ws 7

*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, 23 Nov 2010 14:08:19 +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/Nov/23/t129052124358get5agh3t9wh9.htm/, Retrieved Tue, 23 Nov 2010 15:07:26 +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/23/t129052124358get5agh3t9wh9.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 15 10 12 16 6 12 9 7 12 6 10 10 10 11 5 12 12 7 12 3 15 13 16 18 8 9 12 11 11 4 12 12 14 14 4 11 6 6 9 4 11 5 16 14 6 11 12 11 12 6 15 11 16 11 5 7 14 12 12 4 11 14 7 13 6 11 12 13 11 4 10 12 11 12 6 14 11 15 16 6 10 11 7 9 4 6 7 9 11 4 11 9 7 13 2 15 11 14 15 7 11 11 15 10 5 12 12 7 11 4 14 12 15 13 6 15 11 17 16 6 9 11 15 15 7 13 8 14 14 5 13 9 14 14 6 16 12 8 14 4 13 10 8 8 4 12 10 14 13 7 14 12 14 15 7 11 8 8 13 4 9 12 11 11 4 16 11 16 15 6 12 12 10 15 6 10 7 8 9 5 13 11 14 13 6 16 11 16 16 7 14 12 13 13 6 15 9 5 11 3 5 15 8 12 3 8 11 10 12 4 11 11 8 12 6 16 11 13 14 7 17 11 15 14 5 9 15 6 8 4 9 11 12 13 5 13 12 16 16 6 10 12 5 13 6 6 9 15 11 6 12 12 12 14 5 8 12 8 13 4 14 13 13 13 5 12 11 14 13 5 11 9 12 12 4 16 9 16 16 6 8 11 10 15 2 15 11 15 15 8 7 12 8 12 3 16 12 16 14 6 14 9 19 12 6 16 11 14 15 6 9 9 6 12 5 14 12 13 13 5 11 12 15 12 6 13 12 7 12 5 15 12 13 13 6 5 14 4 5 2 15 11 14 13 5 13 12 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 'RServer@AstonUniversity' @ vre.aston.ac.uk R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation Celebrity [t] = + 0.423591992490597 + 0.154094039023444Popularity[t] -0.0194376966141408FindingFriends[t] + 0.103356510337141KnowingPeople[t] + 0.147677870542411Liked[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) 0.423591992490597 0.705713 0.6002 0.549251 0.274625 Popularity 0.154094039023444 0.038342 4.0189 9.2e-05 4.6e-05 FindingFriends -0.0194376966141408 0.047694 -0.4076 0.68418 0.34209 KnowingPeople 0.103356510337141 0.030848 3.3505 0.001019 0.00051 Liked 0.147677870542411 0.048384 3.0522 0.002685 0.001342 Multiple Linear Regression - Regression Statistics Multiple R 0.677446083231663 R-squared 0.458933195685921 Adjusted R-squared 0.444600300207403 F-TEST (value) 32.0195731821072 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 4.78613250115071 0.213867498849285 3 6 6.14374966442513 -0.143749664425127 4 6 4.59341121011358 1.40658878988641 5 5 4.42817709592157 0.571822904078432 6 3 4.53509812027116 -1.53509812027116 7 8 6.7942183570161 1.20578164298391 8 4 4.33856417400698 -0.338564174006983 9 4 5.55394943371597 -1.55394943371597 10 4 3.95124013896819 0.048759861031813 11 6 5.7426322916658 0.257367708334203 12 6 4.79443012259628 1.20556987740372 13 5 5.79934865644749 -0.799348656447494 14 4 4.24253508361137 -0.242535083611366 15 6 4.48980655856185 1.51019344143815 16 4 4.85346527272815 -0.853465272728154 17 6 4.64033608357284 1.35966391642716 18 6 6.28028745979897 -0.280287459798966 19 4 3.80331412721118 0.19668587278882 20 4 3.76675751933307 0.233242480666927 21 2 4.58699504163255 -2.58699504163255 22 7 6.18334711794286 0.816652882057142 23 5 4.93193811947417 0.0680618805258348 24 4 4.38742024972875 -0.38742024972875 25 6 5.81781615155759 0.182183848442409 26 6 6.6410945194967 -0.641094519496693 27 7 5.36213939413934 1.63786060586067 28 5 5.78579425919598 -0.78579425919598 29 6 5.76635656258184 0.23364343741816 30 4 5.5501865277869 -1.5501865277869 31 4 4.24071258069038 -0.240712580690383 32 