*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, 23 Nov 2010 21:27:31 +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/23/t1290547537itrsvv0lgq81d1u.htm/, Retrieved Tue, 23 Nov 2010 22:25:47 +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/23/t1290547537itrsvv0lgq81d1u.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 «

11 14 11 12 12 11 11 7 8 11 11 6 17 8 14 11 12 10 8 12 11 8 12 9 21 11 10 12 7 12 11 10 11 4 22 11 11 11 11 11 11 16 12 7 10 11 11 13 7 13 11 13 14 12 10 11 12 16 10 8 11 8 11 10 15 11 12 10 8 14 11 11 11 8 10 11 4 15 4 14 11 9 9 9 14 11 8 11 8 11 11 8 17 7 10 11 14 17 11 13 11 15 11 9 7 11 16 18 11 14 11 9 14 13 12 11 14 10 8 14 11 11 11 8 11 11 8 15 9 9 11 9 15 6 11 11 9 13 9 15 11 9 16 9 14 11 9 13 6 13 11 10 9 6 9 11 16 18 16 15 11 11 18 5 10 11 8 12 7 11 11 9 17 9 13 11 16 9 6 8 11 11 9 6 20 11 16 12 5 12 11 12 18 12 10 11 12 12 7 10 11 14 18 10 9 11 9 14 9 14 11 10 15 8 8 11 9 16 5 14 11 10 10 8 11 11 12 11 8 13 11 14 14 10 9 11 14 9 6 11 11 10 12 8 15 11 14 17 7 11 11 16 5 4 10 11 9 12 8 14 11 10 12 8 18 11 6 6 4 14 11 8 24 20 11 11 13 12 8 12 11 10 12 8 13 11 8 14 6 9 11 7 7 4 10 11 15 13 8 15 11 9 12 9 20 11 10 13 6 12 11 12 14 7 12 11 13 8 9 14 11 10 11 5 13 11 11 9 5 11 11 8 11 8 17 11 9 13 8 12 11 13 10 6 13 11 11 11 8 14 11 8 1 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 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 Depression[t] = + 18.7294640774005 -0.457083428977557Month[t] -0.0780147047931104Doubts[t] -0.0134474047661470Expectations[t] -0.0478920443475955Criticism[t] + 0.00711727823524966t + 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) 18.7294640774005 7.033314 2.663 0.008558 0.004279 Month -0.457083428977557 0.631823 -0.7234 0.470495 0.235248 Doubts -0.0780147047931104 0.090654 -0.8606 0.390793 0.195397 Expectations -0.0134474047661470 0.08802 -0.1528 0.878772 0.439386 Criticism -0.0478920443475955 0.108905 -0.4398 0.66072 0.33036 t 0.00711727823524966 0.005404 1.3171 0.189741 0.094871 Multiple Linear Regression - Regression Statistics Multiple R 0.140873739807703 R-squared 0.0198454105674083 Adjusted R-squared -0.0115698006323544 F-TEST (value) 0.631713421922126 F-TEST (DF numerator) 5 F-TEST (DF denominator) 156 p-value 0.675807663433844 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.16183684598457 Sum Squared Residuals 1559.56510953760 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 12 11.8938317851806 0.106168214819405 2 11 12.3803509742498 -1.38035097424985 3 14 12.6430677287892 1.35693227121082 4 12 12.2762286116288 -0.276228611628794 5 21 12.5206178551566 8.4793821448434 6 12 12.4674898125008 -0.467489812500814 7 22 12.631730628545 9.368269371455 8 11 12.2255888915540 -1.22558889155397 9 10 12.0207534184479 -2.02075341844790 10 13 12.4044968158826 0.595503184117442 11 10 12.0026770580275 -2.00267705802746 12 8 12.1566983202187 -4.15669832021872 13 15 12.5431114414571 2.45688855854285 14 14 12.3474013939813 1.65259860601871 15 10 12.4190859722435 -2.41908597224350 16 14 13.1100847423563 0.88991525764368 17 14 12.5683527034849 1.43164729651508 18 11 12.6744819213286 -1.67448192132858 19 10 12.6488068153145 -2.64880681531455 20 13 11.9962676874008 1.00373231259925 21 7 12.1018387781350 -5.10183877813497 22 14 11.8410254295189 2.15897457048111 23 12 12.3522511716753 -0.352251171675305 24 14 12.2625447667476 1.73745523325243 25 11 12.490258754596 -1.490258754596 26 9 12.6297384837984 -3.6297384837984 27 11 12.7025171902833 -1.70251719028332 28 15 12.5928531450081 