WS7 - Multiple regression model (incl. day)

*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 20:47:17 +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/t1290545138l23luvup4fvrwu8.htm/, Retrieved Tue, 23 Nov 2010 21:45:49 +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/t1290545138l23luvup4fvrwu8.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 2 1 12 12 8 13 5 1 1 15 10 12 16 6 0 1 12 9 7 12 6 3 1 10 10 10 11 5 3 1 12 12 7 12 3 1 1 15 13 16 18 8 3 1 9 12 11 11 4 1 1 12 12 14 14 4 4 1 11 6 6 9 4 0 1 11 5 16 14 6 3 1 11 12 11 12 6 2 1 15 11 16 11 5 4 1 7 14 12 12 4 3 1 11 14 7 13 6 1 1 11 12 13 11 4 1 1 10 12 11 12 6 2 1 14 11 15 16 6 3 1 10 11 7 9 4 1 2 6 7 9 11 4 1 2 11 9 7 13 2 2 2 15 11 14 15 7 3 2 11 11 15 10 5 4 2 12 12 7 11 4 2 2 14 12 15 13 6 1 2 15 11 17 16 6 2 2 9 11 15 15 7 2 2 13 8 14 14 5 4 2 13 9 14 14 6 2 2 16 12 8 14 4 3 2 13 10 8 8 4 3 2 12 10 14 13 7 3 2 14 12 14 15 7 4 2 11 8 8 13 4 2 3 9 12 11 11 4 2 3 16 11 16 15 6 4 3 12 12 10 15 6 3 3 10 7 8 9 5 4 3 13 11 14 13 6 2 3 16 11 16 16 7 5 3 14 12 13 13 6 3 3 15 9 5 11 3 1 3 5 15 8 12 3 1 3 8 11 10 12 4 1 3 11 11 8 12 6 2 3 16 11 13 14 7 3 3 17 11 15 14 5 9 3 9 15 6 8 4 0 3 9 11 12 13 5 0 3 13 12 16 16 6 2 3 10 12 5 13 6 2 3 6 9 15 11 6 3 4 12 12 12 14 5 1 4 8 12 8 13 4 2 4 14 13 13 13 5 0 4 12 11 14 13 5 5 4 11 9 1 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 13 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Popularity[t] = + 0.0341957712676926 + 0.106302633229405FindingFriends[t] + 0.211443525990832KnowingPeople[t] + 0.357643540447476Liked[t] + 0.606004881194799Celebrity[t] + 0.212601130536282Sum_friends[t] + 4.11173334192181e-05Day[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) 0.0341957712676926 1.433361 0.0239 0.980999 0.490499 FindingFriends 0.106302633229405 0.095939 1.108 0.269635 0.134818 KnowingPeople 0.211443525990832 0.063848 3.3117 0.001164 0.000582 Liked 0.357643540447476 0.097147 3.6815 0.000324 0.000162 Celebrity 0.606004881194799 0.155956 3.8857 0.000153 7.7e-05 Sum_friends 0.212601130536282 0.12044 1.7652 0.079577 0.039789 Day 4.11173334192181e-05 0.062529 7e-04 0.999476 0.499738 Multiple Linear Regression - Regression Statistics Multiple R 0.713764529068043 R-squared 0.509459802955726 Adjusted R-squared 0.489706506430453 F-TEST (value) 25.7911281949275 F-TEST (DF numerator) 6 F-TEST (DF denominator) 149 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.09777472945348 Sum Squared Residuals 655.698163514507 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 11.2689634149291 1.73103658507088 2 12 10.8934082576081 1.10659174239192 3 15 12.9929114671135 2.00708853288647 4 12 11.0366204337489 0.963379566251083 5 10 10.8136052233086 -0.813605223308552 6 12 9.11231142878019 2.88768857121981 7 15 16.7226937056585 -1.72269370565849 8 9 10.2064468734908 -1.20644687349084 9 12 12.5515114644146 -0.551511464414603 10 11 7.58352523272901 3.41647476727099 11 11 13.2296887156437 -2.22968871564375 12 11 11.9887013068642 -0.98870130686419 13 15 12.4011701430192 2.59882985698077 14 7 11.4133414674605 -4.41334146746052 15 11 11.5005748792709 -0.500574879270867 16 11 10.6293339254725 0.3706660745275 17 10 11.9887013068642 -1.98870130686419 18 14 14.3713480699243 -0.371348069924296 19 10 8.53912417273657 1.46087582726343 20 6 9.25208777269557 -3.25208777269557 21 11 8.75768443621435 2.24231556378565 22 15 14.4083070020142 0.591692997985793 23 11 11.8321241939143 -0.832124193914347 24 12 9.57331501739721 2.42668498260279 25 14 12.9795589380721 1.02044106192787 26 15 14.5816751087031 0.418324891296903 27 9 14.4071493974688 -5.40714939746876 28 13 12.7323469300252 0.267653069974799 29 13 13.0194521833768 -0.0194521833768406 30 16 11.0702902952667 4.92970970473325 31 13 8.71182378612309 4.28817621387691 32 12 