*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: Sat, 21 Nov 2009 05:55:31 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/21/t1258808472lyqpg4d861kbhz4.htm/, Retrieved Sat, 21 Nov 2009 14:01:24 +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/2009/Nov/21/t1258808472lyqpg4d861kbhz4.htm/}, year = {2009}, } @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 = {2009}, 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 «

3.75 0 3.51 3.37 3.21 3 4.11 0 3.75 3.51 3.37 3.21 4.25 0 4.11 3.75 3.51 3.37 4.25 0 4.25 4.11 3.75 3.51 4.5 0 4.25 4.25 4.11 3.75 4.7 0 4.5 4.25 4.25 4.11 4.75 0 4.7 4.5 4.25 4.25 4.75 0 4.75 4.7 4.5 4.25 4.75 0 4.75 4.75 4.7 4.5 4.75 0 4.75 4.75 4.75 4.7 4.75 0 4.75 4.75 4.75 4.75 4.75 0 4.75 4.75 4.75 4.75 4.58 0 4.75 4.75 4.75 4.75 4.5 0 4.58 4.75 4.75 4.75 4.5 0 4.5 4.58 4.75 4.75 4.49 0 4.5 4.5 4.58 4.75 4.03 0 4.49 4.5 4.5 4.58 3.75 0 4.03 4.49 4.5 4.5 3.39 0 3.75 4.03 4.49 4.5 3.25 0 3.39 3.75 4.03 4.49 3.25 0 3.25 3.39 3.75 4.03 3.25 0 3.25 3.25 3.39 3.75 3.25 0 3.25 3.25 3.25 3.39 3.25 0 3.25 3.25 3.25 3.25 3.25 0 3.25 3.25 3.25 3.25 3.25 0 3.25 3.25 3.25 3.25 3.25 0 3.25 3.25 3.25 3.25 3.25 0 3.25 3.25 3.25 3.25 3.25 0 3.25 3.25 3.25 3.25 3.25 0 3.25 3.25 3.25 3.25 3.25 0 3.25 3.25 3.25 3.25 2.85 0 3.25 3.25 3.25 3.25 2.75 0 2.85 3.25 3.25 3.25 2.75 0 2.75 2.85 3.25 3.25 2.55 0 2.75 2.75 2.85 3.25 2.5 0 2.55 2.75 2.75 2.85 2.5 0 2.5 2.55 2.75 2.75 2.1 0 2.5 2.5 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y(t)[t] = + 0.103460639622265 -0.119452797409169`X(t)`[t] + 1.52190634840442`Y(t-1)`[t] -0.619397555123749`Y(t-2)`[t] + 0.254793166385373`Y(t-3)`[t] -0.190018800639385`Y(t-4)`[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) 0.103460639622265 0.035236 2.9363 0.00406 0.00203 `X(t)` -0.119452797409169 0.039381 -3.0333 0.00303 0.001515 `Y(t-1)` 1.52190634840442 0.094088 16.1753 0 0 `Y(t-2)` -0.619397555123749 0.17246 -3.5915 0.000496 0.000248 `Y(t-3)` 0.254793166385373 0.171865 1.4825 0.141114 0.070557 `Y(t-4)` -0.190018800639385 0.091765 -2.0707 0.04077 0.020385 Multiple Linear Regression - Regression Statistics Multiple R 0.994995919607588 R-squared 0.99001688003575 Adjusted R-squared 0.989554698555923 F-TEST (value) 2142.05225273751 F-TEST (DF numerator) 5 F-TEST (DF denominator) 108 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.107112126367783 Sum Squared Residuals 1.23908482242302 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3.75 3.60581182393364 0.144188176066364 2 4.11 3.88521664832076 0.224783351679238 3 4.25 4.2897155557083 -0.0397155557082959 4 4.25 4.31434705248335 -0.0643470524833468 5 4.5 4.27375242251131 0.226247577488695 6 4.7 4.62149328467618 0.0785067153238155 7 4.75 4.74442253348662 0.00557746651338359 8 4.75 4.76033663147843 -0.0103366314784305 9 4.75 4.73282068683947 0.0171793131605282 10 4.75 4.70755658503086 0.0424434149691367 11 4.75 4.69805564499889 0.0519443550011059 12 4.75 4.69805564499889 0.0519443550011059 13 4.58 4.69805564499889 -0.118055644998894 14 4.5 4.43933156577014 0.0606684342298568 15 4.5 4.42287664226883 0.0771233577311728 16 4.49 4.42911360839321 0.0608863916067867 17 4.03 4.42581428770703 -0.395814287707035 18 3.75 3.74713284704339 0.00286715295660920 19 3.39 3.60337401318322 -0.213374013183224 20 3.25 3.11361437466141 0.136385625338595 21 3.25 3.13959716743555 0.110402832564452 22 3.25 3.18779254943317 0.0622074505668336 23 3.25 3.22052827436939 0.0294717256306073 24 3.25 3.24713090645891 0.00286909354109334 25 3.25 3.24713090645891 0.00286909354109334 26 3.25 3.24713090645891 0.00286909354109334 27 3.25 3.24713090645891 0.00286909354109334 28 3.25 3.24713090645891 0.00286909354109334 29 3.25 3.24713090645891 0.00286909354109334 30 3.25 3.24713090645891 0.00286909354109334 31 3.25 3.24713090645891 0.00286909354109334 32 2.85 3.24713090645891 -0.397130906458907 33 2.75 