workshop 7 - tutorial 6

*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: Fri, 19 Nov 2010 16:27:16 +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/19/t1290183948j7nozjxjxlsxayt.htm/, Retrieved Fri, 19 Nov 2010 17:25:48 +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/19/t1290183948j7nozjxjxlsxayt.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 «

1 26 24 24 14 14 11 11 12 12 24 24 1 23 25 25 11 11 7 7 8 8 25 25 0 25 17 0 6 0 17 0 8 0 30 0 1 23 18 18 12 12 10 10 8 8 19 19 1 19 18 18 8 8 12 12 9 9 22 22 0 29 16 0 10 0 12 0 7 0 22 0 1 25 20 20 10 10 11 11 4 4 25 25 1 21 16 16 11 11 11 11 11 11 23 23 1 22 18 18 16 16 12 12 7 7 17 17 1 25 17 17 11 11 13 13 7 7 21 21 1 24 23 23 13 13 14 14 12 12 19 19 1 18 30 30 12 12 16 16 10 10 19 19 1 22 23 23 8 8 11 11 10 10 15 15 1 15 18 18 12 12 10 10 8 8 16 16 1 22 15 15 11 11 11 11 8 8 23 23 1 28 12 12 4 4 15 15 4 4 27 27 1 20 21 21 9 9 9 9 9 9 22 22 1 12 15 15 8 8 11 11 8 8 14 14 1 24 20 20 8 8 17 17 7 7 22 22 1 20 31 31 14 14 17 17 11 11 23 23 1 21 27 27 15 15 11 11 9 9 23 23 1 20 34 34 16 16 18 18 11 11 21 21 1 21 21 21 9 9 14 14 13 13 19 19 1 23 31 31 14 14 10 10 8 8 18 18 1 28 19 19 11 11 11 11 8 8 20 20 1 24 16 16 8 8 15 15 9 9 23 23 1 24 20 20 9 9 15 15 6 6 25 25 1 24 21 21 9 9 13 13 9 9 19 19 1 23 22 22 9 9 16 16 9 9 24 24 1 23 17 17 9 9 13 13 6 6 22 22 1 29 24 24 10 10 9 9 6 6 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 15 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation O[t] = + 29.5494632738198 -15.2181794105889B[t] -0.380081606319416CM[t] + 0.317358735332185CM_B[t] + 0.0209368771515474D[t] + 0.207544690798781D_B[t] -0.541638217696423PE[t] + 0.410737731232436PE_B[t] + 0.275927135451116PC[t] -0.509480209169096PC_B[t] + 0.251134847979600PS[t] + 0.221717890089259PS_B[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) 29.5494632738198 6.411444 4.6089 9e-06 4e-06 B -15.2181794105889 6.7603 -2.2511 0.025862 0.012931 CM -0.380081606319416 0.283486 -1.3407 0.182072 0.091036 CM_B 0.317358735332185 0.290792 1.0914 0.2769 0.13845 D 0.0209368771515474 0.422167 0.0496 0.960513 0.480257 D_B 0.207544690798781 0.438069 0.4738 0.636365 0.318183 PE -0.541638217696423 0.625067 -0.8665 0.387613 0.193806 PE_B 0.410737731232436 0.63394 0.6479 0.518052 0.259026 PC 0.275927135451116 0.744798 0.3705 0.711564 0.355782 PC_B -0.509480209169096 0.756683 -0.6733 0.501809 0.250904 PS 0.251134847979600 0.289765 0.8667 0.387527 0.193763 PS_B 0.221717890089259 0.301174 0.7362 0.462795 0.231397 Multiple Linear Regression - Regression Statistics Multiple R 0.508836076808853 R-squared 0.258914153062225 Adjusted R-squared 0.203458749549874 F-TEST (value) 4.66887150148609 F-TEST (DF numerator) 11 F-TEST (DF denominator) 147 p-value 4.20709262227703e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.48517056052898 Sum Squared Residuals 1785.52283388875 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 26 23.1306003887749 2.86939961122509 2 23 24.3130997927334 -1.31309979273343 3 25 23.7473100514567 1.25268994854331 4 23 21.7508235697893 1.24917643021074 5 19 21.7601014655486 -2.76010146554857 6 29 24.6343243355765 4.3656756644235 7 25 24.8088429287352 0.191157071264768 8 21 22.7076389884709 -1.7076389884709 9 22 21.6907964662429 0.309203533757135 10 25 22.3716219632899 2.6283780367101 11 24 20.2078765420756 3.79212345792443 12 18 19.7456400517226 -1.74564005172261 13 22 18.0338653568764 3.96613464312358 14 15 20.3322653555827 -5.33226535558269 