WS7 Celebrity

*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: Sun, 21 Nov 2010 18:23:11 +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/21/t1290364140wwnw17bonwxyiob.htm/, Retrieved Sun, 21 Nov 2010 19:29:11 +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/21/t1290364140wwnw17bonwxyiob.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 «

13 13 14 13 3 12 12 8 13 5 10 15 12 16 6 9 12 7 12 6 10 10 10 11 5 12 12 7 12 3 13 15 16 18 8 12 9 11 11 4 12 12 14 14 4 6 11 6 9 4 5 11 16 14 6 12 11 11 12 6 11 15 16 11 5 14 7 12 12 4 14 11 7 13 6 12 11 13 11 4 12 10 11 12 6 11 14 15 16 6 11 10 7 9 4 7 6 9 11 4 9 11 7 13 2 11 15 14 15 7 11 11 15 10 5 12 12 7 11 4 12 14 15 13 6 11 15 17 16 6 11 9 15 15 7 8 13 14 14 5 9 13 14 14 6 12 16 8 14 4 10 13 8 8 4 10 12 14 13 7 12 14 14 15 7 8 11 8 13 4 12 9 11 11 4 11 16 16 15 6 12 12 10 15 6 7 10 8 9 5 11 13 14 13 6 11 16 16 16 7 12 14 13 13 6 9 15 5 11 3 15 5 8 12 3 11 8 10 12 4 11 11 8 12 6 11 16 13 14 7 11 17 15 14 5 15 9 6 8 4 11 9 12 13 5 12 13 16 16 6 12 10 5 13 6 9 6 15 11 6 12 12 12 14 5 12 8 8 13 4 13 14 13 13 5 11 12 14 13 5 9 11 12 12 4 9 16 16 16 6 11 8 10 15 2 11 15 15 15 8 12 7 8 12 3 12 16 16 14 6 9 14 19 12 6 11 16 14 15 6 9 9 6 12 5 12 14 13 13 5 12 11 15 12 6 12 13 7 12 5 12 15 13 13 6 14 5 4 5 2 11 15 14 13 5 12 13 13 13 5 11 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 9 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Celebrity[t] = + 0.423591992490579 -0.0194376966141400FindingFriends[t] + 0.154094039023444Popularity[t] + 0.103356510337141KnowingPeople[t] + 0.147677870542413Liked[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) 0.423591992490579 0.705713 0.6002 0.549251 0.274625 FindingFriends -0.0194376966141400 0.047694 -0.4076 0.68418 0.34209 Popularity 0.154094039023444 0.038342 4.0189 9.2e-05 4.6e-05 KnowingPeople 0.103356510337141 0.030848 3.3505 0.001019 0.00051 Liked 0.147677870542413 0.048384 3.0522 0.002685 0.001342 Multiple Linear Regression - Regression Statistics Multiple R 0.677446083231663 R-squared 0.458933195685922 Adjusted R-squared 0.444600300207403 F-TEST (value) 32.0195731821073 F-TEST (DF numerator) 4 F-TEST (DF denominator) 151 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.04372839595306 Sum Squared Residuals 164.494713642332 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3 5.54092790558286 -2.54092790558286 2 5 4.78613250115072 0.213867498849284 3 6 6.14374966442514 -0.143749664425136 4 6 4.59341121011358 1.40658878988642 5 5 4.42817709592157 0.571822904078433 6 3 4.53509812027116 -1.53509812027116 7 8 6.7942183570161 1.2057816429839 8 4 4.33856417400698 -0.338564174006982 9 4 5.55394943371597 -1.55394943371597 10 4 3.95124013896818 0.0487598610318215 11 6 5.74263229166579 0.257367708334207 12 6 4.79443012259628 1.20556987740372 13 5 5.79934865644749 -0.79934865644749 14 4 4.24253508361137 -0.242535083611369 15 6 4.48980655856185 1.51019344143815 16 4 4.85346527272815 -0.853465272728152 17 6 4.64033608357284 1.35966391642716 18 6 6.28028745979897 -0.280287459798969 19 4 3.80331412721118 0.196685872788824 20 4 3.76675751933307 0.233242480666932 21 2 4.58699504163255 -2.58699504163255 22 7 6.18334711794286 0.816652882057141 23 5 4.93193811947416 0.0680618805258387 24 4 4.38742024972875 -0.387420249728749 25 6 5.81781615155759 0.182183848442409 26 6 6.6410945194967 -0.641094519496695 27 7 5.36213939413934 1.63786060586066 28 5 5.78579425919598 -0.785794259195978 29 6 5.76635656258184 0.233643437418162 30 4 5.5501865277869 -1.55018652778690 31 4 4.24071258069038 -0.240712580690376 32 7 5.44514695640184 1.55485304359816 33 7 6.00981538230528 0.990184617694725 34 4 4.70978924858383 -0.709789248583832 35 4 4.33856417400698 -0.338564174006982 36 6 6.54415417764058 -0.544154177640585 37 6 5.28820126290982 0.711798737090177 38 