2.63836836709714 0.111631632902860 34 2.75 2.73393675430620 0.0160632456938030 35 2.55 2.69395924326442 -0.143959243264422 36 2.5 2.44010617720076 0.0598938227992451 37 2.5 2.50689225086922 -0.00689225086922279 38 2.1 2.48690349534834 -0.386903495348335 39 2 1.90340505779518 0.0965949422048237 40 2 2.00847438503620 -0.00847438503620295 41 2 1.96849687399443 0.0315031260055718 42 2 2.01902507761164 -0.0190250776116448 43 2 2.03802695767558 -0.0380269576755834 44 2 2.03802695767558 -0.0380269576755834 45 2 2.03802695767558 -0.0380269576755834 46 2 2.03802695767558 -0.0380269576755834 47 2 2.03802695767558 -0.0380269576755834 48 2 2.03802695767558 -0.0380269576755834 49 2 2.03802695767558 -0.0380269576755834 50 2 2.03802695767558 -0.0380269576755834 51 2 2.03802695767558 -0.0380269576755834 52 2 2.03802695767558 -0.0380269576755834 53 2 2.03802695767558 -0.0380269576755834 54 2 2.03802695767558 -0.0380269576755834 55 2 2.03802695767558 -0.0380269576755834 56 2 2.03802695767558 -0.0380269576755834 57 2 2.03802695767558 -0.0380269576755834 58 2 2.03802695767558 -0.0380269576755834 59 2 2.03802695767558 -0.0380269576755834 60 2 2.03802695767558 -0.0380269576755834 61 2 2.03802695767558 -0.0380269576755834 62 2 2.03802695767558 -0.0380269576755834 63 2 2.03802695767558 -0.0380269576755834 64 2 2.03802695767558 -0.0380269576755834 65 2 2.03802695767558 -0.0380269576755834 66 2 2.03802695767558 -0.0380269576755834 67 2 2.03802695767558 -0.0380269576755834 68 2.21 2.03802695767558 0.171973042324417 69 2.25 2.35762729084051 -0.107627290840511 70 2.25 2.28843005820070 -0.0384300582007008 71 2.45 2.31716072093668 0.132839279063321 72 2.5 2.59182976913871 -0.0918297691387076 73 2.5 2.5364448235086 -0.0364448235086029 74 2.64 2.55643357902949 0.0835664209705096 75 2.75 2.7442363659975 0.00576363400249928 76 2.93 2.81542946657269 0.114570533427308 77 3 3.05690992151583 -0.0569099215158281 78 3.17 3.05337642219474 0.116623577805260 79 3.25 3.29370337444386 -0.0437033744438632 80 3.39 3.29379043547707 0.0962095645229338 81 3.5 3.48731904208454 0.0126809579154582 82 3.5 3.55609333989384 -0.0560933398938371 83 3.65 3.50842914807303 0.141570851926973 84 3.75 3.73813971654657 0.0118602834534337 85 3.75 3.77651865004811 -0.0265186500481137 86 3.9 3.75279786949354 0.147202130506455 87 4 3.97806031829684 0.0219396817031628 88 4 4.01833943980478 -0.0183394398047782 89 4 3.99461865925021 0.0053813407497906 90 4 3.99159515579284 0.00840484420716092 91 4 3.9725932757289 0.0274067242710995 92 4 3.9725932757289 0.0274067242710995 93 4 3.9725932757289 0.0274067242710995 94 4 3.9725932757289 0.0274067242710995 95 4 3.9725932757289 0.0274067242710995 96 4 3.9725932757289 0.0274067242710995 97 4 3.9725932757289 0.0274067242710995 98 4 3.9725932757289 0.0274067242710995 99 4.18 3.9725932757289 0.207406724271099 100 4.25 4.2465364184417 0.00346358155830441 101 4.25 4.24157830290773 0.0084216970922696 102 3.97 4.12463044658926 -0.154630446589265 103 3.42 3.68212880656791 -0.262128806567915 104 2.75 3.00521031433538 -0.255210314335377 105 2.31 2.25485962963457 0.0551403703654259 106 2 1.91328622093661 0.0867137790633864 107 1.66 1.64782909605915 0.0121709039408454 108 1.31 1.33759778290884 -0.0275977829088377 109 1.09 1.02014812041123 0.0698518795887705 110 1 0.874394019682752 0.125605980317248 111 1 0.849118694436089 0.150881305563911 112 1 0.915316558016229 0.0846834419837712 113 1 0.93418930918221 0.0658106908177902 114 1 0.951291001239755 0.0487089987602455 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.596192813611031 0.807614372777937 0.403807186388969 10 0.464381220833799 0.928762441667597 0.535618779166201 11 0.321926475649817 0.643852951299633 0.678073524350183 12 0.209648200070897 0.419296400141794 0.790351799929103 13 0.36451494678391 0.72902989356782 0.63548505321609 14 0.264565225547494 0.529130451094987 0.735434774452506 