Trend wel significant!

*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: Wed, 24 Nov 2010 17:05:14 +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/24/t12906183780sbr2vto5cf50oe.htm/, Retrieved Wed, 24 Nov 2010 18:06:21 +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/24/t12906183780sbr2vto5cf50oe.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 «

14 11 12 11 12 6 6 53 6 18 12 12 8 13 5 3 86 6 11 15 10 12 16 6 0 66 13 12 10 10 10 11 5 4 67 8 16 12 9 7 12 6 7 76 7 18 11 6 6 9 4 0 78 9 14 5 15 8 12 3 3 53 5 14 16 11 16 16 7 10 80 8 15 11 11 8 12 6 3 74 9 15 15 13 16 18 8 6 76 11 17 12 12 7 12 3 1 79 8 19 9 12 11 11 4 3 54 11 10 11 5 16 14 6 5 67 12 18 15 11 16 11 5 6 87 8 14 12 13 12 12 6 6 58 7 14 16 11 13 14 7 7 75 9 17 14 9 19 12 6 2 88 12 14 11 14 7 13 6 2 64 20 16 10 12 8 11 4 0 57 7 18 7 14 12 12 4 6 66 8 14 11 12 13 11 4 1 54 8 12 10 12 11 12 6 5 56 16 17 11 8 8 13 4 4 86 10 9 16 9 16 16 6 7 80 6 16 14 11 15 16 6 7 76 8 14 12 7 11 15 5 2 69 9 11 12 12 12 14 5 2 67 9 16 11 9 7 13 2 3 80 11 13 6 7 9 11 4 3 54 12 17 14 12 15 13 6 3 71 8 15 9 9 6 12 5 8 84 7 14 15 11 14 15 7 7 74 8 16 12 10 14 13 7 6 71 9 9 12 12 7 11 4 6 63 4 15 9 11 15 15 7 5 71 8 17 13 8 14 14 5 10 76 8 13 15 11 17 16 6 5 69 8 15 11 8 14 15 5 5 74 6 16 10 12 5 13 6 5 75 8 16 13 9 14 14 6 2 54 4 12 16 12 8 14 4 6 69 14 11 13 10 8 8 4 4 68 10 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 8 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation Happiness[t] = + 7.3773915218063 -0.0353446594951485Popularity[t] + 0.150287278822863FindingFriends[t] + 0.0685444408465139KnowingPeople[t] + 0.067513834434165Liked[t] + 0.0171804895305078Celebrity[t] -0.215996939893678WeightedSum[t] + 0.0814495958066655BelongingstoSports[t] -0.0503427071174557ParentalCriticism[t] -0.00806458497342902t + 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) 7.3773915218063 2.105264 3.5043 0.000622 0.000311 Popularity -0.0353446594951485 0.090051 -0.3925 0.69531 0.347655 FindingFriends 0.150287278822863 0.105711 1.4217 0.157424 0.078712 KnowingPeople 0.0685444408465139 0.074002 0.9263 0.355967 0.177983 Liked 0.067513834434165 0.108103 0.6245 0.533331 0.266666 Celebrity 0.0171804895305078 0.186539 0.0921 0.926754 0.463377 WeightedSum -0.215996939893678 0.063692 -3.3913 0.000913 0.000456 BelongingstoSports 0.0814495958066655 0.018287 4.4541 1.8e-05 9e-06 ParentalCriticism -0.0503427071174557 0.074649 -0.6744 0.501215 0.250607 t -0.00806458497342902 0.004451 -1.8118 0.072232 0.036116 Multiple Linear Regression - Regression Statistics Multiple R 0.452136711340557 R-squared 0.204427605741854 Adjusted R-squared 0.151389446124644 F-TEST (value) 3.854349532813 F-TEST (DF numerator) 9 F-TEST (DF denominator) 135 p-value 0.000228534429356664 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.18838776189796 Sum Squared Residuals 646.52053451734 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14 13.1700115236517 0.829988476348288 2 18 16.3071297828483 1.69287021715173 3 11 15.0529563716883 -4.05295637168826 4 12 14.1989519126154 -2.19895191261545 5 16 13.9843699809504 2.0156300190496 6 18 14.8295336524277 3.17046634757233 7 14 14.2257125429181 -0.225712542918069 8 14 14.6509727970092 -0.650972797009207 9 15 