workshop 7

*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 13:26:39 +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/t1291383045g9b194f6q7jal4j.htm/, Retrieved Fri, 03 Dec 2010 14:30:56 +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/t1291383045g9b194f6q7jal4j.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 «

4 4 1 4 2 4 2 1 4 2 4 3 2 5 2 4 2 1 3 2 4 2 2 4 2 5 2 1 3 2 4 1 3 4 3 3 1 1 3 3 4 1 1 2 4 4 2 1 4 2 4 2 2 2 3 4 2 4 2 4 4 2 2 2 2 2 2 1 1 3 3 1 1 4 2 4 3 3 4 1 3 2 2 2 2 2 2 2 2 2 4 2 3 3 2 3 2 3 3 2 3 3 1 3 4 4 4 2 4 4 3 2 2 3 3 3 2 2 2 4 4 2 2 2 3 4 1 3 4 2 4 2 2 4 3 4 2 2 3 2 4 2 2 4 2 4 2 2 2 2 5 4 2 4 3 4 2 3 4 4 4 4 2 5 4 4 3 2 5 2 3 1 2 4 2 4 4 2 4 4 3 3 2 4 2 4 2 1 2 3 4 4 2 4 4 3 2 1 4 4 5 3 2 4 5 4 3 2 3 3 3 2 2 2 2 3 1 2 3 2 3 2 2 4 2 4 1 3 3 3 4 2 2 2 3 4 4 2 4 4 4 2 2 4 2 4 2 4 3 4 4 2 1 4 4 4 2 2 3 2 5 2 2 4 2 3 1 1 2 1 3 2 5 4 2 5 3 2 4 3 5 2 2 4 2 4 2 2 4 2 4 1 1 3 2 3 1 2 1 4 4 2 2 3 3 4 2 2 3 2 5 1 2 4 2 4 2 2 2 4 4 1 1 3 2 5 4 1 5 2 4 4 2 4 3 3 1 2 4 2 4 1 1 3 2 4 3 2 4 2 4 4 2 2 2 4 2 1 3 2 4 4 3 4 2 4 4 3 3 4 4 3 3 4 2 3 4 2 4 2 4 2 2 3 4 3 2 2 3 3 5 2 1 2 2 4 2 4 4 2 5 2 3 3 3 5 2 2 2 1 4 2 2 2 4 4 1 2 3 2 4 3 1 2 4 4 3 2 2 3 4 2 3 4 3 5 4 1 4 4 4 4 2 4 4 3 2 2 2 2 4 2 2 2 4 3 1 1 4 1 4 1 1 2 3 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 10 seconds R Server 'George Udny Yule' @ 72.249.76.132 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 neat[t] = + 3.21891279228362 + 0.0516504616509237fail[t] -0.0871109318539845performance[t] + 0.119903178282154goals[t] + 0.0433235060326741`right `[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) 3.21891279228362 0.309951 10.3852 0 0 fail 0.0516504616509237 0.074354 0.6947 0.488326 0.244163 performance -0.0871109318539845 0.074886 -1.1633 0.246539 0.123269 goals 0.119903178282154 0.069172 1.7334 0.085036 0.042518 `right ` 0.0433235060326741 0.07248 0.5977 0.550903 0.275451 Multiple Linear Regression - Regression Statistics Multiple R 0.185351963661483 R-squared 0.0343553504331678 Adjusted R-squared 0.0091097386797866 F-TEST (value) 1.36084444175002 F-TEST (DF numerator) 4 F-TEST (DF denominator) 153 p-value 0.250158771852256 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.792631195123482 Sum Squared Residuals 96.1244243568806 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4 3.90466343222736 0.0953365677726389 2 4 3.80136250892546 0.198637491074545 3 4 3.88580521700455 0.114194782995451 4 4 3.6814593306433 0.318540669356698 5 4 3.71425157707147 0.285748422928529 6 5 3.6814593306433 1.3185406693567 7 4 3.61881368959924 0.381186310400763 8 3 3.67313237502505 -0.673132375025052 9 4 3.59655270277557 0.403447297224429 10 4 3.80136250892546 0.198637491074544 11 4 3.51776872653984 0.482231273460164 12 4 3.38687036886454 0.613129631135458 13 4 3.47444522050716 0.525554779492838 14 2 3.48497648011167 -1.48497648011167 15 3 3.74971204727453 -0.749712047274532 16 4 3.63546760083574 0.364532399164264 17 3 3.47444522050716 -0.474445220507162 18 2 3.47444522050716 -1.47444522050716 19 4 3.50723746693533 0.492762533064668 20 3 3.50723746693533 -0.507237466935332 21 3 3.81975680435957 -0.819756804359573 22 4 