WS 10 - MR: Doubts about actions

*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, 14 Dec 2010 15:54:19 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/14/t1292341978q6gnuu491bj7i0y.htm/, Retrieved Tue, 14 Dec 2010 16:52:58 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/14/t1292341978q6gnuu491bj7i0y.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 «

0 25 11 7 8 25 23 0 17 6 17 8 30 25 0 18 8 12 9 22 19 0 16 10 12 7 22 29 0 20 10 11 4 25 25 0 16 11 11 11 23 21 0 18 16 12 7 17 22 0 17 11 13 7 21 25 0 30 12 16 10 19 18 0 23 8 11 10 15 22 0 18 12 10 8 16 15 0 21 9 9 9 22 20 0 31 14 17 11 23 20 0 27 15 11 9 23 21 0 21 9 14 13 19 21 0 16 8 15 9 23 24 0 20 9 15 6 25 24 0 17 9 13 6 22 23 0 25 16 18 16 26 24 0 26 11 18 5 29 18 0 25 8 12 7 32 25 0 17 9 17 9 25 21 0 32 12 18 12 28 22 0 22 9 14 9 25 23 0 17 9 16 5 25 23 0 20 14 14 10 18 24 0 29 10 12 8 25 23 0 23 14 17 7 25 21 0 20 10 12 8 20 28 0 11 6 6 4 15 16 0 26 13 12 8 24 29 0 22 10 12 8 26 27 0 14 15 13 8 14 16 0 19 12 14 7 24 28 0 20 11 11 8 25 25 0 28 8 12 7 20 22 0 19 9 9 7 21 23 0 30 9 15 9 27 26 0 29 15 18 11 23 23 0 26 9 15 6 25 25 0 23 10 12 8 20 21 0 21 12 14 9 22 24 0 28 11 13 6 25 22 0 23 14 13 10 25 27 0 18 6 11 8 17 26 0 20 8 16 10 25 24 0 21 10 11 5 26 24 0 28 12 16 14 27 22 0 10 5 8 6 19 24 0 22 10 15 6 22 20 0 31 10 21 12 32 26 0 29 13 18 12 21 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 D[t] = + 7.28981769944956 + 0.881039528223467Gender[t] + 0.247509655175127CM[t] -0.088425700420726PE[t] + 0.151038276304408PC[t] -0.175896134084292PS[t] + 0.0764167144019203O[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) 7.28981769944956 1.569054 4.646 7e-06 4e-06 Gender 0.881039528223467 0.428277 2.0572 0.041379 0.020689 CM 0.247509655175127 0.039626 6.2461 0 0 PE -0.088425700420726 0.073669 -1.2003 0.231884 0.115942 PC 0.151038276304408 0.091926 1.643 0.10244 0.05122 PS -0.175896134084292 0.056729 -3.1006 0.002302 0.001151 O 0.0764167144019203 0.058349 1.3097 0.192289 0.096144 Multiple Linear Regression - Regression Statistics Multiple R 0.510045197445894 R-squared 0.260146103437621 Adjusted R-squared 0.23094134436279 F-TEST (value) 8.90766134283299 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 2.48383622558634e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.45594595312024 Sum Squared Residuals 916.81391974645 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 11 11.4270664654548 -0.427066465454784 2 6 7.8360849782289 -1.83608497822890 3 8 9.62543019807488 -1.62543019807488 4 10 9.592501479135 0.407498520864995 5 10 9.38449571148246 0.615504288517541 6 11 9.49785043547371 1.50214956452629 7 16 10.4320844590933 5.56791554090673 8 11 9.62181471036602 1.37818528963398 9 12 12.8441532226489 -0.844153222648853 10 8 12.5629655324714 -4.56296553247144 11 12 10.4009532695100 1.59904673049001 12 9 10.7096529792644 -1.70965297926435 13 14 12.6035243461743 1.39647565382566 14 15 11.9183800897913 3.08161991020871 15 9 11.4757826990331 -2.47578269903315 16 8 9.07132122438775 -1.07132122438775 17 9 9.25645274800645 -0.256452748006450 18 9 9.14204687117348 -0.142046871173476 19 16 11.5632105515797 4.43678944842031 20 11 9.16311047874194 1.83688952125806 21 8 9.75546017726055 -1.75546017726055 22 9 8.56093706734708 0.439062932652920 23 12 12.1869993356155 -0.186999335615527 24 9 10.2165958732887 -1.21659587328873 25 9 8.19804309135401 0.801956908645985 26 14 11.1803044922348 2.81969550776515 27 10 11.9749765840517 -1.97497658405167 