Paper: Multiple Linear Regression (Linear Trend)

*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: Thu, 09 Dec 2010 12:38:52 +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/09/t1291898217tn31igw1jnra9y2.htm/, Retrieved Thu, 09 Dec 2010 13:37:22 +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/09/t1291898217tn31igw1jnra9y2.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

24 14 11 12 24 26 10 25 11 7 8 25 23 14 17 6 17 8 30 25 18 18 12 10 8 19 23 15 18 8 12 9 22 19 18 16 10 12 7 22 29 11 20 10 11 4 25 25 17 16 11 11 11 23 21 19 18 16 12 7 17 22 7 17 11 13 7 21 25 12 23 13 14 12 19 24 13 30 12 16 10 19 18 15 23 8 11 10 15 22 14 18 12 10 8 16 15 14 15 11 11 8 23 22 16 12 4 15 4 27 28 16 21 9 9 9 22 20 12 15 8 11 8 14 12 12 20 8 17 7 22 24 13 31 14 17 11 23 20 16 27 15 11 9 23 21 9 21 9 14 13 19 21 11 31 14 10 8 18 23 12 19 11 11 8 20 28 11 16 8 15 9 23 24 14 20 9 15 6 25 24 18 21 9 13 9 19 24 11 22 9 16 9 24 23 14 17 9 13 6 22 23 17 25 16 18 16 26 24 12 26 11 18 5 29 18 14 25 8 12 7 32 25 14 17 9 17 9 25 21 15 32 16 9 6 29 26 11 33 11 9 6 28 22 15 13 16 12 5 17 22 14 32 12 18 12 28 22 11 25 12 12 7 29 23 12 29 14 18 10 26 30 17 22 9 14 9 25 23 15 18 10 15 8 14 17 9 17 9 16 5 25 23 16 20 10 10 8 26 23 13 15 12 11 8 20 25 15 20 14 14 10 18 24 11 33 14 9 6 32 24 10 29 10 12 8 25 23 16 23 14 17 7 25 21 13 26 16 5 4 23 2 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 Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Multiple Linear Regression - Estimated Regression Equation PS[t] = + 6.96722882487706 + 0.338739169615999CM[t] -0.370733791378405D[t] + 0.173454693435831PE[t] + 0.048155789305374PC[t] + 0.414415238664376O[t] + 0.0195267114176807`H `[t] -0.00254732860272504t + 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) 6.96722882487706 3.106557 2.2427 0.026369 0.013185 CM 0.338739169615999 0.057193 5.9228 0 0 D -0.370733791378405 0.116406 -3.1848 0.00176 0.00088 PE 0.173454693435831 0.101683 1.7058 0.090095 0.045047 PC 0.048155789305374 0.128585 0.3745 0.708553 0.354276 O 0.414415238664376 0.075193 5.5113 0 0 `H ` 0.0195267114176807 0.127692 0.1529 0.878666 0.439333 t -0.00254732860272504 0.006168 -0.413 0.680182 0.340091 Multiple Linear Regression - Regression Statistics Multiple R 0.614545793502647 R-squared 0.377666532311799 Adjusted R-squared 0.348816636458703 F-TEST (value) 13.0907416177475 F-TEST (DF numerator) 7 F-TEST (DF denominator) 151 p-value 4.10338429901458e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.4353914418521 Sum Squared Residuals 1782.08906817135 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 23.3600829066697 0.6399170933303 2 25 22.7568953205311 2.24310467946888 3 30 24.5395878492502 5.46041215074979 4 19 20.5497834763604 -1.54978347636043 5 22 20.8261556690439 1.1738443309561 6 22 23.3158162465616 -1.31581624656163 7 25 22.8098028489195 2.19019715108048 8 23 19.8000480437899 3.19995195621013 9 17 18.7822363353937 -1.78223633539366 10 21 21.8089527605843 -0.80895276058432 11 19 23.1167179796368 -4.11671797963679 12 19 23.6592384288345 -4.65923842883448 13 15 23.5393128544941 -8.53931285449405 14 16 17.1894615696005 -1.18946156960050 15 23 19.65484531045 3.34515468955 16 27 24.2189040611562 2.7810959388438 17 22 21.2179623331316 0.782037666868405 18 14 16.5371454664626 -2.53714546646256 19 22 24.2133759326396 -2.21337593263964 20 23 24.3060990583595 -1.30609905835951 21 23 21.7185497794293 1.28145022057074 22 19 22.6600108417653 -3.66001084176532 23 18 24.1049457209068 -6.1049457209068 24 20 23.3757339063873 -3.37573390638733 25 23 22.6120641857161 0.387935814283944 26 25 23.5273792219535 1.47262077804648 27 19 23.5244420640875 -4.52444206408749 28 24 24.0251628809969 -0.0251628809969272 29 22 21.7226683903436 0.277331609656368 30 26 23.5005109208289 2.49948907917106 31 29 22.7132200272242 6.28677997277577 32 32 25.4406249917871 6.5593750082129 33 25 21.6828813174281 3.31711868257193 34 29 24.6281494256649 4.37185057433512 35 28 25.2384561145834 2.7615438854166 36 17 17.0601380163531 -0.0601380163531021 37 28 26.2958086274675 1.70419137253245 38 29 23.0745219544930 5.92547804550697 39 26 27.8691994778676 -1.86919947786763 40 25 23.6672122623102 1.33278773768976 41 14 19.4606216675032 -5.46062166750324 42 25 22.1422346980926 2.85776530190735 43 26 21.8303301600076 4.16966983999239 44 20 20.433957994168 -0.433957994168018 45 18 21.5077925054716 -3.50779250547162 46 32 24.8294310460586 7.17056895394144 47 25 25.2742828932654 -0.274282893265404 48 25 21.6880724477451 3.31192755225495 49 23 20.8994902264098 2.10050977359018 50 21 22.2866056488887 -1.28660564888866 51 20 24.2875172456324 -4.28751724563239 52 15 16.4933916627726 -1.49339166277261 53 30 27.0387539888558 2.96124601114416 54 24 25.5559440077963 -1.55594400779633 55 26 24.5013376089538 1.49866239104625 56 24 21.7641370528022 2.23586294719776 57 22 21.5950979554049 0.404902044595074 58 14 15.5840538002886 -1.58405380028861 59 24 22.4070382612356 1.59296173876444 60 24 22.9642324837384 1.03576751626160 61 24 23.3829572477102 0.617042752289785 62 24 20.1664929785397 3.83350702146025 63 19 18.4990860629835 0.500913937016457 64 31 26.9791594695616 4.02084053043840 65 22 26.9078641570514 -4.90786415705139 66 27 21.4562164040507 5.54378359594928 67 19 17.6829076437667 1.31709235623332 68 25 22.437251747161 2.56274825283898 69 20 25.1583990491765 -5.15839904917651 70 21 21.6109898495906 -0.610989849590591 71 27 27.7343855534004 -0.734385553400403 72 23 24.5225995384187 -1.52259953841868 73 25 25.7763981883151 -0.776398188315096 74 20 22.3637662373848 -2.36376623738476 75 22 22.482950321875 -0.482950321874988 76 23 23.1330262843134 -0.133026284313445 77 25 24.0144309704262 0.98556902957381 78 25 23.5292659044047 1.47073409559533 79 17 24.0388904116908 -7.03889041169081 80 19 21.4002460073737 -2.40024600737372 81 25 24.085034368004 0.914965631995982 82 19 22.3524440420347 -3.35244404203470 83 20 23.1424834269455 -3.14248342694555 84 26 22.5861382667667 3.41386173323331 85 23 20.9378549293207 2.06214507067932 86 27 24.5849617506268 2.41503824937321 87 17 20.8884850749446 -3.88848507494460 88 17 23.4710677945635 -6.47106779456346 89 17 19.6695405130879 -2.66954051308790 90 22 21.9548536503222 0.0451463496778307 91 21 23.7260603697963 -2.72606036979633 92 32 28.8536192709296 3.14638072907044 93 21 24.8145503105897 -3.81455031058973 94 21 24.3882977810568 -3.38829778105680 95 18 21.1802601032482 -3.18026010324816 96 18 21.1964497861098 -3.19644978610981 97 23 22.8827999156050 0.117200084395035 98 19 20.5695533666805 -1.56955336668047 99 20 20.8539641213514 -0.853964121351367 100 21 22.395925037391 -1.39592503739102 101 20 24.0307052826698 -4.03070528266981 102 17 18.5849371598002 -1.58493715980023 103 18 20.2816301091783 -2.28163010917832 104 19 20.7410407575224 -1.74104075752237 105 22 22.1051202498069 -0.105120249806918 106 15 18.6315165374418 -3.63151653744184 107 14 18.7567940134575 -4.75679401345753 108 18 26.8029547198515 -8.8029547198515 109 24 21.4701801830877 