Multiple Regression X2

*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, 28 Dec 2010 18:54:18 +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/28/t1293562360eeg519rdlccik22.htm/, Retrieved Tue, 28 Dec 2010 19:52:42 +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/28/t1293562360eeg519rdlccik22.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 «

621 0 587 0 655 0 517 0 646 0 657 0 382 0 345 0 625 0 654 0 606 0 510 0 614 0 647 0 580 0 614 0 636 0 388 0 356 0 639 0 753 0 611 0 639 0 630 0 586 0 695 0 552 0 619 0 681 0 421 0 307 0 754 0 690 0 644 0 643 0 608 0 651 0 691 0 627 0 634 0 731 0 475 0 337 0 803 0 722 0 590 0 724 0 627 0 696 0 825 0 677 0 656 0 785 0 412 0 352 0 839 0 729 0 696 0 641 0 695 0 638 0 762 0 635 0 721 0 854 0 418 0 367 0 824 0 687 0 601 0 676 0 740 0 691 0 683 0 594 0 729 0 731 0 386 0 331 0 706 0 715 0 657 0 653 0 642 0 643 0 718 0 654 0 632 0 731 0 392 0 344 0 792 0 852 0 649 0 629 0 685 0 617 0 715 0 715 0 629 0 916 0 531 0 357 0 917 0 828 0 708 0 858 0 775 0 785 0 1006 0 789 0 734 0 906 0 532 0 387 0 991 1 841 1 892 1 782 1 813 1 793 1 978 1 775 1 797 1 946 1 594 1 438 1 1022 1 868 1 795 1

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 6 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation Y[t] = + 639.947826086957 + 181.71884057971X2[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) 639.947826086957 13.417934 47.6935 0 0 X2 181.71884057971 39.50133 4.6003 1e-05 5e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.376667146038657 R-squared 0.141878138904907 Adjusted R-squared 0.135174061865102 F-TEST (value) 21.1629636805345 F-TEST (DF numerator) 1 F-TEST (DF denominator) 128 p-value 1.00085251950599e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 143.891316958371 Sum Squared Residuals 2650203.02028986 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 621 639.947826086955 -18.9478260869546 2 587 639.947826086956 -52.9478260869563 3 655 639.947826086957 15.0521739130435 4 517 639.947826086957 -122.947826086957 5 646 639.947826086957 6.05217391304346 6 657 639.947826086957 17.0521739130435 7 382 639.947826086957 -257.947826086957 8 345 639.947826086957 -294.947826086957 9 625 639.947826086957 -14.9478260869565 10 654 639.947826086957 14.0521739130435 11 606 639.947826086957 -33.9478260869565 12 510 639.947826086957 -129.947826086957 13 614 639.947826086957 -25.9478260869565 14 647 639.947826086957 7.05217391304346 15 580 639.947826086957 -59.9478260869565 16 614 639.947826086957 -25.9478260869565 17 636 639.947826086957 -3.94782608695654 18 388 639.947826086957 -251.947826086957 19 356 639.947826086957 -283.947826086957 20 639 639.947826086957 -0.947826086956538 21 753 639.947826086957 113.052173913043 22 611 639.947826086957 -28.9478260869565 23 639 639.947826086957 -0.947826086956538 24 630 639.947826086957 -9.94782608695654 25 586 639.947826086957 -53.9478260869565 26 695 639.947826086957 55.0521739130435 27 552 639.947826086957 -87.9478260869565 28 619 639.947826086957 -20.9478260869565 29 681 639.947826086957 41.0521739130435 30 421 639.947826086957 -218.947826086957 31 307 639.947826086957 -332.947826086957 32 754 639.947826086957 114.052173913043 33 690 639.947826086957 50.0521739130435 34 644 639.947826086957 4.05217391304346 35 643 639.947826086957 3.05217391304346 36 608 639.947826086957 -31.9478260869565 37 651 639.947826086957 11.0521739130435 38 691 639.947826086957 51.0521739130435 39 627 639.947826086957 -12.9478260869565 40 634 639.947826086957 -5.94782608695654 41 731 639.947826086957 91.0521739130435 42 475 639.947826086957 -164.947826086957 43 337 639.947826086957 -302.947826086957 44 803 639.947826086957 163.052173913043 45 722 639.947826086957 82.0521739130435 46 590 639.947826086957 -49.9478260869565 47 724 639.947826086957 84.0521739130435 48 627 639.947826086957 -12.9478260869565 49 696 639.947826086957 56.0521739130435 50 825 639.947826086957 185.052173913043 51 677 639.947826086957 37.0521739130435 52 656 639.947826086957 16.0521739130435 53 785 639.947826086957 145.052173913043 54 412 639.947826086957 -227.947826086957 55 352 