15 0.204120514176133 0.408241028352265 0.795879485823867 16 0.145165991807863 0.290331983615725 0.854834008192137 17 0.95819901596784 0.0836019680643205 0.0418009840321602 18 0.935931983217985 0.12813603356403 0.064068016782015 19 0.991978973447512 0.0160420531049758 0.00802102655248791 20 0.996158211336097 0.00768357732780503 0.00384178866390252 21 0.994562591849704 0.0108748163005928 0.00543740815029642 22 0.991377023479837 0.0172459530403268 0.0086229765201634 23 0.98772391638902 0.0245521672219584 0.0122760836109792 24 0.98412875203906 0.0317424959218782 0.0158712479609391 25 0.978675302098263 0.0426493958034739 0.0213246979017370 26 0.970987602536733 0.058024794926535 0.0290123974632675 27 0.960567113881305 0.0788657722373898 0.0394328861186949 28 0.946852807000816 0.106294385998367 0.0531471929991837 29 0.929268873723969 0.141462252552063 0.0707311262760313 30 0.907274904140037 0.185450191719925 0.0927250958599626 31 0.880420028165533 0.239159943668934 0.119579971834467 32 0.99857183708365 0.00285632583270026 0.00142816291635013 33 0.99843309026715 0.00313381946569921 0.00156690973284961 34 0.997479692994839 0.00504061401032232 0.00252030700516116 35 0.998089801415298 0.0038203971694034 0.0019101985847017 36 0.997252488891891 0.00549502221621701 0.00274751110810851 37 0.99574943639707 0.00850112720586102 0.00425056360293051 38 0.999991164642495 1.76707150100390e-05 8.83535750501948e-06 39 0.999991767776044 1.64644479127333e-05 8.23222395636666e-06 40 0.999984556785835 3.0886428330954e-05 1.5443214165477e-05 41 0.999978396862047 4.3206275906652e-05 2.1603137953326e-05 42 0.99996197413485 7.60517302979685e-05 3.80258651489842e-05 43 0.999936105402834 0.0001277891943319 6.389459716595e-05 44 0.999894166828347 0.000211666343306229 0.000105833171653114 45 0.999827475445936 0.000345049108128598 0.000172524554064299 46 0.999723476814157 0.000553046371686031 0.000276523185843016 47 0.999564483265553 0.0008710334688942 0.0004355167344471 48 0.999326237297076 0.00134752540584816 0.00067376270292408 49 0.998976399512638 0.00204720097472384 0.00102360048736192 50 0.998473136517497 0.00305372696500498 0.00152686348250249 51 0.997764076903653 0.00447184619269329 0.00223592309634665 52 0.99678600683724 0.0064279863255185 0.00321399316275925 53 0.995465780372792 0.00906843925441578 0.00453421962720789 54 0.9937230093142 0.0125539813715996 0.00627699068579978 55 0.991475156942774 0.0170496861144513 0.00852484305722563 56 0.988645673663683 0.0227086526726335 0.0113543263363168 57 0.9851757691965 0.0296484616069999 0.0148242308035000 58 0.981040310986274 0.0379193780274518 0.0189596890137259 59 0.976268173991232 0.0474636520175363 0.0237318260087682 60 0.970967140870586 0.058065718258827 0.0290328591294135 61 0.96535312426867 0.0692937514626605 0.0346468757313303 62 0.959782887866388 0.080434224267224 0.040217112133612 63 0.954788059954476 0.090423880091048 0.045211940045524 64 0.951104617905578 0.0977907641888445 0.0488953820944222 65 0.94968238482308 0.100635230353841 0.0503176151769204 66 0.951633947319137 0.096732105361726 0.048366052680863 67 0.9580203831753 0.0839592336494 0.0419796168247 68 0.964102331464142 0.071795337071716 0.035897668535858 69 0.985340126498857 0.029319747002286 0.014659873501143 70 0.987689731443744 0.0246205371125127 0.0123102685562563 71 0.985755816374864 0.0284883672502718 0.0142441836251359 72 0.995558591792018 0.0088828164159642 0.0044414082079821 73 0.997245126016366 0.00550974796726816 0.00275487398363408 74 0.995815927402692 0.00836814519461604 0.00418407259730802 75 0.996438206774812 0.00712358645037524 0.00356179322518762 76 0.995322186829989 0.00935562634002227 0.00467781317001113 77 0.997781965214724 0.00443606957055196 0.00221803478527598 78 0.996981265342451 0.00603746931509735 0.00301873465754868 79 0.998479247981446 0.00304150403710772 0.00152075201855386 80 