*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 22:02:00 +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/t1290549609kvdspg8il57ojul.htm/, Retrieved Tue, 23 Nov 2010 23:00:09 +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/t1290549609kvdspg8il57ojul.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 «

41 12 14 12 39 11 18 11 30 15 11 14 31 6 12 12 34 13 16 21 35 10 18 12 39 12 14 22 34 14 14 11 36 12 15 10 37 6 15 13 38 10 17 10 36 12 19 8 38 12 10 15 39 11 16 14 33 15 18 10 32 12 14 14 36 10 14 14 38 12 17 11 39 11 14 10 32 12 16 13 32 11 18 7 31 12 11 14 39 13 14 12 37 11 12 14 39 9 17 11 41 13 9 9 36 10 16 11 33 14 14 15 33 12 15 14 34 10 11 13 31 12 16 9 27 8 13 15 37 10 17 10 34 12 15 11 34 12 14 13 32 7 16 8 29 6 9 20 36 12 15 12 29 10 17 10 35 10 13 10 37 10 15 9 34 12 16 14 38 15 16 8 35 10 12 14 38 10 12 11 37 12 11 13 38 13 15 9 33 11 15 11 36 11 17 15 38 12 13 11 32 14 16 10 32 10 14 14 32 12 11 18 34 13 12 14 32 5 12 11 37 6 15 12 39 12 16 13 29 12 15 9 37 11 12 10 35 10 12 15 30 7 8 20 38 12 13 12 34 14 11 12 31 11 14 14 34 12 15 13 35 13 10 11 36 14 11 17 30 11 12 12 39 12 15 13 35 12 15 14 38 8 14 13 31 11 16 15 34 14 15 13 38 14 15 10 34 12 13 11 39 9 12 19 37 13 17 13 34 11 13 17 28 12 15 13 37 12 13 9 33 12 15 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 7 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Connected[t] = + 32.3319878002113 + 0.073693050794334Software[t] + 0.158414769830047Happiness[t] -0.0578124530341171Depression[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) 32.3319878002113 3.213735 10.0606 0 0 Software 0.073693050794334 0.124931 0.5899 0.556121 0.27806 Happiness 0.158414769830047 0.13519 1.1718 0.243045 0.121523 Depression -0.0578124530341171 0.100457 -0.5755 0.565776 0.282888 Multiple Linear Regression - Regression Statistics Multiple R 0.158387868304105 R-squared 0.0250867168259186 Adjusted R-squared 0.00657570512008154 F-TEST (value) 1.35523207615974 F-TEST (DF numerator) 3 F-TEST (DF denominator) 158 p-value 0.258572965130434 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.36401381269592 Sum Squared Residuals 1788.02105125741 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 41 34.7403617509547 6.25963824904534 2 39 35.3581402325145 3.64185976748549 3 30 34.3705716877792 -4.37057168777917 4 31 33.9813739065284 -2.98137390652845 5 34 34.6105722641019 -0.610572264101918 6 35 35.2266347286861 -0.226634728686063 7 39 34.1622372206134 4.83776277938663 8 34 34.9455603055773 -0.94556030557733 9 36 35.0144014268528 0.985598573147175 10 37 34.3988057629845 2.60119423701553 11 38 35.1838448649243 2.81615513507575 12 36 35.7636854122412 0.236314587758754 13 38 33.933265312532 4.06673468746799 14 39 34.8678733337521 4.13212666624793 15 33 35.710724888726 -2.71072488872597 16 32 34.6247368448863 -2.62473684488631 17 36 34.4773507432976 1.52264925670236 18 38 35.2734185134788 2.7265814865212 19 39 34.7822936062284 4.21770639377156 20 32 34.9993788375805 -2.99937883758052 21 32 35.589390044651 -3.58939004465098 22 31 34.1494925353962 -3.14949253539617 23 39 34.8140548017489 4.18594519825112 24 37 34.2342142544319 2.76578574556812 25 39 35.0523393610958 3.9476606389042 26 41 34.195418311701 6.804581688299 27 36 34.9676176420601 1.03238235793991 28 33 34.7143104934409 -1.71431049344086 29 33 34.7831516147164 -1.78315161471636 30 34 34.0599188868416 -0.0599188868416191 31 31 35.230628649717 -4.23062864971699 32 27 34.1137374188448 -7.11373741884481 33 37 35.1838448649243 1.81615513507575 34 34 34.9565889738187 -0.956588973818708 35 34 34.6825492979204 -0.682549297920427 36 32 34.9199758487794 -2.91997584877944 37 29 33.0436299727654 -4.04362997276537 38 36 34.8987765207846 1.10122347921541 39 29 35.1838448649243 -6.18384486492425 40 35 34.5501857856041 0.449814214395936 41 37 34.9248277782983 2.07517222170173 42 34 34.9415663845464 -0.941566384546404 43 38 35.5095202551341 2.49047974486589 