W7

*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 17:40:07 +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/t1290533915c92zv1j1f1e8rtq.htm/, Retrieved Tue, 23 Nov 2010 18:38:45 +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/t1290533915c92zv1j1f1e8rtq.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 12 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Organization[t] = + 29.5494632738196 -15.2181794105887Browser[t] -0.380081606319418CoM[t] + 0.317358735332188CoM_b[t] + 0.0209368771515603DaA[t] + 0.207544690798768DaA_b[t] -0.541638217696424PExp[t] + 0.410737731232435PExp_b[t] + 0.275927135451115PCri[t] -0.509480209169093PCri_b[t] + 0.251134847979606PSta[t] + 0.221717890089252PSta_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) 29.5494632738196 6.411444 4.6089 9e-06 4e-06 Browser -15.2181794105887 6.7603 -2.2511 0.025862 0.012931 CoM -0.380081606319418 0.283486 -1.3407 0.182072 0.091036 CoM_b 0.317358735332188 0.290792 1.0914 0.2769 0.13845 DaA 0.0209368771515603 0.422167 0.0496 0.960513 0.480257 DaA_b 0.207544690798768 0.438069 0.4738 0.636365 0.318183 PExp -0.541638217696424 0.625067 -0.8665 0.387613 0.193806 PExp_b 0.410737731232435 0.63394 0.6479 0.518052 0.259026 PCri 0.275927135451115 0.744798 0.3705 0.711564 0.355782 PCri_b -0.509480209169093 0.756683 -0.6733 0.501809 0.250904 PSta 0.251134847979606 0.289765 0.8667 0.387527 0.193763 PSta_b 0.221717890089252 0.301174 0.7362 0.462795 0.231397 Multiple Linear Regression - Regression Statistics Multiple R 0.508836076808852 R-squared 0.258914153062224 Adjusted R-squared 0.203458749549874 F-TEST (value) 4.66887150148608 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 23.1306003887746 2.86939961122538 2 23 24.3130997927335 -1.31309979273345 3 25 23.7473100514567 1.25268994854331 4 23 21.7508235697893 1.24917643021073 5 19 21.7601014655486 -2.76010146554857 6 29 24.6343243355765 4.3656756644235 7 25 24.8088429287352 0.191157071264772 8 21 22.7076389884709 -1.70763898847091 9 22 21.6907964662429 0.309203533757118 10 25 22.3716219632899 2.6283780367101 11 24 20.2078765420756 3.79212345792442 12 18 19.7456400517226 -1.74564005172262 13 22 18.0338653568764 3.96613464312358 14 15 20.3322653555827 -5.3322653555827 15 22 23.4710210806121 -1.47102108061208 16 28 24.3618400192129 3.63815998078714 17 20 22.1931158799292 -2.19311587992918 18 12 18.5299017341414 -6.52990173414137 19 24 21.4472594386901 2.55274056130987 20 20 21.6668377087295 -1.66683770872951 21 21 23.3987198268486 -2.39871982684864 22 20 20.8590262690668 -0.859026269066769 23 21 19.1858429385307 1.81415706146925 24 23 20.9195366447871 2.08046335521293 25 28 21.8015713824566 6.19842861754342 26 24 21.9656984861999 2.03430151380007 27 24 23.589653267493 0.410346732507013 28 24 20.2509557198666 3.74904428013335 29 23 22.1597950798317 0.840204920168255 30 23 22.6210646391761 0.378935360823919 31 29 24.3526462702783 4.64735372972168 32 24 22.6200304297062 1.37996957029375 33 18 25.4025417440717 -7.40254174407171 34 25 26.5166748967625 -1.5166748967625 35 21 22.8153616863728 -1.81536168637277 36 26 27.1131636623579 -1.11316366235788 37 22 25.4351802135502 -3.43518021355015 38 22 22.471516968615 -0.471516968614979 39 22 18.2315078477236 3.76849215227641 40 23 26.0120429543572 -3.01204295435724 41 30 23.3134942521645 6.68650574783547 42 23 22.8944487908286 0.105551209171420 43 17 18.2750943112244 -1.27509431122438 44 23 23.8804744677087 -0.880474467708669 45 23 