2.40714685499192 29 14 12.5596282089449 1.44037179105511 30 13 12.7507638345214 0.249236165478633 31 9 12.7336560270281 -3.73365602702810 32 15 11.6727379901334 3.32726200986659 33 10 12.5967412801578 -2.59674128015776 34 11 12.8228030126740 -1.82280301267403 35 13 12.5888844735902 0.411115526409759 36 8 12.3011541894457 -4.30115418944568 37 20 12.6983449916465 7.30165500835352 38 12 12.3229385759653 -0.322938575965334 39 10 12.2261859343430 -2.22618593434298 40 10 12.5534478629131 -2.55344786291308 41 9 12.1801751699224 -3.18017516992245 42 14 12.6790476355354 1.32095236446457 43 8 12.6425948485590 -4.64259484855902 44 14 12.8579555598640 1.14204444013598 45 11 12.7240664288603 -1.72406642886025 46 13 12.5617068927431 0.438293107256866 47 9 12.2766684583985 -3.27666845839853 48 11 12.5425909378549 -1.54259093785490 49 15 12.7256407322690 2.27435926773104 50 11 12.4013542118486 -1.40135421184862 51 10 12.5574870707342 -2.55748707073420 52 14 12.8250072717678 1.17499272823218 53 18 12.7541098452100 5.24589015479004 54 14 13.3455385486049 0.65446145139509 55 11 12.1883004219018 -1.18830042190177 56 12 12.5414175655364 -0.541417565536373 57 13 12.7825789581510 0.217421041849046 58 9 13.0146149251353 -4.01461492513532 59 10 13.2896628302219 -3.2896628302219 60 15 12.400409864125 2.59959013587500 61 20 12.8411707315375 7.15882926846253 62 12 12.9005020332562 -0.900502033256246 63 12 12.6902504527915 -0.690250452791532 64 14 12.6042533661354 1.39574663386464 65 13 12.9966407218419 0.00335927815811590 66 11 12.9526381048163 -1.95263810481632 67 17 13.0232285548558 3.97677144514418 68 12 12.9254363187657 -0.925436318765663 69 13 12.7566210808221 0.243378919177897 70 14 12.8105362751822 1.18946372481776 71 13 13.0861423073783 -0.086142307378265 72 15 13.0555870951188 1.94441290488115 73 13 12.8862358560620 0.113764143937978 74 10 12.2891386025450 -2.28913860254498 75 11 13.0441465455753 -2.04414654557531 76 19 12.9178072446207 6.0821927553793 77 13 12.6952023876125 0.304797612387451 78 17 12.7012255376251 4.29877446237491 79 13 12.8100244792725 0.189975520727480 80 9 12.9505983366976 -3.95059833669763 81 11 12.5321033231632 -1.53210332316317 82 10 13.2860171379708 -3.28601713797078 83 9 12.7981513779151 -3.79815137791508 84 12 12.9812011723291 -0.981201172329137 85 12 12.8672696816729 -0.867269681672877 86 13 12.9050677474631 0.0949322525369093 87 13 13.1532208430174 -0.153220843017377 88 12 12.7314979785697 -0.731497978569693 89 15 12.5131605669426 2.48683943305744 90 22 13.0653411842618 8.93465881573822 91 13 12.6856127894447 0.314387210555293 92 15 13.5713309281100 1.42866907188998 93 13 13.1448046171681 -0.144804617168058 94 15 13.1013601272519 1.89863987274806 95 10 13.0487135519545 -3.04871355195451 96 11 12.74755798904 -1.74755798903999 97 16 12.5243950049224 3.47560499507761 98 11 12.5680906454296 -1.56809064542960 99 11 13.2074113931721 -2.20741139317215 100 10 13.0751745175005 -3.07517451750054 101 10 12.9596128975083 -2.95961289750831 102 16 13.4326846818117 2.56731531818829 103 12 12.9980725397073 -0.998072539707328 104 11 13.1369941418003 -2.13699414180028 105 16 12.7298128103415 3.27018718965855 106 19 12.9763903103147 6.02360968968532 107 11 13.3692591333795 -2.36925913337955 108 16 13.1143433594805 2.88565664051954 109 15 12.6566002598703 2.34339974012973 110 24 12.9435199741419 11.0564800258581 111 14 13.3708334367883 0.629166563211748 112 15 13.0847008742209 1.91529912577906 113 11 13.2338420301668 -2.23384203016681 114 15 13.1979473702998 1.80205262970015 