5 3.98442142400488 1.01557857599512 39 6 5.57980329881115 0.420196701188854 40 7 6.691832048183 0.308167951817002 41 6 5.61110313088331 0.388896869116691 42 3 4.70130243596722 -1.70130243596722 43 3 3.50148326760178 -0.501483267601777 44 4 4.24822919180295 -0.24822919180295 45 6 4.503798288199 1.496201711801 46 7 6.08640677608675 0.913593223913251 47 5 6.44721383578447 -1.44721383578447 48 4 3.32043492085162 0.679565079148381 49 5 4.75671412204309 0.243285877956911 50 6 6.21011223449853 -0.210112234498526 51 6 4.16787489209240 1.83212510790760 52 6 4.34802118812764 1.65197881187237 53 5 5.34723641304169 -0.347236413041693 54 4 4.16975634505694 -0.169756345056941 55 5 5.59166543426917 -0.591665434269169 56 5 5.4257092597877 -0.425709259787702 57 4 4.95609972277584 -0.956099722775843 58 6 6.73070744141128 -0.730707441411277 59 2 4.69126280343019 -2.69126280343019 60 8 6.28670362828 1.71329637172 61 3 3.86798443549108 -0.867984435491084 62 6 6.37703861048403 -0.377038610484032 63 6 6.14187741220616 -0.141877412206162 64 6 6.3374411569663 -0.337441156966303 65 5 4.02777258270611 0.97222741729389 66 5 5.61110313088331 -0.611103130883309 67 6 5.20785616394485 0.792143836055153 68 5 4.68919215929461 0.310807840705394 69 6 5.76519716990675 0.234802830093248 70 2 2.07374982907046 -0.0737498290704635 71 5 5.88799137685803 -0.887991376858033 72 5 5.45700909185986 -0.457009091859865 73 5 5.10922356029525 -0.109223560295248 74 6 5.95951518600461 0.0404848139953913 75 6 5.23843393572756 0.76156606427244 76 6 5.5096280735107 0.490371926489297 77 5 5.23915599601701 -0.239155996017010 78 5 5.38066583929298 -0.380665839292981 79 4 5.24199844974002 -1.24199844974002 80 2 3.35949950525095 -1.35949950525095 81 4 3.76462792515394 0.235372074846057 82 6 5.58005144002574 0.419948559974264 83 6 6.07357443912469 -0.0735744391246866 84 5 4.67921147680112 0.320788523198882 85 3 4.48247913862032 -1.48247913862032 86 6 5.03244297534273 0.967557024657273 87 4 3.90025446906729 0.0997455309327137 88 5 5.48874625631766 -0.488746256317664 89 8 6.3374411569663 1.66255884303370 90 4 4.4530607595127 -0.453060759512697 91 6 5.76350490811326 0.236495091886737 92 6 5.3095204124885 0.690479587511501 93 7 6.67239435156886 0.327605648431142 94 6 6.11414209414646 -0.114142094146455 95 5 4.96796185823387 0.0320381417661339 96 4 4.182588682019 -0.182588682019002 97 6 3.85351878677908 2.14648121322092 98 3 3.60392852647842 -0.603928526478421 99 5 5.6252840516915 -0.625284051691504 100 6 5.25029607118558 0.749703928814417 101 7 6.79518855852014 0.204811441479861 102 7 6.4213599706893 0.578640029310696 103 6 6.72404313171566 -0.724043131715656 104 3 4.36084432434413 -1.36084432434413 105 2 2.73579592921564 -0.735795929215643 106 8 5.72462951488498 2.27537048511502 107 3 4.67279530832009 -1.67279530832009 108 8 6.13260958925656 1.86739041074344 109 3 4.56302262950192 -1.56302262950192 110 4 4.66565707954961 -0.665657079549607 111 5 5.23201776724653 -0.232017767246529 112 7 5.58737885996726 1.41262114003274 113 6 4.52868195179013 1.47131804820987 114 6 5.90645887196813 0.093541128031866 115 7 6.10487427119685 0.89512572880315 116 6 6.18976328642389 -0.189763286423890 117 6 6.17032558980975 -0.17032558980975 118 6 5.07507207375451 0.92492792624549 119 6 5.9654940221 0.0345059778999965 120 4 5.3795064466179 -1.37950644661789 121 4 5.19955854249928 -1.19955854249928 122 5 5.79293248796646 -0.792932487966459 123 4 4.14487268146581 -0.144872681465809 124 6 5.79196228646242 0.208037713537580 125 6 6.27368210014689 -0.273682100146891 126 5 4.72709735101885 0.272902648981154 127 8 6.46568133089458 1.53431866910542 128 6 5.5096280735107 0.490371926489297 129 5 5.06418013980053 -0.0641801398005265 130 4 2.09531711986373 1.90468288013627 131 8 6.46568133089458 1.53431866910542 132 6 5.68127835618375 