*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, 28 Dec 2010 12:27:13 +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/Dec/28/t1293539424e739kc3ne541myy.htm/, Retrieved Tue, 28 Dec 2010 13:30:35 +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/Dec/28/t1293539424e739kc3ne541myy.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 «

9 14 11 12 24 26 9 11 7 8 25 23 9 6 17 8 30 25 9 12 10 8 19 23 9 8 12 9 22 19 9 10 12 7 22 29 10 10 11 4 25 25 10 11 11 11 23 21 10 16 12 7 17 22 10 11 13 7 21 25 10 13 14 12 19 24 10 12 16 10 19 18 10 8 11 10 15 22 10 12 10 8 16 15 10 11 11 8 23 22 10 4 15 4 27 28 10 9 9 9 22 20 10 8 11 8 14 12 10 8 17 7 22 24 10 14 17 11 23 20 10 15 11 9 23 21 10 16 18 11 21 20 10 9 14 13 19 21 10 14 10 8 18 23 10 11 11 8 20 28 10 8 15 9 23 24 10 9 15 6 25 24 10 9 13 9 19 24 10 9 16 9 24 23 10 9 13 6 22 23 10 10 9 6 25 29 10 16 18 16 26 24 10 11 18 5 29 18 10 8 12 7 32 25 10 9 17 9 25 21 10 16 9 6 29 26 10 11 9 6 28 22 10 16 12 5 17 22 10 12 18 12 28 22 10 12 12 7 29 23 10 14 18 10 26 30 10 9 14 9 25 23 10 10 15 8 14 17 10 9 16 5 25 23 10 10 10 8 26 23 10 12 11 8 20 25 10 14 14 10 18 24 10 14 9 6 32 24 10 10 12 8 25 23 10 14 17 7 25 21 10 16 5 4 23 24 10 9 12 8 21 24 10 10 12 8 20 28 10 6 6 4 15 16 10 8 24 20 30 20 10 13 12 8 24 29 10 10 12 8 26 27 10 8 14 6 24 22 10 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 9 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation PersonalStandards[t] = + 18.4826788440990 -0.99436172606256Maand[t] -0.112328105823988DoubtsAboutActions[t] + 0.339703753624901ParentalExpectations[t] + 0.093100809713022ParentalCriticism[t] + 0.437231123532580`Organization `[t] -0.00132568663676311t + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 18.4826788440990 16.782381 1.1013 0.272501 0.13625 Maand -0.99436172606256 1.68538 -0.59 0.556072 0.278036 DoubtsAboutActions -0.112328105823988 0.110148 -1.0198 0.309445 0.154723 ParentalExpectations 0.339703753624901 0.109803 3.0938 0.002353 0.001176 ParentalCriticism 0.093100809713022 0.143074 0.6507 0.51621 0.258105 `Organization ` 0.437231123532580 0.081516 5.3637 0 0 t -0.00132568663676311 0.00711 -0.1865 0.852338 0.426169 Multiple Linear Regression - Regression Statistics Multiple R 0.47458145992812 R-squared 0.225227562107506 Adjusted R-squared 0.194644439559118 F-TEST (value) 7.36443970857313 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 6.29173045330056e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.78436635676899 Sum Squared Residuals 2176.85716578124 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 24.1814643596406 -0.181464359640563 2 25 21.4742113665264 3.52578863347358 3 30 26.3060259923238 3.69397400767622 4 19 22.3783431483036 -3.37834314830361 5 22 21.8499137077953 0.150086292204692 6 22 25.8100414254103 -3.81004142541033 7 25 22.4464233358167 2.55357666418329 8 23 21.2355507172168 1.7644492827832 9 17 21.0771161397655 -4.07711613976549 10 21 23.2888281064713 -2.28882810647131 11 19 23.430822886844 -4.430822886844 12 19 21.4116444526595 -2.4116444526595 13 15 21.9100369153245 -6.91003691532451 14 16 17.8728755676128 -1.87287556761278 15 23 21.3841996051530 1.61580039484703 16 27 25.7789691761271 1.22103082387288 17 22 20.1454354989255 1.85456450107452 18 14 17.3448956273888 -3.34489562738884 19 22 24.5354651351794 -2.53546513517943 20 23 22.4836495583205 0.5163504416795 21 23 20.5828027482169 2.41719725178312 22 21 22.5960457270239 -1.59604572702390 23 19 22.6456345096141 -3.64563450961408 24 18 21.1328114778578 -3.13281147785782 25 20 23.9943294799808 -3.99432947998082 26 23 24.0329794408983 -1.03297944089833 27 25 23.6400232192985 1.35997678070149 28 19 23.238592454551 -4.23859245455101 29 24 23.8191469052564 0.180853094743629 30 22 22.5194075286058 -0.519407528605839 31 25 23.6703254628410 1.32967453715903 32 26 24.7972174033517 1.2027825966483 33 29 