28 14 9.74391844578902 4.25608155421097 29 10 11.0089539299066 -1.00895392990658 30 6 8.67024822823558 -2.67024822823558 31 13 11.8668440390221 1.13315596097790 32 10 10.3721797213492 -0.372179721349167 33 15 9.5738465301178 5.4261534698822 34 12 9.72997006124843 2.27002993875157 35 11 9.9886488167001 1.01135118329991 36 8 12.3794926085917 -4.37949260859167 37 9 10.3177033935953 -1.31770339359533 38 9 11.9857052893062 -2.9857052893062 39 15 12.2493294786091 2.75067052139088 40 9 10.8179273934591 -1.81792739345913 41 10 11.2165658946185 -1.21656589461852 42 12 10.5731913347684 1.42680866523160 43 11 11.2605479614451 -0.260547961445076 44 14 11.0092363627967 2.99076363720333 45 6 10.9772152934261 -4.97721529342609 46 8 9.77218015280336 -1.77218015280336 47 10 9.53073079447578 0.469269205524219 48 12 11.8517848024496 0.148215197550421 49 5 8.45571290370601 -3.45571290370601 50 10 9.9734936030019 0.0265063969981023 51 10 11.2762949004487 -1.27629490044874 52 13 12.5993265942783 0.400673405721733 53 10 11.0795893783874 -1.07958937838741 54 10 10.7256769437123 -0.725676943712285 55 9 9.77505000674727 -0.775050006747274 56 8 9.91633765040715 -1.91633765040715 57 14 11.4160841923176 2.58391580768237 58 8 10.7934851193662 -2.79348511936621 59 9 11.3951222496545 -2.39512224965451 60 14 11.5476306644512 2.45236933554876 61 8 9.49297444226475 -1.49297444226476 62 8 13.2856068854032 -5.28560688540323 63 7 8.69003696248559 -1.69003696248559 64 6 7.12801657480809 -1.12801657480809 65 8 8.99581178818015 -0.995811788180153 66 6 8.37000110057948 -2.37000110057948 67 11 11.5606391324515 -0.560639132451452 68 11 8.98354555198125 2.01645444801875 69 14 10.2130055682899 3.78699443171013 70 8 9.77063316074073 -1.77063316074073 71 8 8.6866448238785 -0.686644823878504 72 11 10.2409616651863 0.759038334813698 73 10 10.1593919321312 -0.159391932131153 74 14 13.0303781998924 0.969621800107553 75 11 10.4009106883930 0.599089311607034 76 9 10.1875828447298 -1.1875828447298 77 8 9.6497480014096 -1.64974800140960 78 13 9.77642048581644 3.22357951418356 79 12 9.25440034532692 2.74559965467308 80 13 10.9139550663853 2.08604493361467 81 14 12.3028434553447 1.69715654465532 82 12 11.4792844398343 0.520715560165656 83 14 11.1989464678924 2.80105353210758 84 13 10.2812612232269 2.71873877677309 85 16 11.4859501780969 4.51404982190309 86 9 11.8732388109950 -2.87323881099502 87 9 10.1591115047232 -1.15911150472325 88 9 10.7826642103246 -1.78266421032460 89 8 11.0178646768088 -3.01786467680884 90 7 9.73454081571445 -2.73454081571445 91 16 11.6260769756798 4.37392302432015 92 11 13.0106096506112 -2.01060965061122 93 9 9.97827399046014 -0.978273990460137 94 11 9.74182145651029 1.25817854348971 95 9 9.51690184462251 -0.516901844622511 96 13 10.7304801370234 2.26951986297663 97 16 14.2372411313607 1.76275886863933 98 14 12.7161929193279 1.28380708067209 99 12 11.3656381106959 0.634361889304061 100 13 12.9300534045082 0.0699465954917786 101 11 9.75468219401075 1.24531780598925 102 4 7.80921307165918 -3.80921307165918 103 8 10.5735802567502 -2.57358025675017 104 8 10.6393675539457 -2.63936755394575 105 16 14.4904594076710 1.50954059232896 106 14 14.7591597620569 -0.75915976205688 107 11 11.7309095033756 -0.730909503375649 108 9 12.0703449656655 -3.07034496566547 109 9 11.0966801347550 -2.09668013475504 110 10 12.0401686714644 -2.04016867146438 111 16 13.0874112333225 2.91258876667753 112 11 13.2051501649742 -2.20515016497421 113 16 9.7734991588323 6.22650084116771 114 