Workshop7, Mini-tutorial, 1

*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, 22 Nov 2010 22:25:18 +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/22/t1290464628rpt66829n3i8cbw.htm/, Retrieved Mon, 22 Nov 2010 23:23:48 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464628rpt66829n3i8cbw.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 «

12 12 11 24 11 8 7 25 14 8 17 17 12 8 10 18 21 9 12 18 12 7 12 16 22 4 11 20 11 11 11 16 10 7 12 18 13 7 13 17 10 12 14 23 8 10 16 30 15 10 11 23 14 8 10 18 10 8 11 15 14 4 15 12 14 9 9 21 11 8 11 15 10 7 17 20 13 11 17 31 7 9 11 27 14 11 18 34 12 13 14 21 14 8 10 31 11 8 11 19 9 9 15 16 11 6 15 20 15 9 13 21 14 9 16 22 13 6 13 17 9 6 9 24 15 16 18 25 10 5 18 26 11 7 12 25 13 9 17 17 8 6 9 32 20 6 9 33 12 5 12 13 10 12 18 32 10 7 12 25 9 10 18 29 14 9 14 22 8 8 15 18 14 5 16 17 11 8 10 20 13 8 11 15 9 10 14 20 11 6 9 33 15 8 12 29 11 7 17 23 10 4 5 26 14 8 12 18 18 8 12 20 14 4 6 11 11 20 24 28 12 8 12 26 13 8 12 22 9 6 14 17 10 4 7 12 15 8 13 14 20 9 12 17 12 6 13 21 12 7 14 19 14 9 8 18 13 5 11 10 11 5 9 29 17 8 11 31 12 8 13 19 13 6 10 9 14 8 11 20 13 7 12 28 15 7 9 19 13 9 15 30 10 11 18 29 11 6 15 26 19 8 12 23 13 6 13 13 17 9 14 21 13 8 10 19 9 6 13 28 11 10 13 23 10 8 11 18 9 8 13 21 12 10 16 20 12 5 8 23 13 7 16 21 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 7 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Depression[t] = + 14.1672885277797 -0.0177914965161202ParentalCriticism[t] -0.00187772044554277ParentalExpectations[t] -0.0511333152340301ConcernOverMistakes[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) 14.1672885277797 1.1941 11.8644 0 0 ParentalCriticism -0.0177914965161202 0.116713 -0.1524 0.87904 0.43952 ParentalExpectations -0.00187772044554277 0.092288 -0.0203 0.983793 0.491897 ConcernOverMistakes -0.0511333152340301 0.047063 -1.0865 0.278949 0.139474 Multiple Linear Regression - Regression Statistics Multiple R 0.099713460840092 R-squared 0.00994277427270855 Adjusted R-squared -0.00921962364459383 F-TEST (value) 0.51886900144845 F-TEST (DF numerator) 3 F-TEST (DF denominator) 155 p-value 0.669905215274848 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.15986935243082 Sum Squared Residuals 1547.64002028689 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 12 12.7059360790685 -0.705936079068524 2 11 12.7334796316811 -1.73347963168115 3 14 13.1237689490980 0.87623105090204 4 12 13.0857796769827 -1.08577967698273 5 21 13.0642327395755 7.93576726042448 6 12 13.2020823630758 -1.20208236307582 7 22 13.0528013121336 8.9471986878664 8 11 13.1327940974569 -2.13279409745689 9 10 13.0998157326078 -3.09981573260776 10 13 13.1490713273963 -0.149071327396251 11 10 12.7514362329659 -2.75143623296593 12 8 12.4253305784689 -4.42533057846887 13 15 12.7926523873348 2.20734761266520 14 14 13.0857796769827 0.914220323017271 15 10 13.2373019022393 -3.23730190223928 16 14 13.4543569522237 0.545643047776324 17 14 12.9164659552101 1.08353404478994 18 11 13.2373019022393 -2.23730190223928 19 10 12.988160499912 -2.98816049991199 20 13 12.3545280462732 0.645471953726822 21 7 12.6059106229148 -5.6059106229148 22 14 12.1992503801255 1.80074961987446 23 12 12.8359113669179 -0.835911366917866 24 14 12.4210465789403 1.57895342105966 25 11 13.0327686413032 -2.03276864130316 26 9 13.1608662087070 -4.16086620870696 27 11 13.0097074373192 -2.00970743731920 28 15 12.9089550734279 2.09104492657211 29 14 12.8521885968572 1.14781140314277 30 13 13.1668628239124 -0.166862823912371 31 9 12.8164404990563 -3.81644049905633 32 15 12.5704927346512 2.42950726534879 33 10 12.7150658810945 -2.71506588109451 34 11 12.7418825259696 -1.74188252596955 35 13 13.1059774525818 -0.105977452581839 36 8 12.4073739771841 -4.40737397718409 37 20 12.3562406619501 7.64375933804994 38 12 13.3910653018102 -1.39106530181015 39 10 12.2837255140775 -2.28372551407748 40 10 12.7418825259696 -2.74188252596955 41 9 12.4727084528118 -3.47270845281182 42 14 12.8559440377483 1.14405596225168 43 8 13.0763910747550 -5.07639107475501 44 14 13.1790211590919 0.820978840908137 45 11 12.9835130465147 -1.98351304651467 46 13 13.2373019022393 -0.237301902239276 47 9 12.9404191717003 -3.94041917170026 48 11 12.3562406619501 -1.35624066195006 49 15 12.5195577685173 2.48044223148269 50 11 12.8347605542099 -1.8347605542099 51 10 12.7572677434027 -2.75726774340268 52 14 13.0820242360916 0.917975763908357 53 18 12.9797576056236 5.02024239437642 54 14 13.5223897514676 0.477610248532409 55 11 12.3346604802114 -1.33466048021139 56 12 12.6729577142194 -0.672957714219403 57 13 12.8774909751555 0.122509024844477 58 9 13.1649851034668 -4.16498510346683 59 10 13.4693787157880 -3.46937871578802 60 15 13.2846797765822 1.71532022341778 61 20 13.1153660548096 6.88463394519045 62 12 12.9623295629763 -0.96232956297625 63 12 13.0449269764826 -1.04492697648265 64 14 13.0717436213577 0.928256378642306 65 13 13.5463429679578 -0.546342967957787 66 11 12.5785654194023 -1.5785654194023 67 17 12.4191688584948 4.58083114150520 68 12 13.0290132004121 -1.02901320041207 69 13 13.5815625071212 -0.58156250712124 70 14 12.9816353260691 1.01836467393087 71 13 12.5884825802675 0.411517419732537 72 15 13.0543155787104 1.94568442128964 73 13 12.4449997954305 0.555000204569466 74 10 12.4549169562957 -2.45491695629570 75 11 12.7029075459150 -1.70290754591501 76 19 12.8263576599215 6.17364234007851 77 13 13.3713960848485 -0.371396084848491 78 17 12.9070773529823 4.09292264701765 79 13 13.0346463617487 -0.0346463617486987 80 9 12.6043963563380 -3.60439635633804 81 11 12.7888969464437 -1.78889694644371 82 10 13.0839019565372 -3.08390195653719 83 9 12.926746569944 -3.92674656994401 84 12 12.9366637308092 -0.936663730809171 85 12 12.8872430312520 -0.887243031252025 86 13 12.9389049051235 0.0610950948764978 87 13 12.9838765003835 0.0161234996165435 88 12 13.2410573431304 -1.24105734313036 89 15 12.4564312228724 2.54356877712755 90 22 13.0486824173737 8.95131758262627 91 13 12.6692022733283 0.330797726671683 92 15 13.5341846327783 1.46581536722170 93 13 13.2432985174447 -0.243298517444692 94 15 12.9074408068511 2.09255919314886 95 10 12.9971856482709 -2.99718564827092 96 11 12.3292256679749 -1.32922566797489 97 16 12.3957442006420 3.60425579935795 98 11 12.4371254597796 -1.43712545977957 99 11 13.0486824173737 -2.04868241737373 100 10 12.8756132547100 -2.87561325470998 101 10 12.7851415055526 -2.78514150555262 102 16 13.2710071748260 2.72899282517403 103 12 12.9310305694725 -0.931030569472543 104 11 13.0408080817228 -2.04080808172277 105 16 12.7926523873348 3.20734761266520 106 19 12.7793432394473 6.22065676055266 107 11 12.9501712277968 -1.95017122779676 108 16 12.7377636312097 3.26223636879032 109 15 12.6650833785684 2.33491662143156 110 24 13.1687405443579 10.8312594556421 111 14 13.3554823087779 0.644517691222086 112 15 12.4920142159047 2.50798578409531 113 11 12.8808829621778 -1.88088296217782 114 15 12.6594502172318 2.34054978276818 115 12 13.4963604654317 -1.49636046543172 116 10 13.2357876356625 -3.23578763566252 117 14 13.0215023186299 0.9784976813701 118 13 13.1743737056945 -0.174373705694542 119 9 12.7006663716007 -3.70066637160068 120 15 13.0584344734702 1.94156552652976 121 15 12.6001123568095 2.39988764319049 122 14 13.3043489935439 0.695651006456116 123 11 12.8203610447161 -1.82036104471608 124 8 13.2822734974992 -5.28227349749923 125 11 13.0561932991559 -2.05619329915590 126 11 12.9703690033959 -1.97036900339587 127 8 13.3103456087493 -5.3103456087493 128 10 12.9816353260691 -2.98163532606913 129 11 13.0604772986844 -2.06047729868444 130 13 12.3169022280267 0.683097771973265 131 11 12.8222387651616 -1.82223876516162 132 20 13.1842908665597 6.8157091334403 133 10 13.1884097613196 -3.18840976131958 134 15 13.2610900139608 1.73890998603919 135 12 12.9286242903896 -0.928624290389553 136 14 12.6223529576228 1.37764704237718 137 23 13.1176072291239 9.88239277087612 138 14 13.0623550191300 0.93764498087002 139 16 13.1153660548096 2.88463394519045 140 11 12.7885334925749 -1.78853349257492 141 12 12.4562661181038 -0.456266118103791 142 10 12.4272082989144 -2.42720829891441 143 14 12.5391937411475 1.46080625885249 144 12 12.9913873821656 -0.991387382165628 145 12 12.8658611986135 -0.865861198613479 146 11 12.5570184819951 -1.55701848199510 147 12 12.3901110393054 -0.390111039305418 148 13 12.9994268225852 0.00057317741475386 149 11 13.1664993700436 -2.16649937004358 150 19 12.8381525412322 6.1618474587678 151 12 12.963843829553 -0.963843829553006 152 17 12.5631802019692 4.43681979803083 153 9 12.0602499439173 -3.06024994391728 154 12 12.9093185272967 -0.909318527296678 155 19 12.8757783594786 6.12422164052136 156 18 13.1668628239124 4.83313717608763 157 15 12.5725688041969 2.42743119580311 158 14 12.8362748207867 1.16372517921335 159 11 12.2618151228015 -1.26181512280149 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.979079793972474 0.041840412055052 0.020920206027526 8 0.954929660897036 0.0901406782059277 0.0450703391029639 9 0.97250790233546 0.054984195329082 0.027492097664541 10 0.955605834409479 0.0887883311810423 0.0443941655905212 11 0.93418246973433 0.131635060531341 0.0658175302656706 12 0.93192262484473 0.13615475031054 0.06807737515527 13 0.924620373952865 0.150759252094271 0.0753796260471354 14 0.887553179598543 0.224893640802913 0.112446820401457 15 0.900840183896008 0.198319632207984 0.0991598161039921 16 0.87358773877713 0.252824522445741 0.126412261222870 17 0.829921011472396 0.340157977055208 0.170078988527604 18 0.803732564111893 0.392534871776214 0.196267435888107 19 0.78370885165998 0.432582296680039 0.216291148340019 20 0.754794074254941 0.490411851490117 0.245205925745058 21 0.846287851082258 0.307424297835483 0.153712148917742 22 0.83837207167633 0.323255856647339 0.161627928323669 23 0.802270535152386 0.395458929695229 0.197729464847614 24 0.756334843138885 0.48733031372223 0.243665156861115 25 0.72182257030252 0.556354859394961 0.278177429697481 26 0.721636693371144 0.556726613257711 0.278363306628856 27 0.694500346713588 0.610999306572824 0.305499653286412 28 0.67475122344289 0.650497553114221 0.325248776557111 29 0.6341824700163 0.7316350599674 0.3658175299837 30 0.575827227110197 0.848345545779607 0.424172772889803 31 0.628759854642492 0.742480290715017 0.371240145357508 32 0.640175698708858 0.719648602582284 0.359824301291142 33 0.622236601288308 0.755526797423384 0.377763398711692 34 0.576484208072809 0.847031583854382 0.423515791927191 35 0.519823734349405 0.96035253130119 0.480176265650595 36 0.535187737817266 0.929624524365469 0.464812262182734 37 0.789436284116834 0.421127431766332 0.210563715883166 38 0.752243931767 0.495512136466001 0.247756068233000 39 0.724960953960448 0.550078092079104 0.275039046039552 40 0.707777780171398 0.584444439657203 0.292222219828602 41 0.700839663111283 0.598320673777434 0.299160336888717 42 0.665074737830298 0.669850524339404 0.334925262169702 43 0.712341774960461 0.575316450079078 0.287658225039539 44 0.676039875451244 0.647920249097513 0.323960124548756 45 0.64267596999056 0.71464806001888 0.35732403000944 46 0.594296760206586 0.811406479586829 0.405703239793414 47 0.602853683583893 0.794292632832215 0.397146316416107 48 0.562187562675206 0.875624874649589 0.437812437324794 49 0.548918625391813 0.902162749216374 0.451081374608187 50 0.509968398556534 0.980063202886932 0.490031601443466 51 0.499230566573459 0.998461133146918 0.500769433426541 52 0.459156481125582 0.918312962251165 0.540843518874418 53 0.549434595350338 0.901130809299324 0.450565404649662 54 0.50172957739016 0.99654084521968 0.49827042260984 