21.7100365977962 7.28996340220385 34 32 23.2542921910361 8.74570780896394 35 25 23.2764342919955 1.72356570800447 36 29 21.6780350241155 7.32196497588452 37 28 20.4894253724683 7.51057462753166 38 17 20.8524696078733 -3.85246960787331 39 28 23.9903845342731 4.00961546572694 40 29 21.9225634008544 7.07743659914564 41 26 27.0747243181862 -1.07472431818616 42 25 23.1225054717287 1.87749452827135 43 14 20.6320678819843 -6.6320678819843 44 25 23.4268583668528 1.57314163314716 45 26 21.5542844817817 4.44571551821825 46 20 22.5424685841871 -2.54246858418707 47 18 23.0845684426705 -5.08456844267049 48 32 21.0123207490571 10.9876792509429 49 25 22.2283892424845 2.77161075751550 50 25 22.5087068438981 2.4912931561019 51 23 19.2386708435732 3.76132915642678 52 21 22.7739714119308 -1.77397141193077 53 20 24.4092421136003 -4.40924211360034 54 15 17.1998296072671 -2.19982960726708 55 30 26.3270527237692 3.67294727623077 56 24 24.5055118597507 -0.505511859750671 57 26 23.9667082435207 2.03329175647929 58 24 22.4970890386928 1.50291096130722 59 22 22.6673503042751 -0.667350304275138 60 14 18.931252049257 -4.931252049257 61 24 23.2923721654455 0.707627834554491 62 24 22.801888573938 1.19811142606199 63 24 24.7576357331215 -0.757635733121516 64 24 21.0430365442071 2.95696345579292 65 19 21.5881720735323 -2.58817207353232 66 31 23.8557286385498 7.14427136145017 67 22 22.5267104645784 -0.526710464578415 68 27 21.7807708087697 5.21922919123028 69 19 21.8737443126666 -2.87374431266658 70 25 22.6229802107287 2.37701978927126 71 20 21.8935484148781 -1.89354841487808 72 21 21.1980144850752 -0.198014485075207 73 27 24.7328063102116 2.26719368978837 74 23 23.9511314983339 -0.951131498333947 75 25 24.0136213842665 0.986378615733538 76 20 21.3181334562267 -1.31813345622673 77 21 22.7699219746232 -1.76992197462319 78 22 23.1750275588658 -1.17502755886579 79 23 23.9079416656793 -0.907941665679305 80 25 21.7912358615871 3.20876413841287 81 25 24.0114847139934 0.988515286006611 82 17 23.6059436237401 -6.6059436237401 83 19 21.8611323152789 -2.86113231527889 84 25 24.388894179304 0.611105820696009 85 19 21.8421591507567 -2.84215915075672 86 20 23.7699560594194 -3.76995605941943 87 26 21.9962380910561 4.00376190894389 88 23 23.3316505206756 -0.33165052067556 89 27 23.4308943146111 3.56910568538885 90 17 21.2064730335990 -4.20647303359902 91 17 22.8400366112269 -5.84003661122687 92 19 21.6252397358306 -2.62523973583056 93 17 20.7593172346292 -3.75931723462916 94 22 21.6899496146811 0.310050385318928 95 21 23.8751581229488 -2.87515812294885 96 32 26.9075123626306 5.09248763736943 97 21 23.1377582130039 -2.13775821300392 98 21 23.3626097933475 -2.36260979334747 99 18 21.3068699596921 -3.30686995969214 100 18 20.7515584835042 -2.75155848350416 101 23 22.4903041706084 0.509695829391601 102 19 21.4344483017168 -2.43444830171681 103 20 21.7726402999956 -1.77264029999556 104 21 23.1482144458787 -2.14821444587867 105 20 24.1747229745264 -4.17472297452643 106 17 17.5866575098684 -0.586657509868434 107 18 18.9802605710419 -0.980260571041904 108 19 19.2905582215298 -0.290558221529762 109 22 22.1234870639314 -0.123487063931363 110 15 20.6375460678548 -5.63754606785479 111 14 20.5288275788098 -6.52882757880981 112 18 24.5379765729007 -6.53797657290067 113 24 20.3166993070463 3.68330069295375 114 35 22.1733421382598 12.8266578617402 115 29 21.5106937623935 7.48930623760645 116 21 22.8618568974878 -1.86185689748776 117 25 20.3509936308118 4.64900636918816 118 20 19.0703513842928 0.929648615707217 119 22 23.2357219487354 -1.23572194873543 120 13 15.9184078967728 -2.91840789677283 121 26 19.5124585683044 6.48754143169561 122 17 18.8655673377357 -1.86556733773571 123 25 20.8907614503266 4.10923854967338 124 20 21.0036570622649 -1.00365706226495 125 19 20.4269024227032 -1.42690242270315 126 21 23.7125020337543 -2.71250203375425 127 22 21.7350622738956 