minitutorial 2

*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: Fri, 12 Nov 2010 10:06:44 +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/12/t1289556418db27g053rdp7se4.htm/, Retrieved Fri, 12 Nov 2010 11:06:58 +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/12/t1289556418db27g053rdp7se4.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:

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11 12 7 8 17 8 10 8 12 9 12 7 11 4 11 11 12 7 13 7 14 12 16 10 11 10 10 8 11 8 15 4 9 9 11 8 17 7 17 11 11 9 18 11 14 13 10 8 11 8 15 9 15 6 13 9 16 9 13 6 9 6 18 16 18 5 12 7 17 9 9 6 9 6 12 5 18 12 12 7 18 10 14 9 15 8 16 5 10 8 11 8 14 10 9 6 12 8 17 7 5 4 12 8 12 8 6 4 24 20 12 8 12 8 14 6 7 4 13 8 12 9 13 6 14 7 8 9 11 5 9 5 11 8 13 8 10 6 11 8 12 7 9 7 15 9 18 11 15 6 12 8 13 6 14 9 10 8 13 6 13 10 11 8 13 8 16 10 8 5 16 7 11 5 9 8 16 14 12 7 14 8 8 6 9 5 15 6 11 10 21 12 14 9 18 12 12 7 13 8 15 10 12 6 19 10 15 10 11 10 11 5 10 7 13 10 15 11 12 6 12 7 16 12 9 11 18 11 8 11 13 5 17 8 9 6 15 9 8 4 7 4 12 7 14 11 6 6 8 7 17 8 10 4 11 8 14 9 11 8 13 11 12 8 11 5 9 4 12 8 20 10 12 6 13 9 12 9 12 13 9 9 15 10 24 20 7 5 17 11 11 6 17 9 11 7 12 9 14 10 11 9 16 8 21 7 14 6 20 13 13 6 11 8 15 10 19 16

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 7 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation ParentalExpectations[t] = + 6.4398361021299 + 0.752008775996732ParentalCriticism[t] + 0.00286466829855502t + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 6.4398361021299 0.788598 8.1662 0 0 ParentalCriticism 0.752008775996732 0.082102 9.1594 0 0 t 0.00286466829855502 0.004827 0.5935 0.553736 0.276868 Multiple Linear Regression - Regression Statistics Multiple R 0.594441332727225 R-squared 0.353360498054519 Adjusted R-squared 0.345070248029577 F-TEST (value) 42.6236237738787 F-TEST (DF numerator) 2 F-TEST (DF denominator) 156 p-value 1.66533453693773e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.78835056709640 Sum Squared Residuals 1212.88422606418 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 11 15.4668060823893 -4.46680608238925 2 7 12.4616356467009 -5.46163564670087 3 17 12.4645003149994 4.53549968500058 4 10 12.4673649832980 -2.46736498329798 5 12 13.2222384275933 -1.22223842759327 6 12 11.7210855438984 0.278914456101642 7 11 9.46792388420672 1.53207611579328 8 11 14.7348499844824 -3.73484998448239 9 12 11.7296795487940 0.270320451205977 10 13 11.7325442170926 1.26745578290742 11 14 15.4954527653748 -1.49545276537479 12 16 13.9942998816799 2.00570011832012 13 11 13.9971645499784 -2.99716454997844 14 10 12.4960116662835 -2.49601166628353 15 11 12.4988763345821 -1.49887633458209 16 15 9.49370589889371 5.50629410110629 17 9 13.2566144471759 -4.25661444717593 18 11 12.5074703394778 -1.50747033947775 19 17 11.7583262317796 5.24167376822043 20 17 14.7692260040651 2.23077399593495 21 11 13.2680731203701 -2.26807312037015 22 18 14.7749553406622 3.22504465933784 23 14 16.2818375609542 -2.28183756095418 24 10 12.5246583492691 -2.52465834926908 25 11 12.5275230175676 -1.52752301756764 26 15 13.2823964618629 1.71760353813708 27 15 11.0292348021713 3.97076519782872 28 13 13.2881257984600 -0.288125798460032 29 16 13.2909904667586 2.70900953324141 30 13 11.0378288070669 1.96217119293305 31 9 11.0406934753655 -2.04069347536550 32 18 18.5636459036314 -0.563645903631373 33 18 10.2944140359659 7.70558596403412 34 12 11.8012962562579 0.198703743742101 35 17 13.3081784765499 3.69182152345008 36 9 11.0550168168583 -2.05501681685828 37 9 11.0578814851568 -2.05788148515683 38 12 10.3087373774587 1.69126262254134 39 18 15.5756634777343 2.42433652226567 40 12 11.8184842660492 0.181515733950771 41 18 14.0773752623380 3.92262473766202 42 14 13.3282311546398 0.671768845360198 43 15 12.5790870469416 2.42091295305837 44 16 