Ws4

*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, 30 Nov 2010 12:22:03 +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/Nov/30/t1291121259mewe61pnsibgn2t.htm/, Retrieved Tue, 30 Nov 2010 13:47:50 +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/Nov/30/t1291121259mewe61pnsibgn2t.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:

Ws4

Dataseries X:

» Textbox « » Textfile « » CSV «

13 14 13 3 25 55 147 12 8 13 5 158 7 71 10 12 16 6 0 0 0 9 7 12 6 143 10 0 10 10 11 5 67 74 43 12 7 12 3 0 0 0 13 16 18 8 148 138 8 12 11 11 4 28 0 0 12 14 14 4 114 113 34 6 6 9 4 0 0 0 5 16 14 6 123 115 103 12 11 12 6 145 9 0 11 16 11 5 113 114 73 14 12 12 4 152 59 159 14 7 13 6 0 0 0 12 13 11 4 36 114 113 12 11 12 6 0 0 0 11 15 16 6 8 102 44 11 7 9 4 108 0 0 7 9 11 4 112 86 0 9 7 13 2 51 17 41 11 14 15 7 43 45 74 11 15 10 5 120 123 0 12 7 11 4 13 24 0 12 15 13 6 55 5 0 11 17 16 6 103 123 32 11 15 15 7 127 136 126 8 14 14 5 14 4 154 9 14 14 6 135 76 129 12 8 14 4 38 99 98 10 8 8 4 11 98 82 10 14 13 7 43 67 45 12 14 15 7 141 92 8 8 8 13 4 62 13 0 12 11 11 4 62 24 129 11 16 15 6 135 129 31 12 10 15 6 117 117 117 7 8 9 5 82 11 99 11 14 13 6 145 20 55 11 16 16 7 87 91 132 12 13 13 6 76 111 58 9 5 11 3 124 0 0 15 8 12 3 151 58 0 11 10 12 4 131 0 0 11 8 12 6 127 146 101 11 13 14 7 76 129 31 11 15 14 5 25 48 147 15 6 8 4 0 0 0 11 12 13 5 58 111 132 12 16 16 6 115 32 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 'Gwilym Jenkins' @ 72.249.127.135 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 liked[t] = + 6.89981578359029 + 0.097864463533243findingfriends[t] + 0.167368197229076knowingpeople[t] + 0.571325185382164celebrity[t] + 0.00243721157219217selectfbf[t] -0.00131784757087074selectsbf[t] + 0.00336547427871851`selecttbf `[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) 6.89981578359029 1.064182 6.4837 0 0 findingfriends 0.097864463533243 0.081463 1.2013 0.231527 0.115764 knowingpeople 0.167368197229076 0.05226 3.2026 0.001665 0.000833 celebrity 0.571325185382164 0.123606 4.6221 8e-06 4e-06 selectfbf 0.00243721157219217 0.003014 0.8087 0.419968 0.209984 selectsbf -0.00131784757087074 0.003026 -0.4355 0.663859 0.33193 `selecttbf ` 0.00336547427871851 0.002783 1.2091 0.228524 0.114262 Multiple Linear Regression - Regression Statistics Multiple R 0.599396383338163 R-squared 0.35927602435887 Adjusted R-squared 0.333475058896811 F-TEST (value) 13.9249062166761 F-TEST (DF numerator) 6 F-TEST (DF denominator) 149 p-value 1.54498636106837e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.77612967854698 Sum Squared Residuals 470.040858617294 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 12.7123575187548 0.287642481245227 2 13 12.8845640199319 0.115435980068071 3 16 13.3148298979646 2.68517010203537 4 12 12.7154672274008 -0.715467227400786 5 11 12.6192561672017 -1.61925616720165 6 12 10.9597422827392 1.04025771726075 7 18 15.6263145903790 2.37368540962098 8 11 12.2687821810591 -1.26878218105909 9 14 12.9459963179229 1.05400368207712 10 9 10.7765124896929 -1.77651248969288 11 14 13.9898487726522 0.0101512273477707 12 12 13.6847256776321 -1.68472567763207 13 11 13.8816918719569 -2.88169187195692 14 12 13.3914509439414 -1.39145094394135 15 13 12.8694467659522 0.130553234047775 16 11 12.8530802385107 -1.85308023851071 17 12 13.3431906278020 -1.34319062780204 18 16 13.9479570617974 2.05204293820256 19 9 11.6964218543849 -2.69642185438492 20 11 11.5361143499040 -0.536114349903987 21 13 10.3347025336618 