*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 21:29:39 +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/t12905476694etcg976uxaubrf.htm/, Retrieved Tue, 23 Nov 2010 22:28:00 +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/t12905476694etcg976uxaubrf.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 10 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Connected[t] = + 32.3319878002112 + 0.0736930507943348Software[t] + 0.158414769830048Happiness[t] -0.0578124530341167Depression[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) 32.3319878002112 3.213735 10.0606 0 0 Software 0.0736930507943348 0.124931 0.5899 0.556121 0.27806 Happiness 0.158414769830048 0.13519 1.1718 0.243045 0.121523 Depression -0.0578124530341167 0.100457 -0.5755 0.565776 0.282888 Multiple Linear Regression - Regression Statistics Multiple R 0.158387868304106 R-squared 0.0250867168259188 Adjusted R-squared 0.00657570512008165 F-TEST (value) 1.35523207615975 F-TEST (DF numerator) 3 F-TEST (DF denominator) 158 p-value 0.25857296513043 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.36401381269591 Sum Squared Residuals 1788.02105125741 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 41 34.740361750955 6.25963824904502 2 39 35.3581402325145 3.64185976748549 3 30 34.3705716877792 -4.37057168777918 4 31 33.9813739065284 -2.98137390652844 5 34 34.6105722641019 -0.610572264101924 6 35 35.2266347286861 -0.226634728686064 7 39 34.1622372206134 4.83776277938662 8 34 34.9455603055773 -0.945560305577329 9 36 35.0144014268528 0.985598573147177 10 37 34.3988057629845 2.60119423701554 11 38 35.1838448649242 2.81615513507575 12 36 35.7636854122412 0.236314587758753 13 38 33.933265312532 4.066734687468 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 2.72658148652120 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 6.80458168829901 27 36 34.9676176420601 1.03238235793992 28 33 34.7143104934409 -1.71431049344086 29 33 34.7831516147164 -1.78315161471636 30 34 34.0599188868416 -0.0599188868416135 31 31 35.230628649717 -4.23062864971699 32 27 34.1137374188448 -7.1137374188448 33 37 35.1838448649242 1.81615513507575 34 34 34.9565889738187 -0.956588973818707 35 34 34.6825492979204 -0.682549297920426 36 32 34.9199758487794 -2.91997584877943 37 29 33.0436299727654 -4.04362997276536 38 36 34.8987765207846 1.10122347921541 39 29 35.1838448649242 -6.18384486492425 40 35 34.5501857856041 0.449814214395941 41 37 34.9248277782983 2.07517222170173 42 34 34.9415663845464 -0.941566384546404 43 38 35.5095202551341 2.49047974486589 44 35 34.1605212036375 0.839478796362455 45 38 34.3339585627399 3.66604143726011 46 37 34.2073049884303 2.79269501156972 47 38 35.1459069306813 2.85409306931872 48 33 34.8828959230244 -1.88289592302437 49 36 34.968475650548 1.031524349452 50 38 34.6397594341586 3.36024056584139 51 32 35.3202022982715 -3.32020229827154 52 32 34.4773507432976 -2.47735074329764 53 32 33.9182427232597 -1.9182427232597 54 34 34.3816003560205 -0.381600356020549 55 32 33.9654933087682 -1.96549330876822 56 37 34.4566182160186 2.54338178398142 57 39 34.9993788375805 4.00062116241948 58 29 35.0722138798869 -6.07221387988694 59 37 34.4654640665683 2.53453593343165 60 35 34.1027087506034 0.897291249396572 61 30 32.9589082537296 -2.95890825372965 62 38 34.5819469811245 3.41805301887551 63 34 34.4125035430531 -0.412503543053069 64 31 34.551043794092 -3.55104379409197 65 34 34.8409640677505 -0.840964067750473 66 35 34.2382081754628 0.761791824537197 67 36 34.1234412778825 1.87655872211751 68 30 34.3498391605001 -4.34983916050011 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 -0.988350169339143 74 38 35.1617875284415 2.83821247155851 75 34 34.6397594341586 -0.639759434158611 76 39 33.7977658876726 5.20223411232737 77 37 35.2314866582049 1.76851334179510 78 34 34.2191916651596 -0.219191665159577 79 28 34.8409640677505 -6.84096406775047 80 37 34.7553843402268 2.24461565977316 81 33 34.9565889738187 -1.95658897381871 82 37 35.1728161966829 1.82718380331713 83 35 35.0722138798869 -0.07221387988694 84 37 35.0571912906146 1.94280870938536 85 32 34.8250834699903 -2.82508346999025 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 -0.0533338318030432 91 31 34.9367144550276 -3.93671445502756 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 4.03238235793992 97 37 34.2659754499523 2.73402455004768 98 35 34.5770950516057 0.422904948394345 99 37 35.2734185134788 1.72658148652120 100 32 34.8670153252642 -2.86701532526415 101 38 35.4786170681016 2.52138293189841 102 37 34.1185893483636 2.88141065163635 103 36 35.2782704429976 0.721729557002357 104 32 34.2492368437042 -2.24923684370418 105 33 34.5938336578538 -1.59383365785379 106 40 33.5436007305655 6.45639926943451 107 38 35.1150037436488 