*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, 03 Dec 2010 21:35:27 +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/03/t12914120132sfojpe83fr9xsb.htm/, Retrieved Fri, 03 Dec 2010 22:33:44 +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/Dec/03/t12914120132sfojpe83fr9xsb.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 14 13 3 12 8 13 5 10 12 16 6 9 7 12 6 10 10 11 5 12 7 12 3 13 16 18 8 12 11 11 4 12 14 14 4 6 6 9 4 5 16 14 6 12 11 12 6 11 16 11 5 14 12 12 4 14 7 13 6 12 13 11 4 12 11 12 6 11 15 16 6 11 7 9 4 7 9 11 4 9 7 13 2 11 14 15 7 11 15 10 5 12 7 11 4 12 15 13 6 11 17 16 6 11 15 15 7 8 14 14 5 9 14 14 6 12 8 14 4 10 8 8 4 10 14 13 7 12 14 15 7 8 8 13 4 12 11 11 4 11 16 15 6 12 10 15 6 7 8 9 5 11 14 13 6 11 16 16 7 12 13 13 6 9 5 11 3 15 8 12 3 11 10 12 4 11 8 12 6 11 13 14 7 11 15 14 5 15 6 8 4 11 12 13 5 12 16 16 6 12 5 13 6 9 15 11 6 12 12 14 5 12 8 13 4 13 13 13 5 11 14 13 5 9 12 12 4 9 16 16 6 11 10 15 2 11 15 15 8 12 8 12 3 12 16 14 6 9 19 12 6 11 14 15 6 9 6 12 5 12 13 13 5 12 15 12 6 12 7 12 5 12 13 13 6 14 4 5 2 11 14 13 5 12 13 13 5 11 11 14 5 6 14 17 6 10 12 13 6 12 15 13 6 13 14 12 5 8 13 13 5 12 8 14 4 12 6 11 2 12 7 12 4 6 13 12 6 11 13 16 6 10 11 12 5 12 5 12 3 13 12 12 6 11 8 10 4 7 11 15 5 11 14 15 8 11 9 12 4 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 13 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Liked[t] = + 7.07678977830615 + 0.0887064792188269FindingFriends[t] + 0.180163506492804KnowingFriends[t] + 0.583237749836951Celebrity[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) 7.07678977830615 1.051654 6.7292 0 0 FindingFriends 0.0887064792188269 0.080351 1.104 0.271342 0.135671 KnowingFriends 0.180163506492804 0.049485 3.6408 0.000372 0.000186 Celebrity 0.583237749836951 0.12235 4.767 4e-06 2e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.592277490989078 R-squared 0.350792626332318 Adjusted R-squared 0.337979322904666 F-TEST (value) 27.3772199583827 F-TEST (DF numerator) 3 F-TEST (DF denominator) 152 p-value 3.26405569239796e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.77011811147447 Sum Squared Residuals 476.264355542632 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 12.5019763485613 0.498023651438748 2 13 12.4987643300593 0.50123566994072 3 16 13.6252431474298 2.37475685257020 4 12 12.6357191357470 -0.635719135746955 5 11 12.6816783846072 -1.68167838460724 6 12 11.1521253238926 0.847874676107423 7 18 15.7784921107314 2.2215078892686 8 11 12.4560170997007 -1.45601709970075 9 14 12.9965076191792 1.00349238082084 10 9 11.0229606919238 -2.02296069192376 11 14 13.9023647773069 0.0976352226931168 12 12 13.6224925993746 -1.62249259937465 13 11 13.8513659027829 -2.85136590278289 14 12 12.8135935646312 -0.813593564631204 15 13 13.0792515318411 -0.079251531841085 16 11 12.8163441126864 -1.81634411268635 17 12 13.6224925993746 -1.62249259937465 18 16 14.2544401461270 1.74555985387296 19 9 11.6466565945107 -2.64665659451070 20 11 11.652157690621 -0.652157690621004 21 13 10.3027681363991 2.69723186360085 22 15 14.6575143894712 0.342485610528814 23 10 13.6712023962901 -3.67120239629009 24 11 11.7353630737295 -0.73536307372953 25 13 14.3431466253459 -1.34314662534587 26 16 14.6147671591126 1.38523284088735 27 15 14.837677895964 0.16232210403601 28 14 13.2249194521408 0.775080547859197 29 14 13.8968636811966 0.103136318803419 30 14 11.9155265802223 2.08447341977767 