24.4783838583962 -1.47838385839616 46 25 22.2809444343558 2.71905556564417 47 24 20.6187801323547 3.3812198676453 48 24 28.0120358696766 -4.01203586967657 49 23 23.1792243085143 -0.179224308514249 50 21 24.048538447637 -3.04853844763699 51 24 25.64309255316 -1.64309255316003 52 24 21.7492833691480 2.25071663085198 53 28 21.3794664570550 6.62053354294497 54 16 20.3853975474503 -4.38539754745034 55 20 20.7758050117615 -0.775805011761512 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 22.9970113806239 2.00298861937615 62 24 23.5443601993152 0.455639800684796 63 28 22.9549465314877 5.04505346851227 64 24 24.3718167272939 -0.371816727293888 65 23 22.3654021364764 0.634597863523596 66 30 27.3381829854236 2.66181701457637 67 24 21.3091577028965 2.69084229710346 68 21 24.3927764401100 -3.39277644010995 69 25 23.0109171240606 1.98908287593937 70 25 24.7059046845367 0.294095315463260 71 22 20.6542734269745 1.34572657302549 72 23 22.3128150312707 0.687184968729264 73 26 23.2074708126045 2.79252918739554 74 23 21.8898645321903 1.11013546780969 75 25 23.2133160415696 1.78668395843040 76 21 21.1912978440933 -0.191297844093341 77 25 23.5415112248078 1.45848877519221 78 24 22.2240581514602 1.77594184853978 79 29 23.5795116510775 5.42048834892253 80 22 23.8066344084238 -1.80663440842378 81 27 23.871481172339 3.128518827661 82 26 23.3523047275809 2.64769527241908 83 22 21.1699534974356 0.830046502564387 84 24 22.2960589182068 1.70394108179324 85 27 22.9187946558915 4.08120534410854 86 24 21.2551762818802 2.74482371811984 87 24 24.9854197220989 -0.985419722098875 88 29 24.4182667573910 4.58173324260896 89 22 22.7196954033760 -0.71969540337603 90 21 22.2384052767202 -1.23840527672021 91 24 20.2366963157984 3.76330368420159 92 24 21.3821426823987 2.61785731760125 93 23 24.4726473550171 -1.47264735501707 94 20 22.2741308792623 -2.27413087926228 95 27 21.3503548371888 5.64964516281117 96 26 24.251431059974 1.74856894002601 97 25 22.0379029753204 2.96209702467963 98 21 20.2536428464340 0.746357153566042 99 21 20.5015553576722 0.498444642327803 100 19 20.1774147524789 -1.17741475247887 101 21 21.750048451472 -0.750048451471994 102 21 21.0018895175073 -0.00188951750729827 103 16 19.7675753364208 -3.76757533642083 104 22 20.6609941943698 1.33900580563023 105 29 21.7690184549227 7.23098154507731 106 15 20.0314470942041 -5.03144709420414 107 17 20.4094290206754 -3.40942902067538 108 15 19.829234033187 -4.82923403318698 109 21 21.832123169512 -0.83212316951201 110 21 22.3041191665550 -1.30411916655496 111 19 18.7580000633698 0.241999936630182 112 24 18.0172006363909 5.98279936360905 113 20 22.4432336406806 -2.44323364068061 114 17 22.2694115066078 -5.26941150660785 115 23 25.234109133435 -2.234109133435 116 24 22.2160062778621 1.78399372213790 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 20.7992801104402 -4.79928011044015 123 19 23.2114188566167 -4.21141885661666 124 25 22.4886267423104 2.51137325768959 125 25 24.0113072890506 0.988692710949376 126 23 21.4262983307543 1.57370166924572 127 24 25.2280272166323 -1.22802721663230 128 26 23.6302594637448 2.36974053625522 129 26 21.4824108904524 4.5175891095476 130 25 24.4460123208995 0.553987679100513 131 18 22.5423535276884 -4.54235352768841 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 -1.01138032424792 137 20 22.1846103122476 -2.18461031224758 138 13 22.0702745128170 -9.07027451281704 139 24 21.3499715984669 2.65002840153305 140 15 21.7174055264794 -6.71740552647938 141 