3.90419951243867 0.095800487561333 23 3 3.63767190482199 -0.637671904821991 24 3 3.56109223257251 -0.561092232572511 25 4 3.51776872653984 0.482231273460164 26 4 3.57549018356656 0.424509816433437 27 4 3.75757508310415 0.242424916895855 28 4 3.59434839878932 0.405651601210683 29 4 3.71425157707147 0.285748422928529 30 4 3.47444522050716 0.525554779492838 31 5 3.86087600640599 1.13912399359401 32 4 3.71378765728284 0.286212342717165 33 4 4.02410269072082 -0.0241026907208213 34 4 3.88580521700455 0.114194782995451 35 3 3.66260111542055 -0.662601115420547 36 4 3.90419951243867 0.095800487561333 37 3 3.76590203872239 -0.765902038722395 38 4 3.60487965839382 0.395120341606179 39 4 3.90419951243867 0.095800487561333 40 3 3.8880095209908 -0.888009520990804 41 5 3.89587255682042 1.10412744317958 42 4 3.68932236647291 0.310677633527085 43 3 3.47444522050716 -0.474445220507162 44 3 3.54269793713839 -0.542697937138393 45 3 3.71425157707147 -0.714251577071471 46 4 3.49891051131708 0.501089488682917 47 4 3.51776872653984 0.482231273460164 48 4 3.90419951243867 0.095800487561333 49 4 3.71425157707147 0.285748422928529 50 4 3.5067735471467 0.493226452853304 51 4 3.8880095209908 0.111990479009196 52 4 3.59434839878932 0.405651601210683 53 5 3.71425157707147 1.28574842292853 54 3 3.46658218467755 -0.466582184677549 55 3 3.45291878150952 -0.452918781509518 56 5 3.80922554475507 1.19077445524493 57 5 3.71425157707147 1.28574842292853 58 4 3.71425157707147 0.285748422928529 59 4 3.62980886899238 0.370191131007622 60 3 3.38953859263943 -0.389538592639433 61 4 3.63767190482199 0.362328095178009 62 4 3.59434839878932 0.405651601210683 63 5 3.66260111542055 1.33739888457945 64 4 3.56109223257251 0.438907767427489 65 4 3.62980886899238 0.370191131007622 66 5 4.02456661050946 0.975433389490542 67 4 3.86087600640599 0.139123993594007 68 3 3.66260111542055 -0.662601115420547 69 4 3.62980886899238 0.370191131007622 70 4 3.76590203872240 0.234097961277605 71 4 3.57774614380901 0.42225385619099 72 4 3.6814593306433 0.318540669356699 73 4 3.73044156851933 0.269558431480666 74 4 3.69718540230253 0.302814597697472 75 4 3.67879110686841 0.321208893131589 76 3 3.81755250037332 -0.817552500373319 77 4 3.68099541085467 0.319004589145335 78 3 3.63767190482199 -0.637671904821991 79 5 3.56155615236115 1.43844384763885 80 4 3.5400297133635 0.459970286636498 81 5 3.55056097296801 1.44943902703199 82 5 3.43112171447449 1.56887828552551 83 4 3.56109223257251 0.438907767427489 84 4 3.54269793713839 0.457302062861607 85 4 3.69985362607742 0.300146373922581 86 4 3.56941918819076 0.43058081180924 87 4 3.67046415125016 0.329535848749839 88 5 3.99131044429265 1.00868955570735 89 4 3.90419951243867 0.095800487561333 90 3 3.47444522050716 -0.474445220507162 91 4 3.56109223257251 0.438907767427489 92 3 3.70638854124186 -0.706388541241858 93 4 3.5532291967429 0.446770803257103 94 4 3.54269793713839 0.457302062861607 95 4 3.59434839878932 0.405651601210683 96 4 3.65993289164566 0.340067108354343 97 4 3.73264587250559 0.267354127494411 98 3 3.68665414269802 -0.686654142698024 99 3 3.6814593306433 -0.681459330643301 100 3 3.38733428865318 -0.387334288653178 101 3 3.86087600640599 -0.860876006405993 102 3 3.59434839878932 -0.594348398789317 103 2 3.47177699673227 -1.47177699673227 104 3 3.50723746693533 -0.507237466935332 105 5 3.80089858913682 1.19910141086318 106 2 3.63160090944619 -1.63160090944619 107 2 3.6814593306433 -1.6814593306433 108 3 3.52609568215809 -0.526095682158086 109 3 3.59388447900068 -0.59388447900068 110 NA NA 0.438443847638853 111 4 3.62106964984168 0.378930350158316 112 4 4.76590203872239 -0.765902038722395 113 3 4.7825042937027 -1.78250429370270 114 2 2.91293873158936 -0.91293873158936 115 3 2.54269793713839 0.457302062861607 116 4 5.62714064521749 -1.62714064521749 117 2 1.71425157707147 0.285748422928529 118 4 3.68932236647291 0.310677633527085 119 4 5.59655270277557 -1.59655270277557 120 2 2.93965998264173 -0.939659982641728 121 3 3.46611826488891 -0.466118264888913 122 3 3.63767190482199 -0.637671904821991 123 3 2.50990569071022 0.490094309289777 124 4 3.60441573860518 0.395584261394815 125 4 3.38733428865318 0.612665711346822 126 4 4.85301297057638 -0.85301297057638 127 3 2.75757508310415 0.242424916895855 128 4 3.71425157707147 0.285748422928529 129 4 3.86087600640599 0.139123993594007 130 4 5.55102489275664 -1.55102489275664 131 2 1.52609568215809 0.473904317841914 132 4 2.88800952099080 1.11199047900920 133 5 4.58648536295970 0.413514637040297 134 4 3.51776872653984 0.482231273460164 135 4 3.67832718707977 0.321672812920226 136 4 4.54269793713839 -0.542697937138393 137 3 5.63767190482199 -2.63767190482199 138 1 0.594348398789317 0.405651601210683 139 4 4.68932236647291 -0.689322366472915 140 3 3.68932236647291 -0.689322366472915 141 3 3.76590203872239 -0.765902038722395 142 3 5.80609340119154 -2.80609340119154 143 1 0.751504087728343 0.248495912271657 144 4 2.34354686283187 1.65645313716813 145 5 4.85254905078774 0.147450949212257 146 4 4.60221143461893 -0.60221143461893 147 3 2.59434839878932 0.405651601210683 148 4 4.34621508660676 -0.346215086606758 149 3 2.47444522050716 0.525554779492838 150 4 3.80136250892546 0.198637491074544 151 4 3.94752301847134 0.0524769815286590 152 4 2.67612288309352 1.32387711690648 153 5 6.43112171447449 -1.43112171447449 154 2 2.72211461290108 -0.722114612901085 155 3 3.59434839878932 -0.594348398789317 156 3 2.66439315587436 0.335606844125642 157 4 3.71425157707147 0.285748422928529 158 4 4.49017129216639 -0.490171292166389 159 3 NA NA Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.258056442489701 0.516112884979401 0.741943557510299 9 0.228899234302928 0.457798468605856 0.771100765697072 10 0.138226208481588 0.276452416963177 0.861773791518412 11 0.109256527458384 0.218513054916768 0.890743472541616 12 0.0595100946732793 0.119020189346559 0.94048990532672 13 0.0430956557127221 0.0861913114254443 0.956904344287278 14 0.33506011743388 0.67012023486776 0.66493988256612 15 0.366297198584172 0.732594397168343 0.633702801415828 16 0.299790485665505 0.599580971331011 0.700209514334495 17 0.265090140861291 0.530180281722582 0.734909859138709 18 0.428314812831127 0.856629625662255 0.571685187168873 19 0.364128020381655 0.72825604076331 0.635871979618345 20 0.337418093840094 0.674836187680188 0.662581906159906 21 0.365930556005947 