31 8 11.7381136217847 -3.73811362178468 32 13 14.5688079102524 -1.56880791025236 33 15 14.74622086869 0.253779131309987 34 13 11.5607006633470 1.43929933665297 35 11 12.4560170997007 -1.45601709970075 36 15 14.4346036526198 0.565396347380157 37 15 13.4423290928818 1.55767090711816 38 9 12.0552319339651 -3.05523193396515 39 13 14.0742766396342 -1.07427663963423 40 16 15.0178414024568 0.982158597543205 41 13 13.9828196123603 -0.982819612360257 42 11 10.5256788732505 0.474321126749511 43 12 11.5984082680419 0.401591731958138 44 12 12.1871471139891 -0.187147113989115 45 12 12.9932956006774 -0.99329560067741 46 14 14.4773508829784 -0.477350882978382 47 14 13.6712023962901 0.328797603709913 48 8 11.8213190048932 -3.82131900489321 49 13 13.1307118768117 -0.130711876811675 50 16 14.5233101318387 1.47668986816133 51 13 12.5415115604178 0.458488439582177 52 11 14.0770271876894 -3.07702718768939 53 14 13.2194183560305 0.780581643969498 54 13 11.9155265802223 1.08447341977767 55 13 13.4882883417421 -0.488288341742133 56 13 13.4910388897973 -0.491038889797283 57 12 12.3700611685371 -0.37006116853707 58 16 14.2571906941822 1.74280930581781 59 15 11.0206716143152 3.97932838568479 60 15 15.4209156458009 -0.420915645800941 61 12 11.3322888303854 0.667711169614618 62 14 14.5233101318387 -0.52331013183867 63 12 14.7976812136606 -2.79768121366060 64 15 14.0742766396342 0.925723360365765 65 12 11.8723178794172 0.127682120582804 66 13 13.3995818625233 -0.399581862523306 67 12 14.3431466253459 -2.34314662534587 68 12 12.3186008235665 -0.318600823566480 69 13 13.9828196123603 -0.982819612360257 70 5 10.2058100130149 -5.20581001301487 71 13 13.4910388897973 -0.491038889797283 72 13 13.3995818625233 -0.399581862523306 73 14 12.9505483703189 1.04945162968113 74 17 13.6307442435401 3.3692557564599 75 13 13.6252431474298 -0.6252431474298 76 13 14.3431466253459 -1.34314662534587 77 12 13.6684518482349 -1.66845184823494 78 13 13.044755945648 -0.044755945647999 79 14 11.9155265802223 2.08447341977767 80 11 10.3887240675628 0.611275932437178 81 12 11.7353630737295 0.264636926270471 82 12 13.4505807370473 -1.45058073704730 83 16 13.8941131331414 2.10588686685857 84 12 12.8618418911000 -0.861841891100044 85 12 10.7917983109070 1.20820168909303 86 12 13.8913625850863 -1.89136258508628 87 10 11.8268201010035 -1.82682010100351 88 15 12.5957224534436 2.40427754655644 89 15 15.2407521393081 -0.240752139308137 90 12 12.0069836074963 -0.00698360749631072 91 16 13.3536226136630 2.64637738633698 92 15 13.8941131331414 1.10588686685857 93 16 15.1065478816756 0.893452118324378 94 13 14.3458971734010 -1.34589717340102 95 12 12.9505483703189 -0.95054837031887 96 11 11.9155265802223 -0.915526580222334 97 13 11.9178156578309 1.08218434216911 98 10 11.2408318031114 -1.24083180311140 99 15 13.2249194521408 1.77508054785920 100 13 13.6224925993746 -0.622492599374649 101 16 15.1980049089496 0.801995091050401 102 15 14.9263843751828 0.0736156248171831 103 18 14.8808865967691 3.11911340323087 104 13 10.6143853524693 2.38561464753068 105 10 9.85098409613956 0.149015903860440 106 16 14.6975110717746 1.30248892822543 107 13 11.6953663914261 1.30463360857386 108 15 15.4209156458009 -0.420915645800941 109 14 11.5152028849333 2.48479711506666 110 15 11.652157690621 3.34784230937900 111 14 13.0420053975928 0.957994602407152 112 13 14.5715584583075 -1.57155845830751 113 13 12.9018385734034 0.0981614265965683 