2.66529746633819 22 15 14.6132979948784 0.386702005121559 23 10 13.4738439052489 -3.4738439052489 24 11 11.5311228768590 -0.531122876859011 25 13 14.1401208153346 -1.14012081533456 26 16 14.4461680652809 1.55383193471906 27 15 15.0404724977158 -0.040472497715783 28 14 13.429644790624 0.570355209376008 29 14 14.214715157704 -0.214715157703995 30 14 11.990399274892 2.009600725108 31 8 11.6763358944877 -3.6763358944877 32 13 14.3888421307032 -1.38884213070320 33 15 14.6659490542602 0.334050945739831 34 13 11.4409529102721 1.55904708972789 35 11 12.7541652147674 -1.75416521476742 36 15 14.3455180786581 0.654481921341931 37 15 13.7005485093376 1.29945149066236 38 9 12.2989755122997 -3.29897551229975 39 13 14.259570567836 -1.25957056783599 40 16 15.1898482184187 0.810151781581333 41 13 13.9120715295458 -0.91207152954582 42 11 10.6336267326332 0.366373267366805 43 12 11.7122876588586 0.287712341141435 44 12 12.2545823122326 -0.254582312232569 45 12 13.2002545990534 -1.20025459905342 46 14 14.2709431895937 -0.270943189593668 47 14 13.8358720926776 0.164127907322432 48 8 11.6572926614921 -3.65729266149206 49 13 13.2806889717270 -0.280688971727048 50 16 14.8320931587640 1.16790684123597 51 13 12.6394735177451 0.360526482254932 52 11 14.1509968986372 -3.15099689863719 53 14 13.5925151720557 0.407484827944284 54 13 11.5769790765825 1.42302092341754 55 13 13.2044663004113 -0.204466300411272 56 13 13.5644091448254 -0.564409144825376 57 12 12.5998424589847 -0.599842458984685 58 16 14.6946063645293 1.30539363547074 59 15 10.9369604928847 4.0630395071153 60 15 15.5013037913587 -0.501303791358683 61 12 11.1271104799683 0.872889520031678 62 14 14.4305603414301 -0.4305603414301 63 12 14.4864606211227 -2.48646062112272 64 15 14.1917477097745 0.808252290225537 65 12 12.0054050107979 -0.005405010797859 66 13 13.2998321688632 -0.299832168863224 67 12 14.1279522856312 -2.12795228563121 68 12 12.2949323677068 -0.294932367706756 69 13 14.0785196593001 -1.07851965930009 70 5 10.2389670051693 -5.23896700516926 71 13 13.4703508376377 -0.470350837637678 72 13 13.4021649515127 -0.402164951512716 73 14 13.2001487833488 0.799851216651212 74 17 13.7040940227608 3.29590597723922 75 13 13.8697255980051 -0.869725598005064 76 13 14.4908544275924 -1.49085442759242 77 12 13.7823222143317 -1.78232221433172 78 13 12.8634220057997 0.136577994200268 79 14 12.2882352779481 1.71176472205187 80 11 10.3648443828873 0.635155617112655 81 12 11.6422976000697 0.357702399930296 82 12 13.2433287040626 -1.24332870406259 83 16 13.9919771814129 2.00802281858713 84 12 13.0861354465583 -1.08613544655830 85 12 10.5904949818338 1.40950501816622 86 12 13.7982073841747 -1.79820738417470 87 10 11.6513627003967 -1.65136270039666 88 15 12.4719459389771 2.52805406102288 89 15 15.2625530019638 -0.262553001963804 90 12 12.0114436106825 -0.0114436106825331 91 16 13.2157828140342 2.78421718596579 92 15 13.9740894562125 1.02591054378752 93 16 15.1521059116221 0.84789408837793 94 13 14.6968684676904 -1.6968684676904 95 12 12.6175158882304 -0.617515888230369 96 11 11.9324079762809 -0.932407976280935 97 13 11.6822909295323 1.31770907046770 98 10 11.1087881892885 -1.10878818928852 99 15 13.2211543751644 1.77884562483565 100 13 13.7695983318829 -0.769598331882898 101 16 15.3650985426371 0.634901457362914 102 15 14.9696648326912 0.0303351673087509 103 18 14.5881313109644 3.41186868903559 104 13 10.5242405464358 2.47575945356424 105 10 10.2583143888960 -0.258314388895981 106 16 14.9906577559437 1.00934224405633 