639.947826086957 -287.947826086957 56 839 639.947826086957 199.052173913043 57 729 639.947826086957 89.0521739130435 58 696 639.947826086957 56.0521739130435 59 641 639.947826086957 1.05217391304346 60 695 639.947826086957 55.0521739130435 61 638 639.947826086957 -1.94782608695654 62 762 639.947826086957 122.052173913043 63 635 639.947826086957 -4.94782608695654 64 721 639.947826086957 81.0521739130435 65 854 639.947826086957 214.052173913043 66 418 639.947826086957 -221.947826086957 67 367 639.947826086957 -272.947826086957 68 824 639.947826086957 184.052173913043 69 687 639.947826086957 47.0521739130435 70 601 639.947826086957 -38.9478260869565 71 676 639.947826086957 36.0521739130435 72 740 639.947826086957 100.052173913043 73 691 639.947826086957 51.0521739130435 74 683 639.947826086957 43.0521739130435 75 594 639.947826086957 -45.9478260869565 76 729 639.947826086957 89.0521739130435 77 731 639.947826086957 91.0521739130435 78 386 639.947826086957 -253.947826086957 79 331 639.947826086957 -308.947826086957 80 706 639.947826086957 66.0521739130435 81 715 639.947826086957 75.0521739130435 82 657 639.947826086957 17.0521739130435 83 653 639.947826086957 13.0521739130435 84 642 639.947826086957 2.05217391304346 85 643 639.947826086957 3.05217391304346 86 718 639.947826086957 78.0521739130435 87 654 639.947826086957 14.0521739130435 88 632 639.947826086957 -7.94782608695654 89 731 639.947826086957 91.0521739130435 90 392 639.947826086957 -247.947826086957 91 344 639.947826086957 -295.947826086957 92 792 639.947826086957 152.052173913043 93 852 639.947826086957 212.052173913043 94 649 639.947826086957 9.05217391304346 95 629 639.947826086957 -10.9478260869565 96 685 639.947826086957 45.0521739130435 97 617 639.947826086957 -22.9478260869565 98 715 639.947826086957 75.0521739130435 99 715 639.947826086957 75.0521739130435 100 629 639.947826086957 -10.9478260869565 101 916 639.947826086957 276.052173913043 102 531 639.947826086957 -108.947826086957 103 357 639.947826086957 -282.947826086957 104 917 639.947826086957 277.052173913043 105 828 639.947826086957 188.052173913043 106 708 639.947826086957 68.0521739130435 107 858 639.947826086957 218.052173913043 108 775 639.947826086957 135.052173913043 109 785 639.947826086957 145.052173913043 110 1006 639.947826086957 366.052173913043 111 789 639.947826086957 149.052173913043 112 734 639.947826086957 94.0521739130435 113 906 639.947826086957 266.052173913043 114 532 639.947826086957 -107.947826086957 115 387 639.947826086957 -252.947826086957 116 991 821.666666666667 169.333333333333 117 841 821.666666666667 19.3333333333333 118 892 821.666666666667 70.3333333333333 119 782 821.666666666667 -39.6666666666667 120 813 821.666666666667 -8.66666666666667 121 793 821.666666666667 -28.6666666666667 122 978 821.666666666667 156.333333333333 123 775 821.666666666667 -46.6666666666667 124 797 821.666666666667 -24.6666666666667 125 946 821.666666666667 124.333333333333 126 594 821.666666666667 -227.666666666667 127 438 821.666666666667 -383.666666666667 128 1022 821.666666666667 200.333333333333 129 868 821.666666666667 46.3333333333333 130 795 821.666666666667 -26.6666666666667 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.100255007850212 0.200510015700424 0.899744992149788 6 0.0470961231849996 0.0941922463699992 0.952903876815 7 0.280284213652512 0.560568427305023 0.719715786347488 8 0.491711926663738 0.983423853327476 0.508288073336262 9 0.399303046435818 0.798606092871635 0.600696953564182 10 0.334887527466663 0.669775054933327 0.665112472533337 11 0.247911145280041 0.495822290560083 0.752088854719959 12 0.19001875612265 0.3800375122453 0.80998124387735 13 0.135707926161937 0.271415852323875 0.864292073838063 14 0.102944216957302 0.205888433914604 0.897055783042698 15 0.0671782417677335 0.134356483535467 0.932821758232267 16 0.0439592261900637 0.0879184523801274 0.956040773809936 17 0.0297346021567667 0.0594692043135334 0.970265397843233 18 0.0601848674706255 0.120369734941251 0.939815132529375 19 0.124320787645638 0.248641575291275 0.875679212354362 20 0.0992491540410588 0.198498308082118 