2.52981981691228 110 35 23.5697499835098 11.4302500164902 111 29 19.2114740958044 9.7885259041956 112 21 21.8313873417681 -0.831387341768137 113 20 18.3766920537217 1.62330794627827 114 22 23.1900750069294 -1.19007500692941 115 13 16.6510839127491 -3.65108391274912 116 26 23.2144181423986 2.78558185760142 117 17 16.6755593840826 0.324440615917431 118 25 19.9753954526882 5.02460454731181 119 20 20.7622584686874 -0.762258468687355 120 19 18.0414007867671 0.958599213232875 121 21 22.4946143030851 -1.49461430308515 122 22 20.9767618621827 1.02323813781726 123 24 22.7115639126755 1.28843608732448 124 21 22.9512651944144 -1.95126519441439 125 26 25.5834618476785 0.416538152321532 126 24 20.5184016887368 3.48159831126324 127 16 20.1892640026714 -4.18926400267138 128 23 22.2991366870723 0.700863312927737 129 18 20.6121662423911 -2.61216624239106 130 16 22.3138878394759 -6.31388783947587 131 26 23.9233154494156 2.07668455058441 132 19 18.8408170046833 0.159182995316669 133 21 16.6260188581603 4.37398114183967 134 21 22.1723071687452 -1.17230716874521 135 22 18.4336193177372 3.56638068226279 136 23 19.6819025013261 3.31809749867393 137 29 24.8445553261332 4.1554446738668 138 21 19.0206123985753 1.9793876014247 139 21 19.7228070602223 1.27719293977767 140 23 21.793065487162 1.20693451283801 141 27 22.9160268001213 4.08397319987874 142 25 25.2796869741909 -0.279686974190913 143 21 20.8674377020862 0.132562297913804 144 10 16.8397398735801 -6.83973987358006 145 20 22.5558599122971 -2.55585991229709 146 26 22.6045122006451 3.39548779935495 147 24 23.5841688389319 0.415831161068146 148 29 31.6943493231591 -2.69434932315913 149 19 18.7060451628066 0.293954837193363 150 24 21.9386390844474 2.06136091555264 151 19 20.485430266394 -1.48543026639402 152 24 23.3675194658252 0.632480534174842 153 22 21.6840974973478 0.315902502652156 154 17 23.7914510648184 -6.7914510648184 155 24 22.9677943018502 1.03220569814981 156 25 22.3646067157115 2.63539328428855 157 30 24.1472992444305 5.85270075556945 158 19 20.1574948715408 -1.15749487154078 159 22 20.4338670642242 1.56613293577575 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.421146350042458 0.842292700084915 0.578853649957543 12 0.295393138892056 0.590786277784113 0.704606861107944 13 0.225860318043728 0.451720636087456 0.774139681956272 14 0.205436981507734 0.410873963015468 0.794563018492266 15 0.340962780348358 0.681925560696716 0.659037219651642 16 0.320482413861828 0.640964827723657 0.679517586138171 17 0.486097858965602 0.972195717931203 0.513902141034398 18 0.394749320578378 0.789498641156757 0.605250679421622 19 0.313747794781716 0.627495589563432 0.686252205218284 20 0.298788533982462 0.597577067964924 0.701211466017538 21 0.39711395930483 0.79422791860966 0.60288604069517 22 0.331106194863779 0.662212389727558 0.668893805136221 23 0.363088305040966 0.726176610081933 0.636911694959034 24 0.317283364123517 0.634566728247035 0.682716635876483 25 0.264923137368998 0.529846274737996 0.735076862631002 26 0.210987285544443 0.421974571088885 0.789012714455557 27 0.180463264630792 0.360926529261584 0.819536735369208 28 0.156733072571073 0.313466145142147 0.843266927428927 29 0.118860350394266 0.237720700788533 0.881139649605734 30 0.135720868931431 0.271441737862862 0.864279131068569 31 0.307043266187303 0.614086532374606 0.692956733812697 32 0.579580582283763 0.840838835432473 0.420419417716237 33 0.540862786469022 0.918274427061956 0.459137213530978 34 0.546668381628682 0.906663236742636 0.453331618371318 