10.3259253872500 5.67407461275001 45 10 12.5848163835387 -2.58481638353874 46 11 12.5876810518373 -1.58768105183729 47 14 14.0945632721293 -0.0945632721293087 48 9 11.0893928364409 -2.08939283644094 49 12 12.5962750567330 -0.596275056732956 50 17 11.8471309490348 5.15286905096522 51 5 9.59396928934314 -4.59396928934314 52 12 12.6048690616286 -0.604869061628621 53 12 12.6077337299272 -0.607733729927176 54 6 9.6025632942388 -3.60256329423881 55 24 21.6375683784851 2.36243162151494 56 12 12.6163277348228 -0.616327734822841 57 12 12.6191924031214 -0.619192403121396 58 14 11.1180395194265 2.88196048057351 59 7 9.61688663573158 -2.61688663573158 60 13 12.6277864080171 0.372213591982939 61 12 13.3826598523123 -1.38265985231235 62 13 11.1294981926207 1.87050180737929 63 14 11.884371636916 2.11562836308401 64 8 13.3912538572080 -5.39125385720801 65 11 10.3860834215196 0.613916578480359 66 9 10.3889480898182 -1.38894808981820 67 11 12.6478390861069 -1.64783908610695 68 13 12.6507037544055 0.349296245594499 69 10 11.1495508707106 -1.14955087071059 70 11 12.6564330910026 -1.65643309100261 71 12 11.9072889833044 0.0927110166955656 72 9 11.910153651603 -2.91015365160299 73 15 13.417035871895 1.58296412810499 74 18 14.9239180921870 3.07608190781297 75 15 11.1667388805019 3.83326111949808 76 12 12.6736211007939 -0.673621100793941 77 13 11.1724682170990 1.82753178290097 78 14 13.4313592133878 0.568640786612217 79 10 12.6822151056896 -2.68221510568961 80 13 11.1810622219947 1.81893777800530 81 13 14.1919619942802 -1.19196199428018 82 11 12.6908091105853 -1.69080911058527 83 13 12.6936737788838 0.306326221116174 84 16 14.2005559991758 1.79944400082416 85 8 10.4433767874907 -2.44337678749074 86 16 11.9502590077828 4.04974099221724 87 11 10.4491061240879 0.550893875912148 88 9 12.7079971203766 -3.7079971203766 89 16 17.2229144446555 -1.22291444465555 90 12 11.9617176809770 0.0382823190230201 91 14 12.7165911252723 1.28340887472773 92 8 11.2154382415774 -3.21543824157736 93 9 10.4662941338792 -1.46629413387918 94 15 11.2211675781745 3.77883242182553 95 11 14.2320673504599 -3.23206735045995 96 21 15.7389495707520 5.26105042924803 97 14 13.4857879110603 0.514212088939672 98 18 15.7446789073491 2.25532109265092 99 12 11.9874996956640 0.0125003043360250 100 13 12.7423731399593 0.257626860040738 101 15 14.2492553602513 0.75074463974872 102 12 11.2440849245629 0.755915075437091 103 19 14.2549846968484 4.74501530315161 104 15 14.2578493651469 0.742150634853055 105 11 14.2607140334455 -3.2607140334455 106 11 10.5035348217604 0.496465178239603 107 10 12.0104170420524 -2.01041704205242 108 13 14.2693080383412 -1.26930803834117 109 15 15.0241814826365 -0.0241814826364516 110 12 11.2670022709513 0.732997729048651 111 12 12.0218757152466 -0.0218757152466351 112 16 15.7847842635288 0.215215736471152 113 9 15.0356401558307 -6.03564015583067 114 18 15.0385048241292 2.96149517587077 115 8 15.0413694924278 -7.04136949242778 116 13 10.5321815047459 2.46781849525405 117 17 12.7910725010347 4.2089274989653 118 9 11.2899196173398 -2.28991961733979 119 15 13.5488106136285 1.45118938637146 120 8 9.79163140194344 -1.79163140194344 121 7 9.794496070242 -2.79449607024199 122 12 12.0533870665307 -0.0533870665307405 123 14 15.0642868388162 -1.06428683881622 124 6 11.3071076271311 -5.30710762713112 125 8 12.0619810714264 -4.06198107142641 126 17 12.8168545157217 4.18314548427831 127 10 9.81168408003332 0.188315919966678 128 11 12.8225838523188 -1.82258385231880 129 14 13.5774572966141 0.422542703385911 130 11 12.8283131889159 -1.82831318891591 131 13 15.0872041852047 -2.08720418520466 132 12 12.8340425255130 -0.834042525513022 133 11 10.5808808658214 0.419119134178617 134 9 9.8317367581232 -0.831736758123207 135 12 12.8426365304087 -0.842636530408687 136 20 14.3495187507007 5.65048124929929 137 12 