WS 10 - MR: Parental Expectations

*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 15:56:12 +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/t1292342077ynb0hvnxeinbuzx.htm/, Retrieved Tue, 14 Dec 2010 16:54:40 +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/t1292342077ynb0hvnxeinbuzx.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 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation PE[t] = + 6.09929709007711 -0.572369992530578Gender[t] + 0.0866727583352752CM[t] -0.106187261755795D[t] + 0.654214401976763PC[t] + 0.108281106271803PS[t] -0.0678164122781242O[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) 6.09929709007711 1.769616 3.4467 0.000734 0.000367 Gender -0.572369992530578 0.473541 -1.2087 0.228654 0.114327 CM 0.0866727583352752 0.048169 1.7994 0.073946 0.036973 D -0.106187261755795 0.088466 -1.2003 0.231884 0.115942 PC 0.654214401976763 0.086673 7.5481 0 0 PS 0.108281106271803 0.063497 1.7053 0.090183 0.045092 O -0.0678164122781242 0.064065 -1.0586 0.291481 0.14574 Multiple Linear Regression - Regression Statistics Multiple R 0.642671903267808 R-squared 0.413027175249867 Adjusted R-squared 0.38985719532552 F-TEST (value) 17.8259617228176 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 1.33226762955019e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.69132262201377 Sum Squared Residuals 1100.96905327598 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7 13.4790215593576 -6.4790215593576 2 17 13.7223485082571 3.27765149174287 3 12 13.7915107685519 -1.79151076855189 4 12 11.419197801635 0.580802198365016 5 11 10.3993545969737 0.600645403026295 6 11 14.580680552283 -3.58068055228304 7 12 10.8887291023586 1.11127089764138 8 13 11.5626678410552 1.43733215894484 9 16 14.8040223169915 1.19597768300851 10 11 13.917671981468 -2.91767198146803 11 10 12.3341263310336 -2.33412633103363 12 9 13.8775253695238 -4.8775253695238 13 17 15.6300265543229 1.36997344567709 14 11 13.8009030429944 -2.80090304299436 15 14 16.1017232463373 -2.10172324633732 16 15 13.3873642967625 1.61263570323748 17 15 11.8817870749611 3.11821292503885 18 13 11.364741893418 1.63525810658196 19 18 18.2222651603864 -0.222265160386393 20 18 12.3752575982404 5.6247424017596 21 12 13.7657038619946 -1.76570386199458 22 17 13.78786124272 3.21213875728002 23 18 16.9890609449493 1.0109390550507 24 14 14.0855922098401 -0.0855922098401114 25 16 11.0353708102567 4.96462918974332 26 14 13.2097406301866 0.7902593698134 27 12 13.9318998544545 -1.93189985445448 28 17 12.4685326799991 4.53146732000087 29 12 12.2713574366874 -0.271357436687365 30 6 9.57158546676449 -3.57158546676449 31 12 12.8381402142407 -0.838140214240721 32 12 13.1622060032669 -1.16220600326686 33 13 11.3844948876034 1.61550511239659 34 14 11.751220177951 2.24877982204905 35 11 12.910024943125 -1.91002494312496 36 12 12.9297980985731 -0.929798098573139 37 9 12.0840207057935 -3.08402070579355 38 15 14.7920872522315 0.207912747768452 39 18 15.1470445390622 2.85295546093781 40 15 12.3340072126947 2.66599278730533 41 12 13.0060905976401 -1.00609059764006 42 14 13.2876979351439 0.712302064856083 43 13 12.498427442688 0.501572557311992 44 13 14.0242774122607 -1.02427741226068 45 11 12.3335504727808 -1.33355047278083 46 16 14.604831944624 1.39516805537601 47 11 11.3163392758357 -0.316339275835669 48 16 17.8425176092899 -1.84251760928992 49 8 10.7901219010008 -2.79012190100075 50 15 11.895367660173 3.10463233982701 51 21 17.2766214861003 3.72337851389967 52 18 15.9327040765632 2.06729592343682 53 13 12.8384884513174 0.161511548682574 54 15 14.639362720409 0.360637279591004 55 19 14.4997704497342 