114 15 13.9828196123603 1.01718038763974 115 16 14.3858938557044 1.61410614429560 116 14 14.0742766396342 -0.0742766396342347 117 14 14.1629831188531 -0.162983118853061 118 16 13.0820020798962 2.91799792010376 119 14 14.3431466253459 -0.343146625345866 120 12 12.5474741269747 -0.547474126974723 121 13 12.6361806061935 0.36381939380645 122 12 13.8513659027829 -1.85136590278289 123 12 12.0069836074963 -0.00698360749631072 124 14 14.4318531045647 -0.431853104564693 125 14 14.3431466253459 -0.343146625345866 126 14 12.1384373170737 1.86156268292632 127 16 15.3294586185270 0.670541381473036 128 13 14.3431466253459 -1.34314662534587 129 14 12.5042654261696 1.49573457383041 130 4 11.2003736503614 -7.20037365036142 131 16 15.3294586185270 0.670541381473036 132 13 13.7139496266486 -0.713949626648626 133 16 11.9155265802223 4.08447341977767 134 15 13.7111990785935 1.28880092140652 135 14 13.9828196123603 0.0171803876397428 136 13 12.0956900867151 0.904309913284862 137 14 14.2544401461270 -0.254440146127039 138 12 12.2331063628494 -0.233106362849403 139 15 14.3431466253459 0.656853374654135 140 14 13.4023324105785 0.597667589421543 141 13 13.2681281529459 -0.268128152945941 142 14 14.1629831188531 -0.162983118853061 143 16 12.9965076191792 3.00349238082084 144 6 12.0984406347703 -6.09844063477029 145 13 12.2758535932079 0.724146406792058 146 13 12.4500545331438 0.549945466856154 147 14 12.4987643300593 1.50123566994072 148 15 14.6092660630023 0.390733936997654 149 14 14.4346036526198 -0.434603652619843 150 15 14.9691316055414 0.0308683944586446 151 13 14.2971873764856 -1.29718737648558 152 16 14.9263843751828 1.07361562481718 153 12 12.0069836074963 -0.00698360749631072 154 15 13.6252431474298 1.3747568525702 155 12 14.0742766396342 -2.07427663963423 156 14 11.2008351208080 2.79916487919198 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.506272706266806 0.987454587466387 0.493727293733194 8 0.510099029356319 0.979801941287362 0.489900970643681 9 0.37962776600687 0.75925553201374 0.62037223399313 10 0.262015820422177 0.524031640844354 0.737984179577823 11 0.174826440398121 0.349652880796242 0.825173559601879 12 0.264396177603602 0.528792355207205 0.735603822396398 13 0.524160124740924 0.951679750518151 0.475839875259076 14 0.449159490474247 0.898318980948495 0.550840509525752 15 0.361875680587897 0.723751361175794 0.638124319412103 16 0.33707574409122 0.67415148818244 0.66292425590878 17 0.331560585502796 0.663121171005593 0.668439414497203 18 0.325529353823621 0.651058707647242 0.674470646176379 19 0.325547963061912 0.651095926123823 0.674452036938088 20 0.268013022148459 0.536026044296918 0.731986977851541 21 0.539161511722223 0.921676976555553 0.460838488277777 22 0.46851055034584 0.93702110069168 0.53148944965416 23 0.660704719751795 0.678590560496411 0.339295280248205 24 0.598566777850063 0.802866444299874 0.401433222149937 25 0.556624733001937 0.886750533996126 0.443375266998063 26 0.542506465610961 0.914987068778077 0.457493534389039 27 0.478259557606692 0.956519115213383 0.521740442393308 28 0.434235183028352 0.868470366056704 0.565764816971648 29 0.373188209061207 0.746376418122414 0.626811790938793 30 0.429427122878585 0.85885424575717 0.570572877121415 31 0.583344371542563 0.833311256914874 0.416655628457437 32 0.562942191208503 0.874115617582994 0.437057808791497 33 0.506232413417090 0.987535173165819 0.493767586582910 34 