workshop 8 - 2

*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: Mon, 29 Nov 2010 18:18:02 +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/29/t1291054628hprbl164yg5n6pb.htm/, Retrieved Mon, 29 Nov 2010 19:17:18 +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/29/t1291054628hprbl164yg5n6pb.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 «

24 14 11 12 24 26 25 11 7 8 25 23 17 6 17 8 30 25 18 12 10 8 19 23 18 8 12 9 22 19 16 10 12 7 22 29 20 10 11 4 25 25 16 11 11 11 23 21 18 16 12 7 17 22 17 11 13 7 21 25 23 13 14 12 19 24 30 12 16 10 19 18 23 8 11 10 15 22 18 12 10 8 16 15 15 11 11 8 23 22 12 4 15 4 27 28 21 9 9 9 22 20 15 8 11 8 14 12 20 8 17 7 22 24 31 14 17 11 23 20 27 15 11 9 23 21 34 16 18 11 21 20 21 9 14 13 19 21 31 14 10 8 18 23 19 11 11 8 20 28 16 8 15 9 23 24 20 9 15 6 25 24 21 9 13 9 19 24 22 9 16 9 24 23 17 9 13 6 22 23 24 10 9 6 25 29 25 16 18 16 26 24 26 11 18 5 29 18 25 8 12 7 32 25 17 9 17 9 25 21 32 16 9 6 29 26 33 11 9 6 28 22 13 16 12 5 17 22 32 12 18 12 28 22 25 12 12 7 29 23 29 14 18 10 26 30 22 9 14 9 25 23 18 10 15 8 14 17 17 9 16 5 25 23 20 10 10 8 26 23 15 12 11 8 20 25 20 14 14 10 18 24 33 14 9 6 32 24 29 10 12 8 25 23 23 14 17 7 25 21 26 16 5 4 23 24 18 9 12 8 21 24 20 10 12 8 20 28 11 6 6 4 15 16 28 8 24 20 30 20 26 13 12 8 24 29 22 10 12 8 26 27 17 8 14 6 24 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 10 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Personal-Standards[t] = + 7.35806857088718 + 0.335229845129777`Concern(Mistakes)`[t] -0.366768472039511`Doubts(actions)`[t] + 0.161870869815985`Parental-Expectations`[t] + 0.0620916339294919`Parental-Criticism`[t] + 0.391606185783133Organization[t] -0.0947915214066301M1[t] + 0.289928443126254M2[t] + 0.669863771372266M3[t] + 0.159286592158596M4[t] + 0.365862044388642M5[t] + 1.01199387597801M6[t] + 0.433806865976564M7[t] + 1.67117605285828M8[t] + 1.41863032292718M9[t] + 0.923487622100795M10[t] -0.528232240887845M11[t] -0.00392377145820462t + 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) 7.35806857088718 2.610736 2.8184 0.005521 0.00276 `Concern(Mistakes)` 0.335229845129777 0.059844 5.6018 0 0 `Doubts(actions)` -0.366768472039511 0.116654 -3.1441 0.002032 0.001016 `Parental-Expectations` 0.161870869815985 0.106932 1.5138 0.132323 0.066161 `Parental-Criticism` 0.0620916339294919 0.139806 0.4441 0.657631 0.328815 Organization 0.391606185783133 0.07857 4.9842 2e-06 1e-06 M1 -0.0947915214066301 1.371116 -0.0691 0.94498 0.47249 M2 0.289928443126254 1.372927 0.2112 0.833055 0.416528 M3 0.669863771372266 1.365334 0.4906 0.624456 0.312228 M4 0.159286592158596 1.407608 0.1132 0.910064 0.455032 M5 0.365862044388642 1.402591 0.2608 0.794591 0.397295 M6 1.01199387597801 1.405064 0.7202 0.472565 0.236282 M7 0.433806865976564 1.426762 0.304 0.761538 0.380769 M8 1.67117605285828 1.400483 1.1933 0.234762 0.117381 M9 1.41863032292718 1.385153 1.0242 0.307509 0.153755 M10 0.923487622100795 1.374666 0.6718 0.502816 0.251408 M11 -0.528232240887845 1.425316 -0.3706 0.711486 0.355743 t -0.00392377145820462 0.006235 -0.6293 0.530153 0.265076 Multiple Linear Regression - Regression Statistics Multiple R 0.624037149557158 R-squared 0.389422364027423 Adjusted R-squared 0.315806620683212 F-TEST (value) 5.2899331900592 F-TEST (DF numerator) 17 F-TEST (DF denominator) 141 p-value 6.3415130924227e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.48809878442326 Sum Squared Residuals 1715.5234713152 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 22.8775509580749 1.12244904192510 2 25 22.6232138400667 2.37678615993331 3 30 24.5531500657400 5.44684993426003 4 19 20.2569596676826 -1.25695966768263 5 22 20.7460938670415 1.25390613295854 6 22 23.7761838828064 -1.7761838828064 7 25 22.6204219671288 2.37957803287115 8 23 21.0143962243677 1.98560377563234 9 17 