0.264937726104360 128 24 22.9833215093291 1.01667849067094 129 21 24.206535999104 -3.20653599910401 130 26 22.206454695051 3.79354530494901 131 24 20.440205397547 3.559794602453 132 16 21.356223110392 -5.35622311039199 133 23 22.9220468586542 0.077953141345844 134 18 20.9488475902808 -2.94884759028082 135 16 22.1143801917229 -6.11438019172287 136 26 24.2426707125068 1.75732928749319 137 19 20.2768495109536 -1.27684951095359 138 21 17.9462402481767 3.05375975182328 139 21 22.8640655900694 -1.86406559006939 140 22 18.7384225013716 3.26157749862845 141 23 16.7960230856514 6.20397691434857 142 29 22.6485259303857 6.35147406961428 143 21 21.1641124294643 -0.164112429464339 144 21 20.0002184091411 0.999781590858933 145 23 23.3047290816143 -0.304729081614261 146 27 21.3371547542562 5.66284524574382 147 25 22.2534951416129 2.74650485838710 148 21 20.4649764373333 0.535023562666729 149 10 17.9289382590194 -7.9289382590194 150 20 21.8730668598975 -1.87306685989750 151 26 21.7463194555622 4.25368054443784 152 24 23.2139210219861 0.786078978013853 153 29 27.5658094405437 1.43419055945629 154 19 17.8851837804137 1.11481621958627 155 24 23.8469790601302 0.153020939869807 156 19 21.4779087653085 -2.47790876530853 157 24 21.7334300323258 2.26656996767420 158 22 22.5149868383735 -0.514986838373517 159 17 23.2196344599774 -6.21963445997736 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.0430935223234363 0.0861870446468725 0.956906477676564 11 0.0124772240179591 0.0249544480359183 0.98752277598204 12 0.0109817055028246 0.0219634110056491 0.989018294497175 13 0.0211517539599432 0.0423035079198863 0.978848246040057 14 0.0377136870224718 0.0754273740449436 0.962286312977528 15 0.335254793331306 0.670509586662613 0.664745206668694 16 0.280724452384190 0.561448904768379 0.71927554761581 17 0.300084719995961 0.600169439991921 0.699915280004039 18 0.259797132465425 0.519594264930851 0.740202867534575 19 0.199952105074175 0.399904210148351 0.800047894925825 20 0.29916768587643 0.59833537175286 0.70083231412357 21 0.322505059181782 0.645010118363564 0.677494940818218 22 0.255083169161260 0.510166338322519 0.74491683083874 23 0.214657362431787 0.429314724863575 0.785342637568213 24 0.182560358473396 0.365120716946792 0.817439641526604 25 0.154969275696946 0.309938551393892 0.845030724303054 26 0.118413533291386 0.236827066582772 0.881586466708614 27 0.0981010991063098 0.196202198212620 0.90189890089369 28 0.0861877153645626 0.172375430729125 0.913812284635437 29 0.0682023783710171 0.136404756742034 0.931797621628983 30 0.0483991062143293 0.0967982124286587 0.95160089378567 31 0.0404270717752061 0.0808541435504121 0.959572928224794 32 0.0442636353435930 0.0885272706871861 0.955736364656407 33 0.0737272961585956 0.147454592317191 0.926272703841404 34 0.205586368982547 0.411172737965093 0.794413631017453 35 0.164913789078687 0.329827578157373 0.835086210921313 36 0.188701768828682 0.377403537657365 0.811298231171318 37 0.204134901326610 0.408269802653221 0.79586509867339 38 0.388023300039762 0.776046600079523 0.611976699960239 39 0.361161103542787 0.722322207085574 0.638838896457213 40 0.383932209195462 0.767864418390923 0.616067790804538 41 0.362222538201537 0.724445076403073 0.637777461798463 42 0.320197505498288 0.640395010996575 0.679802494501712 43 0.588300284736411 0.823399430527178 0.411699715263589 44 0.546846943430057 0.906306113139886 0.453153056569943 45 0.516192872008777 0.967614255982445 0.483807127991223 46 0.54834869505589 0.90330260988822 0.45165130494411 47 0.632980903541815 0.73403819291637 0.367019096458185 48 0.817944929621388 0.364110140757225 0.182055070378612 49 0.789357988445915 0.421284023108171 0.210642011554085 50 0.760973850275567 0.478052299448866 0.239026149724433 51 0.747278097932767 0.505443804134466 0.252721902067233 52 0.747210323538218 0.505579352923565 0.252789676461782 53 0.79817430587994 