4.50022955026582 56 15 14.1339948274225 0.866005172577521 57 11 10.8740990162105 0.125900983789524 58 10 12.4456086390732 -2.44560863907323 59 13 14.8059967890816 -1.8059967890816 60 15 14.9338924857613 0.0661075142386731 61 12 11.1834693227476 0.816530677252438 62 16 15.8486750713571 0.151324928642902 63 18 17.3561233486978 0.643876651302167 64 8 15.0189613657897 -7.01896136578966 65 13 10.5539444763119 2.44605552368813 66 17 14.100269028628 2.89973097137198 67 7 11.3849525033416 -4.38495250334156 68 12 11.4798728514652 0.520127148534764 69 14 15.1343503541272 -1.13435035412716 70 6 10.9453886014034 -4.94538860140342 71 10 9.92133842227163 0.0786615777283697 72 11 12.733927424575 -1.73392742457503 73 14 12.9961402528216 1.00385974717837 74 11 13.826490122488 -2.82649012248796 75 13 15.4124474454009 -2.41244744540086 76 12 12.0724441259617 -0.0724441259617144 77 9 9.64270316779782 -0.642703167797816 78 12 10.9052715227491 1.09472847725091 79 13 13.6653790889257 -0.665379088925654 80 12 16.4953887501336 -4.49538875013357 81 9 14.6418234657028 -5.64182346570285 82 15 15.615567730597 -0.61556773059703 83 24 21.3728487740045 2.62715122599552 84 17 14.7338534081697 2.2661465918303 85 11 12.1350932802317 -1.13509328023167 86 17 15.1369126839701 1.86308731602992 87 11 12.3741427009632 -1.37414270096319 88 12 12.6195031885327 -0.61950318853265 89 14 14.508037579048 -0.508037579048024 90 11 14.3007187352311 -3.30071873523108 91 16 13.0320060070345 2.96799399296549 92 21 13.9777789671579 7.02222103284213 93 14 12.2192429013384 1.78075709866163 94 20 16.4118979081276 3.58810209187241 95 13 11.1755313991589 1.82446860084113 96 15 14.0580306582564 0.941969341743591 97 19 18.0390374030643 0.96096259693569 98 11 14.8065442880252 -3.80654428802522 99 10 11.5440683590935 -1.54406835909346 100 14 14.420286084643 -0.420286084642973 101 11 11.8911781832088 -0.891178183208771 102 15 9.78383908400493 5.21616091599507 103 11 11.9133741348112 -0.913374134811166 104 17 11.7449754273477 5.25502457265228 105 18 14.888738100743 3.11126189925704 106 10 12.3501585876686 -2.35015858766865 107 11 11.5061274240657 -0.506127424065716 108 13 12.7090464090653 0.290953590934688 109 16 13.4049411110377 2.59505888896227 110 9 11.2108387926253 -2.21083879262526 111 9 11.9036709506943 -2.90367095069427 112 9 12.6842645606492 -3.68426456064922 113 12 8.57456651419814 3.42543348580186 114 12 12.5793743281817 -0.579374328181662 115 18 13.8767758391792 4.12322416082082 116 15 11.6219358249148 3.37806417508522 117 10 12.6877561431782 -2.68775614317823 118 11 11.2566983658032 -0.256698365803193 119 9 12.6631943759128 -3.6631943759128 120 5 9.56115178365452 -4.56115178365452 121 12 12.0113759446263 -0.0113759446263311 122 24 22.0806592190148 1.91934078098524 123 14 11.182937787465 2.81706221253502 124 7 8.92387176737853 -1.92387176737852 125 12 12.8359444948051 -0.835944494805105 126 13 11.1816214727382 1.81837852726175 127 8 12.5656846183953 -4.56568461839533 128 11 9.10041760999256 1.89958239000744 129 9 11.4656711459218 -2.46567114592177 130 11 13.3525901710125 -2.35259017101251 131 13 12.9511845774268 0.0488154225732003 132 10 9.21376464381042 0.786235356189582 133 13 9.67083062793933 3.32916937206067 134 10 11.6569670688472 -1.65696706884721 135 13 11.8719030463774 1.12809695362259 136 8 9.53114877221546 -1.53114877221546 137 16 11.296524187872 4.703475812128 138 9 11.0979015119945 -2.09790151199452 139 12 11.1079718509762 0.892028149023793 140 14 11.7406972774423 2.25930272255766 141 9 9.29770468570481 -0.297704685704813 142 11 13.2030282700808 -2.20302827008076 143 14 12.981208960393 1.01879103960702 