524840973575870 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 1 0.00793650793650794 OK 5% type I error level 10 0.0793650793650794 NOK 10% type I error level 16 0.126984126984127 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = 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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