workshop 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: Sun, 21 Nov 2010 18:15:20 +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/t1290363256vo1leyp9a0gvz3o.htm/, Retrieved Sun, 21 Nov 2010 19:14:16 +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/t1290363256vo1leyp9a0gvz3o.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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation FindingFriends[t] = + 9.9004545250637 + 0.0682003253664285Popularity[t] -0.0300954894917058KnowingPeople[t] + 0.0519923282704495Liked[t] -0.0593588957098072Celebrity[t] + 0.00368806807662014t + 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) 9.9004545250637 0.892537 11.0925 0 0 Popularity 0.0682003253664285 0.068503 0.9956 0.321055 0.160528 KnowingPeople -0.0300954894917058 0.05444 -0.5528 0.581212 0.290606 Liked 0.0519923282704495 0.085572 0.6076 0.54438 0.27219 Celebrity -0.0593588957098072 0.138575 -0.4284 0.66901 0.334505 t 0.00368806807662014 0.003205 1.1507 0.251679 0.12584 Multiple Linear Regression - Regression Statistics Multiple R 0.154362735607863 R-squared 0.0238278541443429 Adjusted R-squared -0.00871121738417924 F-TEST (value) 0.732284389966589 F-TEST (DF numerator) 5 F-TEST (DF denominator) 150 p-value 0.600311992850885 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.77800336030926 Sum Squared Residuals 474.194392390652 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 10.8672335504064 2.13276644959356 2 12 10.8645764386472 1.13542356135276 3 10 11.0491016139579 -1.04910161395786 4 9 10.7906968403119 -1.79069684031193 5 10 10.5750643566199 -0.575064356619933 6 12 10.9761496635946 1.02385033640541 7 13 10.9287387934188 2.07126120658119 8 12 10.5471916417015 1.45280835829853 9 12 10.8211712022136 1.17882879778640 10 6 10.7374612195052 -4.73746121950520 11 5 10.5814382425974 -5.58143824259739 12 12 10.6316191015916 1.36838089840836 13 11 10.7649975911148 0.235002408885198 14 14 10.4548162382071 3.54518376179293 15 14 10.8150575920588 3.18494240794123 16 12 10.6529058580639 1.34709414193613 17 12 10.5818591166083 1.41814088339169 18 11 10.9459358412656 0.0540641587343793 19 11 10.6723580173366 0.327641982663360 20 7 10.4470384615050 -3.44703846150503 21 9 11.0746215833577 -2.07462158335772 22 11 10.9476327044500 0.0523672955500213 23 11 10.5071801316365 0.492819868363454 24 12 10.9311836649935 1.06881633500650 25 12 10.8157753329906 1.18422466700939 26 11 10.9834497322616 0.0165502677384013 27 11 10.5267756031428 0.473224396857197 28 8 10.900085925326 -2.90008592532601 29 9 10.8444150976928 -1.84441509769282 30 12 11.3519948702386 0.648005129761425 31 10 10.8391279925932 -0.839127992593212 32 10 10.675927752576 -0.675927752575995 33 12 10.9200011279264 1.07999887207363 34 8 10.9737531874425 -2.97375318744246 35 12 10.6467694797702 1.35323052022979 36 11 11.0666338996155 -0.0666338996154848 37 12 10.9780936031766 1.02190639682337 38 7 10.6529769255909 -3.65297692559091 39 11 10.8293034501886 0.170696549811428 40 11 11.0740196044826 -0.0740196044826077 41 12 10.9349754011999 1.06502459880005 42 9 11.3217197411652 -2.32171974116516 43 15 10.6051104153728 4.39488958462717 44 11 10.6938495848555 0.306150415144482 45 11 10.8436118165952 0.156388183404779 46 11 11.0824498248765 -0.0824498248765467 47 11 11.2128650307558 -0.212865030755798 48 15 10.6892148274135 4.31078517258655 49 11 10.7129327041823 0.287067295817722 50 12 10.9656582048593 1.03434179514067 51 12 10.9398186964341 1.06018130356592 52 9 10.2657659115870 -1.26576591158703 53 12 10.9842782808585 1.01572171914151 54 12 10.8429135728756 1.15708642712442 55 13 11.0459672499824 1.95403275001756 56 11 10.8831591778345 0.116840822165507 