*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: Wed, 01 Dec 2010 16:14:58 +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/01/t1291220022cqau8o7vqi6k1v7.htm/, Retrieved Wed, 01 Dec 2010 17:13:42 +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/01/t1291220022cqau8o7vqi6k1v7.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 «

1081 1 213118 162556 309 1 81767 29790 458 1 153198 87550 588 0 -26007 84738 302 1 126942 54660 156 1 157214 42634 481 0 129352 40949 353 1 234817 45187 452 1 60448 37704 109 1 47818 16275 115 0 245546 25830 110 0 48020 12679 239 1 -1710 18014 247 0 32648 43556 505 1 95350 24811 159 0 151352 6575 109 0 288170 7123 519 1 114337 21950 248 1 37884 37597 373 0 122844 17821 119 1 82340 12988 84 1 79801 22330 102 0 165548 13326 295 0 116384 16189 105 0 134028 7146 64 0 63838 15824 282 1 74996 27664 182 0 31080 11920 37 0 32168 8568 361 0 49857 14416 28 1 87161 3369 85 1 106113 11819 45 1 80570 6984 49 1 102129 4519 22 0 301670 2220 155 0 102313 18562 91 0 88577 10327 81 1 112477 5336 79 1 191778 2365 145 0 79804 4069 855 0 128294 8636 61 0 96448 13718 226 0 93811 4525 105 0 117520 6869 62 0 69159 4628 25 1 101792 3689 217 1 210568 4891 322 1 136996 7489 84 0 121920 4901 33 0 76403 2284 108 1 108094 3160 150 1 134759 4150 115 1 188873 7285 162 1 146216 1134 158 1 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 14 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation Trades[t] = -7.05456938936745 + 1.29944764189907Group[t] + 0.000447415121106048Dividends[t] + 0.00677977480379297`Costs `[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) -7.05456938936745 8.995385 -0.7842 0.433332 0.216666 Group 1.29944764189907 8.100498 0.1604 0.872629 0.436315 Dividends 0.000447415121106048 0.000117 3.8086 0.00016 8e-05 `Costs ` 0.00677977480379297 0.000321 21.1017 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.760202925565886 R-squared 0.577908488038932 Adjusted R-squared 0.574942973903375 F-TEST (value) 194.876322155929 F-TEST (DF numerator) 3 F-TEST (DF denominator) 427 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 73.7204617262728 Sum Squared Residuals 2320619.66573658 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1081 1191.69016703778 -110.690167037780 2 309 232.798161865002 76.2018381349976 3 458 656.35726404781 -198.357264047810 4 588 555.814062879836 32.1859371201638 5 302 421.623139331299 -119.623139331299 6 156 353.633718087007 -197.633718087007 7 481 328.444469796460 152.555530203540 8 353 405.663238804283 -52.6632388042834 9 452 276.91485669536 175.085143304640 10 109 125.980209445311 -16.9802094453112 11 115 277.928007119711 -162.928007119711 12 110 100.391069463436 9.60893053656395 13 239 115.610661710967 123.389338289033 14 247 302.852510838509 -55.8525108385094 15 505 205.118902706901 299.881097293099 16 159 105.239623355214 53.7603766447861 17 109 170.169381987180 -61.1693819871797 18 519 194.217037897690 324.782962102310 19 248 266.093945998717 -18.0939459987174 20 373 168.730060526178 204.269939473822 21 119 119.140754476067 -0.140754476066695 22 84 181.341423700612 -97.3414237006124 23 102 157.361388114842 -55.3613881148417 24 295 154.775166364043 140.224833635957 25 105 101.359855210139 3.6401447898615 26 64 128.790673607020 -64.7906736070204 27 282 215.354912847130 66.6450871528705 28 182 87.6660082358207 94.3339917641793 29 37 65.4269907452701 -28.4269907452701 30 361 112.989439875096 248.010560124904 31 28 56.0830889372344 -28.0830889372344 32 85 121.851597404487 -36.8515974044868 33 45 77.643061789736 -32.643061789736 34 49 70.5767394943116 -21.5767394943116 35 22 142.968250259114 -120.968250259114 36 155 164.567993804361 -9.56799380436074 37 91 102.590854191613 -11.5908541916130 38 81 80.7456671822159 0.254332817784141 39 79 96.0834227589776 -17.0834227589776 40 145 56.2378506120132 88.7621493879868 41 855 108.896241363368 746.103758636632 42 61 129.102674969501 -68.1026749695006 43 226 65.5963715238752 160.403628476125 44 105 92.0959287702692 