144 12 11.3224402190038 0.677559780996194 145 12 10.6421904134693 1.35780958653066 146 11 12.7748690638148 -1.77486906381483 147 12 9.6391006727621 2.36089932723789 148 9 14.9363336552461 -5.93633365524615 149 9 10.6347008139448 -1.63470081394476 150 15 12.8496444524428 2.15035554755715 151 8 9.23522101476318 -1.23522101476318 152 8 9.99139579684937 -1.99139579684937 153 17 12.0401633500634 4.95983664993658 154 11 10.0429893683481 0.957010631651875 155 12 11.6916178387955 0.308382161204532 156 20 14.2654761241541 5.73452387584586 157 12 12.6851048500236 -0.685104850023614 158 7 9.6716274431671 -2.6716274431671 159 11 12.6720105380155 -1.67201053801552 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.966779411538558 0.066441176922885 0.0332205884614425 11 0.940169091742564 0.119661816514871 0.0598309082574355 12 0.939965018015625 0.120069963968749 0.0600349819843745 13 0.933423682587285 0.133152634825429 0.0665763174127147 14 0.918539231807907 0.162921536384186 0.081460768192093 15 0.876821646945461 0.246356706109077 0.123178353054539 16 0.855937793985203 0.288124412029595 0.144062206014797 17 0.852072387032613 0.295855225934775 0.147927612967387 18 0.808676049181311 0.382647901637378 0.191323950818689 19 0.757370773750539 0.485258452498923 0.242629226249461 20 0.83588332184247 0.328233356315059 0.164116678157529 21 0.855258627979334 0.289482744041331 0.144741372020666 22 0.863422068311847 0.273155863376306 0.136577931688153 23 0.832198712581362 0.335602574837275 0.167801287418638 24 0.782718532227274 0.434562935545452 0.217281467772726 25 0.818538435539538 0.362923128920925 0.181461564460462 26 0.785525972937995 0.42894805412401 0.214474027062005 27 0.75371795950932 0.49256408098136 0.24628204049068 28 0.768621314981016 0.462757370037969 0.231378685018984 29 0.717440169019046 0.565119661961908 0.282559830980954 30 0.721824443426854 0.556351113146293 0.278175556573146 31 0.683982084090175 0.632035831819649 0.316017915909825 32 0.648635747742433 0.702728504515133 0.351364252257567 33 0.604148354617243 0.791703290765513 0.395851645382757 34 0.560391527889729 0.879216944220541 0.439608472110271 35 0.559105432677874 0.881789134644251 0.440894567322126 36 0.513248870105965 0.97350225978807 0.486751129894035 37 0.515955058606998 0.968089882786003 0.484044941393002 38 0.465031316381868 0.930062632763736 0.534968683618132 39 0.470557574007248 0.941115148014496 0.529442425992752 40 0.463077715414813 0.926155430829626 0.536922284585187 41 0.409988390267911 0.819976780535821 0.590011609732089 42 0.3597387719205 0.719477543841001 0.6402612280795 43 0.312224765337636 0.624449530675272 0.687775234662364 44 0.287238521458278 0.574477042916556 0.712761478541722 45 0.259359059489708 0.518718118979416 0.740640940510292 46 0.239995783269358 0.479991566538715 0.760004216730642 47 0.216253170270383 0.432506340540766 0.783746829729617 48 0.189235864918961 0.378471729837922 0.810764135081039 49 0.176935385122426 0.353870770244851 0.823064614877575 50 0.184862450474873 0.369724900949746 0.815137549525127 51 0.216334523951937 0.432669047903873 0.783665476048063 52 0.219242334064987 0.438484668129974 0.780757665935013 53 0.187577920999049 0.375155841998098 0.81242207900095 54 0.156855153310095 0.313710306620189 0.843144846689905 55 0.251278562709181 0.502557125418362 0.748721437290819 56 0.225700578775367 0.451401157550734 0.774299421224633 57 0.192875489411007 0.385750978822014 0.807124510588993 58 0.180129375579453 0.360258751158905 0.819870624420547 59 0.1581108351822 0.316221670364399 0.8418891648178 60 0.130254587870966 0.260509175741932 0.869745412129034 61 