57 9 10.8862044669675 -1.88620446696745 58 9 11.1997637255716 -2.19976372557158 59 11 11.0238653822358 -0.0238653822357834 60 11 10.9983249061600 0.00167509383996898 61 12 10.8078962914849 1.19210370851515 62 12 11.1105313413372 0.889468658662841 63 9 10.7835476336649 -1.78354763366491 64 11 11.2300907847443 -0.23009078474426 65 9 10.9005224020880 -1.90052240208799 66 12 11.0865359988253 0.913464001174743 67 12 10.7140808878389 1.28591911216108 68 12 11.1542924182919 0.845707581708146 69 12 11.1064416327117 0.893558367288261 70 14 10.5204828092251 3.47951719077494 71 11 11.1430811750831 -0.143081175083081 72 12 11.0404640819186 0.95953591808145 73 11 11.0199348065162 -0.019934806516174 74 6 11.0299544952192 -5.02995449521922 75 10 10.9540645545639 -0.95406455456388 76 12 10.8674661541654 1.13253384583462 77 13 10.9086162791731 2.09138372082693 78 8 10.9943921650118 -2.99439216501184 79 12 11.3963095552601 0.603690444739895 80 12 10.8773268059970 1.12267319400303 81 12 10.8523942467992 1.14760575320085 82 6 11.0341938640709 -5.03419386407092 83 11 11.2458512452293 -0.245851245229341 84 10 10.8883185734517 -0.888318573451668 85 12 11.3958983459974 0.604101654002578 86 13 10.9426409751363 2.05735902486375 87 11 10.8768431599591 0.123156840040875 88 7 11.1954484813024 -4.19544848130236 89 11 11.2035746952401 -0.203574695240149 90 11 11.0299968566046 -0.0299968566046075 91 11 11.3656422583174 -0.365642258317420 92 11 10.9542502281828 0.045749771817241 93 12 11.2694872125435 0.730512787456525 94 10 11.1083568661521 -1.10835686615213 95 11 11.0652879730273 -0.0652879730273464 96 12 11.0302284262856 0.969771573714416 97 7 11.0031646667175 -4.00316466671746 98 13 10.9386659686370 2.06133403136297 99 8 11.0775304363036 -3.07753043630363 100 12 11.1445620713375 0.855437928662482 101 11 11.2688962676647 -0.268896267664730 102 12 11.2807829864543 0.719217013545687 103 14 11.3032153053358 2.69678469466418 104 10 11.3815633169908 -1.38156331699080 105 10 10.8413265078926 -0.841326507892583 106 13 11.3022454880471 1.69775451195289 107 10 11.0756539335376 -1.07565393353757 108 11 11.1071518484714 -0.107151848471369 109 10 11.0969175620865 -1.09691756208653 110 7 11.1233345522155 -4.1233345522155 111 10 11.1299859039360 -1.12998590393603 112 8 10.9408777092139 -2.9408777092139 113 12 11.1764882635675 0.823511736432454 114 12 11.3081890273341 0.691810972665884 115 12 11.4028063428295 0.597193657170487 116 11 11.3698779964581 -0.369877996458058 117 12 11.3735660645347 0.626433935465322 118 12 11.3208100992703 0.67918990072971 119 12 11.2144460604634 0.785553939536644 120 11 11.3231537318938 -0.323153731893808 121 12 11.2424334775080 0.757566522491979 122 11 11.1507890143704 -0.150789014370418 123 11 11.0153024524002 -0.0153024524002152 124 13 11.1646860754800 1.83531392451997 125 12 11.3729751196559 0.627024880344067 126 12 11.434080187402 0.565919812598001 127 12 11.3957136104222 0.604286389577836 128 12 11.0592456941496 0.94075430585037 129 8 11.2565621082986 -3.25656210829861 130 8 10.4426654697824 -2.44266546978236 131 12 11.4104658827286 0.589534117271355 132 11 11.3688854110305 -0.368885411030514 133 12 11.4266485864728 0.573351413527223 134 13 11.3739410424835 1.62605895751650 135 12 11.4018464540391 0.598153545960882 136 12 11.3880409671324 0.61195903286756 137 11 11.2808312858425 -0.280831285842518 138 12 10.9414000859261 1.05859991407393 139 12 11.6812013770984 0.318798622901650 140 10 11.2449492245410 -1.24494922454103 141 11 11.1958128810736 -0.195812881073601 142 12 11.2611667903509 0.738833209649104 143 12 11.6239579571209 0.376042042879113 144 10 10.7507024228948 -0.750702422894835 145 12 11.3911380903303 0.608861909669684 