0.512448451905175 0.97510309618965 0.487551548094825 35 0.479842047851584 0.95968409570317 0.520157952148416 36 0.430774460666582 0.861548921333165 0.569225539333418 37 0.428960970442630 0.857921940885259 0.571039029557370 38 0.501834985446111 0.996330029107778 0.498165014553889 39 0.462798381496901 0.925596762993802 0.537201618503099 40 0.42502850220786 0.85005700441572 0.57497149779214 41 0.385540721887791 0.771081443775581 0.614459278112209 42 0.355136262866545 0.71027252573309 0.644863737133455 43 0.312007337954270 0.624014675908541 0.68799266204573 44 0.267032911041656 0.534065822083313 0.732967088958344 45 0.233274609762255 0.46654921952451 0.766725390237745 46 0.19630441175382 0.39260882350764 0.80369558824618 47 0.163983784670007 0.327967569340014 0.836016215329993 48 0.277943660300146 0.555887320600292 0.722056339699854 49 0.236979445783732 0.473958891567464 0.763020554216268 50 0.225652765622211 0.451305531244422 0.77434723437779 51 0.203392735219390 0.406785470438780 0.79660726478061 52 0.281528745848568 0.563057491697137 0.718471254151432 53 0.25287479798349 0.50574959596698 0.74712520201651 54 0.238550078829236 0.477100157658473 0.761449921170764 55 0.203555427158751 0.407110854317501 0.79644457284125 56 0.171927337550133 0.343854675100265 0.828072662449867 57 0.143384647754043 0.286769295508085 0.856615352245957 58 0.145595591392648 0.291191182785297 0.854404408607352 59 0.299625230822803 0.599250461645606 0.700374769177197 60 0.260390604342807 0.520781208685614 0.739609395657193 61 0.229047265430455 0.458094530860911 0.770952734569545 62 0.197146942996599 0.394293885993198 0.802853057003401 63 0.253809400336403 0.507618800672806 0.746190599663597 64 0.229587822008333 0.459175644016665 0.770412177991667 65 0.198656340097578 0.397312680195155 0.801343659902423 66 0.168307934446550 0.336615868893100 0.83169206555345 67 0.188907281886301 0.377814563772602 0.811092718113699 68 0.159513868215202 0.319027736430403 0.840486131784798 69 0.139172383129603 0.278344766259205 0.860827616870397 70 0.424854969748122 0.849709939496244 0.575145030251878 71 0.382806550950123 0.765613101900247 0.617193449049877 72 0.341615455382052 0.683230910764105 0.658384544617948 73 0.317850592572136 0.635701185144273 0.682149407427864 74 0.44326490001232 0.88652980002464 0.55673509998768 75 0.402324667518423 0.804649335036846 0.597675332481577 76 0.382719564926625 0.765439129853251 0.617280435073375 77 0.381175949257079 0.762351898514158 0.618824050742921 78 0.337644145241632 0.675288290483265 0.662355854758367 79 0.358776748195951 0.717553496391901 0.64122325180405 80 0.323845046539881 0.647690093079762 0.676154953460119 81 0.287365890553947 0.574731781107894 0.712634109446053 82 0.270247208318180 0.540494416636361 0.72975279168182 83 0.289131222194431 0.578262444388862 0.710868777805569 84 0.259854104527086 0.519708209054171 0.740145895472914 85 0.239621077624814 0.479242155249628 0.760378922375186 86 0.248552854669424 0.497105709338849 0.751447145330576 87 0.258466681355484 0.516933362710967 0.741533318644516 88 0.301108155246921 0.602216310493842 0.698891844753079 89 0.262178070729956 0.524356141459912 0.737821929270044 90 0.227058750638332 0.454117501276664 0.772941249361668 91 0.272827668531012 0.545655337062024 0.727172331468988 92 0.249885431555877 0.499770863111754 0.750114568444123 93 0.223447793587396 0.446895587174792 0.776552206412604 94 0.205313639278996 