107 13 11.3939184601062 1.60608153989381 108 15 15.4119168050792 -0.411916805079173 109 14 11.7353498224795 2.2646501775205 110 15 11.4128629388248 3.58713706117522 111 14 13.1365886308155 0.863411369184523 112 13 14.5871194393257 -1.58711943932573 113 13 13.1350473306006 -0.135047330600562 114 15 14.0967466095669 0.903253390433103 115 16 14.6319261533586 1.36807384664139 116 14 14.3258520403142 -0.325852040314200 117 14 14.0619134694722 -0.0619134694722086 118 16 13.1500671971420 2.84993280285799 119 14 14.4556778137955 -0.45567781379547 120 12 12.7073996499909 -0.7073996499909 121 13 12.6921277059988 0.307872294001191 122 12 13.8202722473981 -1.82027224739813 123 12 12.0772875551874 -0.0772875551874363 124 14 14.4647687128416 -0.46476871284163 125 14 14.3526471017900 -0.352647101789961 126 14 11.9350244562745 2.0649755437255 127 16 15.2101495931576 0.78985040684242 128 13 14.4062231737777 -1.40622317377767 129 14 12.8837797357379 1.11622026426210 130 4 10.9722414167594 -6.97224141675937 131 16 15.2154399110779 0.78456008892208 132 13 13.3575331365584 -0.357533136558368 133 16 11.7447426852221 4.25525731477786 134 15 13.4410550913353 1.55894490866471 135 14 13.7372080514755 0.26279194852451 136 13 11.8658316679774 1.13416833202256 137 14 14.2497996829687 -0.249799682968701 138 12 11.9639514661137 0.0360485338862988 139 15 14.1295457774108 0.870454222589154 140 14 13.4724148121724 0.527585187827579 141 13 13.0231492252456 -0.023149225245558 142 14 14.0711827314672 -0.071182731467205 143 16 13.2362025908106 2.76379740918944 144 6 11.9077091725183 -5.90770917251825 145 13 12.5311653622845 0.46883463771553 146 13 12.8107850937838 0.189214906216212 147 14 12.4574261417914 1.54257385820855 148 15 14.5591646573811 0.440835342618876 149 14 14.1153252590265 -0.115325259026515 150 15 14.9927100066851 0.00728999331486742 151 13 13.9437068757845 -0.94370687578452 152 16 14.6525347302235 1.34746526977655 153 12 11.6428708259672 0.357129174032826 154 15 13.7063540772610 1.29364592273898 155 12 14.1001307898994 -2.10013078989944 156 14 11.4768347131229 2.52316528687711 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.626605660759603 0.746788678480794 0.373394339240397 11 0.484636911698697 0.969273823397394 0.515363088301303 12 0.520346848664111 0.959306302671777 0.479653151335889 13 0.700057106752454 0.599885786495091 0.299942893247546 14 0.607191420704711 0.785617158590578 0.392808579295289 15 0.573822910713607 0.852354178572786 0.426177089286393 16 0.539473403270087 0.921053193459825 0.460526596729913 17 0.56529373627126 0.869412527457481 0.434706263728740 18 0.532873163928164 0.934253672143672 0.467126836071836 19 0.50588163949299 0.98823672101402 0.49411836050701 20 0.438740788256906 0.877481576513811 0.561259211743094 21 0.704306430220637 0.591387139558727 0.295693569779363 22 0.635870322700154 0.728259354599692 0.364129677299846 23 0.765067555202112 0.469864889595776 0.234932444797888 24 0.708147319516 0.583705360968 0.291852680484 25 0.658441985766152 0.683116028467697 0.341558014233848 26 0.655488654003096 0.689022691993808 0.344511345996904 27 0.59021280359449 0.819574392811019 0.409787196405510 28 0.525868473627253 0.948263052745494 0.474131526372747 29 0.459544418908209 0.919088837816418 0.540455581091791 30 0.450558675199423 0.901117350398845 0.549441324800577 31 0.676682980560075 0.64663403887985 0.323317019439925 32 0.661030467136266 0.677939065727468 0.338969532863734 33 0.609720104693853 0.780559790612294 0.390279895306147 