12.9040712297308 45 62 55.2650107631596 6.73498923684041 46 25 64.7987475113507 -39.7987475113507 47 217 121.616064038941 95.3839359610587 48 322 106.312693689181 215.687306310819 49 84 80.7219584892713 3.27804151072873 50 33 42.6142937603611 -9.61429376036108 51 108 64.0318567333545 43.9681432666454 52 150 82.6741579934024 67.3258420065976 53 115 128.140173866826 -13.1401738668260 54 162 67.3523922276747 94.6476077723253 55 158 95.8938565747752 62.1061434252248 56 97 36.5564365924888 60.4435634075112 57 9 40.8833779229381 -31.8833779229381 58 66 68.6068555052271 -2.60685550522712 59 107 46.1703242172261 60.8296757827739 60 101 96.5924203194783 4.40757968052175 61 47 74.1901787876006 -27.1901787876006 62 38 30.2956911066717 7.70430889332833 63 34 57.7681247050828 -23.7681247050828 64 87 82.3849469011763 4.61505309882373 65 79 37.4864264130944 41.5135735869056 66 947 123.436054120242 823.563945879758 67 74 35.0587474872491 38.9412525127509 68 53 53.0945246315512 -0.094524631551224 69 94 61.2631109501743 32.7368890498257 70 63 66.4699161388224 -3.46991613882235 71 58 27.1171477899095 30.8828522100905 72 49 45.1177367441078 3.88226325589222 73 34 50.4692535742802 -16.4692535742802 74 11 32.1747337288269 -21.1747337288269 75 35 59.5246428603318 -24.5246428603318 76 20 40.940884726841 -20.9408847268410 77 47 51.1555013311699 -4.15550133116995 78 43 31.552478390369 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3 32.3684505463762 -29.3684505463762 417 66 30.7917603907707 35.2082396092293 418 17 29.8071734729268 -12.8071734729268 419 26 32.5195554827148 -6.51955548271478 420 3 26.9204665392504 -23.9204665392504 421 2 31.0294954864438 -29.0294954864438 422 67 44.7465833999706 22.2534166000294 423 70 65.8944692541695 4.10553074583049 424 26 62.1694271915361 -36.1694271915361 425 24 32.9805226583249 -8.98052265832493 426 97 58.8765626138171 38.1234373861829 427 30 42.9886698379278 -12.9886698379278 428 223 304.83668363827 -81.8366836382703 429 48 91.245883374467 -43.245883374467 430 90 130.889906499675 -40.8899064996746 431 180 127.683574803840 52.3164251961597 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.98221662410654 0.0355667517869208 0.0177833758934604 8 0.965332274408499 0.069335451183002 0.034667725591501 9 0.9979209240692 0.00415815186160183 0.00207907593080092 10 0.996234648028764 0.00753070394247277 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270 1 1.15563435733652e-56 5.77817178668261e-57 271 1 3.73467441812806e-56 1.86733720906403e-56 272 1 1.18878311945621e-55 5.94391559728104e-56 273 1 3.72235923196934e-55 1.86117961598467e-55 274 1 1.45356990909220e-54 7.26784954546099e-55 275 1 5.10417105773472e-54 2.55208552886736e-54 276 1 1.51878562747404e-53 7.59392813737022e-54 277 1 4.11040065744616e-53 2.05520032872308e-53 278 1 1.43727779237691e-52 7.18638896188455e-53 279 1 1.92981700520122e-55 9.64908502600612e-56 280 1 5.96643463366167e-55 2.98321731683084e-55 281 1 2.0336882265369e-54 1.01684411326845e-54 282 1 7.36449238227888e-54 3.68224619113944e-54 283 1 8.7496083808052e-55 4.3748041904026e-55 284 1 3.23781853443649e-54 1.61890926721825e-54 285 1 1.30916079071753e-53 6.54580395358766e-54 286 1 4.80179019533181e-53 2.40089509766591e-53 287 1 1.69803381353895e-52 8.49016906769475e-53 288 1 6.55995333192051e-52 3.27997666596026e-52 289 1 2.16166402259923e-51 1.08083201129961e-51 290 1 7.18459073906468e-52 3.59229536953234e-52 291 1 2.34267763389975e-51 1.17133881694987e-51 292 1 7.90452688727727e-51 3.95226344363863e-51 293 1 2.90984331110132e-50 1.45492165555066e-50 294 1 1.06322655609417e-49 5.31613278047084e-50 295 1 4.15766166174246e-49 2.07883083087123e-49 296 1 1.63694220881507e-48 8.18471104407536e-49 297 1 5.90167659808208e-48 2.95083829904104e-48 298 1 1.85855988897406e-47 9.2927994448703e-48 299 1 6.64312344237071e-47 3.32156172118535e-47 300 1 2.36182134684680e-46 1.18091067342340e-46 301 1 8.00138523655901e-46 4.00069261827951e-46 302 1 2.82443453144938e-45 1.41221726572469e-45 303 1 