14.9569784527705 0.0430215472294594 10 15 15.5101322575977 -0.510132257597746 11 17 15.8252905586515 1.1747094413485 12 19 13.5278424743396 5.47215752566045 13 10 13.5532104637937 -3.5532104637937 14 18 15.7001347256533 2.29986527434669 15 14 13.5974996661138 0.40250033388617 16 14 14.4361952593442 -0.436195259344156 17 17 16.4451052459982 0.554894754001783 18 14 14.1819596216009 -0.181959621600932 19 16 14.3241228330617 1.67587716693829 20 18 14.4510803978201 3.54891960217986 21 14 14.1046827734211 -0.104682773421147 22 12 12.992918554844 -0.992918554843993 23 17 15.1374207847159 1.86257921528405 24 9 14.9528606241741 -5.95286062417405 25 16 14.8210316775286 1.17896832247144 26 14 14.3831300306075 -0.383130030607525 27 11 14.9646332545474 -3.96463325454743 28 16 14.8214363767004 1.17856362329964 29 13 12.5579105253519 0.442089474648093 30 17 15.1851943087232 1.81480569127683 31 15 14.2305996463093 0.769400353690689 32 14 14.4474579458559 -0.447457945855909 33 16 14.181417837033 1.81858216296704 34 9 13.4076643554538 -4.40766435545376 35 15 14.8915216811204 0.108478318879613 36 17 13.448060646921 3.55193935307898 37 13 14.687847589186 -1.68784758918599 38 15 14.5879055524886 0.41209444751141 39 16 14.4623517769171 1.53764822308293 40 16 13.7207253152533 2.27927468474672 41 12 13.4661900704736 -1.46619007047361 42 11 13.4104170121854 -2.41041701218542 43 15 15.5697461072468 -0.56974610724678 44 17 14.421003338834 2.57899666116599 45 13 13.8606408499943 -0.860640849994334 46 16 14.2877454299756 1.71225457002441 47 14 12.2721327766849 1.72786722331511 48 11 13.3098114378352 -2.30981143783517 49 12 13.4132393816781 -1.41323938167814 50 12 12.1312134139001 -0.131213413900067 51 15 14.9862712584556 0.0137287415444296 52 16 14.9029809337773 1.09701906622272 53 15 14.3240699143115 0.675930085688524 54 12 14.851800346505 -2.85180034650496 55 12 13.4935673395746 -1.49356733957459 56 8 13.2776341566667 -5.27763415666668 57 13 15.7932366311729 -2.79323663117294 58 11 12.7004750202958 -1.70047502029582 59 14 13.9057347575484 0.0942652424515951 60 15 13.59870458744 1.40129541255999 61 10 15.0841405489961 -5.08414054899614 62 11 13.5684933385223 -2.56849333852233 63 12 14.7798580881976 -2.77985808819762 64 15 12.7980971236016 2.2019028763984 65 15 14.323244085015 0.676755914985013 66 14 15.3137650079683 -1.31376500796834 67 16 13.0658224818688 2.93417751813121 68 15 16.4256689813268 -1.4256689813268 69 15 15.2056841788117 -0.205684178811719 70 13 14.5755314465422 -1.57553144654221 71 17 15.2519680674717 1.74803193252825 72 13 13.6799515288514 -0.679951528851428 73 15 13.7383447688425 1.26165523115752 74 13 12.696976128585 0.303023871415021 75 15 13.4087480600144 1.59125193998556 76 16 11.1872837737297 4.81271622627033 77 15 13.4530551600805 1.54694483991947 78 16 13.4882007530518 2.51179924694825 79 15 13.3041407327747 1.69585926722529 80 14 13.8054135766838 0.194586423316199 81 15 13.7012737328993 1.29872626710071 82 7 14.1574275007249 -7.15742750072492 83 17 14.3120525305142 2.68794746948578 84 13 12.8497794233069 0.150220576693059 85 15 14.3296136026062 0.670386397393803 86 14 15.4705817388283 -1.47058173882834 87 13 14.4142529843817 -1.41425298438168 88 16 15.0636305452288 0.936369454771155 89 