0.410627278557992 0.794686360721004 95 0.184292153010234 0.368584306020468 0.815707846989766 96 0.169970249948701 0.339940499897401 0.830029750051299 97 0.156722600264236 0.313445200528473 0.843277399735764 98 0.165721522589754 0.331443045179508 0.834278477410246 99 0.186007950464289 0.372015900928579 0.81399204953571 100 0.163549616508577 0.327099233017154 0.836450383491423 101 0.145714309546206 0.291428619092412 0.854285690453794 102 0.119944236158424 0.239888472316847 0.880055763841576 103 0.160076862863489 0.320153725726978 0.839923137136511 104 0.171727959979564 0.343455919959128 0.828272040020436 105 0.145373688546256 0.290747377092511 0.854626311453744 106 0.129095628663198 0.258191257326396 0.870904371336802 107 0.114923473739066 0.229846947478131 0.885076526260934 108 0.092788227865366 0.185576455730732 0.907211772134634 109 0.109280667073625 0.218561334147249 0.890719332926375 110 0.295230204252768 0.590460408505535 0.704769795747233 111 0.286020061576193 0.572040123152385 0.713979938423807 112 0.269028437558052 0.538056875116105 0.730971562441948 113 0.232297620545952 0.464595241091904 0.767702379454048 114 0.202712919810982 0.405425839621963 0.797287080189018 115 0.191866443853118 0.383732887706236 0.808133556146882 116 0.159039987509060 0.318079975018119 0.84096001249094 117 0.129664646012097 0.259329292024195 0.870335353987903 118 0.164019902890618 0.328039805781235 0.835980097109382 119 0.134413198381635 0.268826396763269 0.865586801618365 120 0.108502927033813 0.217005854067625 0.891497072966188 121 0.0856430839622527 0.171286167924505 0.914356916037747 122 0.0812288915400286 0.162457783080057 0.918771108459971 123 0.0619936689922383 0.123987337984477 0.938006331007762 124 0.0538761543921783 0.107752308784357 0.946123845607822 125 0.0415156598786279 0.0830313197572558 0.958484340121372 126 0.0381767301054907 0.0763534602109815 0.96182326989451 127 0.0288720571931718 0.0577441143863435 0.971127942806828 128 0.0272989689861472 0.0545979379722945 0.972701031013853 129 0.0966913297367285 0.193382659473457 0.903308670263271 130 0.406128592310923 0.812257184621845 0.593871407689077 131 0.360448827000933 0.720897654001866 0.639551172999067 132 0.302933844181565 0.60586768836313 0.697066155818435 133 0.473159424934857 0.946318849869714 0.526840575065143 134 0.414108040985012 0.828216081970023 0.585891959014988 135 0.34580284206556 0.69160568413112 0.65419715793444 136 0.285032385875575 0.57006477175115 0.714967614124425 137 0.224940629975126 0.449881259950252 0.775059370024874 138 0.192646360966971 0.385292721933942 0.807353639033029 139 0.145403249030557 0.290806498061115 0.854596750969443 140 0.121118909056275 0.242237818112550 0.878881090943725 141 0.0865697156418018 0.173139431283604 0.913430284358198 142 0.0583855536504176 0.116771107300835 0.941614446349582 143 0.0683053346479645 0.136610669295929 0.931694665352035 144 0.86693090582733 0.26613818834534 0.13306909417267 145 0.799112258209225 0.40177548358155 0.200887741790775 146 0.70480555629447 0.590388887411061 0.295194443705530 147 0.594556237168248 0.810887525663504 0.405443762831752 148 0.455744932429488 0.911489864858976 0.544255067570512 149 0.313503110196108 0.627006220392216 0.686496889803892 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 4 0.0279720279720280 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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