115 12 13.4175534009897 -1.41755340098968 116 10 13.4887565118935 -3.48875651189354 117 14 13.4544374476076 0.54556255239236 118 13 13.2748445287017 -0.274844528701705 119 9 12.8235571309180 -3.82355713091795 120 15 13.3983105786335 1.60168942136646 121 15 13.4188752616349 1.58112473836506 122 14 13.2150793829967 0.784920617003333 123 11 12.7696895599299 -1.76968955992991 124 8 13.5919345267910 -5.59193452679098 125 11 12.5880884936290 -1.58808849362901 126 11 13.1284194277593 -2.12841942775934 127 8 13.6552808311273 -5.65528083112733 128 10 13.2233384128267 -3.22333841282672 129 11 13.2202361372090 -2.22023613720904 130 13 13.0035288549179 -0.00352885491788466 131 11 13.0741193049574 -2.07411930495739 132 20 13.3943895305878 6.60561046941221 133 10 13.5586303466320 -3.55863034663197 134 15 13.7185491835402 1.28145081645978 135 12 13.3377266605004 -1.33772666050043 136 14 12.9074364975320 1.09256350246802 137 23 13.2137011912868 9.78629880871321 138 14 13.1417096365062 0.858290363493787 139 16 13.4743331386801 2.52566686131995 140 11 12.8998087155594 -1.89980871555937 141 12 13.0608216806903 -1.06082168069033 142 10 13.0953918955673 -3.09539189556732 143 14 12.3465326778451 1.65346732215493 144 12 13.2226217975256 -1.22262179752564 145 12 12.9639421716001 -0.963942171600072 146 11 13.0571599857908 -2.05715998579085 147 12 13.3860196359382 -1.38601963593820 148 13 13.5696054314655 -0.569605431465526 149 11 13.4674912162394 -2.46749121623944 150 19 13.4778363453879 5.52216365461209 151 12 13.6512025870623 -1.65120258706230 152 17 12.9368425426764 4.06315745732358 153 9 13.3146883653941 -4.31468836539408 154 12 13.6198589309262 -1.61985893092618 155 19 13.0550180605452 5.94498193945484 156 18 13.6475408921628 4.35245910783718 157 15 13.1956953672696 1.80430463273037 158 14 13.1312536425382 0.868746357461793 159 11 12.5631849212440 -1.56318492124396 160 11 13.1282002824650 -2.12820028246497 161 12 10.9887731023609 1.01122689763906 162 8 13.0561344881952 -5.05613448819524 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.979618051768586 0.0407638964628277 0.0203819482314139 10 0.959736007593238 0.080527984813524 0.040263992406762 11 0.925134279590612 0.149731440818776 0.0748657204093882 12 0.904786774489668 0.190426451020664 0.0952132255103322 13 0.85281192377076 0.294376152458481 0.147188076229240 14 0.789073864919071 0.421852270161857 0.210926135080929 15 0.784870103352979 0.430259793294042 0.215129896647021 16 0.795958623635795 0.408082752728409 0.204041376364205 17 0.731914242246595 0.53617151550681 0.268085757753405 18 0.69040611918847 0.619187761623061 0.309593880811531 19 0.623914620999889 0.752170758000222 0.376085379000111 20 0.749817397495427 0.500365205009146 0.250182602504573 21 0.730250271538145 0.53949945692371 0.269749728461855 22 0.82057307130543 0.358853857389139 0.179426928694569 23 0.775012302346377 0.449975395307246 0.224987697653623 24 0.763538100324418 0.472923799351163 0.236461899675582 25 0.712171191824491 0.575657616351019 0.287828808175509 26 0.701708479333535 0.59658304133293 0.298291520666465 27 0.648392849156116 0.703214301687768 0.351607150843884 28 0.65503277803486 0.68993444393028 0.34496722196514 29 0.623398810309757 0.753202379380486 0.376601189690243 30 0.56250676890213 0.87498646219574 0.43749323109787 31 0.558922843745785 0.88215431250843 0.441077156254215 32 0.641165661255448 0.717668677489105 0.358834338744552 33 0.60059587241888 0.798808255162239 0.399404127581120 34 0.547239617899725 0.90552076420055 0.452760382100275 