44 35 34.1605212036376 0.839478796362451 45 38 34.3339585627399 3.6660414372601 46 37 34.2073049884303 2.79269501156971 47 38 35.1459069306813 2.85409306931872 48 33 34.8828959230244 -1.88289592302437 49 36 34.968475650548 1.031524349452 50 38 34.6397594341586 3.36024056584138 51 32 35.3202022982715 -3.32020229827154 52 32 34.4773507432976 -2.47735074329764 53 32 33.9182427232597 -1.9182427232597 54 34 34.3816003560205 -0.381600356020551 55 32 33.9654933087682 -1.96549330876823 56 37 34.4566182160186 2.54338178398141 57 39 34.9993788375805 4.00062116241948 58 29 35.0722138798869 -6.07221387988694 59 37 34.4654640665684 2.53453593343165 60 35 34.1027087506034 0.897291249396568 61 30 32.9589082537297 -2.95890825372966 62 38 34.5819469811245 3.4180530188755 63 34 34.4125035430531 -0.412503543053072 64 31 34.551043794092 -3.55104379409198 65 34 34.8409640677505 -0.840964067750474 66 35 34.2382081754628 0.761791824537192 67 36 34.1234412778825 1.87655872211751 68 30 34.3498391605001 -4.34983916050012 69 39 34.8409640677505 4.15903593224953 70 35 34.7831516147164 0.216848385283643 71 38 34.3877770947431 3.61222290525691 72 31 34.8100608807180 -3.81006088071795 73 34 34.9883501693391 -0.988350169339142 74 38 35.1617875284415 2.83821247155851 75 34 34.6397594341586 -0.639759434158615 76 39 33.7977658876726 5.20223411232737 77 37 35.2314866582049 1.7685133417951 78 34 34.2191916651596 -0.219191665159578 79 28 34.8409640677505 -6.84096406775047 80 37 34.7553843402268 2.24461565977315 81 33 34.9565889738187 -1.95658897381871 82 37 35.1728161966829 1.82718380331713 83 35 35.0722138798869 -0.0722138798869423 84 37 35.0571912906146 1.94280870938536 85 32 34.8250834699903 -2.82508346999026 86 33 34.5351631963318 -1.53516319633176 87 38 34.6198849153675 3.38011508463253 88 33 34.7403617509545 -1.74036175095454 89 29 34.4085096220221 -5.40850962202215 90 33 33.0533338318030 -0.053333831803046 91 31 34.9367144550276 -3.93671445502757 92 36 34.6295887744051 1.37041122559485 93 35 34.8409640677505 0.159035932249526 94 32 34.5669243918522 -2.56692439185219 95 29 34.6975718871927 -5.69757188719273 96 39 34.9676176420601 4.03238235793991 97 37 34.2659754499523 2.73402455004768 98 35 34.5770950516057 0.422904948394340 99 37 35.2734185134788 1.7265814865212 100 32 34.8670153252642 -2.86701532526416 101 38 35.4786170681016 2.52138293189841 102 37 34.1185893483636 2.88141065163635 103 36 35.2782704429976 0.72172955700236 104 32 34.2492368437042 -2.24923684370419 105 33 34.5938336578538 -1.59383365785379 106 40 33.5436007305655 6.45639926943451 107 38 35.1150037436488 2.88499625635124 108 41 34.6675267086481 6.33247329135188 109 36 33.8595722617377 2.14042773826233 110 43 33.0444879812533 9.95551201874672 111 30 34.7831516147164 -4.78315161471636 112 31 34.2390661839507 -3.23906618395072 113 32 34.5660663833643 -2.56606638336428 114 32 34.4932313410579 -2.49323134105786 115 37 35.2266347286861 1.77336527131394 116 37 35.2465092474772 1.75349075252279 117 33 34.6984298956806 -1.69842989568064 118 34 34.3877770947431 -0.387777094743091 119 33 34.8401060592626 -1.84010605926256 120 38 34.5669243918522 3.43307560814781 121 33 34.1764018013978 -1.17640180139777 122 31 34.6984298956806 -3.69842989568064 123 38 34.9565889738187 3.04341102618129 124 37 35.2774124345097 1.72258756549027 125 33 35.0302820246130 -2.03028202461304 126 31 34.8608385865416 -3.86083858654162 127 39 35.2994697709925 3.70053022900751 128 44 35.2575379157186 8.74246208428142 129 33 35.3691689007559 -2.36916890075589 130 35 34.7672710169561 0.23272898304386 131 32 34.4923733325699 -2.49237333256995 132 28 33.4120952267370 -5.41209522673704 133 40 34.7196292236755 5.28037077632451 134 27 34.6516461108879 -7.6516461108879 135 37 34.8987765207846 2.10122347921541 136 32 34.9415663845464 -2.94156638454640 137 28 33.4081013057061 -5.40810130570611 138 34 34.551043794092 -0.551043794091976 139 30 33.8864815277393 -3.88648152773927 