146 13 11.3202806532047 1.6797193467953 147 12 11.1785373365619 0.821462663438104 148 15 11.1005910614901 3.89940893850992 149 11 11.3631929386367 -0.363192938636682 150 12 11.4887378268974 0.511262173102611 151 11 11.2431991580436 -0.243199158043632 152 12 11.5171787185558 0.482821281444231 153 11 11.1941448200652 -0.194144820065248 154 10 11.4858072398906 -1.48580723989063 155 11 11.2733273441725 -0.273327344172487 156 11 11.5723214693715 -0.572321469371496 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.339567107057235 0.67913421411447 0.660432892942765 10 0.204989413415576 0.409978826831152 0.795010586584424 11 0.902184668604127 0.195630662791747 0.0978153313958733 12 0.98971213060095 0.0205757387981006 0.0102878693990503 13 0.992211746545888 0.0155765069082232 0.00778825345411158 14 0.995991928886074 0.00801614222785146 0.00400807111392573 15 0.997143713632773 0.00571257273445473 0.00285628636722737 16 0.995018702406648 0.00996259518670302 0.00498129759335151 17 0.992084900095078 0.0158301998098447 0.00791509990492237 18 0.99240698369917 0.0151860326016601 0.00759301630083003 19 0.987420893890623 0.0251582122187538 0.0125791061093769 20 0.998339129207552 0.00332174158489628 0.00166087079244814 21 0.99884575246361 0.00230849507277816 0.00115424753638908 22 0.99799453386713 0.00401093226574144 0.00200546613287072 23 0.996834489836317 0.00633102032736546 0.00316551016368273 24 0.995953475202528 0.00809304959494471 0.00404652479747236 25 0.994174396839507 0.0116512063209863 0.00582560316049316 26 0.991375538182124 0.0172489236357515 0.00862446181787577 27 0.98709853418547 0.0258029316290604 0.0129014658145302 28 0.99189936882708 0.0162012623458414 0.00810063117292069 29 0.990592226522257 0.0188155469554867 0.00940777347774336 30 0.987737857285863 0.0245242854282744 0.0122621427141372 31 0.982572396725027 0.034855206549946 0.017427603274973 32 0.975511297181674 0.048977405636652 0.024488702818326 33 0.970321392405598 0.0593572151888036 0.0296786075944018 34 0.976028953353468 0.0479420932930644 0.0239710466465322 35 0.97595219068602 0.0480956186279613 0.0240478093139807 36 0.966841360520335 0.0663172789593305 0.0331586394796652 37 0.961215467601317 0.0775690647973664 0.0387845323986832 38 0.976407469937131 0.0471850601257381 0.0235925300628690 39 0.96864213681618 0.0627157263676419 0.0313578631838209 40 0.957818512350201 0.0843629752995978 0.0421814876497989 41 0.95220170821997 0.095596583560061 0.0477982917800305 42 0.95347601220746 0.0930479755850785 0.0465239877925392 43 0.988439742383408 0.0231205152331844 0.0115602576165922 44 0.984037137689535 0.0319257246209296 0.0159628623104648 45 0.978621203164947 0.0427575936701057 0.0213787968350528 46 0.97170074984242 0.0565985003151599 0.0282992501575799 47 0.962779848096917 0.0744403038061653 0.0372201519030827 48 0.991213678161446 0.0175726436771081 0.00878632183855404 49 0.988223114494784 0.0235537710104325 0.0117768855052163 50 0.985239462050702 0.0295210758985965 0.0147605379492983 51 0.981347342017132 0.037305315965735 0.0186526579828675 52 0.980236204364805 0.0395275912703904 0.0197637956351952 53 0.975443372966988 0.0491132540660244 0.0245566270330122 54 0.970660926610149 0.0586781467797023 0.0293390733898512 55 0.971487191273529 0.0570256174529421 0.0285128087264710 56 0.963214015076901 0.0735719698461971 0.0367859849230986 57 0.96527875016145 0.0694424996771005 0.0347212498385502 58 0.968969685216174 0.0620606295676516 0.0310303147838258 59 0.961766163737813 0.0764676725243736 0.0382338362621868 60 0.950774820594877 0.0984503588102466 0.0492251794051233 61 0.94450322730383 0.110993545392342 0.0554967726961708 62 0.93526156053976 0.129476878920481 