12 11.0113546789331 0.98864532106695 115 14 12.9865593290887 1.01344067091126 116 10 11.3444899926022 -1.34448999260225 117 10 10.6293844824562 -0.629384482456151 118 12 10.5116207394694 1.48837926053062 119 14 12.6543990574409 1.34560094255912 120 16 12.5565229270477 3.44347707295229 121 9 10.9134111560878 -1.91341115608782 122 8 12.2511265540770 -4.25112655407697 123 8 9.50645171640571 -1.50645171640571 124 7 9.39609934544645 -2.39609934544645 125 9 10.3656680893661 -1.36566808936615 126 10 10.7377494663308 -0.737749466330787 127 13 10.8904638318223 2.10953616817774 128 10 8.84402033996097 1.15597966003903 129 11 12.1477185809318 -1.14771858093178 130 8 14.0435662397009 -6.04356623970091 131 9 9.78786816313071 -0.787868163130714 132 13 8.98880809031482 4.01119190968518 133 14 9.36177734158457 4.63822265841543 134 12 11.3680635159454 0.63193648405458 135 12 11.7664732605572 0.233526739442779 136 14 12.6325898161075 1.36741018389252 137 11 11.3270951777102 -0.327095177710184 138 14 10.4664505956656 3.53354940433436 139 10 11.4842169280899 -1.48421692808995 140 14 13.4202215329846 0.579778467015447 141 11 10.8577219400218 0.142278059978229 142 9 11.7806732074983 -2.78067320749825 143 16 14.1816402632293 1.81835973677065 144 9 11.3083207940057 -2.30832079400566 145 7 9.99134776291645 -2.99134776291645 146 14 13.0994413910869 0.900558608913107 147 14 11.1899516096039 2.81004839039613 148 8 11.5409767919281 -3.54097679192805 149 11 10.4229146116407 0.577085388359251 150 14 12.3558437832717 1.64415621672835 151 11 11.7245653771566 -0.72456537715656 152 20 11.7917943192120 8.20820568078805 153 11 10.8898852499325 0.110114750067473 154 9 10.1022535330555 -1.10225353305546 155 10 12.4590040776327 -2.45900407763274 156 13 11.4558452475065 1.54415475249345 157 8 10.8169397772171 -2.81693977721710 158 15 11.6449537948036 3.35504620519639 159 14 12.9492450060069 1.05075499399306 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.920560292559603 0.158879414880793 0.0794397074403965 11 0.870766057191831 0.258467885616338 0.129233942808169 12 0.805534722332077 0.388930555335846 0.194465277667923 13 0.849644630916183 0.300710738167635 0.150355369083817 14 0.88067573675122 0.238648526497558 0.119324263248779 15 0.83028880609617 0.33942238780766 0.16971119390383 16 0.767343977026904 0.465312045946192 0.232656022973096 17 0.709196412373852 0.581607175252296 0.290803587626148 18 0.642396821485437 0.715206357029125 0.357603178514563 19 0.841389313733352 0.317221372533297 0.158610686266648 20 0.79402023518469 0.411959529630618 0.205979764815309 21 0.768475054461398 0.463049891077204 0.231524945538602 22 0.70620224277173 0.587595514456541 0.293797757228270 23 0.644066104636299 0.711867790727402 0.355933895363701 24 0.5928594506332 0.814281098733599 0.407140549366799 25 0.522603776011809 0.954792447976382 0.477396223988191 26 0.514745906432083 0.970508187135834 0.485254093567917 27 0.479560256489632 0.959120512979264 0.520439743510368 28 0.546105612696136 0.907788774607727 0.453894387303864 29 0.489688972260135 0.97937794452027 0.510311027739865 30 0.479035240635118 0.958070481270237 0.520964759364882 31 0.43031389241846 0.86062778483692 0.56968610758154 32 0.368824353546552 0.737648707093104 0.631175646453448 33 0.510525762099101 0.978948475801797 0.489474237900899 34 0.486353736534236 0.972707473068473 0.513646263465763 35 0.447143421402457 0.894286842804915 0.552856578597543 36 0.568552386457343 0.862895227085315 0.431447613542657 37 