0.40365138824012 0.20182569412006 54 0.805986499024039 0.388027001951922 0.194013500975961 55 0.821242800695362 0.357514398609275 0.178757199304638 56 0.798142432701529 0.403715134596943 0.201857567298471 57 0.767461981287649 0.465076037424702 0.232538018712351 58 0.735865387147998 0.528269225704004 0.264134612852002 59 0.708354829846995 0.58329034030601 0.291645170153005 60 0.76366936196166 0.47266127607668 0.23633063803834 61 0.725832976198212 0.548334047603576 0.274167023801788 62 0.68986834893266 0.62026330213468 0.31013165106734 63 0.659131878288876 0.681736243422247 0.340868121711124 64 0.632754702972251 0.734490594055498 0.367245297027749 65 0.624708305693409 0.750583388613183 0.375291694306591 66 0.713066755819257 0.573866488361486 0.286933244180743 67 0.676896767623104 0.646206464753792 0.323103232376896 68 0.706899559160412 0.586200881679175 0.293100440839588 69 0.705999390040326 0.588001219919347 0.294000609959674 70 0.681681385187375 0.636637229625251 0.318318614812625 71 0.656996880470003 0.686006239059993 0.343003119529997 72 0.61722096870831 0.76555806258338 0.38277903129169 73 0.591541026760196 0.816917946479607 0.408458973239804 74 0.552604861480986 0.894790277038028 0.447395138519014 75 0.519577332900652 0.960845334198697 0.480422667099348 76 0.481262383491989 0.962524766983979 0.518737616508011 77 0.453560592988531 0.907121185977062 0.546439407011469 78 0.414066049958702 0.828132099917404 0.585933950041298 79 0.377175107447954 0.754350214895907 0.622824892552046 80 0.377389845751006 0.754779691502012 0.622610154248994 81 0.343191738055341 0.686383476110683 0.656808261944659 82 0.425091053589354 0.850182107178708 0.574908946410646 83 0.399609044121403 0.799218088242806 0.600390955878597 84 0.359763605660405 0.71952721132081 0.640236394339595 85 0.339476483645663 0.678952967291327 0.660523516354337 86 0.328821632769537 0.657643265539074 0.671178367230463 87 0.354442245487837 0.708884490975674 0.645557754512163 88 0.314999199446982 0.629998398893964 0.685000800553018 89 0.325180808491788 0.650361616983577 0.674819191508212 90 0.319186619900998 0.638373239801996 0.680813380099002 91 0.350240798242356 0.700481596484713 0.649759201757644 92 0.319134905763795 0.63826981152759 0.680865094236205 93 0.302795141898261 0.605590283796523 0.697204858101739 94 0.266631352042791 0.533262704085582 0.733368647957209 95 0.242026530575969 0.484053061151937 0.757973469424031 96 0.300929943036907 0.601859886073814 0.699070056963093 97 0.264951338889137 0.529902677778274 0.735048661110863 98 0.231293895660083 0.462587791320166 0.768706104339917 99 0.209687662008849 0.419375324017698 0.790312337991151 100 0.184366627531669 0.368733255063338 0.815633372468331 101 0.157024870074877 0.314049740149753 0.842975129925123 102 0.134111528688235 0.268223057376471 0.865888471311765 103 0.110632588224501 0.221265176449003 0.889367411775499 104 0.0923045057133062 0.184609011426612 0.907695494286694 105 0.0916306275062364 0.183261255012473 0.908369372493764 106 0.0734373075151926 0.146874615030385 0.926562692484807 107 0.0592595763812928 0.118519152762586 0.940740423618707 108 0.0476107842206825 0.095221568441365 0.952389215779317 109 0.0369139061270905 0.0738278122541811 0.96308609387291 110 0.0485602448957144 0.0971204897914289 0.951439755104286 111 0.0820873469878885 0.164174693975777 0.917912653012111 112 0.154336741837009 0.308673483674017 0.845663258162991 113 0.148995476922521 0.297990953845042 0.85100452307748 114 0.554297711472214 0.891404577055572 0.445702288527786 115 0.692840215968647 0.614319568062706 0.307159784031353 116 0.653054444378564 0.693891111242871 0.346945555621436 117 0.705946380661241 0.588107238677518 0.294053619338759 118 0.659001510385771 0.681996979228458 0.340998489614229 119 0.614692351720057 0.770615296559885 0.385307648279943 120 0.615033884269733 0.769932231460535 0.384966115730267 121 