11.3443483150123 0.655651684987666 138 13 13.6032393113011 -0.603239311301084 139 12 13.6061039795996 -1.60610397959964 140 12 16.6170037518851 -4.61700375188512 141 9 13.6118333161967 -4.61183331619675 142 15 14.3667067604920 0.633293239507964 143 24 21.8896591887579 2.11034081124209 144 7 10.6123922171055 -3.61239221710549 145 17 15.1273095413844 1.87269045861557 146 11 11.3701303296993 -0.370130329699329 147 17 13.6290213259881 3.37097867401192 148 11 12.1278684422932 -1.12786844229317 149 12 13.6347506625852 -1.63475066258519 150 14 14.3896241068805 -0.389624106880476 151 11 13.6404799991823 -2.6404799991823 152 16 12.8913358914841 3.10866410851588 153 21 12.1421917837859 8.85780821621406 154 14 11.3930476760878 2.60695232391223 155 20 16.6599737763634 3.34002622363655 156 13 11.3987770126849 1.60122298731512 157 11 12.9056592329769 -1.90565923297690 158 15 14.4125414532689 0.587458546731084 159 19 18.9274587775479 0.0725412224521393 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.913274772068044 0.173450455863912 0.086725227931956 7 0.843457023179191 0.313085953641617 0.156542976820809 8 0.781190557049451 0.437618885901098 0.218809442950549 9 0.67969959160312 0.64060081679376 0.32030040839688 10 0.579466875913652 0.841066248172696 0.420533124086348 11 0.484677297912578 0.969354595825156 0.515322702087422 12 0.4433263469705 0.886652693941 0.5566736530295 13 0.465524269068609 0.931048538137217 0.534475730931391 14 0.484280718162199 0.968561436324399 0.515719281837801 15 0.422300063027936 0.844600126055872 0.577699936972064 16 0.434422562594325 0.86884512518865 0.565577437405675 17 0.511864243241083 0.976271513517833 0.488135756758917 18 0.449409395025903 0.898818790051807 0.550590604974097 19 0.574512532934101 0.850974934131799 0.425487467065899 20 0.607988958980575 0.78402208203885 0.392011041019425 21 0.606614400542868 0.786771198914264 0.393385599457132 22 0.655136515005599 0.689726969988802 0.344863484994401 23 0.606400870727382 0.787198258545236 0.393599129272618 24 0.667279614446659 0.665440771106682 0.332720385553341 25 0.654650520322963 0.690698959354073 0.345349479677037 26 0.605904314298805 0.78819137140239 0.394095685701195 27 0.575178697561499 0.849642604877002 0.424821302438501 28 0.522815451435506 0.954369097128987 0.477184548564494 29 0.487823660630602 0.975647321261204 0.512176339369398 30 0.438605606409658 0.877211212819316 0.561394393590342 31 0.527025680680314 0.945948638639373 0.472974319319687 32 0.493935785932274 0.987871571864548 0.506064214067726 33 0.645307493894959 0.709385012210081 0.354692506105041 34 0.62418985978934 0.75162028042132 0.37581014021066 35 0.612142882593138 0.775714234813724 0.387857117406862 36 0.70079032182078 0.59841935635844 0.29920967817922 37 0.750984923240525 0.498030153518949 0.249015076759475 38 0.714816787036356 0.570366425927288 0.285183212963644 39 0.698082877248577 0.603834245502845 0.301917122751423 40 0.66536587866941 0.66926824266118 0.33463412133059 41 0.676680798318716 0.646638403362568 0.323319201681284 42 0.633180709289713 0.733638581420575 0.366819290710287 43 0.59616996038128 0.80766007923744 0.40383003961872 44 0.648659837600758 0.702680324798484 0.351340162399242 45 0.70948533001455 0.581029339970901 0.290514669985450 46 0.716404727298929 0.567190545402143 0.283595272701071 47 0.677230951993639 0.645538096012723 0.322769048006361 48 0.711768802531127 0.576462394937747 0.288231197468873 49 0.682781364977714 0.634437270044571 0.317218635022286 50 0.739420942629038 0.521158114741925 0.260579057370962 51 0.867280610484149 0.265438779031702 0.132719389515851 52 0.845883328740897 0.308233342518206 0.154116671259103 53 0.821667182098389 0.356665635803223 0.178332817901611 54 0.866509638117373 0.266980723765254 0.133490361882627 55 0.864360131943185 0.27127973611363 0.135639868056815 