0.516734421247039 0.966531157505922 0.483265578752961 38 0.525862075931596 0.948275848136808 0.474137924068404 39 0.508606211681789 0.982787576636423 0.491393788318211 40 0.481201018541067 0.962402037082134 0.518798981458933 41 0.437124433137084 0.874248866274168 0.562875566862916 42 0.393166764501818 0.786333529003635 0.606833235498182 43 0.343606457338632 0.687212914677264 0.656393542661368 44 0.375552156342335 0.75110431268467 0.624447843657665 45 0.540777578302884 0.918444843394231 0.459222421697116 46 0.547708782732924 0.904582434534153 0.452291217267076 47 0.504923492057137 0.990153015885727 0.495076507942863 48 0.453800629730759 0.907601259461518 0.546199370269241 49 0.484610159632274 0.969220319264549 0.515389840367726 50 0.435707809369982 0.871415618739963 0.564292190630018 51 0.425159077101731 0.850318154203462 0.574840922898269 52 0.378233854124927 0.756467708249853 0.621766145875073 53 0.343211230681168 0.686422461362335 0.656788769318832 54 0.306392129826863 0.612784259653726 0.693607870173137 55 0.298308190817282 0.596616381634563 0.701691809182718 56 0.293532033645806 0.587064067291613 0.706467966354194 57 0.302537616058857 0.605075232117715 0.697462383941143 58 0.310810262465321 0.621620524930642 0.689189737534679 59 0.311065069411716 0.622130138823432 0.688934930588284 60 0.306957166704542 0.613914333409084 0.693042833295458 61 0.284210390702237 0.568420781404473 0.715789609297763 62 0.453369111098378 0.906738222196757 0.546630888901621 63 0.444878308590582 0.889756617181164 0.555121691409418 64 0.408061774272904 0.816123548545808 0.591938225727096 65 0.372436086298574 0.744872172597149 0.627563913701426 66 0.380196565702611 0.760393131405223 0.619803434297388 67 0.343432522522803 0.686865045045606 0.656567477477197 68 0.326230420287963 0.652460840575925 0.673769579712037 69 0.382767024264364 0.765534048528727 0.617232975735636 70 0.368329803691718 0.736659607383436 0.631670196308282 71 0.331609475726211 0.663218951452423 0.668390524273789 72 0.297101783183351 0.594203566366701 0.702898216816649 73 0.26082943149197 0.52165886298394 0.73917056850803 74 0.235183472320016 0.470366944640032 0.764816527679984 75 0.201976495527828 0.403952991055656 0.798023504472172 76 0.184516007444063 0.369032014888127 0.815483992555937 77 0.180221766291806 0.360443532583611 0.819778233708194 78 0.193528307630399 0.387056615260798 0.806471692369601 79 0.193880707923050 0.387761415846099 0.80611929207695 80 0.178750146839893 0.357500293679787 0.821249853160107 81 0.161596799327869 0.323193598655739 0.83840320067213 82 0.13488057615116 0.26976115230232 0.86511942384884 83 0.158886375271734 0.317772750543467 0.841113624728266 84 0.162750205961903 0.325500411923805 0.837249794038097 85 0.243599038572092 0.487198077144184 0.756400961427908 86 0.254797349981771 0.509594699963542 0.745202650018229 87 0.226922519404062 0.453845038808123 0.773077480595939 88 0.213676745717185 0.427353491434371 0.786323254282815 89 0.242109304852523 0.484218609705046 0.757890695147477 90 0.273989910457488 0.547979820914975 0.726010089542512 91 0.33488735074803 0.66977470149606 0.66511264925197 92 0.335516379717769 0.671032759435539 0.66448362028223 93 0.306532229077806 0.613064458155611 0.693467770922194 94 0.271542383093073 0.543084766186145 0.728457616906927 95 0.262115393302898 0.524230786605796 0.737884606697102 96 0.236984363352317 0.473968726704633 0.763015636647683 97 0.205390533902447 0.410781067804894 0.794609466097553 98 0.18014853045513 0.36029706091026 