19.8996545729215 -2.89965457292149 10 21 22.2358900428701 -1.23589004287007 11 19 22.1388113888032 -3.13881138880317 12 19 23.2264186032549 -4.22641860325494 13 15 23.0052386766923 -8.00523867669233 14 16 17.2155143178032 -1.21551431780318 15 23 19.8557189815391 3.14428101846091 16 27 23.6516618579992 3.34833814200076 17 22 21.243923249228 0.756076750772009 18 14 17.3703213300574 -3.37032133005742 19 22 24.0727675886107 -2.07276758861067 20 23 25.4750722608101 -2.47507226081009 21 23 22.8071126058904 0.192887394109601 22 21 25.1535597482625 -4.15355974826248 23 19 21.7756134057833 -2.7756134057833 24 18 23.643648688968 -5.64364868896801 25 20 22.7423824693960 -2.74238246939605 26 23 22.3609449132608 0.639055086739163 27 25 23.5248324767398 1.47516752326024 28 19 23.2080945333542 -4.20809453335417 29 24 23.8399824829206 0.160017517079393 30 22 22.1341538061665 -0.134153806166453 31 25 25.2340371040106 -0.234037104010590 32 26 24.7218247710499 1.27817522895007 33 29 23.6017823870647 5.39821761293526 34 32 25.7619928352139 6.23800716478608 35 25 20.6248548414957 4.37514515850427 36 29 24.0870207521947 4.91297924780526 37 28 24.5909529215247 3.40904707847529 38 17 16.8568308273248 0.143169172675234 39 28 26.4751499861387 1.52485001386127 40 29 22.7239629167982 6.27603708320182 41 26 27.4327404551764 -1.43274045517642 42 25 24.1113635459213 0.888636454078658 43 14 19.5717070330908 -5.57170703309077 44 25 23.1619241581503 1.83807584184967 45 26 22.7594254030034 3.2405745969966 46 20 20.7957560023732 -0.795756002373161 47 18 20.50091434102 -2.50091434101998 48 32 24.3254899123388 7.67451008766118 49 25 24.5711188186367 0.428881181363266 50 25 21.4375123963589 3.56248760364113 51 23 21.1317697622261 1.86823023777391 52 21 21.8842719792225 -0.88427197922245 53 20 23.9570396213469 -3.95703962134687 54 15 17.1303869794566 -2.13038697945661 55 30 26.9872131638163 3.01278683618373 56 24 26.5532621558852 -2.55326215588515 57 26 25.272966318529 0.727033681470997 58 24 22.0728151075319 1.92718489246812 59 22 20.4001484776036 1.59985152239642 60 14 15.1810863861930 -1.18108638619296 61 24 21.7133478971162 2.28665210288377 62 24 22.6522847809149 1.34771521908512 63 24 23.4146869502421 0.585313049757879 64 24 19.7847209882315 4.2152790117685 65 19 18.2514792120305 0.748520787969483 66 31 27.3137874184379 3.68621258156212 67 22 26.6628212700780 -4.66282127007797 68 27 22.6556632541872 4.34433674581277 69 19 18.5364502791677 0.463549720832304 70 25 22.7445031850646 2.25549681493536 71 20 23.9959644063116 -3.99596440631164 72 21 21.0424293738690 -0.042429373868957 73 27 26.9014694215360 0.0985305784640425 74 23 24.1814022572013 -1.18140225720133 75 25 25.7394767033077 -0.739476703307729 76 20 21.9246636604855 -1.92466366048551 77 21 18.9120553468911 2.08794465310893 78 22 22.9261786979608 -0.926178697960797 79 23 22.9220640419638 0.0779359580361682 80 25 25.1595325767019 -0.159532576701885 81 25 24.3330058981788 0.66699410182121 82 17 24.2524067832873 -7.25240678328733 83 19 20.3591588484922 -1.35915884849218 84 25 23.4083196098233 1.59168039017671 85 19 21.6840764492848 -2.68407644928478 86 20 22.7390500372559 -2.73905003725591 87 26 22.5482924491443 3.45170755085569 88 23 20.3759026306079 2.62409736939209 89 27 24.4344818339528 2.56551816604722 90 17 21.3194271294415 -4.31942712944146 91 17 23.1775033066431 -6.17750330664306 92 19 21.2527789615909 -2.25277896159087 93 17 20.5152507488465 -3.5152507488465 94 22 22.2528301148561 -0.252830114856086 95 21 22.5003917739954 -1.50039177399538 96 32 28.0319756931785 3.96802430682147 97 21 24.0216723917931 -3.02167239179312 98 21 24.0996479486467 -3.09964794864667 99 18 21.3087515537514 -3.30875155375139 100 18 20.8739217986085 -2.87392179860854 101 23 22.6429407035674 0.357059296432621 102 19 20.9696362736129 -1.96963627361294 103 20 