12 13.4320079541132 -1.4320079541132 90 14 13.8737641980839 0.126235801916119 91 17 14.6356734407509 2.36432655924908 92 15 14.1066625667745 0.893337433225519 93 17 15.1301184506206 1.86988154937938 94 12 14.4103580011544 -2.41035800115444 95 16 14.7690787562917 1.23092124370825 96 11 13.1234122920199 -2.12341229201994 97 15 14.4229739010641 0.577026098935911 98 9 13.0064158841188 -4.00641588411875 99 16 14.3895752797044 1.6104247202956 100 10 11.9445798366188 -1.94457983661876 101 10 11.1108929883659 -1.11089298836588 102 15 14.9303481750662 0.0696518249337507 103 11 12.3611599483093 -1.36115994830927 104 13 15.1402465221191 -2.14024652211911 105 14 13.2507683867453 0.749231613254662 106 18 13.8433312730264 4.1566687269736 107 16 15.1522828882833 0.847717111716747 108 14 12.1746376544887 1.82536234551129 109 14 13.7370676352061 0.262932364793851 110 14 14.2785542342993 -0.278554234299344 111 14 15.3448483794456 -1.34484837944564 112 12 11.9882914298471 0.0117085701528539 113 14 14.158088892604 -0.158088892603962 114 15 16.1854899823522 -1.18548998235222 115 15 13.7553691692275 1.2446308307725 116 13 14.6208459632646 -1.62084596326463 117 17 16.0157086957728 0.984291304227165 118 17 15.6399105856226 1.36008941437743 119 19 15.8078703913156 3.19212960868442 120 15 13.7738781617474 1.22612183825261 121 13 13.3738773925656 -0.373877392565593 122 9 12.4396902136984 -3.43969021369844 123 15 14.3019971688592 0.698002831140823 124 15 13.6386546317338 1.36134536826623 125 16 15.4167750989596 0.583224901040358 126 11 11.8379738092366 -0.837973809236574 127 14 13.5339230157962 0.466076984203817 128 11 11.6396958553392 -0.639695855339171 129 15 12.8573706542261 2.14262934577393 130 13 13.5783167614389 -0.578316761438865 131 16 13.5305064242993 2.46949357570071 132 14 14.4501623086304 -0.450162308630377 133 15 14.1628180743477 0.837181925652303 134 16 15.7031532135189 0.296846786481058 135 16 14.3726567713866 1.62734322861341 136 11 13.4896736638542 -2.48967366385422 137 13 14.5765263690527 -1.5765263690527 138 16 13.5024855964978 2.49751440350224 139 12 14.8783182613892 -2.87831826138916 140 9 12.7408880702764 -3.74088807027638 141 13 13.6775069861062 -0.677506986106245 142 13 12.3820334948481 0.617966505151942 143 14 12.7682898696218 1.23171013037817 144 19 15.6062557669798 3.39374423302015 145 13 14.680662176924 -1.68066217692401 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 13 0.902873876360188 0.194252247279623 0.0971261236398116 14 0.847966994949802 0.304066010100396 0.152033005050198 15 0.76612709614761 0.46774580770478 0.23387290385239 16 0.673788998681948 0.652422002636105 0.326211001318052 17 0.567341327612008 0.865317344775984 0.432658672387992 18 0.68250160900158 0.63499678199684 0.31749839099842 19 0.602883550821108 0.794232898357783 0.397116449178892 20 0.564866578216589 0.870266843566822 0.435133421783411 21 0.496868484902518 0.993736969805036 0.503131515097482 22 0.455040620323468 0.910081240646936 0.544959379676532 23 0.382557745512223 0.765115491024447 0.617442254487777 24 0.60664669525033 0.78670660949934 0.39335330474967 25 0.664704092417134 0.670591815165732 0.335295907582866 26 0.653135248165921 0.693729503668158 0.346864751834079 27 0.737064188728873 0.525871622542254 