0.318721643816249 133 4 4.92097803473107 -0.920978034731066 134 6 5.52621411565627 0.473785884343732 135 6 5.91287504044916 0.087124959550835 136 4 4.88948901148786 -0.889489011487857 137 6 5.98493171871414 0.0150682812858566 138 3 4.38476698717679 -1.38476698717679 139 6 6.88364208775964 -0.883642087759635 140 5 5.59282482694425 -0.592824826944255 141 4 5.63242228046198 -1.63242228046198 142 6 5.70804347273942 0.291956527260581 143 4 6.31158729187113 -2.31158729187113 144 4 3.38159966516261 0.618400334837386 145 4 4.992845521825 -0.992845521824998 146 6 4.04508068514112 1.95491931485888 147 5 4.31743421559935 0.682565784400647 148 6 5.43848264670622 0.561517353293779 149 6 6.24238226807473 -0.242382268074728 150 8 6.11129043967788 1.88870956032212 151 7 5.37309027813686 1.62690972186314 152 7 6.56903784123172 0.430962158768284 153 4 4.29896672048925 -0.298966720489253 154 6 5.84197775485927 0.158022245140727 155 6 5.58621946729218 0.413780532707823 156 2 5.26331759931869 -3.26331759931869 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.456942541526257 0.913885083052514 0.543057458473743 9 0.58160814466977 0.83678371066046 0.41839185533023 10 0.435631460184382 0.871262920368765 0.564368539815618 11 0.570793240841874 0.858413518316252 0.429206759158126 12 0.76914389297211 0.461712214055780 0.230856107027890 13 0.85026384317645 0.299472313647101 0.149736156823551 14 0.787057473314891 0.425885053370218 0.212942526685109 15 0.809999083107689 0.380001833784622 0.190000916892311 16 0.748401610101418 0.503196779797165 0.251598389898582 17 0.786286347979022 0.427427304041956 0.213713652020978 18 0.725896576339637 0.548206847320727 0.274103423660363 19 0.659845740605459 0.680308518789082 0.340154259394541 20 0.617605874472805 0.76478825105439 0.382394125527195 21 0.932495193624231 0.135009612751538 0.067504806375769 22 0.927716105317819 0.144567789364363 0.0722838946821814 23 0.907371162342088 0.185257675315824 0.0926288376579119 24 0.878012929800598 0.243974140398803 0.121987070199402 25 0.847414292259357 0.305171415481285 0.152585707740643 26 0.815041414202185 0.369917171595631 0.184958585797815 27 0.835640083313921 0.328719833372158 0.164359916686079 28 0.81167697746294 0.37664604507412 0.18832302253706 29 0.770575225055105 0.45884954988979 0.229424774944895 30 0.77952745862727 0.440945082745459 0.220472541372730 31 0.744601123625445 0.51079775274911 0.255398876374555 32 0.795286509548177 0.409426980903647 0.204713490451823 33 0.79295356161886 0.414092876762281 0.207046438381140 34 0.770534108073438 0.458931783853124 0.229465891926562 35 0.733280478909927 0.533439042180146 0.266719521090073 36 0.690086978123317 0.619826043753366 0.309913021876683 37 0.656125895624163 0.687748208751674 0.343874104375837 38 0.660392393054405 0.67921521389119 0.339607606945595 39 0.619223182081245 0.76155363583751 0.380776817918755 40 0.574602346977231 0.850795306045537 0.425397653022769 41 0.534529123543423 0.930941752913154 0.465470876456577 42 0.571513787993215 0.85697242401357 0.428486212006785 43 0.557746460688832 0.884507078622336 0.442253539311168 44 0.513529531493348 0.972940937013304 0.486470468506652 45 0.576128644643141 0.847742710713718 0.423871355356859 46 0.576254130480047 0.847491739039906 0.423745869519953 47 0.6035494414739 0.7929011170522 0.3964505585261 48 0.583914909648103 0.832170180703795 0.416085090351897 49 0.536128505931799 0.927742988136402 0.463871494068201 50 0.489927941971274 0.979855883942548 0.510072058028726 51 0.572924330168371 0.854151339663258 0.427075669831629 52 0.621308721679724 0.757382556640551 0.378691278320276 53 0.580345803042144 0.839308393915713 0.419654196957856 54 0.543404601116988 0.913190797766024 0.456595398883012 55 0.505076658735207 0.989846682529586 0.494923341264793 56 0.464307316087952 0.928614632175905 0.535692683912048 