13.5867172878899 -1.58671728788985 33 14 14.7272107657799 -0.727210765779894 34 11 10.0748762086988 0.925123791301208 35 9 10.4191302386940 -1.41913023869396 36 16 14.4378314206708 1.56216857932923 37 12 13.0628717674189 -1.06287176741890 38 10 9.56920655594685 0.430793444053152 39 13 12.8744550267216 0.125544973278405 40 16 15.6140809728493 0.385919027150671 41 14 12.9819152644965 1.01808473550355 42 15 8.01295517132967 6.98704482867033 43 5 9.64274508912607 -4.64274508912607 44 8 10.2464264893849 -2.24642648938491 45 11 11.2481503303291 -0.248150330329128 46 16 13.8392610529093 2.16073894709068 47 17 14.3257451257191 2.67425487428092 48 9 8.18268762601302 0.817312373986978 49 9 11.4203608324726 -2.42036083247257 50 13 14.4765753332751 -1.47657533327509 51 10 11.0777659260335 -1.07776592603351 52 6 12.3706484532284 -6.37064845322837 53 12 12.0969492540191 -0.0969492540191498 54 8 10.5001278589498 -2.50012785894983 55 14 11.8444507422556 2.15554925774437 56 12 12.9062946544691 -0.906294654469062 57 11 10.6693505227775 0.330649477222532 58 16 14.5829108119929 1.41708918800714 59 8 10.5325907267437 -2.53259072674373 60 15 14.5880342522578 0.41196574774217 61 7 9.111277176235 -2.11127717623499 62 16 14.1865316307861 1.81346836921388 63 14 13.1488638365666 0.851136163433394 64 16 13.3771820944137 2.62281790558632 65 9 10.4318965090998 -1.43189650909984 66 14 12.1633503700988 1.83664962990121 67 11 13.2598010239003 -2.25980102390034 68 13 10.3244445431700 2.67555545682996 69 15 13.1945986296996 1.80540137030043 70 5 5.79384205280933 -0.793842052809333 71 15 12.9063357718025 2.09366422819752 72 13 12.5885937485048 0.411406251495228 73 11 12.4170476037412 -1.41704760374118 74 11 14.1988005181039 -3.19880051810387 75 12 12.7705498372499 -0.770549837249929 76 12 13.4048845511450 -1.40488455114495 77 12 12.3360952367413 -0.336095236741251 78 12 11.9507820850509 0.0492179149491302 79 14 10.8578125167307 3.14218748326928 80 6 7.93738395048076 -1.93738395048076 81 7 9.71848077930866 -2.71848077930866 82 14 12.4117404204119 1.58825957958805 83 14 14.1612266178126 -0.161226617812591 84 10 11.1702556285443 -1.17025562854426 85 13 9.11479110720476 3.88520889279524 86 12 12.3066119354181 -0.306611935418104 87 9 9.32097683904484 -0.320976839044838 88 12 11.9243194675319 0.0756805324681113 89 16 14.8018752220064 1.1981247779936 90 10 10.4603085764669 -0.460308576466903 91 14 13.1017348961010 0.89826510389905 92 10 13.5910230641623 -3.59102306416225 93 16 15.5079058275427 0.492094172457290 94 15 13.4037639280104 1.59623607198961 95 12 11.4892005096434 0.510799490356635 96 10 9.35972075164915 0.640279248350845 97 8 10.1223314553596 -2.12233145535963 98 8 8.71613369831802 -0.716133698318018 99 11 12.6649526787338 -1.66495267873379 100 13 12.5591515645150 0.440848435484956 101 16 15.6130467203041 0.386953279695863 102 16 14.9388187611044 1.06118123889560 103 14 15.4034334280837 -1.40343342808366 104 11 9.04726936799056 1.95273063200944 105 4 7.15689033946251 -3.15689033946251 106 14 14.7389510554856 -0.73895105548564 107 9 10.5285727718053 -1.52857277180526 108 14 15.2259609958669 -1.22596099586693 109 8 10.2495705251893 -2.24957052518934 110 8 10.6828675211526 -2.68286752115256 111 11 11.8844673395606 -0.884467339560597 112 12 13.1605588730164 -1.16055887301641 113 11 11.0756151862763 -0.0756151862762893 114 14 13.2721645536525 0.727835446347487 115 15 14.4495717103765 0.550428289623481 116 16 13.4448641670390 2.55513583296097 117 16 12.9133634086596 3.08663659134041 118 11 12.7851915946821 -1.78519159468211 119 14 14.1878125873318 -0.18781258733183 120 14 10.8820791412365 3.11792085876346 121 12 11.5586264454497 0.441373554550302 122 14 12.5464592569309 1.45354074306906 123 8 10.8855519548729 -2.88555195487289 124 13 14.0815140900250 -1.08151409002495 125 16 13.9752114567955 2.02478854320445 126 12 10.6158103195381 1.38418968046187 127 16 15.4784636435530 0.521536356447018 128 12 12.7671633942029 -0.767163394202944 129 11 11.4615761516564 -0.461576151656406 130 4 6.00815950095096 -2.00815950095096 131 16 16.1162670351618 -0.116267035161828 132 15 12.6643335746099 2.33566642539011 133 10 11.3605807017562 -1.36058070175623 134 13 14.0185857875817 -1.01858578758166 135 15 13.1271221437413 1.87287785625868 136 12 10.4990936064046 1.50090639359536 137 14 13.6563076930299 0.343692306970139 138 7 10.3812604060591 -3.38126040605911 139 19 13.9076938535039 5.09230614649612 140 12 12.9451989004845 -0.945198900484526 141 12 11.8729367724445 0.127063227555525 142 13 13.3386067870656 -0.338606787065571 143 15 12.4166818444984 2.58331815550164 144 8 8.84487272228288 -0.84487272228288 145 12 10.9231793802652 1.07682061973483 146 10 10.7602294894029 -0.7602294894029 147 8 11.2513396193895 -3.2513396193895 148 10 14.6518040142647 -4.65180401426466 149 15 13.8677923363541 1.13220766364589 150 16 14.0602118941818 1.93978810581817 151 13 13.2704618078049 -0.270461807804946 152 16 15.0840256403493 0.915974359650727 153 9 9.82283412352541 -0.82283412352541 154 14 13.0610047130731 0.938995286926912 155 14 13.1550671685506 0.844932831449423 156 12 10.174200755085 1.82579924491501 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.128079867154562 0.256159734309124 0.871920132845438 11 0.148704773894552 0.297409547789104 0.851295226105448 12 0.0779372660984226 0.155874532196845 0.922062733901577 13 0.566237799252258 0.867524401495485 0.433762200747742 14 0.833055446551984 0.333889106896031 0.166944553448016 15 0.763198982970391 0.473602034059217 0.236801017029609 16 0.68026238252849 0.63947523494302 0.31973761747151 17 0.62377927399084 0.75244145201832 0.37622072600916 18 0.536276733406086 0.927446533187828 0.463723266593914 19 0.451020282283459 0.902040564566918 0.548979717716541 20 0.631854791922907 0.736290416154187 0.368145208077093 21 0.60074943380197 0.79850113239606 0.39925056619803 22 0.639619034877265 0.72076193024547 0.360380965122735 23 0.575053590561901 0.849892818876198 0.424946409438099 24 0.561079106335497 0.877841787329006 0.438920893664503 25 0.514013716193205 0.97197256761359 0.485986283806795 26 0.44602143502875 0.8920428700575 0.55397856497125 27 0.705620085007535 0.58875982998493 0.294379914992465 28 0.651861572192064 0.696276855615872 0.348138427807936 29 0.592036994137575 0.81592601172485 0.407963005862425 30 0.726888331102834 0.546223337794331 0.273111668897166 31 0.810341760501073 0.379316478997855 0.189658239498928 32 0.774144088144499 0.451711823711002 0.225855911855501 33 0.727292089994434 0.545415820011131 0.272707910005566 34 0.696904985842906 0.606190028314187 0.303095014157094 35 0.693027474314328 0.613945051371344 0.306972525685672 36 0.689741424513968 0.620517150972063 0.310258575486032 37 0.66319201393369 0.67361597213262 0.33680798606631 38 0.614488850293377 0.771022299413246 0.385511149706623 39 0.565758375552833 0.868483248894333 0.434241624447167 40 0.522458123954239 0.955083752091523 0.477541876045761 41 0.483866201385057 0.967732402770115 0.516133798614943 42 0.784511647238391 0.430976705523218 0.215488352761609 43 0.95211140483037 0.0957771903392612 0.0478885951696306 44 0.956332597632802 0.0873348047343958 0.0436674023671979 45 0.943297702913536 0.113404594172929 0.0567022970864644 46 0.950826279850052 0.0983474402998962 0.0491737201499481 47 0.95068812849458 0.0986237430108407 0.0493118715054203 48 0.940243280498854 0.119513439002291 0.0597567195011456 49 0.937808849747203 0.124382300505594 0.0621911502527971 50 0.92607799714878 0.147844005702439 0.0739220028512195 51 0.919333692181 0.161332615638000 0.0806663078189998 52 