0.731861112011895 0.634069443994053 22 0.297136070794873 0.594272141589747 0.702863929205127 23 0.276727864440871 0.553455728881743 0.723272135559129 24 0.230136355649043 0.460272711298086 0.769863644350957 25 0.219690413223624 0.439380826447248 0.780309586776376 26 0.172812478766274 0.345624957532548 0.827187521233726 27 0.132588532708735 0.265177065417470 0.867411467291265 28 0.107601256854298 0.215202513708597 0.892398743145702 29 0.0801333644642729 0.160266728928546 0.919866635535727 30 0.0731616942943376 0.146323388588675 0.926838305705662 31 0.0891074909145762 0.178214981829152 0.910892509085424 32 0.0664273818126927 0.132854763625385 0.933572618187307 33 0.0525115269881186 0.105023053976237 0.947488473011881 34 0.039517058443254 0.079034116886508 0.960482941556746 35 0.04064672255237 0.08129344510474 0.95935327744763 36 0.0291486897015699 0.0582973794031398 0.97085131029843 37 0.0365914619305305 0.073182923861061 0.96340853806947 38 0.0333328952606818 0.0666657905213636 0.966667104739318 39 0.0238256088918145 0.0476512177836289 0.976174391108185 40 0.0238252039815093 0.0476504079630185 0.97617479601849 41 0.0341030331351418 0.0682060662702836 0.965896966864858 42 0.025449168889705 0.05089833777941 0.974550831110295 43 0.0205109214143943 0.0410218428287886 0.979489078585606 44 0.0167938974682495 0.0335877949364991 0.98320610253175 45 0.0170083821908976 0.0340167643817952 0.982991617809102 46 0.0134357371761648 0.0268714743523297 0.986564262823835 47 0.0112005972606251 0.0224011945212502 0.988799402739375 48 0.00793456816375024 0.0158691363275005 0.99206543183625 49 0.00570972177777282 0.0114194435555456 0.994290278222227 50 0.00405582049913825 0.0081116409982765 0.995944179500862 51 0.00280101728351006 0.00560203456702012 0.99719898271649 52 0.00211568189167593 0.00423136378335187 0.997884318108324 53 0.00452743227075656 0.00905486454151311 0.995472567729243 54 0.00325684357936909 0.00651368715873818 0.996743156420631 55 0.00415639568225366 0.00831279136450732 0.995843604317746 56 0.00633462471417605 0.0126692494283521 0.993665375285824 57 0.0115554195023807 0.0231108390047614 0.98844458049762 58 0.00851740971531214 0.0170348194306243 0.991482590284688 59 0.00692883060799633 0.0138576612159927 0.993071169392004 60 0.00515265192806713 0.0103053038561343 0.994847348071933 61 0.00384007543683977 0.00768015087367954 0.99615992456316 62 0.00290275148795374 0.00580550297590749 0.997097248512046 63 0.00589533325963139 0.0117906665192628 0.994104666740369 64 0.00471894809770392 0.00943789619540784 0.995281051902296 65 0.00366034754705992 0.00732069509411985 0.99633965245294 66 0.00420362830400119 0.00840725660800238 0.995796371696 67 0.00303858312213761 0.00607716624427522 0.996961416877862 68 0.00310860199949831 0.00621720399899661 0.996891398000502 69 0.00240625650814625 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0.99979403661633 102 0.000168780662299901 0.000337561324599802 0.9998312193377 103 0.000506721465525861 0.00101344293105172 0.999493278534474 104 0.000387535845655542 0.000775071691311083 0.999612464154344 105 0.000877698540129075 0.00175539708025815 0.999122301459871 106 0.00323041547210096 0.00646083094420191 