55 0.459301594437984 0.918603188875969 0.540698405562016 56 0.41255612034754 0.82511224069508 0.58744387965246 57 0.36699131258175 0.7339826251635 0.63300868741825 58 0.390810084273374 0.781620168546749 0.609189915726626 59 0.394928103577449 0.789856207154898 0.605071896422551 60 0.370289359210243 0.740578718420487 0.629710640789757 61 0.558303742857391 0.883392514285218 0.441696257142609 62 0.514832419987753 0.970335160024494 0.485167580012247 63 0.472182637569448 0.944365275138897 0.527817362430552 64 0.429411741603545 0.858823483207089 0.570588258396455 65 0.385594132379595 0.77118826475919 0.614405867620405 66 0.350039544941586 0.700079089883172 0.649960455058414 67 0.406806870314481 0.813613740628962 0.593193129685519 68 0.366435338251157 0.732870676502313 0.633564661748843 69 0.325803623104129 0.651607246208258 0.674196376895871 70 0.289856192486688 0.579712384973376 0.710143807513312 71 0.252641524118503 0.505283048237006 0.747358475881497 72 0.230385444114601 0.460770888229202 0.769614555885399 73 0.198741046166670 0.397482092333339 0.80125895383333 74 0.183628275726193 0.367256551452386 0.816371724273807 75 0.162614543346180 0.325229086692361 0.83738545665382 76 0.25994525555766 0.51989051111532 0.74005474444234 77 0.226382856614627 0.452765713229253 0.773617143385373 78 0.252475255621152 0.504950511242304 0.747524744378848 79 0.216957745087408 0.433915490174816 0.783042254912592 80 0.225876620632567 0.451753241265134 0.774123379367433 81 0.202353545349337 0.404707090698673 0.797646454650663 82 0.201260675036249 0.402521350072498 0.798739324963751 83 0.220047601449087 0.440095202898174 0.779952398550913 84 0.191562940864352 0.383125881728705 0.808437059135648 85 0.164008996667490 0.328017993334981 0.83599100333251 86 0.139823833852434 0.279647667704869 0.860176166147566 87 0.116506245247396 0.233012490494792 0.883493754752604 88 0.0987464304693105 0.197492860938621 0.90125356953069 89 0.0934506604557493 0.186901320911499 0.90654933954425 90 0.296854444384500 0.593708888769001 0.7031455556155 91 0.258810646619120 0.517621293238241 0.74118935338088 92 0.228362905691082 0.456725811382163 0.771637094308918 93 0.195290129422465 0.39058025884493 0.804709870577535 94 0.176751105900071 0.353502211800141 0.82324889409993 95 0.172566481127002 0.345132962254004 0.827433518872998 96 0.151395889698920 0.302791779397841 0.84860411030108 97 0.158789548668279 0.317579097336557 0.841210451331721 98 0.137884898443316 0.275769796886632 0.862115101556684 99 0.125084555640439 0.250169111280878 0.87491544435956 100 0.122796305963744 0.245592611927488 0.877203694036256 101 0.119613278668193 0.239226557336386 0.880386721331807 102 0.110142352873164 0.220284705746328 0.889857647126836 103 0.0954833273707528 0.190966654741506 0.904516672629247 104 0.0873690473717062 0.174738094743412 0.912630952628294 105 0.0881852816075434 0.176370563215087 0.911814718392457 106 0.149054454184715 0.298108908369431 0.850945545815285 107 0.131856107455939 0.263712214911878 0.868143892544061 108 0.132270758756771 0.264541517513542 0.867729241243229 109 0.119270361685283 0.238540723370565 0.880729638314717 110 0.513940776222505 0.97211844755499 0.486059223777495 111 0.464278698354544 0.928557396709088 0.535721301645456 112 0.443794781439984 0.887589562879968 0.556205218560016 113 0.40454090042955 0.8090818008591 0.59545909957045 114 0.374871595684148 0.749743191368295 0.625128404315852 115 0.336023790802683 0.672047581605367 0.663976209197316 116 0.353620738576363 0.707241477152726 0.646379261423637 117 0.308594977626925 0.61718995525385 0.691405022373075 118 0.263748661637691 0.527497323275382 0.736251338362309 119 0.284376368272246 0.568752736544492 0.715623631727754 120 0.257371248512524 0.514742497025048 0.742628751487476 121 0.266771603203028 0.533543206406057 0.733228396796972 122 0.224513749385986 0.449027498771972 