0.98658497260755 0.0268300547849002 0.0134150273924501 53 0.982593876497837 0.0348122470043256 0.0174061235021628 54 0.985632879267855 0.0287342414642890 0.0143671207321445 55 0.991124744881208 0.0177505102375837 0.00887525511879184 56 0.988204763276293 0.0235904734474131 0.0117952367237066 57 0.984202348923762 0.0315953021524765 0.0157976510762383 58 0.982591731177798 0.0348165376444048 0.0174082688222024 59 0.988060945528115 0.0238781089437693 0.0119390544718847 60 0.987076700614869 0.0258465987702622 0.0129232993851311 61 0.986673693462526 0.0266526130749479 0.0133263065374740 62 0.987367399357383 0.0252652012852341 0.0126326006426171 63 0.985850536502448 0.0282989269951039 0.0141494634975520 64 0.989104555393154 0.0217908892136916 0.0108954446068458 65 0.98776173114636 0.0244765377072806 0.0122382688536403 66 0.987381458938028 0.0252370821239431 0.0126185410619716 67 0.987446398928657 0.0251072021426865 0.0125536010713433 68 0.990360199865787 0.0192796002684264 0.0096398001342132 69 0.98995578139262 0.0200884372147610 0.0100442186073805 70 0.98686062692741 0.026278746145182 0.013139373072591 71 0.98746388178776 0.0250722364244817 0.0125361182122409 72 0.983371608934805 0.0332567821303891 0.0166283910651946 73 0.980298626596252 0.0394027468074963 0.0197013734037482 74 0.9861815553876 0.0276368892248014 0.0138184446124007 75 0.981739541944851 0.0365209161102975 0.0182604580551487 76 0.978303224777073 0.0433935504458542 0.0216967752229271 77 0.971565821428782 0.0568683571424353 0.0284341785712176 78 0.962942949352355 0.0741141012952905 0.0370570506476452 79 0.976970462191356 0.046059075617288 0.023029537808644 80 0.974956288094458 0.0500874238110844 0.0250437119055422 81 0.977416042029847 0.0451679159403056 0.0225839579701528 82 0.977358642351664 0.0452827152966729 0.0226413576483364 83 0.970057249538305 0.0598855009233898 0.0299427504616949 84 0.962736771992479 0.0745264560150421 0.0372632280075211 85 0.988826932582823 0.0223461348343531 0.0111730674171766 86 0.984892181994422 0.0302156360111567 0.0151078180055783 87 0.979832142454912 0.0403357150901754 0.0201678575450877 88 0.974004111737015 0.0519917765259692 0.0259958882629846 89 0.969317300147167 0.0613653997056654 0.0306826998528327 90 0.9604921571153 0.0790156857694 0.0395078428847 91 0.953781361713128 0.0924372765737438 0.0462186382868719 92 0.971591777283056 0.0568164454338878 0.0284082227169439 93 0.963663791262621 0.0726724174747576 0.0363362087373788 94 0.960409418749607 0.0791811625007853 0.0395905812503926 95 0.95115765513406 0.0976846897318783 0.0488423448659391 96 0.940429892070924 0.119140215858152 0.0595701079290762 97 0.933728131967063 0.132543736065874 0.0662718680329369 98 0.917146318373977 0.165707363252046 0.082853681626023 99 0.908064004375226 0.183871991249547 0.0919359956247737 100 0.888924852861152 0.222150294277696 0.111075147138848 101 0.864636295194498 0.270727409611004 0.135363704805502 102 0.843986922667751 0.312026154664498 0.156013077332249 103 0.849693407506405 0.300613184987189 0.150306592493595 104 0.898955280253977 0.202089439492047 0.101044719746023 105 0.89668656819555 0.206626863608902 0.103313431804451 106 0.872463442863565 0.255073114272870 0.127536557136435 107 0.847684038967963 0.304631922064074 0.152315961032037 108 0.840121853234237 0.319756293531526 0.159878146765763 109 0.830526839947247 0.338946320105506 0.169473160052753 110 0.848534971040357 0.302930057919286 0.151465028959643 111 0.832573636327333 0.334852727345334 0.167426363672667 112 0.875924106553221 0.248151786893558 0.124075893446779 113 0.845739256879454 0.308521486241091 0.154260743120546 114 0.815756589203797 0.368486821592406 0.184243410796203 115 0.777487948425372 0.445024103149257 0.222512051574628 116 0.781167428419542 0.437665143160916 0.218832571580458 