0.119082191816173 0.238164383632346 0.880917808183827 62 0.112155343486853 0.224310686973707 0.887844656513147 63 0.0973147939441823 0.194629587888365 0.902685206055818 64 0.252494488677236 0.504988977354473 0.747505511322764 65 0.245966305927588 0.491932611855176 0.754033694072412 66 0.262567715704239 0.525135431408478 0.737432284295761 67 0.393719831456051 0.787439662912102 0.606280168543949 68 0.350361291226664 0.700722582453328 0.649638708773336 69 0.319256039958456 0.638512079916913 0.680743960041544 70 0.424617304746242 0.849234609492484 0.575382695253758 71 0.378704879969507 0.757409759939013 0.621295120030493 72 0.356942649087228 0.713885298174456 0.643057350912772 73 0.323937506818168 0.647875013636335 0.676062493181832 74 0.348494619336173 0.696989238672346 0.651505380663827 75 0.341661370725868 0.683322741451737 0.658338629274132 76 0.307110064407145 0.614220128814289 0.692889935592855 77 0.276452714894196 0.552905429788393 0.723547285105804 78 0.240706443598245 0.48141288719649 0.759293556401755 79 0.208567884184758 0.417135768369516 0.791432115815242 80 0.272228444465567 0.544456888931135 0.727771555534433 81 0.430739193808435 0.861478387616869 0.569260806191565 82 0.391841977949965 0.783683955899929 0.608158022050036 83 0.405610524768198 0.811221049536395 0.594389475231802 84 0.381040178666372 0.762080357332744 0.618959821333628 85 0.354135388527263 0.708270777054527 0.645864611472737 86 0.32610169338674 0.65220338677348 0.67389830661326 87 0.309771538437517 0.619543076875034 0.690228461562483 88 0.297260135263193 0.594520270526385 0.702739864736807 89 0.282593972378593 0.565187944757185 0.717406027621407 90 0.380362643903924 0.760725287807848 0.619637356096076 91 0.356183232150662 0.712366464301324 0.643816767849338 92 0.549810913954294 0.900378172091412 0.450189086045706 93 0.513521533890916 0.972956932218168 0.486478466109084 94 0.523385528699341 0.953228942601318 0.476614471300659 95 0.488007483592213 0.976014967184426 0.511992516407787 96 0.442093368098805 0.88418673619761 0.557906631901195 97 0.397496149223594 0.794992298447188 0.602503850776406 98 0.406292425672514 0.812584851345029 0.593707574327486 99 0.385588611209518 0.771177222419035 0.614411388790482 100 0.356294468883437 0.712588937766874 0.643705531116563 101 0.321049850655612 0.642099701311225 0.678950149344388 102 0.499659823681798 0.999319647363597 0.500340176318202 103 0.493332582305717 0.986665164611434 0.506667417694283 104 0.641049609352423 0.717900781295154 0.358950390647577 105 0.63411163247452 0.73177673505096 0.36588836752548 106 0.6355103391277 0.7289793217446 0.3644896608723 107 0.590361005727276 0.819277988545447 0.409638994272724 108 0.540874716044979 0.918250567910042 0.459125283955021 109 0.535727136212754 0.928545727574492 0.464272863787246 110 0.508790865011774 0.982418269976452 0.491209134988226 111 0.495386180679796 0.990772361359591 0.504613819320204 112 0.498225531580964 0.996451063161928 0.501774468419036 113 0.514165858626285 0.97166828274743 0.485834141373715 114 0.466290725251463 0.932581450502926 0.533709274748537 115 0.581887570186869 0.836224859626263 0.418112429813131 116 0.564503542258399 0.870992915483201 0.435496457741601 117 0.553647665200042 0.892704669599915 0.446352334799958 118 0.50035312025066 0.99929375949868 0.49964687974934 119 0.489440042632618 0.978880085265236 0.510559957367382 120 0.563457466196512 0.873085067606977 0.436542533803488 121 0.506195396078436 0.987609207843128 0.493804603921564 122 0.47691276465641 0.95382552931282 0.52308723534359 123 0.483207066115303 0.966414132230606 0.516792933884697 124 0.444115200594394 0.888230401188787 