WS7 - Multiple regression model (incl. month)

*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 20:19:24 +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/t12905436462ra742ajwpssq04.htm/, Retrieved Tue, 23 Nov 2010 21:20:57 +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/t12905436462ra742ajwpssq04.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 «

13 13 14 13 3 2 9 12 12 8 13 5 1 9 15 10 12 16 6 0 9 12 9 7 12 6 3 9 10 10 10 11 5 3 9 12 12 7 12 3 1 9 15 13 16 18 8 3 9 9 12 11 11 4 1 9 12 12 14 14 4 4 9 11 6 6 9 4 0 9 11 5 16 14 6 3 9 11 12 11 12 6 2 9 15 11 16 11 5 4 9 7 14 12 12 4 3 9 11 14 7 13 6 1 9 11 12 13 11 4 1 9 10 12 11 12 6 2 9 14 11 15 16 6 3 9 10 11 7 9 4 1 9 6 7 9 11 4 1 9 11 9 7 13 2 2 9 15 11 14 15 7 3 9 11 11 15 10 5 4 9 12 12 7 11 4 2 9 14 12 15 13 6 1 9 15 11 17 16 6 2 9 9 11 15 15 7 2 9 13 8 14 14 5 4 9 13 9 14 14 6 2 9 16 12 8 14 4 3 9 13 10 8 8 4 3 9 12 10 14 13 7 3 9 14 12 14 15 7 4 9 11 8 8 13 4 2 9 9 12 11 11 4 2 9 16 11 16 15 6 4 9 12 12 10 15 6 3 9 10 7 8 9 5 4 9 13 11 14 13 6 2 9 16 11 16 16 7 5 9 14 12 13 13 6 3 9 15 9 5 11 3 1 9 5 15 8 12 3 1 9 8 11 10 12 4 1 9 11 11 8 12 6 2 9 16 11 13 14 7 3 9 17 11 15 14 5 9 9 9 15 6 8 4 0 9 9 11 12 13 5 0 9 13 12 16 16 6 2 9 10 12 5 13 6 2 9 6 9 15 11 6 3 10 12 12 12 14 5 1 10 8 12 8 13 4 2 10 14 13 13 13 5 0 10 12 11 14 13 5 5 10 1 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 Popularity[t] = + 2.39535698605526 + 0.108109507398842FindingFriends[t] + 0.211437082159555KnowingPeople[t] + 0.366476681384955Liked[t] + 0.601540871476521Celebrity[t] + 0.213410758679599Sum_friends[t] -0.255965716461004Month[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) 2.39535698605526 3.624285 0.6609 0.509685 0.254843 FindingFriends 0.108109507398842 0.09571 1.1296 0.260478 0.130239 KnowingPeople 0.211437082159555 0.063732 3.3176 0.001141 0.000571 Liked 0.366476681384955 0.096894 3.7822 0.000224 0.000112 Celebrity 0.601540871476521 0.155782 3.8614 0.000168 8.4e-05 Sum_friends 0.213410758679599 0.120235 1.7749 0.077949 0.038974 Month -0.255965716461004 0.361236 -0.7086 0.47969 0.239845 Multiple Linear Regression - Regression Statistics Multiple R 0.71491764765422 R-squared 0.511107242927444 Adjusted R-squared 0.491420286266804 F-TEST (value) 25.9617193118173 F-TEST (DF numerator) 6 F-TEST (DF denominator) 149 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.09424916265587 Sum Squared Residuals 653.49605373744 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 11.4528492741181 1.54715072588193 2 12 11.0657882580354 0.934211741964616 3 15 13.1828777288277 1.81712227117231 4 12 11.1919083611301 0.808091638869943 5 10 10.9663115621461 -0.966311562146098 6 12 9.28479275153784 2.71520724846216 7 15 16.9292219614242 -1.92922196142420 8 9 10.3656052702676 -1.36560527026762 9 12 12.7395788369399 -0.739578836939947 10 11 7.71339869362729 3.28660130637271 11 11 13.3953574337406 -2.39535743374061 12 11 12.1485744532852 -1.14857445328522 13 15 12.5564543211819 2.44354567881813 14 7 11.5865595659690 -4.58655956596901 15 11 11.6721110621500 -0.67211106215004 16 11 10.7884794345867 0.211520565413267 17 10 12.1485744532852 -2.14857445328522 18 14 14.565530758744 -0.565530758744012 19 10 8.67879407146065 1.32120592853935 20 6 9.4021835689543 -3.40218356895430 21 11 8.93881079792934 2.06118920207066 22 15 14.5891578666760 0.410842133323976 23 11 11.9785405576374 -0.978540557637362 24 12 9.733267700309 2.26673229969100 25 14 13.1473887046288 0.852611295371206 26 15 14.7749941643835 0.225005835616476 27 9 14.5871841901560 -5.58718419015598 28 13 12.9086816788211 0.0913183211789004 29 13 13.1915105403373 -0.191510540337265 30 16 11.2575455853030 4.74245441469698 31 13 8.8424664821956 4.15753351780439 32 12 13.7480949965073 -1.74809499650727 33 14 14.9106781327545 -0.910678132754465 34 11 