35 0.494339321327967 0.988678642655935 0.505660678672033 36 0.465196102444659 0.930392204889317 0.534803897555341 37 0.772111505712896 0.455776988574208 0.227888494287104 38 0.733434095519253 0.533131808961493 0.266565904480747 39 0.697659595979957 0.604680808040086 0.302340404020043 40 0.664574406351508 0.670851187296985 0.335425593648492 41 0.63683901567886 0.72632196864228 0.36316098432114 42 0.601082681004067 0.797834637991866 0.398917318995933 43 0.62664646746116 0.746707065077681 0.373353532538840 44 0.595596971264938 0.808806057470124 0.404403028735062 45 0.550358547761068 0.899282904477863 0.449641452238932 46 0.509228045558506 0.981543908882987 0.490771954441494 47 0.485669545758708 0.971339091517416 0.514330454241292 48 0.440464555368276 0.880929110736551 0.559535444631724 49 0.433204811989541 0.866409623979082 0.566795188010459 50 0.392302700824637 0.784605401649274 0.607697299175363 51 0.362795772556303 0.725591545112606 0.637204227443697 52 0.327648883745766 0.655297767491533 0.672351116254234 53 0.425123837649754 0.850247675299508 0.574876162350246 54 0.37911403719302 0.75822807438604 0.62088596280698 55 0.338296309941879 0.676592619883759 0.661703690058121 56 0.297011638081985 0.59402327616397 0.702988361918015 57 0.256451038216212 0.512902076432423 0.743548961783788 58 0.277297656954837 0.554595313909675 0.722702343045163 59 0.28207431042673 0.56414862085346 0.71792568957327 60 0.298462964191241 0.596925928382482 0.701537035808759 61 0.489127816997931 0.978255633995862 0.510872183002069 62 0.444393705478666 0.888787410957331 0.555606294521334 63 0.400662972419656 0.801325944839312 0.599337027580344 64 0.363522270478471 0.727044540956942 0.636477729521529 65 0.320186338711709 0.640372677423418 0.679813661288291 66 0.293546348413034 0.587092696826068 0.706453651586966 67 0.309347378711026 0.618694757422053 0.690652621288974 68 0.272987452966228 0.545974905932456 0.727012547033772 69 0.237065758680556 0.474131517361111 0.762934241319444 70 0.20632351446695 0.4126470289339 0.79367648553305 71 0.174731407036978 0.349462814073955 0.825268592963022 72 0.154164394549293 0.308328789098586 0.845835605450707 73 0.127922496231561 0.255844992463121 0.87207750376844 74 0.115833349878197 0.231666699756394 0.884166650121803 75 0.102754143720427 0.205508287440854 0.897245856279573 76 0.167500803967243 0.335001607934486 0.832499196032757 77 0.143182962745036 0.286365925490072 0.856817037254964 78 0.165030358472474 0.330060716944949 0.834969641527526 79 0.138133710148841 0.276267420297683 0.861866289851159 80 0.154343513386904 0.308687026773809 0.845656486613096 81 0.135372574585085 0.27074514917017 0.864627425414915 82 0.147473494425164 0.294946988850327 0.852526505574836 83 0.162004926173185 0.32400985234637 0.837995073826815 84 0.138543040811329 0.277086081622658 0.861456959188671 85 0.118233370123741 0.236466740247482 0.881766629876259 86 0.0996135036827563 0.199227007365513 0.900386496317244 87 0.0816161542773882 0.163232308554776 0.918383845722612 88 0.0676342111055145 0.135268422211029 0.932365788894485 89 0.0600098469517951 0.120019693903590 0.939990153048205 90 0.212665592216278 0.425331184432555 0.787334407783722 91 0.182500126451025 0.365000252902050 0.817499873548975 92 0.163310487359645 0.326620974719291 0.836689512640355 93 0.136407966463337 0.272815932926674 0.863592033536663 94 0.119626432710637 0.239252865421274 0.880373567289363 95 0.122041089543075 0.244082179086150 0.877958910456925 96 0.108679562388928 0.217359124777855 0.891320437611072 97 