35 0.499756390346927 0.999512780693855 0.500243609653073 36 0.516992028848683 0.966015942302634 0.483007971151317 37 0.480865569466204 0.961731138932408 0.519134430533796 38 0.543130356129887 0.913739287740226 0.456869643870113 39 0.598670958322274 0.802658083355452 0.401329041677726 40 0.545451377188666 0.909097245622667 0.454548622811334 41 0.607236772453054 0.785526455093892 0.392763227546946 42 0.57265822216421 0.85468355567158 0.42734177783579 43 0.56872346802615 0.8625530639477 0.43127653197385 44 0.538472712743044 0.923054574513912 0.461527287256956 45 0.539398182562411 0.921203634875177 0.460601817437589 46 0.639536237547459 0.720927524905083 0.360463762452541 47 0.622799660682211 0.754400678635578 0.377200339317789 48 0.605645706147193 0.788708587705614 0.394354293852807 49 0.563511641985517 0.872976716028967 0.436488358014483 50 0.530944543431120 0.93811091313776 0.46905545656888 51 0.604229408324064 0.791541183351872 0.395770591675936 52 0.56694348011788 0.86611303976424 0.43305651988212 53 0.607906669687226 0.784186660625548 0.392093330312774 54 0.582268362204929 0.835463275590141 0.417731637795071 55 0.539110909374918 0.921778181250163 0.460889090625082 56 0.507567995615684 0.984864008768631 0.492432004384316 57 0.458760197252434 0.917520394504867 0.541239802747566 58 0.420459780269622 0.840919560539244 0.579540219730378 59 0.383570965101833 0.767141930203666 0.616429034898167 60 0.343540995370397 0.687081990740794 0.656459004629603 61 0.301215273961807 0.602430547923614 0.698784726038193 62 0.313398097265309 0.626796194530619 0.686601902734691 63 0.278419004074647 0.556838008149294 0.721580995925353 64 0.282885927504942 0.565771855009884 0.717114072495058 65 0.389109909231050 0.778219818462101 0.610890090768950 66 0.48120580502645 0.9624116100529 0.51879419497355 67 0.447292343030426 0.894584686060853 0.552707656969574 68 0.432427489975911 0.864854979951822 0.567572510024089 69 0.519696187875784 0.960607624248433 0.480303812124216 70 0.475411471183907 0.950822942367815 0.524588528816093 71 0.438655174228514 0.877310348457028 0.561344825771486 72 0.408198960760971 0.816397921521943 0.591801039239029 73 0.377419684136791 0.754839368273582 0.622580315863209 74 0.350308189929836 0.700616379859673 0.649691810070164 75 0.309599783942413 0.619199567884827 0.690400216057587 76 0.271429423838847 0.542858847677694 0.728570576161153 77 0.246968209176075 0.49393641835215 0.753031790823925 78 0.226404816809047 0.452809633618093 0.773595183190953 79 0.328189711110747 0.656379422221494 0.671810288889253 80 0.297592619014268 0.595185238028536 0.702407380985732 81 0.267302330728723 0.534604661457445 0.732697669271277 82 0.255787399255827 0.511574798511653 0.744212600744173 83 0.243580420587619 0.487160841175239 0.75641957941238 84 0.263906824767243 0.527813649534486 0.736093175232757 85 0.254973348887600 0.509946697775201 0.7450266511124 86 0.254562874707113 0.509125749414226 0.745437125292887 87 0.246497125758044 0.492994251516088 0.753502874241956 88 0.320202052190444 0.640404104380888 0.679797947809556 89 0.288355514860942 0.576711029721884 0.711644485139058 90 0.255484079708122 0.510968159416243 0.744515920291878 91 0.229815081047294 0.459630162094588 0.770184918952706 92 0.247007679096849 0.494015358193698 0.752992320903151 93 0.235749236100587 0.471498472201174 0.764250763899413 94 0.214642500705125 0.42928500141025 0.785357499294875 95 0.192504816899054 0.385009633798109 0.807495183100946 96 0.173170305306774 0.346340610613549 0.826829694693226 