10.2452201156431 0.754779884356902 35 9 10.5790160289472 -1.57901602894722 36 16 14.6239019181982 1.37609808180179 37 12 13.2499781739601 -1.24997817396013 38 10 9.69956627154015 0.300433728459845 39 13 13.04125287375 -0.0412528737499953 40 16 15.8053302297393 0.194669770260715 41 14 13.1513360576689 0.848663942331119 42 15 8.17111338363724 6.82888661636275 43 5 9.82055835589392 -4.82055835589392 44 8 10.4125353620942 -2.41253536209418 45 11 11.4061536994077 -0.406153699407712 46 16 14.0112441031315 1.98875589686849 47 17 14.5115010765752 2.48849892342483 48 9 8.31990757883191 0.680092421168087 49 9 11.5900163205952 -2.59001632059517 50 13 14.6716665896228 -1.67166658962281 51 10 11.2464286417128 -1.24642864171284 52 6 12.2609626205605 -6.26096262056055 53 12 12.0220475515976 -0.0220475515975586 54 8 10.4216924287775 -2.42169242877746 55 14 11.7617067010914 2.2382932989086 56 12 12.8239785618513 -0.823978561851266 57 11 10.5766355538342 0.423364446165799 58 16 14.5181938683245 1.48180613167552 59 8 10.4797394641942 -2.47973946419419 60 15 14.5059378278123 0.4940621721877 61 7 9.02685335855679 -2.02685335855679 62 16 14.1095690277511 1.89043097224890 63 14 13.0463661132245 0.953633886775472 64 16 13.3048297613793 2.6951702386207 65 9 10.3363754497126 -1.33637544971259 66 14 12.0804187110518 1.91958128894824 67 11 13.1651785828216 -2.16517858282163 68 13 10.2319087780299 2.76809122197012 69 15 13.1087810998875 1.89121890011252 70 5 5.65726792090425 -0.657267920904248 71 15 12.8239785618513 2.17602143814873 72 13 12.5072402284110 0.492759771589045 73 11 12.3427332380780 -1.34273323807796 74 11 14.1374678631938 -3.13746786319380 75 12 12.6811250029302 -0.681125002930237 76 12 13.318244505527 -1.31824450552699 77 12 12.2468993779048 -0.246899377904798 78 12 11.8613914401360 0.138608559864013 79 14 10.7881691101624 3.21183088983758 80 6 7.8493724000558 -1.84937240005580 81 7 9.63036790655335 -2.63036790655335 82 14 12.3070581327891 1.69294186721093 83 14 14.1001016366435 -0.100101636643497 84 10 11.07484885055 -1.07484885055001 85 13 9.03277438811692 3.96722561188308 86 12 12.2121553263826 -0.212155326382611 87 9 9.21415287722376 -0.214152877223756 88 12 11.8499503725083 0.150049627491654 89 16 14.7213222630119 1.27867773698806 90 10 10.3719540808328 -0.371954080832819 91 14 13.0389688728056 0.961031127194365 92 10 13.5202141965789 -3.52021419657894 93 16 15.4440632619975 0.555936738002475 94 15 13.3134625728889 1.68653742711114 95 12 11.3963691166284 0.60363088337155 96 10 9.26191754864836 0.738082451351644 97 8 10.0250675474185 -2.02506754741848 98 8 8.61739393838537 -0.617393938385365 99 11 12.5923711263859 -1.59237112638585 100 13 12.4724961768888 0.527503823111233 101 16 15.5473908367582 0.452609163241762 102 16 14.8661494984530 1.13385050154698 103 14 15.3628995742094 -1.36289957420936 104 11 8.9696212960246 2.03037870397541 105 4 7.05721329823365 -3.05721329823365 106 14 14.6716803892360 -0.67168038923596 107 9 10.4516545476615 -1.45165454766152 108 14 15.1461701038511 -1.14617010385110 109 8 10.1798726295277 -2.17987262952772 110 8 10.6121245780331 -2.61212457803312 111 11 11.8058285367999 -0.805828536799874 112 12 13.0605258300489 -1.06052583004894 113 11 10.9865155722118 0.0134844277882477 114 14 13.2015021866186 0.798497813381411 115 15 14.3849041746797 0.615095825320293 116 16 13.3651745973535 2.63482540264646 117 16 12.8330518287136 3.16694817128641 118 11 12.7242042158854 -1.72420421588537 119 14 14.1115427042711 -0.111542704271138 120 14 10.7928545686319 3.20714543136811 121 12 11.4808515160953 0.51914848390472 122 14 12.4535545274262 1.54644547257378 123 8 10.7987755981920 -2.79877559819202 124 13 14.0062414529904 -1.00624145299038 125 16 13.8981319455915 2.10186805440846 126 12 10.5400142999606 1.45998570003937 127 16 15.4093192104753 0.590680789524662 