20.7535694692373 -0.75356946923735 104 21 23.3854773018757 -2.38547730187568 105 20 24.6983060151162 -4.69830601511618 106 17 19.0767544624798 -2.07675446247982 107 18 19.2263270493602 -1.22632704936020 108 19 20.2782317218098 -1.27823172180982 109 22 21.4163744021375 0.583625597862532 110 15 18.3192610550785 -3.31926105507852 111 14 18.8338433259475 -4.83384332594752 112 18 26.2637626300494 -8.26376263004936 113 24 21.3581929291388 2.64180707086116 114 35 23.9901081128231 11.0098918871769 115 29 19.1420166978655 9.85798330213452 116 21 22.8169448164045 -1.81694481640451 117 25 21.2173983177046 3.78260168229537 118 20 18.7529104974917 1.24708950250826 119 22 21.9943312575646 0.00566874243537843 120 13 16.1915736154901 -3.19157361549010 121 26 22.4725117310255 3.52748826897454 122 17 16.4708523833231 0.529147616676901 123 25 20.1753241177299 4.82467588227008 124 20 20.2590370699101 -0.259037069910140 125 19 17.7872198402884 1.21278015971159 126 21 22.8012910846120 -1.80129108461204 127 22 20.6534800549753 1.34651994502468 128 24 23.6562190570294 0.343780942970601 129 21 23.6437625807975 -2.64376258079749 130 26 25.7667594681409 0.233240531859075 131 24 19.4926662943236 4.50733370567641 132 16 19.5658054227985 -3.56580542279853 133 23 21.4122051323747 1.58779486762532 134 18 20.2638880214482 -2.26388802144823 135 16 22.3164910049718 -6.31649100497182 136 26 23.4053779044340 2.59462209556598 137 19 18.5996449583555 0.400355041644462 138 21 17.2155239616487 3.78447603835126 139 21 21.9110543970158 -0.911054397015845 140 22 19.7107175415605 2.28928245843955 141 23 20.6437329982208 2.35626700177922 142 29 25.0443698091057 3.95563019089431 143 21 18.2222900980423 2.77770990195765 144 21 19.1734478651929 1.82655213480712 145 23 21.0163156465776 1.98368435342239 146 27 22.4801741675949 4.51982583240513 147 25 25.2934939106875 -0.293493910687525 148 21 20.3876623626164 0.612337637383651 149 10 16.7942055000621 -6.79420550006212 150 20 22.9416377770548 -2.94163777705485 151 26 22.291343905564 3.70865609443602 152 24 24.4361869203868 -0.436186920386799 153 29 32.0711518745589 -3.07115187455891 154 19 19.0894519433223 -0.08945194332227 155 24 20.7685278172043 3.23147218279573 156 19 19.8445523548884 -0.844552354888397 157 24 22.5747830838300 1.42521691617004 158 22 21.2994230537222 0.700576946277849 159 17 23.8290187118340 -6.82901871183404 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.79485807418249 0.41028385163502 0.20514192581751 22 0.679019108696912 0.641961782606176 0.320980891303088 23 0.554098259347953 0.891803481304094 0.445901740652047 24 0.456518782748368 0.913037565496737 0.543481217251632 25 0.371054876012169 0.742109752024338 0.628945123987831 26 0.267875081129891 0.535750162259783 0.732124918870109 27 0.188207925191981 0.376415850383962 0.811792074808019 28 0.171084783151800 0.342169566303599 0.8289152168482 29 0.116658049308368 0.233316098616737 0.883341950691632 30 0.114745600232955 0.22949120046591 0.885254399767045 31 0.0754855530206753 0.150971106041351 0.924514446979325 32 0.056867818518768 0.113735637037536 0.943132181481232 33 0.187234529875725 0.374469059751451 0.812765470124275 34 0.31974362883225 0.6394872576645 0.68025637116775 35 0.403238555727362 0.806477111454724 0.596761444272638 36 0.525144249917283 0.949711500165434 0.474855750082717 37 0.491770702366490 0.983541404732979 0.508229297633510 38 0.440137517216526 0.880275034433052 0.559862482783474 39 0.377930657897996 0.755861315795992 0.622069342102004 40 0.483404058790478 0.966808117580957 0.516595941209522 41 0.449279826414309 0.898559652828618 0.550720173585691 42 0.399995885190672 0.799991770381344 0.600004114809328 43 0.395130302891557 0.790260605783115 0.604869697108443 44 0.408941794454662 0.817883588909324 0.591058205545338 45 0.359506295567679 0.719012591135359 0.640493704432321 46 