15 22 23.4710210806121 -1.47102108061207 16 28 24.3618400192129 3.63815998078713 17 20 22.1931158799292 -2.19311587992917 18 12 18.5299017341414 -6.52990173414137 19 24 21.4472594386901 2.55274056130986 20 20 21.6668377087295 -1.66683770872951 21 21 23.3987198268486 -2.39871982684864 22 20 20.8590262690668 -0.85902626906677 23 21 19.1858429385307 1.81415706146926 24 23 20.9195366447871 2.08046335521293 25 28 21.8015713824566 6.19842861754342 26 24 21.9656984861999 2.03430151380007 27 24 23.589653267493 0.410346732507007 28 24 20.2509557198666 3.74904428013335 29 23 22.1597950798317 0.840204920168254 30 23 22.6210646391761 0.378935360823917 31 29 24.3526462702783 4.64735372972168 32 24 22.6200304297062 1.37996957029377 33 18 25.4025417440717 -7.40254174407172 34 25 26.5166748967625 -1.51667489676250 35 21 22.8153616863728 -1.81536168637277 36 26 27.1131636623579 -1.11316366235788 37 22 25.4351802135502 -3.43518021355015 38 22 22.471516968615 -0.471516968614977 39 22 18.2315078477236 3.76849215227642 40 23 26.0120429543572 -3.01204295435724 41 30 23.3134942521645 6.68650574783546 42 23 22.8944487908286 0.105551209171422 43 17 18.2750943112244 -1.27509431122438 44 23 23.8804744677087 -0.880474467708677 45 23 24.4783838583962 -1.47838385839615 46 25 22.2809444343558 2.71905556564417 47 24 20.6187801323547 3.38121986764531 48 24 28.0120358696766 -4.01203586967657 49 23 23.1792243085142 -0.179224308514248 50 21 24.048538447637 -3.04853844763699 51 24 25.64309255316 -1.64309255316002 52 24 21.749283369148 2.25071663085198 53 28 21.3794664570550 6.62053354294497 54 16 20.3853975474503 -4.38539754745034 55 20 20.7758050117615 -0.775805011761506 56 29 23.5799848872581 5.42001511274193 57 27 24.0911371434937 2.90886285650628 58 22 23.2073880608995 -1.20738806089948 59 28 23.7302249244315 4.26977507556854 60 16 19.9301946078529 -3.93019460785292 61 25 22.9970113806238 2.00298861937616 62 24 23.5443601993152 0.455639800684793 63 28 22.9549465314877 5.0450534685123 64 24 24.3718167272939 -0.371816727293876 65 23 22.3654021364764 0.634597863523598 66 30 27.3381829854236 2.66181701457637 67 24 21.3091577028965 2.69084229710346 68 21 24.3927764401100 -3.39277644010995 69 25 23.0109171240606 1.98908287593938 70 25 24.7059046845367 0.294095315463281 71 22 20.6542734269745 1.34572657302549 72 23 22.3128150312707 0.687184968729269 73 26 23.2074708126045 2.79252918739554 74 23 21.8898645321903 1.11013546780969 75 25 23.2133160415696 1.78668395843039 76 21 21.1912978440933 -0.191297844093338 77 25 23.5415112248078 1.45848877519221 78 24 22.2240581514602 1.77594184853978 79 29 23.5795116510775 5.42048834892254 80 22 23.8066344084238 -1.80663440842378 81 27 23.871481172339 3.128518827661 82 26 23.352304727581 2.64769527241898 83 22 21.1699534974356 0.83004650256439 84 24 22.2960589182068 1.70394108179324 85 27 22.9187946558914 4.08120534410856 86 24 21.2551762818802 2.74482371811984 87 24 24.9854197220989 -0.985419722098878 88 29 24.4182667573910 4.58173324260897 89 22 22.719695403376 -0.719695403376022 90 21 22.2384052767203 -1.23840527672025 91 24 20.2366963157984 3.76330368420159 92 24 21.3821426823987 2.61785731760126 93 23 24.4726473550171 -1.47264735501708 94 20 22.2741308792623 -2.27413087926229 95 27 21.3503548371888 5.64964516281118 96 26 24.251431059974 1.74856894002601 97 25 22.0379029753204 2.96209702467963 98 21 20.2536428464340 0.746357153566045 99 21 20.5015553576722 0.498444642327805 100 19 20.1774147524789 -1.17741475247886 101 21 21.750048451472 -0.750048451471991 102 21 21.0018895175073 -0.00188951750729945 103 16 19.7675753364208 -3.76757533642083 104 22 20.6609941943698 1.33900580563023 105 29 21.7690184549227 7.23098154507732 106 15 20.0314470942041 -5.03144709420414 107 17 20.4094290206754 -3.40942902067538 108 15 19.8292340331870 -4.82923403318697 109 21 21.832123169512 -0.832123169512005 110 21 22.3041191665550 -1.30411916655496 111 19 18.7580000633698 0.241999936630185 112 24 18.0172006363909 5.98279936360905 113 20 22.4432336406806 -2.44323364068060 114 17 22.2694115066078 -5.26941150660783 115 23 25.234109133435 -2.23410913343498 116 24 22.2160062778621 1.78399372213789 117 14 22.2380243142653 -8.2380243142653 118 19 22.6559242447950 -3.65592424479497 119 24 22.2992293169480 1.70077068305203 120 13 19.7557930992512 -6.75579309925122 121 22 25.4692733417253 -3.46927334172529 122 16 20.7992801104401 -4.79928011044015 123 19 23.2114188566166 -4.21141885661661 124 25 22.4886267423104 2.51137325768959 125 25 24.0113072890506 0.988692710949389 126 23 21.4262983307543 1.57370166924572 127 24 25.2280272166323 -1.22802721663232 128 26 23.6302594637448 2.36974053625522 129 26 21.4824108904524 4.51758910954761 130 25 24.4460123208995 0.553987679100515 131 18 22.5423535276884 -4.5423535276884 132 21 19.5104654207782 1.48953457922181 133 26 23.5892714238909 2.41072857610911 134 23 21.5546030832295 1.44539691677054 135 23 19.4253326337924 3.57466736620763 136 22 23.0113803242479 -1.01138032424793 137 20 22.1846103122476 -2.18461031224758 138 13 22.0702745128170 -9.07027451281704 139 24 21.3499715984669 2.65002840153306 140 15 21.7174055264794 -6.71740552647937 141 14 23.2438706188646 -9.2438706188646 142 22 20.3158662905290 1.68413370947095 143 10 18.1419112607927 -8.14191126079267 144 24 24.2871658173622 -0.287165817362175 145 22 22.0655848506515 -0.0655848506514833 146 24 26.0938258262539 -2.09382582625388 147 19 21.9372414925515 -2.93724149255154 148 20 23.3835644028641 -3.38356440286411 149 13 16.4397959186471 -3.43979591864706 150 20 20.0681504588160 -0.0681504588159777 151 22 23.4284855943632 -1.42848559436320 152 24 23.6163819032786 0.383618096721359 153 29 23.7900596853970 5.20994031460296 154 12 20.7579915835694 -8.75799158356937 155 20 21.284389716979 -1.28438971697899 156 21 21.2025064249695 -0.202506424969507 157 24 23.8139211996979 0.18607880030208 158 22 22.0253632882413 -0.0253632882413480 159 20 17.8571180746991 2.14288192530086 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 15 0.910952404085674 0.178095191828652 0.0890475959143262 16 0.871980473468124 0.256039053063753 0.128019526531876 17 0.804268671087644 0.391462657824712 0.195731328912356 18 0.833764164723694 0.332471670552612 0.166235835276306 19 0.757143769756681 0.485712460486638 0.242856230243319 20 0.7816483364017 0.4367033271966 0.2183516635983 21 0.723861243473009 0.552277513053982 0.276138756526991 22 0.652161982398576 0.695676035202848 0.347838017601424 23 0.572663309211792 0.854673381576416 0.427336690788208 24 0.586142800261919 0.827714399476162 0.413857199738081 25 0.741411063114461 0.517177873771078 0.258588936885539 26 0.677637473957032 0.644725052085935 0.322362526042968 27 0.608004512256241 0.783990975487518 0.391995487743759 28 0.596970965765154 0.806058068469691 0.403029034234846 29 0.525835847449189 0.948328305101622 0.474164152550811 30 0.45269970982136 0.90539941964272 0.54730029017864 31 0.477398229280014 