128 12 12.6780122294882 -0.678012229488191 129 11 11.3801461163627 -0.380146116362679 130 4 5.8412685850392 -1.84126858503920 131 16 16.0495514865141 -0.0495514865141337 132 15 12.5758237516495 2.42417624835052 133 10 11.3077117142527 -1.30771171425273 134 13 13.9537913230963 -0.953791323096314 135 15 13.0484362639132 1.95156373608677 136 12 10.4197187522574 1.58028124774258 137 14 13.5766116795131 0.423388320486901 138 7 10.2974495280342 -3.29744952803416 139 19 13.8377871096173 5.1622128903827 140 12 12.8689349771578 -0.86893497715778 141 12 11.7916688199755 0.20833118002454 142 13 13.2598733460728 -0.259873346072788 143 15 12.3629234485305 2.63707655146954 144 8 8.703243084643 -0.703243084643001 145 12 10.8445665930966 1.15543340690343 146 10 10.6737245918115 -0.673724591811528 147 8 11.1762992229593 -3.17629922295934 148 10 14.5889371491730 -4.58893714917302 149 15 13.7880487616727 1.21195123832735 150 16 13.9797360887325 2.02026391126752 151 13 13.177364623126 -0.177364623126001 152 16 15.0192154211584 0.980784578841628 153 9 9.73172180479402 -0.731721804794023 154 14 12.9872568483409 1.01274315165905 155 14 13.0590427519428 0.940957248057168 156 12 10.1112891062892 1.88871089371080 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.127891435208484 0.255782870416968 0.872108564791516 11 0.148786160625616 0.297572321251233 0.851213839374384 12 0.0780975221103143 0.156195044220629 0.921902477889686 13 0.565769576087115 0.86846084782577 0.434230423912885 14 0.834551472369617 0.330897055260766 0.165448527630383 15 0.765397977192753 0.469204045614493 0.234602022807247 16 0.682640577516971 0.634718844966057 0.317359422483029 17 0.627862766508355 0.744274466983291 0.372137233491645 18 0.541147043920611 0.917705912158779 0.458852956079389 19 0.459312550753235 0.91862510150647 0.540687449246765 20 0.74280399893436 0.514392002131281 0.257196001065641 21 0.684296996404343 0.631406007191314 0.315703003595657 22 0.652496879700231 0.695006240599538 0.347503120299769 23 0.584636569680495 0.83072686063901 0.415363430319505 24 0.564201395716613 0.871597208566775 0.435798604283387 25 0.523000649204438 0.953998701591124 0.476999350795562 26 0.459701943012236 0.919403886024472 0.540298056987764 27 0.71719242453584 0.565615150928319 0.282807575464160 28 0.663069401328821 0.673861197342357 0.336930598671179 29 0.604044439687815 0.79191112062437 0.395955560312185 30 0.735450615906114 0.529098768187771 0.264549384093886 31 0.823372015790588 0.353255968418824 0.176627984209412 32 0.788885237884124 0.422229524231752 0.211114762115876 33 0.745928830600179 0.508142338799642 0.254071169399821 34 0.704230684387494 0.591538631225012 0.295769315612506 35 0.694758234870179 0.610483530259642 0.305241765129821 36 0.693676570662987 0.612646858674026 0.306323429337013 37 0.66490032201647 0.670199355967061 0.335099677983531 38 0.614375406028553 0.771249187942894 0.385624593971447 39 0.567455347111986 0.865089305776028 0.432544652888014 40 0.52658727219048 0.94682545561904 0.47341272780952 41 0.491865861723546 0.983731723447092 0.508134138276454 42 0.813225177999172 0.373549644001657 0.186774822000828 43 0.950230645269395 0.0995387094612093 0.0497693547306046 44 0.955255314656835 0.0894893706863304 0.0447446853431652 45 0.942146721738118 0.115706556523764 0.057853278261882 46 0.948658196373985 0.102683607252030 0.0513418036260152 47 0.95268483685115 0.0946303262976987 0.0473151631488494 48 0.946734666625133 0.106530666749734 0.0532653333748668 49 0.93907560281203 0.12184879437594 0.06092439718797 50 0.923835711546406 0.152328576907188 0.076164288453594 51 0.917045576373746 0.165908847252507 0.0829544236262537 52 0.960944094385291 0.078111811229418 0.039055905614709 53 0.97507692614946 0.0498461477010793 0.0249230738505397 54 0.971837159425216 0.0563256811495677 0.0281628405747839 