*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, 30 Nov 2010 14:14:25 +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/30/t12911263790iwwqa5ss1qm5nj.htm/, Retrieved Tue, 30 Nov 2010 15:12:59 +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/30/t12911263790iwwqa5ss1qm5nj.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 «

2 12 2 11 2 14 1 12 2 21 2 12 2 22 2 11 2 10 2 13 1 10 2 8 1 15 2 14 2 10 1 14 1 14 2 11 1 10 2 13 1 7 2 14 2 12 2 14 1 11 2 9 1 11 2 15 2 14 1 13 2 9 1 15 2 10 2 11 1 13 1 8 1 20 1 12 2 10 1 10 1 9 2 14 1 8 1 14 2 11 2 13 2 9 2 11 2 15 1 11 2 10 1 14 1 18 2 14 1 11 2 12 2 13 2 9 1 10 2 15 1 20 1 12 2 12 2 14 2 13 1 11 2 17 1 12 2 13 1 14 1 13 2 15 2 13 1 10 1 11 2 19 2 13 2 17 1 13 1 9 1 11 1 10 2 9 1 12 2 12 2 13 1 13 2 12 2 15 2 22 2 13 2 15 2 13 2 15 2 10 2 11 2 16 2 11 1 11 1 10 2 10 1 16 2 12 1 11 2 16 1 19 2 11 1 16 1 15 2 24 2 14 2 15 2 11 1 15 2 12 1 10 2 14 2 13 2 9 2 15 2 15 2 14 2 11 2 8 2 11 2 11 1 8 2 10 2 11 2 13 1 11 1 20 2 10 1 15 1 12 2 14 1 23 1 14 2 16 2 11 1 12 2 10 1 14 2 12 1 12 2 11 2 12 1 13 1 11 1 19 2 12 2 17 1 9 2 12 2 19 2 18 2 15 2 14 2 11 2 9 2 18 2 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 y[t] = + 12.2907451492279 + 0.276580143314847x[t] + 0.970866601147538M1[t] -0.485826440139703M2[t] -1.85133518547589M3[t] -0.625659634861006M4[t] + 0.917647323851751M5[t] + 1.2147514458952M6[t] -0.859972086470695M7[t] -1.07783180979365M8[t] -1.89797925849695M9[t] -0.696851311560647M10[t] -1.87216024360439M11[t] + 0.00836588819332487t + 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) 12.2907451492279 1.265789 9.7099 0 0 x 0.276580143314847 0.504304 0.5484 0.584217 0.292108 M1 0.970866601147538 1.186296 0.8184 0.414444 0.207222 M2 -0.485826440139703 1.184941 -0.41 0.682398 0.341199 M3 -1.85133518547589 1.184868 -1.5625 0.12031 0.060155 M4 -0.625659634861006 1.186105 -0.5275 0.598643 0.299321 M5 0.917647323851751 1.18479 0.7745 0.439857 0.219929 M6 1.2147514458952 1.18609 1.0242 0.307429 0.153714 M7 -0.859972086470695 1.207112 -0.7124 0.477326 0.238663 M8 -1.07783180979365 1.208852 -0.8916 0.374046 0.187023 M9 -1.89797925849695 1.206359 -1.5733 0.117782 0.058891 M10 -0.696851311560647 1.206946 -0.5774 0.564569 0.282284 M11 -1.87216024360439 1.208743 -1.5488 0.123554 0.061777 t 0.00836588819332487 0.005179 1.6154 0.10836 0.05418 Multiple Linear Regression - Regression Statistics Multiple R 0.364293777347871 R-squared 0.132709956214381 Adjusted R-squared 0.0565290739899679 F-TEST (value) 1.74203753408165 F-TEST (DF numerator) 13 F-TEST (DF denominator) 148 p-value 0.0578919379739506 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.07536929794538 Sum Squared Residuals 1399.76865517427 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 12 13.8231379251985 -1.82313792519848 2 11 12.3748107721045 -1.37481077210453 3 14 11.0176679149617 2.98233208503832 4 12 11.9751292104550 0.0248707895449669 5 21 13.8033822006760 7.19661779932404 6 12 14.1088522109127 -2.10885221091274 7 22 12.0424945667402 9.95750543325984 8 11 11.8330007316105 -0.83300073161054 9 10 11.0212191711006 -1.02121917110056 10 13 12.2307130062302 0.769286993769811 11 10 10.7871898190649 -0.787189819064924 12 8 12.9442960941775 -4.94429609417748 13 15 13.6469484402035 1.35305155979650 14 14 12.4752014304244 1.52479856957557 15 10 11.1180585732816 -1.11805857328157 16 14 12.0755198687749 1.92448013122507 17 14 13.6271927156810 0.372807284318985 18 11 14.2092428692326 -3.20924286923264 19 10 11.8663050817452 -1.86630508174522 20 13 11.9333913899304 1.06660861006956 21 7 10.8450296861056 -3.84502968610561 22 14 12.3311036645501 1.66889633544991 23 12 11.1641606206997 0.835839379300332 24 14 13.0446867524974 0.955313247502616 25 11 13.7473390985234 -2.7473390985234 26 9 12.5755920887443 -3.57559208874433 27 11 10.9418690882866 0.0581309117133738 28 15 12.4524906704097 2.54750932959032 29 14 14.0041635173158 -0.00416351731575923 30 13 14.0330533842377 -1.03305338423769 31 9 