0.954796458560028 0.522601770719986 32 0.410270669291817 0.820541338583635 0.589729330708183 33 0.662138434369221 0.675723131261558 0.337861565630779 34 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0.820968381639517 52 0.156219523557644 0.312439047115288 0.843780476442356 53 0.248674089914811 0.497348179829621 0.75132591008519 54 0.271914854299299 0.543829708598598 0.728085145700701 55 0.264838102081066 0.529676204162132 0.735161897918934 56 0.334204332547487 0.668408665094974 0.665795667452513 57 0.320777330582086 0.641554661164173 0.679222669417914 58 0.280632365499211 0.561264730998423 0.719367634500789 59 0.303334479916919 0.606668959833837 0.696665520083081 60 0.326888374073780 0.653776748147561 0.67311162592622 61 0.292748478639951 0.585496957279902 0.707251521360049 62 0.251390077254097 0.502780154508194 0.748609922745903 63 0.288273738234971 0.576547476469942 0.711726261765029 64 0.248001795243686 0.496003590487372 0.751998204756314 65 0.210610363147337 0.421220726294674 0.789389636852663 66 0.201194471230638 0.402388942461277 0.798805528769362 67 0.18491944914274 0.36983889828548 0.81508055085726 68 0.187077140484833 0.374154280969665 0.812922859515167 69 0.165430477685314 0.330860955370628 0.834569522314686 70 0.136373421453063 0.272746842906125 0.863626578546937 71 0.114023617050086 0.228047234100171 0.885976382949914 72 0.0925954919920433 0.185190983984087 0.907404508007957 73 0.0849127350199873 0.169825470039975 0.915087264980013 74 0.0687095079727903 0.137419015945581 0.93129049202721 75 0.0573166526532019 0.114633305306404 0.942683347346798 76 0.0449067678286596 0.0898135356573193 0.95509323217134 77 0.0362812072260439 0.0725624144520877 0.963718792773956 78 0.0293642297445423 0.0587284594890846 0.970635770255458 79 0.0434756103174697 0.0869512206349394 0.95652438968253 80 0.0357388996744 0.0714777993488 0.9642611003256 81 0.0339319281052531 0.0678638562105063 0.966068071894747 82 0.0277032300289706 0.0554064600579411 0.97229676997103 83 0.0211157411753775 0.042231482350755 0.978884258824622 84 0.0168432248792483 0.0336864497584967 0.983156775120752 85 0.0139075337093626 0.0278150674187253 0.986092466290637 86 0.0123520199837555 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0.00215403027429581 0.00430806054859161 0.997845969725704 104 0.00162274923757532 0.00324549847515063 0.998377250762425 105 0.00748111752403738 0.0149622350480748 0.992518882475963 106 0.0117329779207750 0.0234659558415501 0.988267022079225 107 0.0111482285196903 0.0222964570393806 0.98885177148031 108 0.0141247968261094 0.0282495936522188 0.98587520317389 109 0.0105307564580442 0.0210615129160883 0.989469243541956 110 0.00750977849723533 0.0150195569944707 0.992490221502765 111 0.00530557284380624 0.0106111456876125 0.994694427156194 112 0.0148173158258302 0.0296346316516603 0.98518268417417 113 0.0124479414753574 0.0248958829507148 0.987552058524643 114 0.0157131625792882 0.0314263251585765 0.984286837420712 115 0.0124501788772014 0.0249003577544029 0.987549821122799 116 0.00954947377854751 0.0190989475570950 0.990450526221452 117 0.0390327947946147 0.0780655895892295 0.960967205205385 118 0.0363102590286553 0.0726205180573105 0.963689740971345 119 0.03015275226836 0.06030550453672 0.96984724773164 120 0.0555318602089327 0.111063720417865 0.944468139791067 121 0.0524284084597929 0.104856816919586 0.947571591540207 122 0.0644266181930372 0.128853236386074 0.935573381806963 123 0.0588139234319808 