0.109280598721279 0.218561197442558 0.890719401278721 98 0.0970649635191059 0.194129927038212 0.902935036480894 99 0.0888242600802065 0.177648520160413 0.911175739919794 100 0.0913883041382813 0.182776608276563 0.908611695861719 101 0.094477786481005 0.18895557296201 0.905522213518995 102 0.0851185861700531 0.170237172340106 0.914881413829947 103 0.0734035503019881 0.146807100603976 0.926596449698012 104 0.0683526915509708 0.136705383101942 0.93164730844903 105 0.0638960991585423 0.127792198317085 0.936103900841458 106 0.097995202072946 0.195990404145892 0.902004797927054 107 0.0903355545846531 0.180671109169306 0.909664445415347 108 0.0830452084599832 0.166090416919966 0.916954791540017 109 0.0711110299985358 0.142222059997072 0.928888970001464 110 0.431086462804772 0.862172925609544 0.568913537195228 111 0.388623428474217 0.777246856948435 0.611376571525783 112 0.363627860111720 0.727255720223441 0.63637213988828 113 0.334829304059473 0.669658608118946 0.665170695940527 114 0.309557511987299 0.619115023974598 0.690442488012701 115 0.274852270479618 0.549704540959236 0.725147729520382 116 0.271156624191395 0.542313248382791 0.728843375808605 117 0.232719977043140 0.465439954086281 0.76728002295686 118 0.197954768974582 0.395909537949164 0.802045231025418 119 0.204737500352522 0.409475000705043 0.795262499647478 120 0.186978839739789 0.373957679479577 0.813021160260211 121 0.176415202261778 0.352830404523557 0.823584797738222 122 0.152086860002084 0.304173720004168 0.847913139997916 123 0.126347890953389 0.252695781906778 0.873652109046611 124 0.150994545980006 0.301989091960012 0.849005454019994 125 0.123778639033733 0.247557278067466 0.876221360966267 126 0.10764122955921 0.21528245911842 0.89235877044079 127 0.157447891121889 0.314895782243778 0.842552108878111 128 0.15724860778731 0.31449721557462 0.84275139221269 129 0.149117114508939 0.298234229017877 0.850882885491061 130 0.118363592138061 0.236727184276121 0.88163640786194 131 0.110897270540874 0.221794541081747 0.889102729459126 132 0.184605636509068 0.369211273018136 0.815394363490932 133 0.208259961084448 0.416519922168895 0.791740038915552 134 0.167418584872425 0.33483716974485 0.832581415127575 135 0.145779492625584 0.291558985251168 0.854220507374416 136 0.116128949453763 0.232257898907527 0.883871050546237 137 0.488996263458012 0.977992526916025 0.511003736541988 138 0.426965188081926 0.853930376163852 0.573034811918074 139 0.419872573069995 0.83974514613999 0.580127426930005 140 0.356611882638064 0.713223765276129 0.643388117361936 141 0.290314946027215 0.58062989205443 0.709685053972785 142 0.274200440353856 0.548400880707713 0.725799559646144 143 0.214261626996405 0.42852325399281 0.785738373003595 144 0.160391857864604 0.320783715729207 0.839608142135396 145 0.123956436027997 0.247912872055995 0.876043563972003 146 0.109021733848922 0.218043467697844 0.890978266151078 147 0.0935107171533767 0.187021434306753 0.906489282846623 148 0.0677045815166447 0.135409163033289 0.932295418483355 149 0.103145316131872 0.206290632263744 0.896854683868128 150 0.0940797996306536 0.188159599261307 0.905920200369346 151 0.105393072113514 0.210786144227028 0.894606927886486 152 0.0617071992798439 0.123414398559688 0.938292800720156 153 0.207994607650606 0.415989215301212 0.792005392349394 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 1 0.00689655172413793 OK 10% type I error level 2 0.0137931034482759 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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