7 5.44514695640184 1.55485304359816 33 7 6.00981538230527 0.990184617694727 34 4 4.70978924858383 -0.709789248583834 35 4 4.33856417400698 -0.338564174006983 36 6 6.54415417764058 -0.544154177640584 37 6 5.28820126290982 0.71179873709018 38 5 3.98442142400488 1.01557857599512 39 6 5.57980329881115 0.420196701188853 40 7 6.691832048183 0.308167951817004 41 6 5.61110313088331 0.388896869116691 42 3 4.70130243596722 -1.70130243596722 43 3 3.50148326760177 -0.501483267601773 44 4 4.24822919180295 -0.24822919180295 45 6 4.503798288199 1.496201711801 46 7 6.08640677608675 0.91359322391325 47 5 6.44721383578448 -1.44721383578448 48 4 3.32043492085162 0.67956507914838 49 5 4.75671412204309 0.243285877956912 50 6 6.21011223449852 -0.210112234498523 51 6 4.1678748920924 1.8321251079076 52 6 4.34802118812764 1.65197881187236 53 5 5.34723641304169 -0.347236413041691 54 4 4.16975634505694 -0.169756345056939 55 5 5.59166543426917 -0.591665434269168 56 5 5.4257092597877 -0.425709259787703 57 4 4.95609972277585 -0.956099722775846 58 6 6.73070744141128 -0.730707441411277 59 2 4.69126280343018 -2.69126280343019 60 8 6.28670362828 1.71329637172 61 3 3.86798443549108 -0.867984435491083 62 6 6.37703861048403 -0.377038610484032 63 6 6.14187741220617 -0.141877412206167 64 6 6.3374411569663 -0.337441156966302 65 5 4.02777258270611 0.972227417293889 66 5 5.61110313088331 -0.611103130883309 67 6 5.20785616394485 0.792143836055152 68 5 4.68919215929461 0.310807840705394 69 6 5.76519716990675 0.234802830093247 70 2 2.07374982907047 -0.0737498290704678 71 5 5.88799137685803 -0.887991376858035 72 5 5.45700909185986 -0.457009091859865 73 5 5.10922356029525 -0.109223560295247 74 6 5.95951518600461 0.0404848139953915 75 6 5.23843393572756 0.761566064272439 76 6 5.5096280735107 0.490371926489297 77 5 5.23915599601701 -0.23915599601701 78 5 5.38066583929298 -0.380665839292984 79 4 5.24199844974001 -1.24199844974001 80 2 3.35949950525094 -1.35949950525094 81 4 3.76462792515394 0.235372074846058 82 6 5.58005144002574 0.419948559974258 83 6 6.07357443912468 -0.0735744391246839 84 5 4.67921147680112 0.32078852319888 85 3 4.48247913862032 -1.48247913862032 86 6 5.03244297534273 0.967557024657273 87 4 3.90025446906729 0.099745530932711 88 5 5.48874625631767 -0.488746256317665 89 8 6.3374411569663 1.6625588430337 90 4 4.4530607595127 -0.453060759512697 91 6 5.76350490811326 0.23649509188674 92 6 5.3095204124885 0.690479587511504 93 7 6.67239435156885 0.327605648431145 94 6 6.11414209414646 -0.114142094146458 95 5 4.96796185823387 0.0320381417661324 96 4 4.182588682019 -0.182588682019004 97 6 3.85351878677908 2.14648121322092 98 3 3.60392852647842 -0.603928526478422 99 5 5.6252840516915 -0.625284051691504 100 6 5.25029607118558 0.749703928814418 101 7 6.79518855852014 0.204811441479863 102 7 6.4213599706893 0.578640029310698 103 6 6.72404313171565 -0.72404313171565 104 3 4.36084432434413 -1.36084432434413 105 2 2.73579592921564 -0.735795929215645 106 8 5.72462951488498 2.27537048511502 107 3 4.67279530832009 -1.67279530832009 108 8 6.13260958925656 1.86739041074345 109 3 4.56302262950191 -1.56302262950191 110 4 4.66565707954961 -0.665657079549607 111 5 5.23201776724653 -0.232017767246529 112 7 5.58737885996727 1.41262114003273 113 6 4.52868195179013 1.47131804820987 114 6 5.90645887196813 0.0935411280318684 115 7 6.10487427119685 0.895125728803154 116 