0.69511703949931 0.60976592100138 0.30488296050069 122 0.661617907659615 0.676764184680771 0.338382092340385 123 0.660021383097385 0.67995723380523 0.339978616902615 124 0.603808376218762 0.792383247562476 0.396191623781238 125 0.628292935561315 0.74341412887737 0.371707064438685 126 0.60173829702899 0.79652340594202 0.39826170297101 127 0.54080059932483 0.91839880135034 0.45919940067517 128 0.481003428751953 0.962006857503905 0.518996571248047 129 0.452971332431305 0.90594266486261 0.547028667568695 130 0.414936843811246 0.829873687622491 0.585063156188754 131 0.407254770565382 0.814509541130764 0.592745229434618 132 0.449179404637095 0.89835880927419 0.550820595362905 133 0.381801602849775 0.76360320569955 0.618198397150225 134 0.370689770189077 0.741379540378154 0.629310229810923 135 0.595533640302884 0.808932719394233 0.404466359697116 136 0.529721570252418 0.940556859495165 0.470278429747582 137 0.612441904815406 0.775116190369189 0.387558095184594 138 0.540197549400927 0.919604901198146 0.459802450599073 139 0.631932711169707 0.736134577660586 0.368067288830293 140 0.555819565349045 0.88836086930191 0.444180434650955 141 0.597137935052324 0.805724129895352 0.402862064947676 142 0.594142258893877 0.811715482212246 0.405857741106123 143 0.6099652774308 0.7800694451384 0.3900347225692 144 0.561858686393421 0.876282627213159 0.438141313606579 145 0.458765177782758 0.917530355565515 0.541234822217242 146 0.407107410044724 0.814214820089447 0.592892589955276 147 0.38977486923475 0.7795497384695 0.61022513076525 148 0.266748948964248 0.533497897928497 0.733251051035752 149 0.444502658067576 0.889005316135152 0.555497341932424 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 3 0.0214285714285714 OK 10% type I error level 11 0.0785714285714286 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293539424e739kc3ne541myy/109sev1293539222.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293539424e739kc3ne541myy/109sev1293539222.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293539424e739kc3ne541myy/13rh11293539222.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293539424e739kc3ne541myy/13rh11293539222.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293539424e739kc3ne541myy/23rh11293539222.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293539424e739kc3ne541myy/23rh11293539222.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293539424e739kc3ne541myy/3d0z41293539222.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293539424e739kc3ne541myy/3d0z41293539222.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293539424e739kc3ne541myy/4d0z41293539222.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293539424e739kc3ne541myy/4d0z41293539222.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293539424e739kc3ne541myy/5d0z41293539222.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293539424e739kc3ne541myy/5d0z41293539222.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293539424e739kc3ne541myy/6oayp1293539222.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293539424e739kc3ne541myy/6oayp1293539222.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293539424e739kc3ne541myy/7oayp1293539222.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293539424e739kc3ne541myy/7oayp1293539222.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293539424e739kc3ne541myy/8hjxs1293539222.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293539424e739kc3ne541myy/8hjxs1293539222.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293539424e739kc3ne541myy/9hjxs1293539222.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293539424e739kc3ne541myy/9hjxs1293539222.ps (open in new window)

Parameters (Session):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

Copyright

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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