0.900750845958941 21 0.132128987825773 0.264257975651547 0.867871012174226 22 0.0989748588540176 0.197949717708035 0.901025141145982 23 0.0760875047236394 0.152175009447279 0.923912495276361 24 0.0563683213282901 0.11273664265658 0.94363167867171 25 0.0393541750218919 0.0787083500437838 0.960645824978108 26 0.0353408770247964 0.0706817540495928 0.964659122975204 27 0.0251420846741688 0.0502841693483377 0.97485791532583 28 0.017237844821409 0.034475689642818 0.98276215517859 29 0.014060749792796 0.0281214995855921 0.985939250207204 30 0.0206674256398474 0.0413348512796947 0.979332574360153 31 0.0788178835149424 0.157635767029885 0.921182116485058 32 0.0937109435103784 0.187421887020757 0.906289056489622 33 0.083119839846298 0.166239679692596 0.916880160153702 34 0.0655130033481307 0.131026006696261 0.93448699665187 35 0.0508397526054029 0.101679505210806 0.949160247394597 36 0.0376312513890815 0.075262502778163 0.962368748610918 37 0.028811482882591 0.057622965765182 0.971188517117409 38 0.0243139529158949 0.0486279058317898 0.975686047084105 39 0.0175387521601749 0.0350775043203497 0.982461247839825 40 0.0125619098707421 0.0251238197414843 0.987438090129258 41 0.012332524428739 0.024665048857478 0.98766747557126 42 0.01279578200018 0.0255915640003599 0.98720421799982 43 0.0387142421457459 0.0774284842914918 0.961285757854254 44 0.0548645586644382 0.109729117328876 0.945135441335562 45 0.050791869901505 0.10158373980301 0.949208130098495 46 0.0389896667980929 0.0779793335961859 0.961010333201907 47 0.0358481342494114 0.0716962684988228 0.964151865750589 48 0.0268774918275489 0.0537549836550977 0.97312250817245 49 0.0221907904022031 0.0443815808044063 0.977809209597797 50 0.0336622030238113 0.0673244060476227 0.96633779697619 51 0.0264243751240183 0.0528487502480365 0.973575624875982 52 0.019874026318733 0.039748052637466 0.980125973681267 53 0.0226702580765792 0.0453405161531584 0.97732974192342 54 0.0353470511563347 0.0706941023126694 0.964652948843665 55 0.0786751699000962 0.157350339800192 0.921324830099904 56 0.10806258364299 0.216125167285981 0.89193741635701 57 0.0975996129715923 0.195199225943185 0.902400387028408 58 0.0821022301254246 0.164204460250849 0.917897769874575 59 0.0650393906811291 0.130078781362258 0.934960609318871 60 0.0535363832389117 0.107072766477823 0.946463616761088 61 0.0414147381369132 0.0828294762738264 0.958585261863087 62 0.0399502447573963 0.0799004895147927 0.960049755242604 63 0.0304191968542745 0.0608383937085489 0.969580803145726 64 0.0255280215882194 0.0510560431764388 0.97447197841178 65 0.0380315432626363 0.0760630865252726 0.961968456737364 66 0.0558448617808764 0.111689723561753 0.944155138219124 67 0.106998033775805 0.213996067551611 0.893001966224195 68 0.12378966706074 0.24757933412148 0.87621033293926 69 0.102738886705838 0.205477773411676 0.897261113294162 70 0.0842321000267899 0.16846420005358 0.91576789997321 71 0.0677533475833701 0.13550669516674 0.93224665241663 72 0.0595754726449011 0.119150945289802 0.940424527355099 73 0.0476561235172378 0.0953122470344756 0.952343876482762 74 0.0373432261909669 0.0746864523819337 0.962656773809033 75 0.0294233675617908 0.0588467351235815 0.97057663243821 76 0.0243889243813326 0.0487778487626652 0.975611075618667 77 0.0201478685612842 0.0402957371225683 0.979852131438716 78 0.039718272571176 0.0794365451423521 0.960281727428824 79 0.1082405462247 0.2164810924494 0.8917594537753 80 0.0898537798701289 0.179707559740258 0.910146220129871 81 0.0746108401231106 0.149221680246221 0.925389159876889 82 0.0588063399657983 0.117612679931597 0.941193660034202 83 0.0457475660464342 0.0914951320928685 0.954252433953566 84 0.0352348236632926 0.0704696473265852 0.964765176336707 85 0.0267842272079635 0.053568454415927 0.973215772792037 86 0.0210176418464884 0.0420352836929768 0.978982358153512 87 0.0154987424911578 0.0309974849823157 0.984501257508842 88 0.0114222035776411 0.0228444071552822 0.98857779642236 89 0.00884502544774458 0.0176900508954892 0.991154974552255 90 0.0210907933881007 0.0421815867762013 0.9789092066119 91 0.0736366079564381 0.147273215912876 