6 6.18976328642389 -0.18976328642389 117 6 6.17032558980975 -0.170325589809749 118 6 5.0750720737545 0.924927926245495 119 6 5.9654940221 0.0345059778999974 120 4 5.3795064466179 -1.3795064466179 121 4 5.19955854249928 -1.19955854249928 122 5 5.79293248796646 -0.792932487966462 123 4 4.14487268146581 -0.144872681465809 124 6 5.79196228646242 0.208037713537582 125 6 6.27368210014689 -0.273682100146891 126 5 4.72709735101884 0.272902648981156 127 8 6.46568133089457 1.53431866910543 128 6 5.5096280735107 0.490371926489297 129 5 5.06418013980053 -0.0641801398005278 130 4 2.09531711986374 1.90468288013626 131 8 6.46568133089457 1.53431866910543 132 6 5.68127835618375 0.318721643816248 133 4 4.92097803473106 -0.920978034731061 134 6 5.52621411565626 0.473785884343736 135 6 5.91287504044916 0.0871249595508358 136 4 4.88948901148786 -0.889489011487856 137 6 5.98493171871414 0.0150682812858566 138 3 4.38476698717679 -1.38476698717679 139 6 6.88364208775963 -0.883642087759634 140 5 5.59282482694425 -0.592824826944255 141 4 5.63242228046199 -1.63242228046199 142 6 5.70804347273942 0.291956527260583 143 4 6.31158729187113 -2.31158729187113 144 4 3.38159966516262 0.618400334837378 145 4 4.992845521825 -0.992845521824997 146 6 4.04508068514112 1.95491931485888 147 5 4.31743421559935 0.68256578440065 148 6 5.43848264670622 0.561517353293784 149 6 6.24238226807473 -0.242382268074729 150 8 6.11129043967788 1.88870956032212 151 7 5.37309027813686 1.62690972186314 152 7 6.56903784123171 0.430962158768286 153 4 4.29896672048925 -0.298966720489253 154 6 5.84197775485927 0.158022245140728 155 6 5.58621946729218 0.413780532707821 156 2 5.26331759931869 -3.26331759931869 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.456942541526259 0.913885083052518 0.543057458473741 9 0.58160814466977 0.83678371066046 0.41839185533023 10 0.435631460184383 0.871262920368767 0.564368539815617 11 0.570793240841873 0.858413518316253 0.429206759158127 12 0.76914389297211 0.461712214055779 0.23085610702789 13 0.850263843176449 0.299472313647102 0.149736156823551 14 0.78705747331489 0.425885053370219 0.21294252668511 15 0.809999083107689 0.380001833784622 0.190000916892311 16 0.748401610101416 0.503196779797167 0.251598389898584 17 0.786286347979021 0.427427304041958 0.213713652020979 18 0.725896576339636 0.548206847320728 0.274103423660364 19 0.659845740605457 0.680308518789086 0.340154259394543 20 0.617605874472807 0.764788251054386 0.382394125527193 21 0.932495193624232 0.135009612751537 0.0675048063757683 22 0.927716105317818 0.144567789364363 0.0722838946821815 23 0.907371162342088 0.185257675315824 0.0926288376579122 24 0.878012929800599 0.243974140398803 0.121987070199401 25 0.847414292259358 0.305171415481285 0.152585707740642 26 0.815041414202183 0.369917171595633 0.184958585797817 27 0.835640083313922 0.328719833372156 0.164359916686078 28 0.811676977462941 0.376646045074118 0.188323022537059 29 0.770575225055102 0.458849549889796 0.229424774944898 30 0.779527458627272 0.440945082745457 0.220472541372728 31 0.744601123625445 0.51079775274911 0.255398876374555 32 0.795286509548175 0.409426980903649 0.204713490451825 33 0.79295356161886 0.414092876762281 0.207046438381141 34 0.77053410807344 0.458931783853121 0.229465891926561 35 0.733280478909924 0.533439042180152 0.266719521090076 36 0.690086978123318 0.619826043753364 0.309913021876682 