2.88499625635125 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 -0.387777094743087 119 33 34.8401060592626 -1.84010605926256 120 38 34.5669243918522 3.43307560814781 121 33 34.1764018013978 -1.17640180139776 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 3.70053022900752 128 44 35.2575379157186 8.74246208428142 129 33 35.3691689007559 -2.36916890075589 130 35 34.7672710169561 0.232728983043861 131 32 34.4923733325699 -2.49237333256994 132 28 33.412095226737 -5.41209522673704 133 40 34.7196292236755 5.28037077632452 134 27 34.6516461108879 -7.65164611088791 135 37 34.8987765207846 2.10122347921541 136 32 34.9415663845464 -2.94156638454640 137 28 33.4081013057061 -5.40810130570611 138 34 34.551043794092 -0.551043794091975 139 30 33.8864815277393 -3.88648152773926 140 35 34.6618167706414 0.338183229358632 141 31 34.3608678287415 -3.36086782874149 142 32 34.7196292236755 -2.71962922367548 143 30 34.7204872321634 -4.7204872321634 144 30 34.9614409033375 -4.96144090333755 145 31 34.8250834699903 -3.82508346999025 146 40 34.8202315404714 5.17976845952859 147 32 35.1308843414090 -3.13088434140897 148 36 34.2073049884303 1.79269501156972 149 32 34.4813446643286 -2.48134466432856 150 35 33.3225215781825 1.67747842181752 151 38 34.6887260366430 3.31127396335704 152 42 34.3665777667482 7.63342223325175 153 34 35.009549497334 -1.00954949733398 154 35 33.9813739065284 1.01862609347156 155 35 33.2488285273881 1.75117147261185 156 33 33.9403000597425 -0.940300059742456 157 36 34.6295887744051 1.37041122559485 158 32 34.1825785401203 -2.1825785401203 159 33 35.3691689007559 -2.36916890075589 160 34 34.6816912894325 -0.68169128943251 161 32 33.7818852899124 -1.78188528991241 162 34 34.0559249658107 -0.0559249658106891 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.929659075304176 0.140681849391647 0.0703409246958236 8 0.870659096202935 0.25868180759413 0.129340903797065 9 0.789247800990525 0.421504398018951 0.210752199009475 10 0.709257444500982 0.581485110998036 0.290742555499018 11 0.611716275015886 0.776567449968227 0.388283724984114 12 0.546414132086734 0.907171735826533 0.453585867913266 13 0.615502417731021 0.768995164537958 0.384497582268979 14 0.57228354989207 0.85543290021586 0.42771645010793 15 0.562643120204438 0.874713759591123 0.437356879795562 16 0.563675151147818 0.872649697704365 0.436324848852182 17 0.480453028170069 0.960906056340138 0.519546971829931 18 0.427044418069858 0.854088836139715 0.572955581930142 19 0.44554169871525 0.8910833974305 0.55445830128475 20 0.477776092827352 0.955552185654705 0.522223907172648 21 0.503182229559139 0.993635540881721 0.496817770440861 22 0.504026072219556 0.991947855560888 0.495973927780444 23 0.54238850291575 0.9152229941685 0.45761149708425 24 0.498331859640095 0.99666371928019 0.501668140359905 25 0.474111122542173 0.948222245084346 0.525888877457827 26 0.63711736104083 0.72576527791834 0.36288263895917 27 0.57650188584546 0.84699622830908 0.42349811415454 28 0.54167556863967 0.91664886272066 0.45832443136033 29 0.513347789517612 0.973304420964776 0.486652210482388 30 0.469563960907515 0.93912792181503 0.530436039092485 31 0.521579432448991 0.956841135102018 0.478420567551009 32 0.775578328763462 0.448843342473075 0.224421671236538 33 0.738096671700776 0.523806656598447 0.261903328299224 34 0.696928626117836 0.606142747764327 0.303071373882164 35 0.650615577725834 0.698768844548333 0.349384422274166 36 0.645413598920834 0.709172802158332 0.354586401079166 37 0.664139219925208 0.671721560149584 0.335860780074792 38 0.615426309200372 0.769147381599255 0.384573690799627 39 0.725094717009549 0.549810565980903 0.274905282990451 40 0.678922828913815 0.642154342172371 0.321077171086185 41 0.646442291919472 0.707115416161056 0.353557708080528 42 0.60073035635871 0.79853928728258 0.39926964364129 43 0.564906732629374 0.870186534741252 0.435093267370626 44 0.515481570987824 0.969036858024352 0.484518429012176 45 0.51522376495573 0.96955247008854 0.48477623504427 46 0.487067172979463 0.974134345958925 0.512932827020537 47 0.46021890192189 0.92043780384378 0.53978109807811 48 0.430102492103341 0.860204984206682 0.569897507896659 49 0.387117413364021 0.774234826728043 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0.869219900651295 85 0.123175556672534 0.246351113345069 0.876824443327466 86 0.105326298547718 0.210652597095436 0.894673701452282 87 0.105609078996284 0.211218157992568 0.894390921003716 88 0.090890399515752 0.181780799031504 0.909109600484248 89 0.122307145943385 0.244614291886770 0.877692854056615 90 0.100554126810489 0.201108253620979 0.89944587318951 91 0.108333499879953 0.216666999759906 0.891666500120047 92 0.091999092779674 0.183998185559348 0.908000907220326 93 0.0744652627744585 0.148930525548917 