0.117627846863962 0.94118607656802 124 0.0562002442168259 0.112400488433652 0.943799755783174 125 0.0485435566702981 0.0970871133405963 0.951456443329702 126 0.0356817783153974 0.0713635566307949 0.964318221684603 127 0.02547686528839 0.05095373057678 0.97452313471161 128 0.0249796448187472 0.0499592896374945 0.975020355181253 129 0.0388028939823763 0.0776057879647527 0.961197106017624 130 0.0299620045440525 0.059924009088105 0.970037995455947 131 0.0245692625037148 0.0491385250074297 0.975430737496285 132 0.0192922727653276 0.0385845455306551 0.980707727234672 133 0.0161717547665161 0.0323435095330321 0.983828245233484 134 0.0116761893164846 0.0233523786329693 0.988323810683515 135 0.0171254360605619 0.0342508721211238 0.982874563939438 136 0.0106847014541643 0.0213694029083287 0.989315298545836 137 0.00636112265935153 0.0127222453187031 0.993638877340648 138 0.0214760925568549 0.0429521851137099 0.978523907443145 139 0.0325366646781546 0.0650733293563091 0.967463335321845 140 0.0256465477347436 0.0512930954694873 0.974353452265256 141 0.0897987089241462 0.179597417848292 0.910201291075854 142 0.0518632442750284 0.103726488550057 0.948136755724972 143 0.157261793021036 0.314523586042072 0.842738206978964 144 0.100360520063917 0.200721040127835 0.899639479936083 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 5 0.0384615384615385 NOK 5% type I error level 43 0.330769230769231 NOK 10% type I error level 60 0.461538461538462 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/19/t1290183948j7nozjxjxlsxayt/10lo7v1290184016.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290183948j7nozjxjxlsxayt/10lo7v1290184016.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290183948j7nozjxjxlsxayt/17erm1290184016.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290183948j7nozjxjxlsxayt/17erm1290184016.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290183948j7nozjxjxlsxayt/27erm1290184016.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290183948j7nozjxjxlsxayt/27erm1290184016.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290183948j7nozjxjxlsxayt/37erm1290184016.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290183948j7nozjxjxlsxayt/37erm1290184016.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290183948j7nozjxjxlsxayt/4io971290184016.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290183948j7nozjxjxlsxayt/4io971290184016.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290183948j7nozjxjxlsxayt/5io971290184016.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290183948j7nozjxjxlsxayt/5io971290184016.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290183948j7nozjxjxlsxayt/6io971290184016.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290183948j7nozjxjxlsxayt/6io971290184016.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290183948j7nozjxjxlsxayt/7sfqs1290184016.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290183948j7nozjxjxlsxayt/7sfqs1290184016.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290183948j7nozjxjxlsxayt/8lo7v1290184016.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290183948j7nozjxjxlsxayt/8lo7v1290184016.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290183948j7nozjxjxlsxayt/9lo7v1290184016.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290183948j7nozjxjxlsxayt/9lo7v1290184016.ps (open in new window)

Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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