56 0.841422477030512 0.317155045938976 0.158577522969488 57 0.815671192649649 0.368657614700703 0.184328807350351 58 0.809074969134897 0.381850061730205 0.190925030865103 59 0.816455510812596 0.367088978374807 0.183544489187404 60 0.784296587259719 0.431406825480563 0.215703412740281 61 0.760823698436576 0.478352603126848 0.239176301563424 62 0.736529784323981 0.526940431352037 0.263470215676019 63 0.715691580407241 0.568616839185517 0.284308419592759 64 0.817659859052267 0.364680281895467 0.182340140947733 65 0.787125645658268 0.425748708683464 0.212874354341732 66 0.76352705590053 0.472945888198939 0.236472944099469 67 0.740271276675196 0.519457446649607 0.259728723324804 68 0.701850997368305 0.59629800526339 0.298149002631695 69 0.668617884014882 0.662764231970236 0.331382115985118 70 0.640773214483345 0.718453571033311 0.359226785516655 71 0.59679900717627 0.80640198564746 0.40320099282373 72 0.599431246553442 0.801137506893115 0.400568753446558 73 0.569391906527871 0.861216186944258 0.430608093472129 74 0.578611874419167 0.842776251161667 0.421388125580833 75 0.615114244088506 0.769771511822989 0.384885755911494 76 0.573641950305086 0.852716099389828 0.426358049694914 77 0.548085612866452 0.903828774267096 0.451914387133548 78 0.504770931762359 0.990458136475283 0.495229068237641 79 0.500497315593199 0.999005368813603 0.499502684406801 80 0.475403269307778 0.950806538615556 0.524596730692222 81 0.437405697597092 0.874811395194184 0.562594302402908 82 0.407907322803616 0.815814645607231 0.592092677196384 83 0.364888153376616 0.729776306753232 0.635111846623384 84 0.341140649835784 0.682281299671569 0.658859350164216 85 0.329912202456449 0.659824404912899 0.67008779754355 86 0.380483056927035 0.76096611385407 0.619516943072965 87 0.341975629621703 0.683951259243405 0.658024370378297 88 0.368042969692741 0.736085939385483 0.631957030307259 89 0.332346985972441 0.664693971944881 0.667653014027559 90 0.291937583658499 0.583875167316998 0.708062416341501 91 0.26324565201075 0.5264913040215 0.73675434798925 92 0.270081239092781 0.540162478185562 0.729918760907219 93 0.241098905257632 0.482197810515263 0.758901094742368 94 0.277540317331690 0.555080634663381 0.72245968266831 95 0.284919441742165 0.56983888348433 0.715080558257835 96 0.397384217226252 0.794768434452503 0.602615782773748 97 0.356493494028688 0.712986988057377 0.643506505971312 98 0.347747532672528 0.695495065345056 0.652252467327472 99 0.307375778275085 0.614751556550171 0.692624221724914 100 0.27035312456301 0.54070624912602 0.72964687543699 101 0.239746269145527 0.479492538291054 0.760253730854473 102 0.212671368906193 0.425342737812387 0.787328631093807 103 0.314614411929374 0.629228823858749 0.685385588070626 104 0.289107883151862 0.578215766303725 0.710892116848138 105 0.284661006491103 0.569322012982206 0.715338993508897 106 0.256269204765059 0.512538409530118 0.743730795234941 107 0.229030700988225 0.458061401976451 0.770969299011775 108 0.197106382998135 0.39421276599627 0.802893617001865 109 0.168956334218739 0.337912668437478 0.83104366578126 110 0.150506391397406 0.301012782794812 0.849493608602594 111 0.128210302021722 0.256420604043443 0.871789697978278 112 0.110012566899149 0.220025133798297 0.889987433100851 113 0.173310218511186 0.346620437022372 0.826689781488814 114 0.203223126593566 0.406446253187131 0.796776873406434 115 0.365154641651962 0.730309283303924 0.634845358348038 116 0.385114491783828 0.770228983567655 0.614885508216172 117 0.516154130155693 0.967691739688615 0.483845869844307 118 0.476005578373473 0.952011156746945 0.523994421626527 119 0.474538807395428 0.949077614790855 0.525461192604572 120 0.42855172806391 0.85710345612782 0.57144827193609 121 0.39561966926665 0.7912393385333 0.60438033073335 122 0.355429892350302 0.710859784700604 