140 35 34.6618167706414 0.338183229358628 141 31 34.3608678287415 -3.36086782874150 142 32 34.7196292236755 -2.71962922367549 143 30 34.7204872321634 -4.7204872321634 144 30 34.9614409033375 -4.96144090333755 145 31 34.8250834699903 -3.82508346999026 146 40 34.8202315404714 5.17976845952858 147 32 35.130884341409 -3.13088434140897 148 36 34.2073049884303 1.79269501156971 149 32 34.4813446643286 -2.48134466432857 150 35 33.3225215781825 1.67747842181751 151 38 34.688726036643 3.31127396335703 152 42 34.3665777667482 7.63342223325176 153 34 35.009549497334 -1.00954949733399 154 35 33.9813739065284 1.01862609347155 155 35 33.2488285273882 1.75117147261185 156 33 33.9403000597425 -0.940300059742459 157 36 34.6295887744051 1.37041122559485 158 32 34.1825785401203 -2.18257854012031 159 33 35.3691689007559 -2.36916890075589 160 34 34.6816912894325 -0.681691289432515 161 32 33.7818852899124 -1.78188528991241 162 34 34.0559249658107 -0.0559249658106935 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.929659075304176 0.140681849391648 0.0703409246958238 8 0.870659096202935 0.258681807594131 0.129340903797065 9 0.789247800990526 0.421504398018948 0.210752199009474 10 0.709257444500983 0.581485110998034 0.290742555499017 11 0.611716275015885 0.776567449968231 0.388283724984115 12 0.546414132086728 0.907171735826544 0.453585867913272 13 0.615502417731021 0.768995164537958 0.384497582268979 14 0.572283549892069 0.855432900215863 0.427716450107931 15 0.562643120204438 0.874713759591125 0.437356879795562 16 0.563675151147817 0.872649697704366 0.436324848852183 17 0.480453028170067 0.960906056340135 0.519546971829933 18 0.427044418069858 0.854088836139716 0.572955581930142 19 0.445541698715246 0.891083397430493 0.554458301284754 20 0.477776092827349 0.955552185654698 0.522223907172651 21 0.503182229559139 0.993635540881721 0.496817770440861 22 0.504026072219558 0.991947855560884 0.495973927780442 23 0.54238850291575 0.9152229941685 0.45761149708425 24 0.4983318596401 0.9966637192802 0.5016681403599 25 0.47411112254217 0.94822224508434 0.52588887745783 26 0.63711736104083 0.725765277918341 0.362882638959170 27 0.576501885845466 0.846996228309068 0.423498114154534 28 0.541675568639671 0.916648862720659 0.458324431360329 29 0.513347789517614 0.973304420964772 0.486652210482386 30 0.469563960907513 0.939127921815027 0.530436039092487 31 0.521579432448997 0.956841135102007 0.478420567551003 32 0.775578328763467 0.448843342473066 0.224421671236533 33 0.738096671700776 0.523806656598449 0.261903328299224 34 0.696928626117837 0.606142747764325 0.303071373882163 35 0.650615577725834 0.698768844548332 0.349384422274166 36 0.645413598920836 0.709172802158329 0.354586401079164 37 0.664139219925207 0.671721560149587 0.335860780074794 38 0.61542630920037 0.769147381599261 0.384573690799631 39 0.725094717009548 0.549810565980904 0.274905282990452 40 0.678922828913816 0.642154342172368 0.321077171086184 41 0.646442291919472 0.707115416161056 0.353557708080528 42 0.600730356358704 0.798539287282592 0.399269643641296 43 0.564906732629371 0.870186534741257 0.435093267370629 44 0.515481570987828 0.969036858024345 0.484518429012172 45 0.515223764955728 0.969552470088543 0.484776235044272 46 0.487067172979462 0.974134345958924 0.512932827020538 47 0.46021890192189 0.92043780384378 0.53978109807811 48 0.430102492103342 0.860204984206684 0.569897507896658 49 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0.446895458572196 0.776552270713902 119 0.200577048551343 0.401154097102685 0.799422951448657 120 0.226011608769766 0.452023217539532 0.773988391230234 121 0.190733300042144 0.381466600084288 0.809266699957856 122 0.180400905413666 0.360801810827333 0.819599094586334 123 0.177594013170332 0.355188026340664 0.822405986829668 124 0.153418652837038 0.306837305674077 0.846581347162962 125 0.128928756925719 0.257857513851438 0.87107124307428 126 0.127234034480165 0.25446806896033 0.872765965519835 127 