0.309575241643481 0.619150483286961 0.690424758356519 47 0.29015150093885 0.5803030018777 0.70984849906115 48 0.405475843774796 0.810951687549592 0.594524156225204 49 0.348548123466319 0.697096246932639 0.651451876533681 50 0.336709661008017 0.673419322016035 0.663290338991983 51 0.374802066056817 0.749604132113633 0.625197933943183 52 0.334035045896182 0.668070091792365 0.665964954103818 53 0.397705035957663 0.795410071915326 0.602294964042337 54 0.368172204705612 0.736344409411224 0.631827795294388 55 0.47664760901474 0.95329521802948 0.52335239098526 56 0.5250019141373 0.9499961717254 0.4749980858627 57 0.493881641422653 0.987763282845306 0.506118358577347 58 0.448463470051761 0.896926940103522 0.551536529948239 59 0.401276424224926 0.802552848449852 0.598723575775074 60 0.357981832208801 0.715963664417602 0.642018167791199 61 0.333496530647462 0.666993061294925 0.666503469352538 62 0.307571156252691 0.615142312505382 0.69242884374731 63 0.285538565186749 0.571077130373498 0.714461434813251 64 0.309544692243620 0.619089384487241 0.69045530775638 65 0.269678566283126 0.539357132566251 0.730321433716874 66 0.265398678770029 0.530797357540057 0.734601321229971 67 0.332116220247255 0.66423244049451 0.667883779752745 68 0.340493311194692 0.680986622389384 0.659506688805308 69 0.300535588985991 0.601071177971981 0.69946441101401 70 0.274362915029195 0.548725830058389 0.725637084970805 71 0.309052886330456 0.618105772660912 0.690947113669544 72 0.271850665401351 0.543701330802702 0.728149334598649 73 0.232659807020176 0.465319614040352 0.767340192979824 74 0.205118753549364 0.410237507098727 0.794881246450636 75 0.210499524336718 0.420999048673435 0.789500475663282 76 0.189539124607252 0.379078249214505 0.810460875392748 77 0.182781467049027 0.365562934098054 0.817218532950973 78 0.150998495866249 0.301996991732498 0.849001504133751 79 0.123473202225298 0.246946404450597 0.876526797774702 80 0.105035279954074 0.210070559908147 0.894964720045926 81 0.0886035315968984 0.177207063193797 0.911396468403102 82 0.1855106221806 0.3710212443612 0.8144893778194 83 0.153935185067222 0.307870370134445 0.846064814932778 84 0.133687737225402 0.267375474450804 0.866312262774598 85 0.119025599180853 0.238051198361705 0.880974400819147 86 0.109953073411056 0.219906146822111 0.890046926588944 87 0.149915198416528 0.299830396833056 0.850084801583472 88 0.160815204096792 0.321630408193585 0.839184795903208 89 0.156582734507291 0.313165469014582 0.843417265492709 90 0.160206907443564 0.320413814887129 0.839793092556436 91 0.222502105391899 0.445004210783797 0.777497894608101 92 0.198522158890717 0.397044317781433 0.801477841109284 93 0.187422748091565 0.374845496183129 0.812577251908435 94 0.155608268548472 0.311216537096943 0.844391731451528 95 0.131378961974625 0.26275792394925 0.868621038025375 96 0.177620603828038 0.355241207656077 0.822379396171962 97 0.167406583820928 0.334813167641856 0.832593416179072 98 0.151929514468709 0.303859028937418 0.848070485531291 99 0.138361081696634 0.276722163393268 0.861638918303366 100 0.117374295913193 0.234748591826386 0.882625704086807 101 0.0995395840724173 0.199079168144835 0.900460415927583 102 0.0864127053841176 0.172825410768235 0.913587294615882 103 0.0828389306230848 0.165677861246170 0.917161069376915 104 0.0679213132949603 0.135842626589921 0.93207868670504 105 0.0820383409206879 0.164076681841376 0.917961659079312 106 0.0784228562924296 0.156845712584859 0.92157714370757 107 0.074788054562921 0.149576109125842 0.925211945437079 108 0.0583368728978555 0.116673745795711 0.941663127102145 109 0.0551755774523347 0.110351154904669 0.944824422547665 110 0.0657583346374708 0.131516669274942 0.93424166536253 111 0.0641770372460662 0.128354074492132 0.935822962753934 112 0.315903238931130 0.631806477862261 0.68409676106887 113 0.291067870239367 