9.89443193117943e-45 4.94721596558972e-45 304 1 2.94517471071034e-44 1.47258735535517e-44 305 1 2.40963488103885e-44 1.20481744051942e-44 306 1 9.23020230172593e-44 4.61510115086297e-44 307 1 2.67164777513963e-43 1.33582388756981e-43 308 1 9.82998467089073e-43 4.91499233544536e-43 309 1 3.40233949093380e-42 1.70116974546690e-42 310 1 9.35492281092196e-42 4.67746140546098e-42 311 1 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332 1 6.66641490402042e-33 3.33320745201021e-33 333 1 2.18513372254972e-32 1.09256686127486e-32 334 1 7.54996718717096e-32 3.77498359358548e-32 335 1 2.51930661714731e-31 1.25965330857366e-31 336 1 8.46133951304307e-31 4.23066975652153e-31 337 1 1.03024784581638e-31 5.15123922908191e-32 338 1 3.42576283404470e-31 1.71288141702235e-31 339 1 1.14692609085761e-30 5.73463045428807e-31 340 1 4.07130884822564e-30 2.03565442411282e-30 341 1 1.42596429644617e-29 7.12982148223083e-30 342 1 4.62708939610443e-29 2.31354469805221e-29 343 1 1.49054226440453e-28 7.45271132202266e-29 344 1 4.76628936459565e-28 2.38314468229782e-28 345 1 6.26264212163189e-28 3.13132106081594e-28 346 1 2.01217864192327e-27 1.00608932096164e-27 347 1 6.8246528537337e-27 3.41232642686685e-27 348 1 2.16061104054370e-26 1.08030552027185e-26 349 1 6.78739457424858e-26 3.39369728712429e-26 350 1 2.27686367299472e-25 1.13843183649736e-25 351 1 7.62734738764677e-25 3.81367369382338e-25 352 1 2.53980220967152e-24 1.26990110483576e-24 353 1 8.37144987692684e-24 4.18572493846342e-24 354 1 2.5844292135796e-23 1.2922146067898e-23 355 1 7.77645847038063e-23 3.88822923519031e-23 356 1 2.32029566161379e-22 1.16014783080689e-22 357 1 2.3338538193211e-22 1.16692690966055e-22 358 1 7.03172744042354e-22 3.51586372021177e-22 359 1 2.10024724462628e-21 1.05012362231314e-21 360 1 6.21786232645913e-21 3.10893116322957e-21 361 1 1.91506071451779e-20 9.57530357258897e-21 362 1 5.57030797001239e-20 2.78515398500620e-20 363 1 1.60529990556222e-19 8.02649952781108e-20 364 1 4.04441880797068e-19 2.02220940398534e-19 365 1 1.24670397208321e-18 6.23351986041605e-19 366 1 3.51284112468550e-18 1.75642056234275e-18 367 1 9.80179082827072e-18 4.90089541413536e-18 368 1 2.70785967792334e-17 1.35392983896167e-17 369 1 7.4052316051755e-17 3.70261580258775e-17 370 1 2.11622479119962e-16 1.05811239559981e-16 371 1 5.69929163556451e-16 2.84964581778225e-16 372 1 1.13427171350354e-15 5.67135856751768e-16 373 0.999999999999998 3.27360335612217e-15 1.63680167806108e-15 374 0.999999999999996 8.72592457552425e-15 4.36296228776212e-15 375 0.999999999999989 2.29280597476733e-14 1.14640298738366e-14 376 0.99999999999997 5.95632811926981e-14 2.97816405963491e-14 377 0.999999999999921 1.57148288579509e-13 7.85741442897545e-14 378 0.999999999999785 4.30202962624634e-13 2.15101481312317e-13 379 0.999999999999453 1.09396613140784e-12 5.46983065703922e-13 380 0.999999999998632 2.73570221705750e-12 1.36785110852875e-12 381 0.999999999996622 6.75572301878685e-12 3.37786150939343e-12 382 0.999999999996816 6.36876819451802e-12 3.18438409725901e-12 383 0.999999999999053 1.89358633012299e-12 9.46793165061494e-13 384 0.99999999999747 5.05893827659305e-12 2.52946913829652e-12 385 0.999999999993024 1.39522730705198e-11 6.97613653525989e-12 386 0.999999999982904 3.41924635624326e-11 1.70962317812163e-11 387 0.999999999953654 9.26924468831027e-11 4.63462234415513e-11 388 0.999999999878452 2.43096434065980e-10 1.21548217032990e-10 389 0.999999999684646 6.3070881572267e-10 3.15354407861335e-10 390 0.999999999169167 1.66166569830283e-09 8.30832849151415e-10 391 0.999999997846148 4.3077032775298e-09 2.1538516387649e-09 392 0.999999994548326 1.09033485264647e-08 5.45167426323234e-09 393 0.999999986566857 2.68662850866604e-08 1.34331425433302e-08 394 0.999999967221284 6.5557432475906e-08 3.2778716237953e-08 395 0.999999962281977 7.5436045411756e-08 3.7718022705878e-08 396 0.999999906345972 1.87308056376986e-07 9.3654028188493e-08 397 0.999999770978924 4.5804215221578e-07 2.2902107610789e-07 398 0.999999985590722 