0.262935811271127 28 0.679524685133234 0.640950629733532 0.320475314866766 29 0.614139660840548 0.771720678318903 0.385860339159452 30 0.613969303733918 0.772061392532165 0.386030696266082 31 0.579402720757843 0.841194558484315 0.420597279242157 32 0.518198563929438 0.963602872141125 0.481801436070562 33 0.497218496326392 0.994436992652783 0.502781503673608 34 0.739810691758349 0.520378616483302 0.260189308241651 35 0.686150946373979 0.627698107252042 0.313849053626021 36 0.78806982396068 0.423860352078641 0.211930176039321 37 0.749471580896537 0.501056838206926 0.250528419103463 38 0.71074375138362 0.578512497232759 0.289256248616379 39 0.677078190843653 0.645843618312694 0.322921809156347 40 0.77720155644602 0.44559688710796 0.22279844355398 41 0.737235987340523 0.525528025318953 0.262764012659477 42 0.794147530138564 0.411704939722873 0.205852469861436 43 0.751503042203319 0.496993915593362 0.248496957796681 44 0.772423747535981 0.455152504928037 0.227576252464019 45 0.730226800576867 0.539546398846266 0.269773199423133 46 0.701674747297575 0.59665050540485 0.298325252702425 47 0.699424247468409 0.601151505063183 0.300575752531591 48 0.696448882849741 0.607102234300519 0.303551117150259 49 0.654157485903322 0.691685028193355 0.345842514096678 50 0.609925839917494 0.780148320165013 0.390074160082506 51 0.559066032505218 0.881867934989564 0.440933967494782 52 0.519050965652332 0.961898068695335 0.480949034347668 53 0.47332813648806 0.94665627297612 0.52667186351194 54 0.514389647964941 0.971220704070118 0.485610352035059 55 0.473091540122984 0.946183080245969 0.526908459877016 56 0.693764366378448 0.612471267243103 0.306235633621552 57 0.755766360524878 0.488467278950243 0.244233639475122 58 0.73062955923992 0.53874088152016 0.26937044076008 59 0.698722262983028 0.602555474033944 0.301277737016972 60 0.715482021128287 0.569035957743426 0.284517978871713 61 0.876130543312481 0.247738913375038 0.123869456687519 62 0.874766962290935 0.250466075418129 0.125233037709065 63 0.879770130342163 0.240459739315675 0.120229869657837 64 0.888419191221555 0.223161617556891 0.111580808778445 65 0.869105513113799 0.261788973772402 0.130894486886201 66 0.852210495477712 0.295579009044576 0.147789504522288 67 0.884446303717809 0.231107392564383 0.115553696282191 68 0.875887352912496 0.248225294175008 0.124112647087504 69 0.852411581032044 0.295176837935912 0.147588418967956 70 0.83683817865747 0.326323642685061 0.16316182134253 71 0.837348772946777 0.325302454106445 0.162651227053223 72 0.807301331895095 0.385397336209809 0.192698668104905 73 0.784751860054238 0.430496279891523 0.215248139945762 74 0.752006619610029 0.495986760779942 0.247993380389971 75 0.740177583543394 0.519644832913212 0.259822416456606 76 0.87402126239702 0.251957475205959 0.125978737602979 77 0.864129361523947 0.271741276952106 0.135870638476053 78 0.869903177791304 0.260193644417393 0.130096822208696 79 0.863865590162526 0.272268819674948 0.136134409837474 80 0.835852583990559 0.328294832018883 0.164147416009441 81 0.820581143110475 0.35883771377905 0.179418856889525 82 0.98646351529389 0.0270729694122186 0.0135364847061093 83 0.988192043646509 0.0236159127069826 0.0118079563534913 84 0.983639293709178 0.0327214125816436 