0.582135740478734 0.708932129760633 114 0.695309146877793 0.609381706244414 0.304690853122207 115 0.903817611862067 0.192364776275865 0.0961823881379325 116 0.875991700575682 0.248016598848636 0.124008299424318 117 0.910079976345476 0.179840047309048 0.0899200236545238 118 0.882784433655623 0.234431132688754 0.117215566344377 119 0.90480240381364 0.190395192372721 0.0951975961863604 120 0.937260376211633 0.125479247576733 0.0627396237883666 121 0.922107870579205 0.15578425884159 0.077892129420795 122 0.904650715664149 0.190698568671703 0.0953492843358513 123 0.966943652515063 0.066112694969873 0.0330563474849365 124 0.94962586376738 0.100748272465241 0.0503741362326204 125 0.92925432878797 0.141491342424061 0.0707456712120305 126 0.907561962737454 0.184876074525092 0.0924380372625458 127 0.885547611234631 0.228904777530738 0.114452388765369 128 0.84324045742242 0.31351908515516 0.15675954257758 129 0.81656057965859 0.366878840682821 0.183439420341410 130 0.805137921345937 0.389724157308126 0.194862078654063 131 0.756705800465242 0.486588399069516 0.243294199534758 132 0.729965395332664 0.540069209334672 0.270034604667336 133 0.638564426853821 0.722871146292359 0.361435573146179 134 0.649741849342605 0.70051630131479 0.350258150657395 135 0.737947568264606 0.524104863470788 0.262052431735394 136 0.626036729752965 0.74792654049407 0.373963270247035 137 0.595394569974860 0.809210860050281 0.404605430025141 138 0.69254411302319 0.614911773953619 0.307455886976809 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 0 0 OK 10% type I error level 1 0.00847457627118644 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291054628hprbl164yg5n6pb/1018ax1291054671.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291054628hprbl164yg5n6pb/1018ax1291054671.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291054628hprbl164yg5n6pb/1c7cm1291054671.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291054628hprbl164yg5n6pb/1c7cm1291054671.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291054628hprbl164yg5n6pb/25zup1291054671.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291054628hprbl164yg5n6pb/25zup1291054671.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291054628hprbl164yg5n6pb/35zup1291054671.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291054628hprbl164yg5n6pb/35zup1291054671.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291054628hprbl164yg5n6pb/45zup1291054671.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291054628hprbl164yg5n6pb/45zup1291054671.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291054628hprbl164yg5n6pb/55zup1291054671.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291054628hprbl164yg5n6pb/55zup1291054671.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291054628hprbl164yg5n6pb/6y8ts1291054671.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291054628hprbl164yg5n6pb/6y8ts1291054671.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291054628hprbl164yg5n6pb/7qzsc1291054671.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291054628hprbl164yg5n6pb/7qzsc1291054671.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291054628hprbl164yg5n6pb/8qzsc1291054671.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291054628hprbl164yg5n6pb/8qzsc1291054671.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291054628hprbl164yg5n6pb/9qzsc1291054671.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291054628hprbl164yg5n6pb/9qzsc1291054671.ps (open in new window)

Parameters (Session):

par1 = 5 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 5 ; par2 = Include Monthly 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') }

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Software written by Ed van Stee & Patrick Wessa

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