0.0647384394602403 63 0.93015071206945 0.139698575861099 0.0698492879305494 64 0.91270739467265 0.174585210654701 0.0872926053273505 65 0.915505137359936 0.168989725280129 0.0844948626400644 66 0.902531979729124 0.194936040541752 0.097468020270876 67 0.896540990459842 0.206918019080316 0.103459009540158 68 0.878990910468432 0.242018179063136 0.121009089531568 69 0.86177936335065 0.276441273298699 0.138220636649349 70 0.924972120736212 0.150055758527576 0.0750278792637881 71 0.906892584213886 0.186214831572228 0.0931074157861142 72 0.895421876555955 0.209156246888090 0.104578123444045 73 0.875736486806505 0.248527026386990 0.124263513193495 74 0.973204668267415 0.0535906634651691 0.0267953317325845 75 0.966570799942948 0.0668584001141042 0.0334292000570521 76 0.963387874940876 0.073224250118249 0.0366121250591245 77 0.97180928300223 0.0563814339955402 0.0281907169977701 78 0.980670336344428 0.0386593273111446 0.0193296636555723 79 0.975905146171043 0.0481897076579133 0.0240948538289566 80 0.97556383574449 0.0488723285110213 0.0244361642555106 81 0.975750450945674 0.048499098108651 0.0242495490543255 82 0.996879181800234 0.00624163639953112 0.00312081819976556 83 0.995534612034688 0.0089307759306245 0.00446538796531225 84 0.99392149075503 0.0121570184899405 0.00607850924497023 85 0.99243994792981 0.0151201041403781 0.00756005207018907 86 0.994857154145012 0.0102856917099766 0.0051428458549883 87 0.993642286302261 0.0127154273954778 0.00635771369773889 88 0.998696950448533 0.0026060991029338 0.0013030495514669 89 0.99809924493333 0.00380151013333985 0.00190075506666993 90 0.997344650163343 0.0053106996733146 0.0026553498366573 91 0.996183682243393 0.00763263551321405 0.00381631775660703 92 0.994606475826335 0.0107870483473299 0.00539352417366496 93 0.993049550029318 0.0139008999413644 0.0069504499706822 94 0.991038702882749 0.0179225942345022 0.0089612971172511 95 0.987731113293012 0.0245377734139754 0.0122688867069877 96 0.987695812619506 0.0246083747609884 0.0123041873804942 97 0.996751279638499 0.00649744072300285 0.00324872036150143 98 0.9988361735163 0.00232765296740171 0.00116382648370085 99 0.999579209281457 0.00084158143708547 0.000420790718542735 100 0.999499713317156 0.00100057336568703 0.000500286682843515 101 0.999261763397972 0.00147647320405631 0.000738236602028157 102 0.998962575758926 0.00207484848214772 0.00103742424107386 103 0.999466988031667 0.00106602393666611 0.000533011968333054 104 0.999228233030314 0.00154353393937267 0.000771766969686336 105 0.998891077160161 0.00221784567967791 0.00110892283983896 106 0.998914437484635 0.00217112503073029 0.00108556251536514 107 0.998358788333901 0.00328242333219776 0.00164121166609888 108 0.997472853490434 0.00505429301913132 0.00252714650956566 109 0.996317914191123 0.00736417161775407 0.00368208580887703 110 0.999827060253454 0.000345879493091514 0.000172939746545757 111 0.999810799136828 0.00037840172634481 0.000189200863172405 112 0.999988638551462 2.27228970768488e-05 1.13614485384244e-05 113 0.999980911756465 3.81764870706583e-05 1.90882435353291e-05 114 0.99996497163381 7.00567323781508e-05 3.50283661890754e-05 115 0.999937776788062 0.000124446423875225 6.22232119376127e-05 116 0.999892743815354 0.000214512369291564 0.000107256184645782 117 0.999819096912102 0.000361806175795743 0.000180903087897872 118 0.999706495594146 0.000587008811708792 0.000293504405854396 119 0.99949549721834 0.00100900556331960 0.000504502781659801 120 0.999132821042562 0.00173435791487549 0.000867178957437744 121 0.998730019808695 0.0025399603826101 0.00126998019130505 122 0.99784492976532 0.00431014046936123 0.00215507023468062 123 0.996446488845342 0.00710702230931687 