14 23.2438706188646 -9.2438706188646 142 22 20.3158662905291 1.68413370947092 143 10 18.1419112607927 -8.14191126079268 144 24 24.2871658173622 -0.28716581736218 145 22 22.0655848506515 -0.0655848506514869 146 24 26.0938258262539 -2.09382582625388 147 19 21.9372414925515 -2.93724149255154 148 20 23.3835644028641 -3.38356440286408 149 13 16.4397959186471 -3.43979591864706 150 20 20.068150458816 -0.0681504588159815 151 22 23.4284855943632 -1.42848559436321 152 24 23.6163819032786 0.383618096721361 153 29 23.790059685397 5.20994031460298 154 12 20.7579915835694 -8.75799158356937 155 20 21.284389716979 -1.28438971697900 156 21 21.2025064249695 -0.202506424969506 157 24 23.8139211996979 0.186078800302076 158 22 22.0253632882414 -0.0253632882413528 159 20 17.8571180746991 2.14288192530085 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 15 0.91095240408567 0.178095191828659 0.0890475959143296 16 0.871980473468123 0.256039053063753 0.128019526531877 17 0.804268671087647 0.391462657824705 0.195731328912353 18 0.833764164723689 0.332471670552622 0.166235835276311 19 0.757143769756683 0.485712460486634 0.242856230243317 20 0.781648336401702 0.436703327196597 0.218351663598299 21 0.72386124347302 0.55227751305396 0.27613875652698 22 0.65216198239857 0.695676035202861 0.347838017601430 23 0.572663309211814 0.854673381576371 0.427336690788186 24 0.586142800261916 0.827714399476167 0.413857199738084 25 0.741411063114472 0.517177873771056 0.258588936885528 26 0.677637473957033 0.644725052085934 0.322362526042967 27 0.608004512256232 0.783990975487535 0.391995487743768 28 0.596970965765145 0.80605806846971 0.403029034234855 29 0.525835847449182 0.948328305101636 0.474164152550818 30 0.452699709821376 0.905399419642753 0.547300290178624 31 0.477398229280002 0.954796458560005 0.522601770719998 32 0.410270669291806 0.820541338583612 0.589729330708194 33 0.662138434369226 0.675723131261548 0.337861565630774 34 0.616638438541656 0.766723122916687 0.383361561458344 35 0.574059994071729 0.851880011856541 0.425940005928271 36 0.511436431145244 0.977127137709512 0.488563568854756 37 0.488347416629952 0.976694833259905 0.511652583370048 38 0.426191382640305 0.85238276528061 0.573808617359695 39 0.385503168221057 0.771006336442113 0.614496831778943 40 0.353624897917595 0.70724979583519 0.646375102082405 41 0.516638596074912 0.966722807850176 0.483361403925088 42 0.457579603115513 0.915159206231027 0.542420396884487 43 0.413692044642815 0.82738408928563 0.586307955357185 44 0.359976523640211 0.719953047280422 0.640023476359789 45 0.315213168464165 0.63042633692833 0.684786831535835 46 0.293093309829983 0.586186619659965 0.706906690170017 47 0.278522131962022 0.557044263924044 0.721477868037978 48 0.267062340341989 0.534124680683979 0.73293765965801 49 0.223858909486799 0.447717818973598 0.776141090513201 50 0.211085705508355 0.42217141101671 0.788914294491645 51 0.179031618360484 0.358063236720967 0.820968381639516 52 0.156219523557641 0.312439047115282 0.84378047644236 53 0.248674089914808 0.497348179829615 0.751325910085192 54 0.2719148542993 0.5438297085986 0.7280851457007 55 0.264838102081069 0.529676204162138 0.735161897918931 56 0.334204332547485 0.668408665094971 0.665795667452515 57 0.320777330582086 0.641554661164172 0.679222669417914 58 0.280632365499212 0.561264730998424 0.719367634500788 59 0.303334479916916 0.606668959833832 0.696665520083084 60 0.32688837407378 0.65377674814756 0.67311162592622 61 0.292748478639950 