0.775486250614014 123 0.19941832355173 0.39883664710346 0.80058167644827 124 0.259439933808429 0.518879867616858 0.740560066191571 125 0.232007306219726 0.464014612439451 0.767992693780274 126 0.22978000096964 0.45956000193928 0.77021999903036 127 0.394753000214475 0.78950600042895 0.605246999785525 128 0.414303810062288 0.828607620124576 0.585696189937712 129 0.44128740047138 0.88257480094276 0.55871259952862 130 0.42368026414278 0.84736052828556 0.57631973585722 131 0.396060495099564 0.792120990199127 0.603939504900436 132 0.492684023174575 0.98536804634915 0.507315976825425 133 0.616253380958344 0.767493238083313 0.383746619041656 134 0.559830271138723 0.880339457722555 0.440169728861278 135 0.525980765083543 0.948038469832914 0.474019234916457 136 0.461863441170004 0.923726882340007 0.538136558829996 137 0.820496528359726 0.359006943280549 0.179503471640274 138 0.770888287819828 0.458223424360343 0.229111712180172 139 0.723321032118189 0.553357935763623 0.276678967881811 140 0.684501972767311 0.630996054465377 0.315498027232689 141 0.625643547194246 0.748712905611509 0.374356452805754 142 0.573726388399793 0.852547223200413 0.426273611600207 143 0.503502259224098 0.992995481551805 0.496497740775902 144 0.421105231798579 0.842210463597158 0.578894768201421 145 0.417964715798079 0.835929431596157 0.582035284201921 146 0.329622131119262 0.659244262238525 0.670377868880738 147 0.246602171988648 0.493204343977296 0.753397828011352 148 0.181948745644261 0.363897491288521 0.81805125435574 149 0.324813003825240 0.649626007650479 0.67518699617476 150 0.371627595109802 0.743255190219605 0.628372404890198 151 0.399139692020334 0.798279384040668 0.600860307979666 152 0.474304630071168 0.948609260142336 0.525695369928832 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 1 0.00684931506849315 OK 10% type I error level 4 0.0273972602739726 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464628rpt66829n3i8cbw/102iwn1290464707.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464628rpt66829n3i8cbw/102iwn1290464707.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464628rpt66829n3i8cbw/1dh0b1290464707.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464628rpt66829n3i8cbw/1dh0b1290464707.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464628rpt66829n3i8cbw/2dh0b1290464707.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464628rpt66829n3i8cbw/2dh0b1290464707.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464628rpt66829n3i8cbw/3dh0b1290464707.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464628rpt66829n3i8cbw/3dh0b1290464707.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464628rpt66829n3i8cbw/4orzw1290464707.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464628rpt66829n3i8cbw/4orzw1290464707.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464628rpt66829n3i8cbw/5orzw1290464707.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464628rpt66829n3i8cbw/5orzw1290464707.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464628rpt66829n3i8cbw/6h0yh1290464707.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464628rpt66829n3i8cbw/6h0yh1290464707.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464628rpt66829n3i8cbw/799x21290464707.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464628rpt66829n3i8cbw/799x21290464707.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464628rpt66829n3i8cbw/899x21290464707.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464628rpt66829n3i8cbw/899x21290464707.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464628rpt66829n3i8cbw/999x21290464707.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290464628rpt66829n3i8cbw/999x21290464707.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') }

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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