2.8818555807345e-08 1.44092779036725e-08 399 0.9999999610262 7.79476018269558e-08 3.89738009134779e-08 400 0.999999999807767 3.84465283344168e-10 1.92232641672084e-10 401 0.999999999408702 1.18259512432386e-09 5.91297562161931e-10 402 0.9999999980803 3.83940182912413e-09 1.91970091456206e-09 403 0.999999993958322 1.20833562023762e-08 6.04167810118808e-09 404 0.999999980896847 3.82063049383554e-08 1.91031524691777e-08 405 0.99999994223291 1.15534180324744e-07 5.7767090162372e-08 406 0.999999823458895 3.53082210016453e-07 1.76541105008226e-07 407 0.99999946111064 1.07777871844708e-06 5.38889359223541e-07 408 0.999998470637485 3.05872502989070e-06 1.52936251494535e-06 409 0.999995637257676 8.7254846486753e-06 4.36274232433765e-06 410 0.999989031312896 2.19373742072089e-05 1.09686871036045e-05 411 0.99998855335533 2.28932893393050e-05 1.14466446696525e-05 412 0.999982154370516 3.56912589678946e-05 1.78456294839473e-05 413 0.999949466541121 0.000101066917757396 5.05334588786978e-05 414 0.999857743081739 0.00028451383652281 0.000142256918261405 415 0.999615906364284 0.000768187271431436 0.000384093635715718 416 0.999070065892057 0.00185986821588499 0.000929934107942497 417 0.9984481041618 0.00310379167639934 0.00155189583819967 418 0.996414450511877 0.00717109897624688 0.00358554948812344 419 0.991278832512605 0.0174423349747894 0.0087211674873947 420 0.980229308020659 0.0395413839586827 0.0197706919793414 421 0.95952575970321 0.0809484805935814 0.0404742402967907 422 0.941937152083502 0.116125695832997 0.0580628479164984 423 0.996635644525051 0.00672871094989731 0.00336435547494866 424 0.992785666344469 0.0144286673110622 0.00721433365553109 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 411 0.983253588516746 NOK 5% type I error level 415 0.992822966507177 NOK 10% type I error level 417 0.997607655502392 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291220022cqau8o7vqi6k1v7/101p941291220076.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291220022cqau8o7vqi6k1v7/101p941291220076.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291220022cqau8o7vqi6k1v7/1u6us1291220076.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291220022cqau8o7vqi6k1v7/1u6us1291220076.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291220022cqau8o7vqi6k1v7/2u6us1291220076.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291220022cqau8o7vqi6k1v7/2u6us1291220076.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291220022cqau8o7vqi6k1v7/34xtd1291220076.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291220022cqau8o7vqi6k1v7/34xtd1291220076.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291220022cqau8o7vqi6k1v7/44xtd1291220076.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291220022cqau8o7vqi6k1v7/44xtd1291220076.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291220022cqau8o7vqi6k1v7/54xtd1291220076.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291220022cqau8o7vqi6k1v7/54xtd1291220076.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291220022cqau8o7vqi6k1v7/6xpby1291220076.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291220022cqau8o7vqi6k1v7/6xpby1291220076.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291220022cqau8o7vqi6k1v7/78ga11291220076.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291220022cqau8o7vqi6k1v7/78ga11291220076.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291220022cqau8o7vqi6k1v7/88ga11291220076.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291220022cqau8o7vqi6k1v7/88ga11291220076.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291220022cqau8o7vqi6k1v7/98ga11291220076.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291220022cqau8o7vqi6k1v7/98ga11291220076.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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

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

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

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