37 0.656125895624162 0.687748208751676 0.343874104375838 38 0.660392393054406 0.679215213891188 0.339607606945594 39 0.619223182081248 0.761553635837505 0.380776817918752 40 0.574602346977233 0.850795306045535 0.425397653022767 41 0.534529123543426 0.930941752913147 0.465470876456574 42 0.571513787993217 0.856972424013567 0.428486212006783 43 0.557746460688835 0.88450707862233 0.442253539311165 44 0.513529531493348 0.972940937013303 0.486470468506652 45 0.576128644643143 0.847742710713714 0.423871355356857 46 0.576254130480048 0.847491739039905 0.423745869519952 47 0.603549441473903 0.792901117052194 0.396450558526097 48 0.583914909648102 0.832170180703797 0.416085090351898 49 0.536128505931802 0.927742988136397 0.463871494068198 50 0.489927941971271 0.979855883942542 0.510072058028729 51 0.572924330168376 0.854151339663247 0.427075669831624 52 0.621308721679727 0.757382556640546 0.378691278320273 53 0.580345803042145 0.83930839391571 0.419654196957855 54 0.543404601116988 0.913190797766023 0.456595398883012 55 0.505076658735205 0.98984668252959 0.494923341264795 56 0.464307316087953 0.928614632175907 0.535692683912047 57 0.461789365255341 0.923578730510683 0.538210634744659 58 0.432537690134226 0.865075380268453 0.567462309865774 59 0.724677442669575 0.550645114660849 0.275322557330425 60 0.793390370237009 0.413219259525982 0.206609629762991 61 0.783385182328557 0.433229635342885 0.216614817671443 62 0.750599257700746 0.498801484598509 0.249400742299254 63 0.712161510645378 0.575676978709243 0.287838489354622 64 0.674429055515128 0.651141888969744 0.325570944484872 65 0.665333871513328 0.669332256973344 0.334666128486672 66 0.634731547549665 0.73053690490067 0.365268452450335 67 0.616739001216384 0.766521997567231 0.383260998783616 68 0.577280470541102 0.845439058917795 0.422719529458898 69 0.534523143568329 0.930953712863343 0.465476856431671 70 0.488953197025897 0.977906394051794 0.511046802974103 71 0.475126206237542 0.950252412475085 0.524873793762458 72 0.436371246774293 0.872742493548586 0.563628753225707 73 0.390847361434077 0.781694722868154 0.609152638565923 74 0.347629904742389 0.695259809484777 0.652370095257611 75 0.327187249902987 0.654374499805973 0.672812750097013 76 0.296282266103192 0.592564532206384 0.703717733896808 77 0.258458366293151 0.516916732586302 0.741541633706849 78 0.226768711649548 0.453537423299096 0.773231288350452 79 0.246301688738849 0.492603377477698 0.753698311261151 80 0.273223815240407 0.546447630480813 0.726776184759593 81 0.237908407841391 0.475816815682781 0.76209159215861 82 0.20721254411193 0.41442508822386 0.79278745588807 83 0.175449053373228 0.350898106746456 0.824550946626772 84 0.149467139277227 0.298934278554453 0.850532860722773 85 0.203227193567774 0.406454387135548 0.796772806432226 86 0.19811775210036 0.39623550420072 0.80188224789964 87 0.167058400859031 0.334116801718063 0.832941599140969 88 0.14491547418226 0.289830948364519 0.85508452581774 89 0.188284743075859 0.376569486151718 0.81171525692414 90 0.164394653576699 0.328789307153397 0.835605346423301 91 0.13954243193523 0.279084863870459 0.86045756806477 92 0.13313456080957 0.26626912161914 0.86686543919043 93 0.112076019107942 0.224152038215883 0.887923980892058 94 0.0911844811581388 0.182368962316278 0.908815518841861 95 0.0732880572252212 0.146576114450442 0.926711942774779 96 0.0595972326385806 