0.0163607062908218 85 0.97828702842432 0.0434259431513609 0.0217129715756805 86 0.97470059720753 0.0505988055849397 0.0252994027924699 87 0.969493366885433 0.0610132662291349 0.0305066331145674 88 0.961676758602146 0.0766464827957081 0.0383232413978541 89 0.955022493222562 0.0899550135548757 0.0449775067774378 90 0.940886846587373 0.118226306825255 0.0591131534126273 91 0.950238520397626 0.0995229592047488 0.0497614796023744 92 0.9383562907716 0.123287418456801 0.0616437092284007 93 0.93686138714056 0.12627722571888 0.0631386128594402 94 0.94368190165541 0.11263619668918 0.0563180983445902 95 0.940306763400735 0.11938647319853 0.0596932365992651 96 0.934200540897764 0.131598918204472 0.0657994591022358 97 0.916901904075923 0.166196191848154 0.0830980959240772 98 0.95105749432986 0.0978850113402815 0.0489425056701407 99 0.941642824034408 0.116714351931185 0.0583571759655923 100 0.934922634821942 0.130154730356115 0.0650773651780577 101 0.916788212637174 0.166423574725651 0.0832117873628255 102 0.894494124278027 0.211011751443945 0.105505875721973 103 0.884373290067123 0.231253419865754 0.115626709932877 104 0.923623936292058 0.152752127415883 0.0763760637079415 105 0.90123243130861 0.197535137382782 0.098767568691391 106 0.9444733760845 0.111053247830999 0.0555266239154995 107 0.929262236061065 0.141475527877869 0.0707377639389347 108 0.93197192793206 0.136056144135879 0.0680280720679396 109 0.908248514149141 0.183502971701717 0.0917514858508586 110 0.880546370448098 0.238907259103803 0.119453629551902 111 0.851188312908785 0.29762337418243 0.148811687091215 112 0.809689855470186 0.380620289059628 0.190310144529814 113 0.789081776160246 0.421836447679509 0.210918223839754 114 0.777822045156518 0.444355909686963 0.222177954843482 115 0.731764822456411 0.536470355087177 0.268235177543589 116 0.735455467781212 0.529089064437576 0.264544532218788 117 0.708132654040492 0.583734691919017 0.291867345959508 118 0.64672342210521 0.706553155789581 0.353276577894791 119 0.605749417420415 0.78850116515917 0.394250582579585 120 0.545043172613554 0.909913654772892 0.454956827386446 121 0.465670552751138 0.931341105502275 0.534329447248862 122 0.520395507997001 0.959208984005997 0.479604492002999 123 0.446429441174351 0.892858882348701 0.553570558825649 124 0.363718692300631 0.727437384601261 0.63628130769937 125 0.282141241893151 0.564282483786303 0.717858758106849 126 0.209292543287856 0.418585086575711 0.790707456712144 127 0.174373095719379 0.348746191438758 0.825626904280621 128 0.117765757421846 0.235531514843691 0.882234242578154 129 0.138065734173595 0.276131468347189 0.861934265826405 130 0.0858334852583974 0.171666970516795 0.914166514741603 131 0.154282642858426 0.308565285716852 0.845717357141574 132 0.210998339588535 0.42199667917707 0.789001660411465 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 4 0.0333333333333333 OK 10% type I error level 10 0.0833333333333333 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

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

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

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Software written by Ed van Stee & Patrick Wessa

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