55 0.988982381555178 0.0220352368896448 0.0110176184448224 56 0.985210960943165 0.02957807811367 0.014789039056835 57 0.981010684421946 0.0379786311561071 0.0189893155780536 58 0.980633391742666 0.0387332165146681 0.0193666082573340 59 0.985253208163603 0.0294935836727950 0.0147467918363975 60 0.985555438472469 0.0288891230550616 0.0144445615275308 61 0.984538482096426 0.0309230358071472 0.0154615179035736 62 0.986442420533483 0.0271151589330342 0.0135575794665171 63 0.98509894013097 0.0298021197380623 0.0149010598690312 64 0.988687193031725 0.0226256139365493 0.0113128069682746 65 0.986794778167644 0.0264104436647128 0.0132052218323564 66 0.986499967988942 0.0270000640221167 0.0135000320110583 67 0.986634075104435 0.0267318497911292 0.0133659248955646 68 0.989704745532994 0.0205905089340127 0.0102952544670063 69 0.989202194390346 0.0215956112193081 0.0107978056096541 70 0.985867530935757 0.0282649381284853 0.0141324690642427 71 0.98628220282973 0.0274355943405408 0.0137177971702704 72 0.981769266103638 0.0364614677927242 0.0182307338963621 73 0.9785160596516 0.0429678806967993 0.0214839403483997 74 0.985161944024766 0.0296761119504678 0.0148380559752339 75 0.98052919607703 0.0389416078459408 0.0194708039229704 76 0.977311033104489 0.0453779337910227 0.0226889668955113 77 0.970457932201994 0.059084135596012 0.029542067798006 78 0.961502157950696 0.076995684098608 0.038497842049304 79 0.975122841854285 0.0497543162914295 0.0248771581457147 80 0.973372974593985 0.0532540508120308 0.0266270254060154 81 0.976560291652205 0.0468794166955905 0.0234397083477953 82 0.97604724143845 0.0479055171231011 0.0239527585615505 83 0.968388046065408 0.0632239078691843 0.0316119539345921 84 0.961192097383956 0.0776158052320889 0.0388079026160445 85 0.9871212122698 0.0257575754604011 0.0128787877302006 86 0.982915998782178 0.0341680024356442 0.0170840012178221 87 0.977252992712076 0.0454940145758482 0.0227470072879241 88 0.970550090305963 0.0588998193880742 0.0294499096940371 89 0.964825571767684 0.070348856464632 0.035174428232316 90 0.954833385232667 0.0903332295346658 0.0451666147673329 91 0.946382285350417 0.107235429299166 0.053617714649583 92 0.968459416169427 0.0630811676611466 0.0315405838305733 93 0.959598822973557 0.0808023540528861 0.0404011770264430 94 0.954719984594765 0.0905600308104694 0.0452800154052347 95 0.943535878580419 0.112928242839163 0.0564641214195815 96 0.930370551534034 0.139258896931932 0.0696294484659659 97 0.923459803751226 0.153080392497548 0.0765401962487741 98 0.904881903310375 0.190236193379250 0.0951180966896251 99 0.898100579583368 0.203798840833264 0.101899420416632 100 0.87619510532684 0.24760978934632 0.12380489467316 101 0.850179425098482 0.299641149803037 0.149820574901518 102 0.82590686861214 0.348186262775719 0.174093131387860 103 0.838554170863019 0.322891658273963 0.161445829136981 104 0.882816730637804 0.234366538724391 0.117183269362196 105 0.882992594097098 0.234014811805804 0.117007405902902 106 0.857655586636667 0.284688826726666 0.142344413363333 107 0.833677975400939 0.332644049198122 0.166322024599061 108 0.82756098697927 0.344878026041461 0.172439013020730 109 0.823048918768799 0.353902162462402 0.176951081231201 110 0.84870981002075 0.302580379958498 0.151290189979249 111 0.834726792630815 0.33054641473837 0.165273207369185 112 0.879707548657549 0.240584902684902 0.120292451342451 113 0.849731550748274 0.300536898503451 0.150268449251726 114 0.818803497057266 0.362393005885468 0.181196502942734 115 0.780187265662848 0.439625468674304 0.219812734337152 116 0.78055290142237 0.438894197155258 0.219447098577629 117 0.796134345179927 0.407731309640146 0.203865654820073 118 0.783285729316027 0.433428541367946 0.216714270683973 119 0.737280914472618 0.525438171054764 0.262719085527382 120 0.80488337677909 0.39023324644182 