0.926363392043562 92 0.067868372925812 0.135736745851624 0.932131627074188 93 0.0767277921308624 0.153455584261725 0.923272207869138 94 0.06089873301786 0.12179746603572 0.93910126698214 95 0.0490188498504858 0.0980376997009716 0.950981150149514 96 0.0374596018627573 0.0749192037255146 0.962540398137243 97 0.0304327766704681 0.0608655533409363 0.969567223329532 98 0.0228854931672481 0.0457709863344961 0.977114506832752 99 0.016917669171659 0.033835338343318 0.98308233082834 100 0.0131245702125683 0.0262491404251367 0.986875429787432 101 0.0206551460488982 0.0413102920977963 0.979344853951102 102 0.0229124161662875 0.0458248323325749 0.977087583833713 103 0.106112336121117 0.212224672242234 0.893887663878883 104 0.131132762818706 0.262265525637411 0.868867237181294 105 0.119221036197808 0.238442072395616 0.880778963802192 106 0.0935527708291201 0.18710554165824 0.90644722917088 107 0.0919189633896814 0.183837926779363 0.908081036610319 108 0.0729951375812658 0.145990275162532 0.927004862418734 109 0.058275652356827 0.116551304713654 0.941724347643173 110 0.15709731800858 0.314194636017161 0.84290268199142 111 0.147865744639035 0.295731489278071 0.852134255360965 112 0.126576315373223 0.253152630746446 0.873423684626777 113 0.374011003320634 0.748022006641268 0.625988996679366 114 0.336304553083842 0.672609106167684 0.663695446916158 115 0.28940717658677 0.57881435317354 0.71059282341323 116 0.302378142705396 0.604756285410791 0.697621857294604 117 0.237323786362135 0.474647572724271 0.762676213637865 118 0.190852202991735 0.38170440598347 0.809147797008265 119 0.137276511697068 0.274553023394136 0.862723488302932 120 0.0918261635160826 0.183652327032165 0.908173836483917 121 0.057464079952317 0.114928159904634 0.942535920047683 122 0.0613821954413412 0.122764390882682 0.938617804558659 123 0.0342797972534725 0.068559594506945 0.965720202746527 124 0.016944140378733 0.033888280757466 0.983055859621267 125 0.0150711707693408 0.0301423415386816 0.98492882923066 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 25 0.206611570247934 NOK 10% type I error level 56 0.462809917355372 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562360eeg519rdlccik22/103aai1293562448.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562360eeg519rdlccik22/103aai1293562448.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562360eeg519rdlccik22/14hst1293562447.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562360eeg519rdlccik22/14hst1293562447.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562360eeg519rdlccik22/24hst1293562447.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562360eeg519rdlccik22/24hst1293562447.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562360eeg519rdlccik22/3f89e1293562447.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562360eeg519rdlccik22/3f89e1293562447.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562360eeg519rdlccik22/4f89e1293562447.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562360eeg519rdlccik22/4f89e1293562447.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562360eeg519rdlccik22/5f89e1293562447.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562360eeg519rdlccik22/5f89e1293562447.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562360eeg519rdlccik22/6i9tu1293562448.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562360eeg519rdlccik22/6i9tu1293562448.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562360eeg519rdlccik22/7t0sx1293562448.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562360eeg519rdlccik22/7t0sx1293562448.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562360eeg519rdlccik22/8t0sx1293562448.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562360eeg519rdlccik22/8t0sx1293562448.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562360eeg519rdlccik22/9t0sx1293562448.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293562360eeg519rdlccik22/9t0sx1293562448.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

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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