0.644570107649698 123 0.307466706076244 0.614933412152488 0.692533293923756 124 0.371801750571231 0.743603501142463 0.628198249428769 125 0.392120543141801 0.784241086283603 0.607879456858199 126 0.5127262817462 0.9745474365076 0.4872737182538 127 0.466702179629954 0.933404359259908 0.533297820370046 128 0.414093945598525 0.82818789119705 0.585906054401475 129 0.371916467895118 0.743832935790237 0.628083532104882 130 0.321822523768204 0.643645047536407 0.678177476231796 131 0.279454657836296 0.558909315672592 0.720545342163704 132 0.230189874950054 0.460379749900108 0.769810125049946 133 0.192213050070226 0.384426100140452 0.807786949929774 134 0.152231170564699 0.304462341129397 0.847768829435301 135 0.117768887305860 0.235537774611721 0.88223111269414 136 0.303251968609739 0.606503937219478 0.696748031390261 137 0.282599664659245 0.56519932931849 0.717400335340755 138 0.236308287118105 0.47261657423621 0.763691712881895 139 0.187063904531805 0.374127809063611 0.812936095468195 140 0.214057986539424 0.428115973078849 0.785942013460576 141 0.276475766155471 0.552951532310942 0.723524233844529 142 0.217934740870687 0.435869481741375 0.782065259129313 143 0.183686671696859 0.367373343393719 0.81631332830314 144 0.231382977431623 0.462765954863246 0.768617022568377 145 0.191764762125860 0.383529524251719 0.80823523787414 146 0.147295724208739 0.294591448417479 0.85270427579126 147 0.152207942535366 0.304415885070732 0.847792057464634 148 0.116462989057331 0.232925978114663 0.883537010942669 149 0.102058168082889 0.204116336165778 0.897941831917111 150 0.0813901087007167 0.162780217401433 0.918609891299283 151 0.488395734483036 0.976791468966072 0.511604265516964 152 0.631171898304443 0.737656203391114 0.368828101695557 153 0.85932949610366 0.281341007792680 0.140670503896340 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 0 0 OK 10% type I error level 0 0 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556418db27g053rdp7se4/10x8di1289556390.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556418db27g053rdp7se4/10x8di1289556390.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556418db27g053rdp7se4/18pz71289556390.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556418db27g053rdp7se4/18pz71289556390.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556418db27g053rdp7se4/28pz71289556390.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556418db27g053rdp7se4/28pz71289556390.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556418db27g053rdp7se4/31ygs1289556390.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556418db27g053rdp7se4/31ygs1289556390.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556418db27g053rdp7se4/41ygs1289556390.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556418db27g053rdp7se4/41ygs1289556390.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556418db27g053rdp7se4/51ygs1289556390.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556418db27g053rdp7se4/51ygs1289556390.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556418db27g053rdp7se4/6uqfd1289556390.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556418db27g053rdp7se4/6uqfd1289556390.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556418db27g053rdp7se4/74hef1289556390.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556418db27g053rdp7se4/74hef1289556390.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556418db27g053rdp7se4/84hef1289556390.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556418db27g053rdp7se4/84hef1289556390.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556418db27g053rdp7se4/94hef1289556390.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556418db27g053rdp7se4/94hef1289556390.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

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