0.19511662322091 121 0.771422196067994 0.457155607864013 0.228577803932006 122 0.741815375785039 0.516369248429921 0.258184624214961 123 0.737583153508597 0.524833692982805 0.262416846491403 124 0.691400887372585 0.61719822525483 0.308599112627415 125 0.687011648050497 0.625976703899007 0.312988351949503 126 0.668733614861058 0.662532770277885 0.331266385138942 127 0.609345952397273 0.781308095205454 0.390654047602727 128 0.575283686154436 0.849432627691128 0.424716313845564 129 0.590936279322617 0.818127441354767 0.409063720677383 130 0.581619857332299 0.836760285335402 0.418380142667701 131 0.512533893330391 0.974932213339218 0.487466106669609 132 0.498465836191323 0.996931672382646 0.501534163808677 133 0.463611742282113 0.927223484564226 0.536388257717887 134 0.394957592629450 0.789915185258899 0.605042407370550 135 0.368037545036676 0.736075090073353 0.631962454963324 136 0.360543483951051 0.721086967902103 0.639456516048948 137 0.290790798057117 0.581581596114235 0.709209201942883 138 0.363706140509017 0.727412281018034 0.636293859490983 139 0.718987445670285 0.56202510865943 0.281012554329715 140 0.739664531501608 0.520670936996784 0.260335468498392 141 0.684094092137304 0.631811815725393 0.315905907862697 142 0.584421476124033 0.831157047751933 0.415578523875967 143 0.530379105427788 0.939241789144423 0.469620894572212 144 0.405352823036498 0.810705646072997 0.594647176963502 145 0.371890674606971 0.743781349213942 0.628109325393029 146 0.507389047636315 0.985221904727371 0.492610952363685 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 29 0.211678832116788 NOK 10% type I error level 45 0.328467153284672 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t12905436462ra742ajwpssq04/10z15n1290543551.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905436462ra742ajwpssq04/10z15n1290543551.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905436462ra742ajwpssq04/1ai9b1290543551.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905436462ra742ajwpssq04/1ai9b1290543551.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905436462ra742ajwpssq04/2ai9b1290543551.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905436462ra742ajwpssq04/2ai9b1290543551.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905436462ra742ajwpssq04/3ai9b1290543551.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905436462ra742ajwpssq04/3ai9b1290543551.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905436462ra742ajwpssq04/4la8w1290543551.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905436462ra742ajwpssq04/4la8w1290543551.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905436462ra742ajwpssq04/5la8w1290543551.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905436462ra742ajwpssq04/5la8w1290543551.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905436462ra742ajwpssq04/6v17z1290543551.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905436462ra742ajwpssq04/6v17z1290543551.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905436462ra742ajwpssq04/7v17z1290543551.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905436462ra742ajwpssq04/7v17z1290543551.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905436462ra742ajwpssq04/8oao21290543551.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905436462ra742ajwpssq04/8oao21290543551.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905436462ra742ajwpssq04/9oao21290543551.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905436462ra742ajwpssq04/9oao21290543551.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

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

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

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

Software written by Ed van Stee & Patrick Wessa

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