0.124528061904202 0.249056123808403 0.875471938095798 128 0.390516466514242 0.781032933028484 0.609483533485758 129 0.346245166835564 0.692490333671128 0.653754833164436 130 0.302360382687314 0.604720765374629 0.697639617312686 131 0.278005716473108 0.556011432946217 0.721994283526892 132 0.318029218513993 0.636058437027986 0.681970781486007 133 0.406198916083822 0.812397832167644 0.593801083916178 134 0.569361466260225 0.86127706747955 0.430638533739775 135 0.560053903870438 0.879892192259125 0.439946096129562 136 0.510954730122379 0.978090539755242 0.489045269877621 137 0.628267178053729 0.743465643892542 0.371732821946271 138 0.561863954942012 0.876272090115975 0.438136045057988 139 0.600027969486316 0.799944061027368 0.399972030513684 140 0.540649215230144 0.918701569539713 0.459350784769856 141 0.522556801283205 0.95488639743359 0.477443198716795 142 0.470777055965781 0.941554111931561 0.529222944034219 143 0.520770445464045 0.95845910907191 0.479229554535955 144 0.589458416266228 0.821083167467544 0.410541583733772 145 0.62103273935169 0.75793452129662 0.37896726064831 146 0.793037218784583 0.413925562430834 0.206962781215417 147 0.81835606889633 0.36328786220734 0.18164393110367 148 0.752783778544037 0.494432442911925 0.247216221455963 149 0.765991940978936 0.468016118042128 0.234008059021064 150 0.676056936549415 0.64788612690117 0.323943063450585 151 0.811852270431641 0.376295459136718 0.188147729568359 152 0.995965614938796 0.00806877012240894 0.00403438506120447 153 0.987078569122982 0.0258428617540360 0.0129214308770180 154 0.985911722762896 0.0281765544742077 0.0140882772371038 155 0.980147880738194 0.0397042385236122 0.0198521192618061 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 1 0.00671140939597315 OK 5% type I error level 4 0.0268456375838926 OK 10% type I error level 7 0.0469798657718121 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290549609kvdspg8il57ojul/10qvck1290549709.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290549609kvdspg8il57ojul/10qvck1290549709.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290549609kvdspg8il57ojul/1jcg91290549709.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290549609kvdspg8il57ojul/1jcg91290549709.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290549609kvdspg8il57ojul/2c3fu1290549709.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290549609kvdspg8il57ojul/2c3fu1290549709.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290549609kvdspg8il57ojul/3c3fu1290549709.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290549609kvdspg8il57ojul/3c3fu1290549709.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290549609kvdspg8il57ojul/4c3fu1290549709.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290549609kvdspg8il57ojul/4c3fu1290549709.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290549609kvdspg8il57ojul/5c3fu1290549709.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290549609kvdspg8il57ojul/5c3fu1290549709.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290549609kvdspg8il57ojul/6muex1290549709.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290549609kvdspg8il57ojul/6muex1290549709.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290549609kvdspg8il57ojul/7fmdi1290549709.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290549609kvdspg8il57ojul/7fmdi1290549709.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290549609kvdspg8il57ojul/8fmdi1290549709.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290549609kvdspg8il57ojul/8fmdi1290549709.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290549609kvdspg8il57ojul/9fmdi1290549709.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290549609kvdspg8il57ojul/9fmdi1290549709.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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Software written by Ed van Stee & Patrick Wessa

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