0.9967695845279 107 0.00943039359902337 0.0188607871980467 0.990569606400977 108 0.0080973096193158 0.0161946192386316 0.991902690380684 109 0.00679511553559019 0.0135902310711804 0.99320488446441 110 0.00531755555998849 0.0106351111199770 0.994682444440012 111 0.00395843255794164 0.00791686511588329 0.996041567442058 112 0.00357802929508722 0.00715605859017445 0.996421970704913 113 0.00942670262294213 0.0188534052458843 0.990573297377058 114 0.0087485490211253 0.0174970980422506 0.991251450978875 115 0.00736177819721754 0.0147235563944351 0.992638221802782 116 0.0158955054420111 0.0317910108840222 0.984104494557989 117 0.0124482511979280 0.0248965023958560 0.987551748802072 118 0.00955925761016903 0.0191185152203381 0.99044074238983 119 0.0202141855010451 0.0404283710020902 0.979785814498955 120 0.0196471078754386 0.0392942157508772 0.980352892124561 121 0.0158079788401159 0.0316159576802317 0.984192021159884 122 0.0133109743059531 0.0266219486119063 0.986689025694047 123 0.0102443321626630 0.0204886643253260 0.989755667837337 124 0.00753758152782254 0.0150751630556451 0.992462418472178 125 0.00634391680992272 0.0126878336198454 0.993656083190077 126 0.00584954628736857 0.0116990925747371 0.994150453712631 127 0.00418535611165527 0.00837071222331054 0.995814643888345 128 0.00301599113063861 0.00603198226127722 0.996984008869361 129 0.00200957202581084 0.00401914405162168 0.99799042797419 130 0.0048748713530403 0.0097497427060806 0.99512512864696 131 0.00346603871145267 0.00693207742290534 0.996533961288547 132 0.00812569362423728 0.0162513872484746 0.991874306375763 133 0.00606449803805523 0.0121289960761105 0.993935501961945 134 0.00499696163404758 0.00999392326809516 0.995003038365952 135 0.00487162252443029 0.00974324504886057 0.99512837747557 136 0.00311982248480472 0.00623964496960943 0.996880177515195 137 0.0414733775209906 0.0829467550419812 0.95852662247901 138 0.030808950849449 0.061617901698898 0.96919104915055 139 0.0240096112416285 0.048019222483257 0.975990388758372 140 0.0186545391384461 0.0373090782768921 0.981345460861554 141 0.0167294900135779 0.0334589800271558 0.983270509986422 142 0.384687601101842 0.769375202203685 0.615312398898158 143 0.392143988088127 0.784287976176254 0.607856011911873 144 0.595341614301844 0.809316771396311 0.404658385698156 145 0.491464996022963 0.982929992045926 0.508535003977037 146 0.44075780319076 0.88151560638152 0.55924219680924 147 0.375612140174905 0.75122428034981 0.624387859825095 148 0.326560772636601 0.653121545273202 0.673439227363399 149 0.630585439354407 0.738829121291185 0.369414560645593 150 0.474835801710989 0.949671603421978 0.525164198289011 151 0.382292902979532 0.764585805959063 0.617707097020469 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 60 0.416666666666667 NOK 5% type I error level 99 0.6875 NOK 10% type I error level 109 0.756944444444444 NOK

Charts produced by software:

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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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Software written by Ed van Stee & Patrick Wessa

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