0.81985146954487 99 0.150746693442547 0.301493386885095 0.849253306557453 100 0.126626058500074 0.253252117000148 0.873373941499926 101 0.109640033544546 0.219280067089093 0.890359966455454 102 0.166019214987134 0.332038429974267 0.833980785012866 103 0.152623838817585 0.305247677635171 0.847376161182415 104 0.156141782922664 0.312283565845327 0.843858217077336 105 0.163475311188926 0.326950622377852 0.836524688811074 106 0.134677989522881 0.269355979045763 0.865322010477119 107 0.114800491626555 0.229600983253110 0.885199508373445 108 0.120292285295007 0.240584570590013 0.879707714704993 109 0.105696262499609 0.211392524999219 0.89430373750039 110 0.1113284271949 0.2226568543898 0.8886715728051 111 0.126362703464412 0.252725406928825 0.873637296535588 112 0.111709095223264 0.223418190446529 0.888290904776736 113 0.280940811139448 0.561881622278897 0.719059188860552 114 0.249881169166168 0.499762338332337 0.750118830833832 115 0.214724247556329 0.429448495112658 0.785275752443671 116 0.180872363677695 0.36174472735539 0.819127636322305 117 0.148045745048186 0.296091490096372 0.851954254951814 118 0.127074353705162 0.254148707410324 0.872925646294838 119 0.114070412324093 0.228140824648187 0.885929587675907 120 0.138558760450007 0.277117520900015 0.861441239549993 121 0.127388569466693 0.254777138933386 0.872611430533307 122 0.128455058254028 0.256910116508056 0.871544941745972 123 0.107359360293524 0.214718720587048 0.892640639706476 124 0.157105539555202 0.314211079110404 0.842894460444798 125 0.135578933478434 0.271157866956868 0.864421066521566 126 0.110142038405405 0.220284076810809 0.889857961594595 127 0.107479284476083 0.214958568952166 0.892520715523917 128 0.0870976943139808 0.174195388627962 0.91290230568602 129 0.0846098267434806 0.169219653486961 0.91539017325652 130 0.260084616987087 0.520169233974174 0.739915383012913 131 0.212369551179317 0.424739102358635 0.787630448820683 132 0.255291038808177 0.510582077616355 0.744708961191823 133 0.369201145737146 0.738402291474293 0.630798854262854 134 0.312511870397302 0.625023740794604 0.687488129602698 135 0.256284412586973 0.512568825173946 0.743715587413027 136 0.251176236637339 0.502352473274677 0.748823763362661 137 0.200428368562623 0.400856737125245 0.799571631437377 138 0.221422529643532 0.442845059287064 0.778577470356468 139 0.174111007667818 0.348222015335637 0.825888992332181 140 0.134316009915565 0.268632019831130 0.865683990084435 141 0.0966495206990035 0.193299041398007 0.903350479300997 142 0.0843895094180379 0.168779018836076 0.915610490581962 143 0.0621277084946032 0.124255416989206 0.937872291505397 144 0.0508476942242718 0.101695388448544 0.949152305775728 145 0.0440895796437044 0.0881791592874088 0.955910420356296 146 0.0274164351618264 0.0548328703236528 0.972583564838174 147 0.0215212742218939 0.0430425484437878 0.978478725778106 148 0.0175934924084013 0.0351869848168026 0.982406507591599 149 0.00744838902495838 0.0148967780499168 0.992551610975042 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 3 0.0214285714285714 OK 10% type I error level 5 0.0357142857142857 OK

Charts produced by software:

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Parameters (Session):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 3 ; 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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Software written by Ed van Stee & Patrick Wessa

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