57 0.461789365255345 0.92357873051069 0.538210634744655 58 0.432537690134231 0.865075380268463 0.567462309865769 59 0.724677442669572 0.550645114660856 0.275322557330428 60 0.793390370237008 0.413219259525983 0.206609629762992 61 0.783385182328559 0.433229635342882 0.216614817671441 62 0.750599257700745 0.498801484598509 0.249400742299255 63 0.712161510645375 0.57567697870925 0.287838489354625 64 0.674429055515129 0.651141888969743 0.325570944484871 65 0.665333871513326 0.669332256973349 0.334666128486674 66 0.634731547549665 0.73053690490067 0.365268452450335 67 0.616739001216388 0.766521997567224 0.383260998783612 68 0.577280470541103 0.845439058917795 0.422719529458897 69 0.534523143568331 0.930953712863338 0.465476856431669 70 0.488953197025902 0.977906394051805 0.511046802974098 71 0.475126206237542 0.950252412475083 0.524873793762458 72 0.436371246774293 0.872742493548586 0.563628753225707 73 0.39084736143408 0.78169472286816 0.60915263856592 74 0.34762990474239 0.69525980948478 0.65237009525761 75 0.327187249902991 0.654374499805983 0.672812750097008 76 0.296282266103194 0.592564532206388 0.703717733896806 77 0.258458366293145 0.516916732586291 0.741541633706855 78 0.226768711649551 0.453537423299103 0.773231288350449 79 0.246301688738855 0.49260337747771 0.753698311261145 80 0.273223815240399 0.546447630480798 0.726776184759601 81 0.237908407841389 0.475816815682779 0.76209159215861 82 0.207212544111931 0.414425088223863 0.792787455888069 83 0.175449053373234 0.350898106746469 0.824550946626766 84 0.149467139277225 0.29893427855445 0.850532860722775 85 0.203227193567775 0.406454387135551 0.796772806432225 86 0.198117752100360 0.396235504200719 0.80188224789964 87 0.167058400859033 0.334116801718066 0.832941599140967 88 0.144915474182261 0.289830948364522 0.855084525817739 89 0.188284743075860 0.376569486151719 0.81171525692414 90 0.164394653576699 0.328789307153399 0.8356053464233 91 0.139542431935228 0.279084863870456 0.860457568064772 92 0.133134560809571 0.266269121619142 0.86686543919043 93 0.112076019107943 0.224152038215887 0.887923980892056 94 0.0911844811581383 0.182368962316277 0.908815518841862 95 0.0732880572252197 0.146576114450439 0.92671194277478 96 0.0595972326385815 0.119194465277163 0.940402767361418 97 0.114064863195602 0.228129726391204 0.885935136804398 98 0.104649658564899 0.209299317129798 0.895350341435101 99 0.0903641436849533 0.180728287369907 0.909635856315047 100 0.0787848635920172 0.157569727184034 0.921215136407983 101 0.0642226815171045 0.128445363034209 0.935777318482895 102 0.0539830161188285 0.107966032237657 0.946016983881172 103 0.0448792234169341 0.0897584468338682 0.955120776583066 104 0.0624390396941538 0.124878079388308 0.937560960305846 105 0.0570680364828296 0.114136072965659 0.94293196351717 106 0.113463365461395 0.226926730922789 0.886536634538605 107 0.141597999846768 0.283195999693536 0.858402000153232 108 0.234402979314345 0.468805958628689 0.765597020685655 109 0.262099585600219 0.524199171200439 0.73790041439978 110 0.230140180982935 0.46028036196587 0.769859819017065 111 0.193406395319838 0.386812790639677 0.806593604680162 112 0.277215998298629 0.554431996597258 0.722784001701371 113 0.279675445981658 0.559350891963315 0.720324554018342 114 0.237544908314449 0.475089816628897 0.762455091685551 115 0.224906736563864 0.449813473127727 0.775093263436136 116 0.187272895543949 0.374545791087898 0.812727104456051 117 0.154669916550935 0.30933983310187 0.845330083449065 118 0.145717375151959 0.291434750303917 0.854282624848041 119 0.117643857180124 0.235287714360247 0.882356142819877 120 0.156235625930721 0.312471251861443 0.843764374069279 121 0.171214170395716 0.342428340791431 0.828785829604284 122 0.153878187753764 0.307756375507528 0.846121812246236 123 0.122333865406632 0.244667730813264 