34 0.621515450853456 0.756969098293087 0.378484549146544 35 0.599584653686105 0.800830692627789 0.400415346313895 36 0.553430319691868 0.893139360616265 0.446569680308132 37 0.536903818117344 0.926192363765312 0.463096181882656 38 0.620537935798791 0.758924128402417 0.379462064201209 39 0.579285884367846 0.841428231264309 0.420714115632154 40 0.534518478619203 0.930963042761595 0.465481521380797 41 0.495485345224264 0.990970690448529 0.504514654775736 42 0.470305868808528 0.940611737617057 0.529694131191472 43 0.422990175885572 0.845980351771144 0.577009824114428 44 0.373970956515633 0.747941913031265 0.626029043484367 45 0.338213364775215 0.67642672955043 0.661786635224785 46 0.291335422001395 0.58267084400279 0.708664577998605 47 0.248636731176697 0.497273462353393 0.751363268823303 48 0.375048706115342 0.750097412230685 0.624951293884658 49 0.326640039978192 0.653280079956385 0.673359960021808 50 0.303678565397221 0.607357130794442 0.696321434602779 51 0.272631556549256 0.545263113098511 0.727368443450744 52 0.357333928618386 0.714667857236773 0.642666071381614 53 0.319472786572987 0.638945573145974 0.680527213427013 54 0.308208038600901 0.616416077201801 0.691791961399099 55 0.265455253703486 0.530910507406971 0.734544746296514 56 0.227757825804347 0.455515651608693 0.772242174195653 57 0.194566084094292 0.389132168188583 0.805433915905708 58 0.187452539620762 0.374905079241523 0.812547460379238 59 0.351029386760414 0.702058773520827 0.648970613239586 60 0.309488122765953 0.618976245531906 0.690511877234047 61 0.278782500719443 0.557565001438886 0.721217499280557 62 0.240995461656116 0.481990923312231 0.759004538343884 63 0.289989478751717 0.579978957503435 0.710010521248283 64 0.264049867668584 0.528099735337168 0.735950132331416 65 0.230096481353080 0.460192962706161 0.76990351864692 66 0.195913093038669 0.391826186077338 0.804086906961331 67 0.206209365942371 0.412418731884742 0.793790634057629 68 0.174927492648356 0.349854985296711 0.825072507351644 69 0.155260345930577 0.310520691861154 0.844739654069423 70 0.457804563031556 0.915609126063112 0.542195436968444 71 0.413007996052974 0.826015992105948 0.586992003947026 72 0.369188841114309 0.738377682228617 0.630811158885692 73 0.337579923430674 0.675159846861348 0.662420076569326 74 0.454855562351489 0.909711124702978 0.545144437648511 75 0.417679806992468 0.835359613984936 0.582320193007532 76 0.406443495534585 0.812886991069169 0.593556504465415 77 0.408662969389943 0.817325938779887 0.591337030610056 78 0.364266115350939 0.728532230701877 0.635733884649061 79 0.362155250556527 0.724310501113055 0.637844749443472 80 0.32676734161317 0.65353468322634 0.67323265838683 81 0.290287181503088 0.580574363006176 0.709712818496912 82 0.265828683955170 0.531657367910341 0.73417131604483 83 0.280004841610118 0.560009683220235 0.719995158389882 84 0.255415485879630 0.510830971759261 0.74458451412037 85 0.24182185309562 0.48364370619124 0.75817814690438 86 0.248067619354358 0.496135238708716 0.751932380645642 87 0.252003539218687 0.504007078437373 0.747996460781313 88 0.292876276312184 0.585752552624368 0.707123723687816 89 0.253943644770861 0.507887289541721 0.74605635522914 90 0.218910747904128 0.437821495808257 0.781089252095872 91 0.270881540162896 0.541763080325793 0.729118459837104 92 0.246080856661528 0.492161713323056 0.753919143338472 93 0.217393645449175 0.434787290898349 0.782606354550825 94 0.218248043259423 0.436496086518846 0.781751956740577 95 0.188399588413989 