0.997771657784045 0.0044566844319108 0.0022283422159554 81 0.997315630523956 0.00536873895208884 0.00268436947604442 82 0.998292543761142 0.00341491247771547 0.00170745623885773 83 0.998495240049271 0.00300951990145713 0.00150475995072856 84 0.998568961840543 0.00286207631891415 0.00143103815945707 85 0.997981619380393 0.00403676123921382 0.00201838061960691 86 0.999090833751536 0.00181833249692860 0.000909166248464302 87 0.99891322568516 0.00217354862968281 0.00108677431484141 88 0.997999536062183 0.00400092787563344 0.00200046393781672 89 0.99627571511424 0.00744856977151825 0.00372428488575913 90 0.99422003029413 0.0115599394117393 0.00577996970586964 91 0.989934744812815 0.0201305103743696 0.0100652551871848 92 0.983013155563142 0.0339736888737169 0.0169868444368585 93 0.97226366545695 0.0554726690860994 0.0277363345430497 94 0.956280424012992 0.0874391519740157 0.0437195759870078 95 0.933681788161396 0.132636423677208 0.066318211838604 96 0.903681388181757 0.192637223636486 0.0963186118182428 97 0.867388779065267 0.265222441869466 0.132611220934733 98 0.831274455261593 0.337451089476814 0.168725544738407 99 0.940190171919675 0.11961965616065 0.059809828080325 100 0.970072781457326 0.0598544370853483 0.0299272185426741 101 0.940016119684102 0.119967760631797 0.0599838803158983 102 0.913624298899143 0.172751402201713 0.0863757011008567 103 0.912602533152274 0.174794933695453 0.0873974668477265 104 0.93577797909424 0.128444041811521 0.0642220209057607 105 0.982225092677804 0.0355498146443914 0.0177749073221957 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 41 0.422680412371134 NOK 5% type I error level 60 0.618556701030928 NOK 10% type I error level 74 0.762886597938144 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/21/t1258808472lyqpg4d861kbhz4/107agz1258808125.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258808472lyqpg4d861kbhz4/107agz1258808125.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258808472lyqpg4d861kbhz4/1iiti1258808125.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258808472lyqpg4d861kbhz4/1iiti1258808125.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258808472lyqpg4d861kbhz4/25d2b1258808125.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258808472lyqpg4d861kbhz4/25d2b1258808125.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258808472lyqpg4d861kbhz4/3w1091258808125.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258808472lyqpg4d861kbhz4/3w1091258808125.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258808472lyqpg4d861kbhz4/4u9lo1258808125.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258808472lyqpg4d861kbhz4/4u9lo1258808125.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258808472lyqpg4d861kbhz4/5u5ch1258808125.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258808472lyqpg4d861kbhz4/5u5ch1258808125.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258808472lyqpg4d861kbhz4/63da71258808125.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258808472lyqpg4d861kbhz4/63da71258808125.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258808472lyqpg4d861kbhz4/7efu31258808125.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258808472lyqpg4d861kbhz4/7efu31258808125.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258808472lyqpg4d861kbhz4/884401258808125.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258808472lyqpg4d861kbhz4/884401258808125.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258808472lyqpg4d861kbhz4/9ti1h1258808125.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/21/t1258808472lyqpg4d861kbhz4/9ti1h1258808125.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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

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

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

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