0.877666134593368 124 0.096645169493269 0.193290338986538 0.903354830506731 125 0.0771292258168415 0.154258451633683 0.922870774183159 126 0.0606389121879251 0.121277824375850 0.939361087812075 127 0.0845615340492701 0.169123068098540 0.91543846595073 128 0.0720864360321491 0.144172872064298 0.927913563967851 129 0.0608930660556173 0.121786132111235 0.939106933944383 130 0.083855649239921 0.167711298479842 0.91614435076008 131 0.118428590644808 0.236857181289616 0.881571409355192 132 0.089330679254932 0.178661358509864 0.910669320745068 133 0.0716991503697098 0.143398300739420 0.92830084963029 134 0.0520255359935979 0.104051071987196 0.947974464006402 135 0.0359390360193623 0.0718780720387246 0.964060963980638 136 0.041762985975061 0.083525971950122 0.95823701402494 137 0.0313787681916426 0.0627575363832852 0.968621231808357 138 0.0264089467474253 0.0528178934948506 0.973591053252575 139 0.0306369485889353 0.0612738971778706 0.969363051411065 140 0.0253797316865256 0.0507594633730512 0.974620268313474 141 0.0193201778691544 0.0386403557383088 0.980679822130846 142 0.0118689031077122 0.0237378062154245 0.988131096892288 143 0.0426730701360779 0.0853461402721558 0.957326929863922 144 0.0279665082245043 0.0559330164490085 0.972033491775496 145 0.0481484327466246 0.0962968654932491 0.951851567253375 146 0.0334312446114262 0.0668624892228524 0.966568755388574 147 0.0334611985729549 0.0669223971459098 0.966538801427045 148 0.0289184415192506 0.0578368830385012 0.97108155848075 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 2 0.0141843971631206 OK 10% type I error level 15 0.106382978723404 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290364140wwnw17bonwxyiob/10f6rb1290363780.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290364140wwnw17bonwxyiob/10f6rb1290363780.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290364140wwnw17bonwxyiob/1rnbz1290363780.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290364140wwnw17bonwxyiob/1rnbz1290363780.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290364140wwnw17bonwxyiob/2rnbz1290363780.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290364140wwnw17bonwxyiob/2rnbz1290363780.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290364140wwnw17bonwxyiob/3jwt21290363780.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290364140wwnw17bonwxyiob/3jwt21290363780.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290364140wwnw17bonwxyiob/4jwt21290363780.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290364140wwnw17bonwxyiob/4jwt21290363780.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290364140wwnw17bonwxyiob/5jwt21290363780.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290364140wwnw17bonwxyiob/5jwt21290363780.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290364140wwnw17bonwxyiob/6uos51290363780.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290364140wwnw17bonwxyiob/6uos51290363780.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290364140wwnw17bonwxyiob/7nfrq1290363780.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290364140wwnw17bonwxyiob/7nfrq1290363780.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290364140wwnw17bonwxyiob/8nfrq1290363780.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290364140wwnw17bonwxyiob/8nfrq1290363780.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290364140wwnw17bonwxyiob/9nfrq1290363780.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290364140wwnw17bonwxyiob/9nfrq1290363780.ps (open in new window)

Parameters (Session):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 5 ; 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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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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