0.555884799405606 125 0.387042689885584 0.774085379771167 0.612957310114416 126 0.361189398866449 0.722378797732898 0.638810601133551 127 0.458374426696394 0.916748853392788 0.541625573303606 128 0.418102383021859 0.836204766043718 0.581897616978141 129 0.375084521337691 0.750169042675382 0.624915478662309 130 0.357790920898801 0.715581841797603 0.642209079101199 131 0.298507147485611 0.597014294971222 0.701492852514389 132 0.251834127689038 0.503668255378077 0.748165872310962 133 0.312491733669882 0.624983467339765 0.687508266330118 134 0.264286719547978 0.528573439095957 0.735713280452022 135 0.215926627366841 0.431853254733682 0.784073372633159 136 0.208881914036179 0.417763828072357 0.791118085963821 137 0.273485838086986 0.546971676173972 0.726514161913014 138 0.220460481652622 0.440920963305243 0.779539518347378 139 0.170597835388591 0.341195670777181 0.82940216461141 140 0.137792907493941 0.275585814987883 0.862207092506059 141 0.0971157532493388 0.194231506498678 0.902884246750661 142 0.0772499628127193 0.154499925625439 0.922750037187281 143 0.050102221013551 0.100204442027102 0.94989777898645 144 0.0309109576610268 0.0618219153220535 0.969089042338973 145 0.0200899926085775 0.040179985217155 0.979910007391423 146 0.0162264183342963 0.0324528366685926 0.983773581665704 147 0.0142033092684797 0.0284066185369594 0.98579669073152 148 0.209173249039185 0.41834649807837 0.790826750960815 149 0.180304093064731 0.360608186129461 0.81969590693527 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:

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292342077ynb0hvnxeinbuzx/101njx1292342161.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292342077ynb0hvnxeinbuzx/101njx1292342161.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292342077ynb0hvnxeinbuzx/1um431292342161.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292342077ynb0hvnxeinbuzx/1um431292342161.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292342077ynb0hvnxeinbuzx/25v3o1292342161.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292342077ynb0hvnxeinbuzx/25v3o1292342161.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292342077ynb0hvnxeinbuzx/35v3o1292342161.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292342077ynb0hvnxeinbuzx/35v3o1292342161.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292342077ynb0hvnxeinbuzx/45v3o1292342161.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292342077ynb0hvnxeinbuzx/45v3o1292342161.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292342077ynb0hvnxeinbuzx/5g5391292342161.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292342077ynb0hvnxeinbuzx/5g5391292342161.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292342077ynb0hvnxeinbuzx/6g5391292342161.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292342077ynb0hvnxeinbuzx/6g5391292342161.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292342077ynb0hvnxeinbuzx/7qwkc1292342161.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292342077ynb0hvnxeinbuzx/7qwkc1292342161.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292342077ynb0hvnxeinbuzx/81njx1292342161.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292342077ynb0hvnxeinbuzx/81njx1292342161.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292342077ynb0hvnxeinbuzx/91njx1292342161.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292342077ynb0hvnxeinbuzx/91njx1292342161.ps (open in new window)

Parameters (Session):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 4 ; 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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