97 0.146938903046447 0.293877806092894 0.853061096953553 98 0.121406558941832 0.242813117883664 0.878593441058168 99 0.098807662794169 0.197615325588338 0.90119233720583 100 0.0798317917117787 0.159663583423557 0.920168208288221 101 0.080994253781883 0.161988507563766 0.919005746218117 102 0.0644416655442469 0.128883331088494 0.935558334455753 103 0.0547264281508925 0.109452856301785 0.945273571849108 104 0.0467699720392488 0.0935399440784976 0.953230027960751 105 0.0368775495268784 0.0737550990537567 0.963122450473122 106 0.0346701229874316 0.0693402459748633 0.965329877012568 107 0.0443808027390602 0.0887616054781203 0.95561919726094 108 0.230469097454290 0.460938194908580 0.76953090254571 109 0.239402047361746 0.478804094723493 0.760597952638254 110 0.646307414314944 0.707385171370112 0.353692585685056 111 0.884187389093037 0.231625221813926 0.115812610906963 112 0.855728278249613 0.288543443500775 0.144271721750387 113 0.83080921614876 0.338381567702479 0.169190783851240 114 0.80024093637436 0.39951812725128 0.19975906362564 115 0.828529488635187 0.342941022729626 0.171470511364813 116 0.808526422949083 0.382947154101835 0.191473577050918 117 0.769899402415356 0.460201195169288 0.230100597584644 118 0.819902891773485 0.360194216453029 0.180097108226515 119 0.780671272713017 0.438657454573967 0.219328727286983 120 0.741672920352702 0.516654159294595 0.258327079647298 121 0.697287739875408 0.605424520249184 0.302712260124592 122 0.64657485499902 0.706850290001961 0.353425145000980 123 0.596467327486696 0.807065345026609 0.403532672513304 124 0.547679472659693 0.904641054680614 0.452320527340307 125 0.489880368107411 0.979760736214821 0.510119631892589 126 0.489690975739743 0.979381951479486 0.510309024260257 127 0.522494103228841 0.955011793542318 0.477505896771159 128 0.4588394063328 0.9176788126656 0.5411605936672 129 0.421374640504679 0.842749281009358 0.578625359495321 130 0.675995728072305 0.64800854385539 0.324004271927695 131 0.62536132496651 0.749277350066981 0.374638675033490 132 0.585362152162429 0.829275695675141 0.414637847837571 133 0.567074606788364 0.865850786423272 0.432925393211636 134 0.634671445341941 0.730657109316118 0.365328554658059 135 0.579697889559414 0.840604220881171 0.420302110440586 136 0.554960304679724 0.890079390640552 0.445039695320276 137 0.52795320090575 0.9440935981885 0.47204679909425 138 0.757730231129452 0.484539537741095 0.242269768870548 139 0.683885079907542 0.632229840184915 0.316114920092458 140 0.60493691427425 0.7901261714515 0.39506308572575 141 0.65930375533992 0.681392489320159 0.340696244660080 142 0.663954574708272 0.672090850583456 0.336045425291728 143 0.563430695215875 0.87313860956825 0.436569304784125 144 0.671504060067124 0.656991879865751 0.328495939932876 145 0.680080703079928 0.639838593840143 0.319919296920072 146 0.877286159321744 0.245427681356513 0.122713840678256 147 0.840559488182601 0.318881023634798 0.159440511817399 148 0.756735015975613 0.486529968048773 0.243264984024387 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 0.0289855072463768 OK

Charts produced by software:

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Parameters (Session):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

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

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

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Software written by Ed van Stee & Patrick Wessa

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