0.119194465277161 0.94040276736142 97 0.114064863195603 0.228129726391206 0.885935136804397 98 0.1046496585649 0.2092993171298 0.8953503414351 99 0.0903641436849548 0.18072828736991 0.909635856315045 100 0.0787848635920181 0.157569727184036 0.921215136407982 101 0.0642226815171038 0.128445363034208 0.935777318482896 102 0.0539830161188293 0.107966032237659 0.94601698388117 103 0.0448792234169343 0.0897584468338686 0.955120776583066 104 0.0624390396941522 0.124878079388304 0.937560960305848 105 0.0570680364828306 0.114136072965661 0.94293196351717 106 0.113463365461395 0.22692673092279 0.886536634538605 107 0.141597999846767 0.283195999693534 0.858402000153233 108 0.234402979314341 0.468805958628682 0.765597020685659 109 0.262099585600218 0.524199171200437 0.737900414399782 110 0.230140180982932 0.460280361965863 0.769859819017068 111 0.19340639531984 0.38681279063968 0.80659360468016 112 0.277215998298628 0.554431996597256 0.722784001701372 113 0.279675445981655 0.559350891963309 0.720324554018345 114 0.237544908314447 0.475089816628893 0.762455091685553 115 0.224906736563862 0.449813473127724 0.775093263436138 116 0.187272895543951 0.374545791087902 0.812727104456049 117 0.154669916550936 0.309339833101872 0.845330083449064 118 0.145717375151958 0.291434750303917 0.854282624848042 119 0.117643857180125 0.23528771436025 0.882356142819875 120 0.15623562593072 0.312471251861441 0.84376437406928 121 0.171214170395715 0.34242834079143 0.828785829604285 122 0.153878187753763 0.307756375507525 0.846121812246237 123 0.122333865406633 0.244667730813267 0.877666134593367 124 0.0966451694932681 0.193290338986536 0.903354830506732 125 0.0771292258168414 0.154258451633683 0.922870774183159 126 0.060638912187926 0.121277824375852 0.939361087812074 127 0.0845615340492695 0.169123068098539 0.91543846595073 128 0.0720864360321478 0.144172872064296 0.927913563967852 129 0.0608930660556176 0.121786132111235 0.939106933944382 130 0.0838556492399191 0.167711298479838 0.91614435076008 131 0.118428590644809 0.236857181289618 0.881571409355191 132 0.0893306792549315 0.178661358509863 0.910669320745069 133 0.0716991503697118 0.143398300739424 0.928300849630288 134 0.0520255359935979 0.104051071987196 0.947974464006402 135 0.035939036019362 0.0718780720387241 0.964060963980638 136 0.0417629859750609 0.0835259719501217 0.95823701402494 137 0.0313787681916433 0.0627575363832867 0.968621231808357 138 0.0264089467474254 0.0528178934948509 0.973591053252575 139 0.0306369485889358 0.0612738971778716 0.969363051411064 140 0.0253797316865251 0.0507594633730502 0.974620268313475 141 0.0193201778691543 0.0386403557383086 0.980679822130846 142 0.0118689031077121 0.0237378062154241 0.988131096892288 143 0.0426730701360782 0.0853461402721563 0.957326929863922 144 0.0279665082245041 0.0559330164490083 0.972033491775496 145 0.0481484327466246 0.0962968654932491 0.951851567253375 146 0.0334312446114263 0.0668624892228525 0.966568755388574 147 0.0334611985729551 0.0669223971459102 0.966538801427045 148 0.0289184415192507 0.0578368830385014 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:

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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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Software written by Ed van Stee & Patrick Wessa

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