0.925534737225541 94 0.0675550661999526 0.135110132399905 0.932444933800047 95 0.0958948339105571 0.191789667821114 0.904105166089443 96 0.103869743271535 0.207739486543070 0.896130256728465 97 0.0972699394593445 0.194539878918689 0.902730060540656 98 0.0791268860280612 0.158253772056122 0.920873113971939 99 0.0672596026400878 0.134519205280176 0.932740397359912 100 0.062115291120374 0.124230582240748 0.937884708879626 101 0.0568796836969927 0.113759367393985 0.943120316303007 102 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0.200577048551344 0.401154097102689 0.799422951448656 120 0.226011608769761 0.452023217539522 0.773988391230239 121 0.190733300042145 0.381466600084290 0.809266699957855 122 0.180400905413667 0.360801810827335 0.819599094586333 123 0.177594013170327 0.355188026340654 0.822405986829673 124 0.153418652837038 0.306837305674075 0.846581347162962 125 0.128928756925716 0.257857513851432 0.871071243074284 126 0.127234034480163 0.254468068960327 0.872765965519837 127 0.124528061904201 0.249056123808403 0.875471938095799 128 0.390516466514242 0.781032933028484 0.609483533485758 129 0.346245166835563 0.692490333671126 0.653754833164437 130 0.302360382687316 0.604720765374632 0.697639617312684 131 0.278005716473104 0.556011432946208 0.721994283526896 132 0.318029218513996 0.636058437027992 0.681970781486004 133 0.40619891608382 0.81239783216764 0.59380108391618 134 0.569361466260226 0.861277067479547 0.430638533739774 135 0.56005390387044 0.879892192259121 0.439946096129560 136 0.510954730122382 0.978090539755236 0.489045269877618 137 0.628267178053731 0.743465643892537 0.371732821946269 138 0.561863954942018 0.876272090115965 0.438136045057982 139 0.600027969486317 0.799944061027367 0.399972030513683 140 0.540649215230142 0.918701569539717 0.459350784769858 141 0.522556801283207 0.954886397433586 0.477443198716793 142 0.470777055965781 0.941554111931561 0.529222944034219 143 0.520770445464045 0.95845910907191 0.479229554535955 144 0.589458416266226 0.821083167467549 0.410541583733774 145 0.62103273935169 0.75793452129662 0.37896726064831 146 0.793037218784582 0.413925562430836 0.206962781215418 147 0.81835606889633 0.36328786220734 0.18164393110367 148 0.752783778544038 0.494432442911924 0.247216221455962 149 0.765991940978937 0.468016118042127 0.234008059021063 150 0.676056936549409 0.647886126901182 0.323943063450591 151 0.811852270431641 0.376295459136718 0.188147729568359 152 0.995965614938796 0.0080687701224088 0.0040343850612044 153 0.987078569122982 0.0258428617540362 0.0129214308770181 154 0.985911722762896 0.0281765544742076 0.0140882772371038 155 0.980147880738194 0.0397042385236123 0.0198521192618062 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/t12905476694etcg976uxaubrf/10ienb1290547768.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905476694etcg976uxaubrf/10ienb1290547768.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905476694etcg976uxaubrf/1tdpz1290547768.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905476694etcg976uxaubrf/1tdpz1290547768.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905476694etcg976uxaubrf/2tdpz1290547768.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905476694etcg976uxaubrf/2tdpz1290547768.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905476694etcg976uxaubrf/3m4pk1290547768.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905476694etcg976uxaubrf/3m4pk1290547768.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905476694etcg976uxaubrf/4m4pk1290547768.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905476694etcg976uxaubrf/4m4pk1290547768.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905476694etcg976uxaubrf/5m4pk1290547768.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905476694etcg976uxaubrf/5m4pk1290547768.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905476694etcg976uxaubrf/6wv6n1290547768.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905476694etcg976uxaubrf/6wv6n1290547768.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905476694etcg976uxaubrf/77n5q1290547768.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905476694etcg976uxaubrf/77n5q1290547768.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905476694etcg976uxaubrf/87n5q1290547768.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905476694etcg976uxaubrf/87n5q1290547768.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905476694etcg976uxaubrf/97n5q1290547768.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905476694etcg976uxaubrf/97n5q1290547768.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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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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