0.585496957279901 0.70725152136005 62 0.251390077254090 0.502780154508181 0.74860992274591 63 0.288273738234971 0.576547476469943 0.711726261765029 64 0.248001795243687 0.496003590487375 0.751998204756313 65 0.210610363147336 0.421220726294673 0.789389636852664 66 0.201194471230637 0.402388942461274 0.798805528769363 67 0.184919449142737 0.369838898285474 0.815080550857263 68 0.187077140484833 0.374154280969665 0.812922859515167 69 0.165430477685315 0.330860955370630 0.834569522314685 70 0.136373421453062 0.272746842906124 0.863626578546938 71 0.114023617050083 0.228047234100166 0.885976382949917 72 0.0925954919920418 0.185190983984084 0.907404508007958 73 0.0849127350199887 0.169825470039977 0.915087264980011 74 0.0687095079727914 0.137419015945583 0.931290492027209 75 0.0573166526532019 0.114633305306404 0.942683347346798 76 0.0449067678286603 0.0898135356573205 0.95509323217134 77 0.0362812072260449 0.0725624144520897 0.963718792773955 78 0.0293642297445436 0.0587284594890872 0.970635770255456 79 0.0434756103174695 0.086951220634939 0.95652438968253 80 0.0357388996744008 0.0714777993488016 0.9642611003256 81 0.0339319281052541 0.0678638562105083 0.966068071894746 82 0.0277032300289709 0.0554064600579419 0.97229676997103 83 0.0211157411753774 0.0422314823507548 0.978884258824623 84 0.0168432248792482 0.0336864497584963 0.983156775120752 85 0.0139075337093625 0.0278150674187249 0.986092466290638 86 0.0123520199837556 0.0247040399675112 0.987647980016244 87 0.00912119797188984 0.0182423959437797 0.99087880202811 88 0.0123161322709192 0.0246322645418385 0.98768386772908 89 0.0094425409779795 0.0188850819559590 0.99055745902202 90 0.0111885521550941 0.0223771043101882 0.988811447844906 91 0.0117499198244435 0.023499839648887 0.988250080175556 92 0.0105559399645568 0.0211118799291136 0.989444060035443 93 0.0090303621301118 0.0180607242602236 0.990969637869888 94 0.00743158292117126 0.0148631658423425 0.992568417078829 95 0.0137739179974519 0.0275478359949037 0.986226082002548 96 0.0110115904398982 0.0220231808797964 0.988988409560102 97 0.0101804739953407 0.0203609479906815 0.98981952600466 98 0.0075717998884536 0.0151435997769072 0.992428200111546 99 0.0054859870262589 0.0109719740525178 0.994514012973741 100 0.00405902651696245 0.0081180530339249 0.995940973483038 101 0.00290887429078832 0.00581774858157665 0.997091125709212 102 0.00200386428763807 0.00400772857527614 0.997996135712362 103 0.00215403027429583 0.00430806054859166 0.997845969725704 104 0.00162274923757524 0.00324549847515049 0.998377250762425 105 0.00748111752403735 0.0149622350480747 0.992518882475963 106 0.0117329779207750 0.0234659558415501 0.988267022079225 107 0.0111482285196904 0.0222964570393807 0.98885177148031 108 0.0141247968261095 0.028249593652219 0.98587520317389 109 0.0105307564580442 0.0210615129160883 0.989469243541956 110 0.00750977849723533 0.0150195569944707 0.992490221502765 111 0.00530557284380623 0.0106111456876125 0.994694427156194 112 0.0148173158258304 0.0296346316516607 0.98518268417417 113 0.0124479414753572 0.0248958829507145 0.987552058524643 114 0.0157131625792883 0.0314263251585766 0.984286837420712 115 0.0124501788772014 0.0249003577544029 0.987549821122799 116 0.00954947377854742 0.0190989475570948 0.990450526221453 117 0.0390327947946151 0.0780655895892301 0.960967205205385 118 0.0363102590286551 0.0726205180573102 0.963689740971345 119 0.0301527522683604 0.0603055045367208 0.96984724773164 120 0.0555318602089322 