0.376799176827979 0.81160041158601 96 0.178838420100661 0.357676840201322 0.821161579899339 97 0.171755452191583 0.343510904383166 0.828244547808417 98 0.177418759392209 0.354837518784418 0.822581240607791 99 0.202207917407672 0.404415834815345 0.797792082592328 100 0.193037326214067 0.386074652428134 0.806962673785933 101 0.167110839450987 0.334221678901974 0.832889160549013 102 0.138362597943410 0.276725195886820 0.86163740205659 103 0.193130643170219 0.386261286340439 0.80686935682978 104 0.207888410244812 0.415776820489624 0.792111589755188 105 0.180859287357751 0.361718574715501 0.81914071264225 106 0.156186060152569 0.312372120305138 0.84381393984743 107 0.150461286637543 0.300922573275086 0.849538713362457 108 0.123218786226758 0.246437572453516 0.876781213773242 109 0.136145312561381 0.272290625122762 0.86385468743862 110 0.421800702746304 0.843601405492608 0.578199297253696 111 0.399484515847186 0.798969031694373 0.600515484152814 112 0.377673576822669 0.755347153645338 0.622326423177331 113 0.346021710897982 0.692043421795965 0.653978289102018 114 0.305211055403091 0.610422110806183 0.694788944596909 115 0.273119570494567 0.546239140989135 0.726880429505433 116 0.232718536888901 0.465437073777802 0.767281463111099 117 0.193661742554469 0.387323485108937 0.806338257445531 118 0.234161620363707 0.468323240727413 0.765838379636293 119 0.210982401926002 0.421964803852004 0.789017598073998 120 0.175912920314809 0.351825840629617 0.824087079685191 121 0.142143541846721 0.284287083693442 0.857856458153279 122 0.130407970282829 0.260815940565659 0.86959202971717 123 0.102118012279423 0.204236024558845 0.897881987720577 124 0.092057723457829 0.184115446915658 0.907942276542171 125 0.0748950828149751 0.149790165629950 0.925104917185025 126 0.080328979723429 0.160657959446858 0.919671020276571 127 0.0603565250983604 0.120713050196721 0.93964347490164 128 0.0670544592100745 0.134108918420149 0.932945540789926 129 0.0930650572418516 0.186130114483703 0.906934942758148 130 0.354383128786614 0.708766257573228 0.645616871213386 131 0.30514448313802 0.61028896627604 0.69485551686198 132 0.24641519766001 0.49283039532002 0.75358480233999 133 0.468604875560527 0.937209751121054 0.531395124439473 134 0.441075467932021 0.882150935864042 0.558924532067979 135 0.372044962022081 0.744089924044162 0.62795503797792 136 0.330558538171301 0.661117076342602 0.669441461828699 137 0.266105128118774 0.532210256237547 0.733894871881226 138 0.200583478555536 0.401166957111072 0.799416521444464 139 0.149547386887267 0.299094773774534 0.850452613112733 140 0.107930059693819 0.215860119387637 0.892069940306181 141 0.0700660512997336 0.140132102599467 0.929933948700266 142 0.042465611330776 0.084931222661552 0.957534388669224 143 0.0318707359795203 0.0637414719590407 0.96812926402048 144 0.718990272693581 0.562019454612838 0.281009727306419 145 0.577332554994687 0.845334890010626 0.422667445005313 146 0.427104158357889 0.854208316715777 0.572895841642111 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 2 0.0145985401459854 OK

Charts produced by software:

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Parameters (Session):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

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

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

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Software written by Ed van Stee & Patrick Wessa

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