0.00355351115465844 124 0.99618570677753 0.00762858644493815 0.00381429322246907 125 0.994674834637163 0.0106503307256741 0.00532516536283704 126 0.99234086610313 0.0153182677937409 0.00765913389687046 127 0.987827863732758 0.0243442725344843 0.0121721362672422 128 0.983033159111004 0.0339336817779918 0.0169668408889959 129 0.999227225792248 0.00154554841550408 0.00077277420775204 130 0.999495645356046 0.00100870928790868 0.000504354643954341 131 0.99910639663319 0.00178720673362146 0.00089360336681073 132 0.998382798405757 0.00323440318848512 0.00161720159424256 133 0.998012177244092 0.00397564551181606 0.00198782275590803 134 0.996385621669467 0.0072287566610657 0.00361437833053285 135 0.993209528218543 0.0135809435629145 0.00679047178145724 136 0.98797365260293 0.0240526947941388 0.0120263473970694 137 0.982571834837174 0.0348563303256524 0.0174281651628262 138 0.969313989047768 0.0613720219044644 0.0306860109522322 139 0.961920400263093 0.0761591994738149 0.0380795997369075 140 0.984274984469264 0.0314500310614715 0.0157250155307357 141 0.978913005186102 0.0421739896277965 0.0210869948138982 142 0.96463252359058 0.0707349528188383 0.0353674764094191 143 0.937316056922994 0.125367886154012 0.0626839430770062 144 0.892999324026027 0.214001351947946 0.107000675973973 145 0.809796062222932 0.380407875554137 0.190203937777068 146 0.844896674256676 0.310206651486647 0.155103325743324 147 0.730160544437383 0.539678911125234 0.269839455562617 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 48 0.345323741007194 NOK 5% type I error level 95 0.683453237410072 NOK 10% type I error level 118 0.848920863309353 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290363256vo1leyp9a0gvz3o/10ha8s1290363307.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290363256vo1leyp9a0gvz3o/10ha8s1290363307.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290363256vo1leyp9a0gvz3o/13is21290363307.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290363256vo1leyp9a0gvz3o/13is21290363307.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290363256vo1leyp9a0gvz3o/23is21290363307.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290363256vo1leyp9a0gvz3o/23is21290363307.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290363256vo1leyp9a0gvz3o/33is21290363307.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290363256vo1leyp9a0gvz3o/33is21290363307.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290363256vo1leyp9a0gvz3o/4e99m1290363307.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290363256vo1leyp9a0gvz3o/4e99m1290363307.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290363256vo1leyp9a0gvz3o/5e99m1290363307.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290363256vo1leyp9a0gvz3o/5e99m1290363307.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290363256vo1leyp9a0gvz3o/6pjr81290363307.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290363256vo1leyp9a0gvz3o/6pjr81290363307.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290363256vo1leyp9a0gvz3o/7pjr81290363307.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290363256vo1leyp9a0gvz3o/7pjr81290363307.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290363256vo1leyp9a0gvz3o/8ha8s1290363307.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290363256vo1leyp9a0gvz3o/8ha8s1290363307.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290363256vo1leyp9a0gvz3o/9ha8s1290363307.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290363256vo1leyp9a0gvz3o/9ha8s1290363307.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = 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') }

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by