0.111063720417864 0.944468139791068 121 0.0524284084597928 0.104856816919586 0.947571591540207 122 0.0644266181930378 0.128853236386076 0.935573381806962 123 0.0588139234319798 0.117627846863960 0.94118607656802 124 0.0562002442168255 0.112400488433651 0.943799755783175 125 0.048543556670299 0.097087113340598 0.951456443329701 126 0.0356817783153973 0.0713635566307947 0.964318221684603 127 0.0254768652883900 0.0509537305767801 0.97452313471161 128 0.0249796448187475 0.0499592896374949 0.975020355181253 129 0.038802893982376 0.077605787964752 0.961197106017624 130 0.0299620045440523 0.0599240090881045 0.970037995455948 131 0.0245692625037149 0.0491385250074299 0.975430737496285 132 0.0192922727653276 0.0385845455306552 0.980707727234672 133 0.0161717547665162 0.0323435095330324 0.983828245233484 134 0.0116761893164848 0.0233523786329696 0.988323810683515 135 0.0171254360605619 0.0342508721211238 0.982874563939438 136 0.0106847014541643 0.0213694029083286 0.989315298545836 137 0.00636112265935149 0.0127222453187030 0.993638877340649 138 0.0214760925568553 0.0429521851137107 0.978523907443145 139 0.0325366646781542 0.0650733293563085 0.967463335321846 140 0.0256465477347433 0.0512930954694866 0.974353452265257 141 0.0897987089241468 0.179597417848294 0.910201291075853 142 0.051863244275028 0.103726488550056 0.948136755724972 143 0.157261793021037 0.314523586042074 0.842738206978963 144 0.100360520063918 0.200721040127835 0.899639479936082 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/23/t1290533915c92zv1j1f1e8rtq/10cwe81290533994.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290533915c92zv1j1f1e8rtq/10cwe81290533994.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290533915c92zv1j1f1e8rtq/15vhf1290533994.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290533915c92zv1j1f1e8rtq/15vhf1290533994.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290533915c92zv1j1f1e8rtq/25vhf1290533994.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290533915c92zv1j1f1e8rtq/25vhf1290533994.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290533915c92zv1j1f1e8rtq/3x4y01290533994.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290533915c92zv1j1f1e8rtq/3x4y01290533994.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290533915c92zv1j1f1e8rtq/4x4y01290533994.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290533915c92zv1j1f1e8rtq/4x4y01290533994.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290533915c92zv1j1f1e8rtq/5x4y01290533994.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290533915c92zv1j1f1e8rtq/5x4y01290533994.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290533915c92zv1j1f1e8rtq/6qvg31290533994.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290533915c92zv1j1f1e8rtq/6qvg31290533994.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290533915c92zv1j1f1e8rtq/71nfo1290533994.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290533915c92zv1j1f1e8rtq/71nfo1290533994.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290533915c92zv1j1f1e8rtq/81nfo1290533994.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290533915c92zv1j1f1e8rtq/81nfo1290533994.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290533915c92zv1j1f1e8rtq/9cwe81290533994.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290533915c92zv1j1f1e8rtq/9cwe81290533994.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') }

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by