117 0.799776585613042 0.400446828773916 0.200223414386958 118 0.785412141312459 0.429175717375082 0.214587858687541 119 0.739529139064996 0.520941721870007 0.260470860935004 120 0.811410086224054 0.377179827551893 0.188589913775946 121 0.780572793346612 0.438854413306777 0.219427206653388 122 0.754757734574798 0.490484530850405 0.245242265425202 123 0.746039563795274 0.507920872409452 0.253960436204726 124 0.699331152701279 0.601337694597443 0.300668847298721 125 0.700103667502263 0.599792664995473 0.299896332497737 126 0.68713561496015 0.625728770079701 0.312864385039851 127 0.627867839390222 0.744264321219555 0.372132160609778 128 0.590287770921604 0.819424458156792 0.409712229078396 129 0.594142841031002 0.811714317937997 0.405857158968998 130 0.585586085035124 0.828827829929752 0.414413914964876 131 0.517099397344465 0.96580120531107 0.482900602655535 132 0.501211851611816 0.997576296776368 0.498788148388184 133 0.468678804538642 0.937357609077284 0.531321195461358 134 0.398534551495579 0.797069102991158 0.601465448504421 135 0.370425734924566 0.740851469849131 0.629574265075434 136 0.367127678584287 0.734255357168574 0.632872321415713 137 0.294820146990136 0.589640293980272 0.705179853009864 138 0.366272950938823 0.732545901877646 0.633727049061177 139 0.732867165495646 0.534265669008707 0.267132834504354 140 0.745324383451238 0.509351233097523 0.254675616548762 141 0.694316230160992 0.611367539678016 0.305683769839008 142 0.59806828235943 0.80386343528114 0.40193171764057 143 0.532759158396127 0.934481683207745 0.467240841603873 144 0.410260787972307 0.820521575944614 0.589739212027693 145 0.387764349515841 0.775528699031683 0.612235650484159 146 0.566723446609808 0.866553106780384 0.433276553390192 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 31 0.226277372262774 NOK 10% type I error level 48 0.35036496350365 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545138l23luvup4fvrwu8/108wo21290545223.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545138l23luvup4fvrwu8/108wo21290545223.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545138l23luvup4fvrwu8/16gge1290545223.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545138l23luvup4fvrwu8/16gge1290545223.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545138l23luvup4fvrwu8/26gge1290545223.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545138l23luvup4fvrwu8/26gge1290545223.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545138l23luvup4fvrwu8/36gge1290545223.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545138l23luvup4fvrwu8/36gge1290545223.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545138l23luvup4fvrwu8/4umqb1290545223.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545138l23luvup4fvrwu8/4umqb1290545223.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545138l23luvup4fvrwu8/5umqb1290545223.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545138l23luvup4fvrwu8/5umqb1290545223.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545138l23luvup4fvrwu8/6mvpe1290545223.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545138l23luvup4fvrwu8/6mvpe1290545223.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545138l23luvup4fvrwu8/7mvpe1290545223.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545138l23luvup4fvrwu8/7mvpe1290545223.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545138l23luvup4fvrwu8/8fmoz1290545223.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545138l23luvup4fvrwu8/8fmoz1290545223.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545138l23luvup4fvrwu8/9fmoz1290545223.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290545138l23luvup4fvrwu8/9fmoz1290545223.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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