12.2432758833800 -3.24327588337996 32 15 11.7572019049355 3.24279809506451 33 10 11.2220004877404 -1.22200048774036 34 11 12.4314943228700 -1.43149432286999 35 13 10.9879711357047 2.01202886429528 36 8 12.8684972675024 -4.86849726750243 37 20 13.8477297568433 6.1522702431567 38 12 12.3994026037494 -0.399402603749383 39 10 11.3188398899214 -1.31883988992137 40 10 12.2763011854147 -2.27630118541473 41 9 13.8279740323208 -4.82797403232081 42 14 14.4100241858724 -0.410024185872432 43 8 12.0670863983850 -4.06708639838501 44 14 11.8575925632554 2.14240743674461 45 11 11.3223911460603 -0.322391146060258 46 13 12.5318849811899 0.468115018810115 47 9 11.3649419373395 -2.36494193733946 48 11 13.2454680691372 -2.24546806913718 49 15 14.2247005584780 0.775299441521956 50 11 12.4997932620693 -1.49979326206928 51 10 11.4192305482413 -1.41923054824127 52 14 12.3766918437346 1.62330815626537 53 18 13.9283646906407 4.07163530935929 54 14 14.5104148441923 -0.510414844192331 55 11 12.1674770567049 -1.16747705670491 56 12 12.2345633648901 -0.234563364890132 57 13 11.4227818043802 1.57721819561984 58 9 12.6322756395098 -3.63227563950978 59 10 11.1887524523445 -1.18875245234452 60 15 13.3458587274571 1.65414127254292 61 20 14.0485110734831 5.9514889265169 62 12 12.6001839203892 -0.600183920389179 63 12 11.5196212065612 0.48037879343883 64 14 12.7536626453694 1.24633735463063 65 13 14.3053354922755 -1.30533549227546 66 11 14.3342253591974 -3.33422535919738 67 17 12.5444478583397 4.45555214166034 68 12 12.0583738798952 -0.0583738798951842 69 13 11.5231724627001 1.47682753729995 70 14 12.4560861545148 1.54391384548516 71 13 11.2891431106644 1.71085688933558 72 15 13.4462493857770 1.55375061422302 73 13 14.4254818751178 -1.42548187511784 74 10 12.7005745787091 -2.70057457870908 75 11 11.3434317215662 -0.343431721566221 76 19 12.8540533036893 6.14594669631073 77 13 14.4057261505954 -1.40572615059535 78 17 14.7111961608321 2.28880383916787 79 13 12.3682583733447 0.63174162665529 80 9 12.1587645382151 -3.15876453821508 81 11 11.3469829777051 -0.346982977705106 82 10 12.5564768128347 -2.55647681283473 83 9 11.6661139122992 -2.66611391229916 84 12 13.2700599007820 -1.27005990078203 85 12 14.5258725334377 -2.52587253343774 86 13 13.0775453803438 -0.077545380343823 87 13 11.4438223798861 1.55617762011388 88 12 12.9544439620092 -0.95444396200917 89 15 14.5061168089153 0.493883191084749 90 22 14.8115868191520 7.18841318084797 91 13 12.7452291749795 0.254770825020545 92 15 12.5357353398498 2.46426466015017 93 13 11.7239537793399 1.27604622066015 94 15 12.9334476144695 2.06655238553052 95 10 11.7665045706191 -1.76650457061906 96 11 13.6470307024168 -2.64703070241677 97 16 14.6262631917576 1.37373680824236 98 11 13.1779360386637 -2.17793603866372 99 11 11.5442130382060 -0.544213038206017 100 10 12.7782544770142 -2.77825447701422 101 10 14.6065074672351 -4.60650746723515 102 16 14.6353973341571 1.36460266584292 103 12 12.8456198332994 -0.845619833299353 104 11 12.3595458548549 -1.35954585485488 105 16 11.8243444376597 4.17565556234025 106 19 12.7572581294745 6.24274187052547 107 11 11.8668952289390 -0.866895228938958 108 16 13.4708412174218 2.52915878257817 109 15 14.4500737067627 0.549926293237312 110 24 13.2783266969836 10.7216733030164 111 14 11.9211838398408 2.07881616015924 112 15 13.1552252786490 1.84477472135103 113 11 14.7068981255550 -3.70689812555505 114 15 14.7357879924770 0.264212007523024 115 12 12.9460104916193 -0.946010491619252 116 10 12.4599365131748 -2.45993651317478 117 14 11.9247350959796 2.07526490402035 118 13 13.1342289311093 -0.134228931109275 119 9 11.9672858872589 -2.96728588725886 120 15 13.8478120190566 1.15218798094343 121 15 14.8270445083974 0.172955491602566 122 14 13.3787173553035 0.621282644696481 123 11 12.0215744981607 -1.02157449816066 124 8 13.2556159369689 -5.25561593696886 125 11 14.8072887838749 -3.80728878387495 126 11 15.1127587941117 -4.11275879411172 127 8 12.7698210066243 -4.7698210066243 128 10 12.8369073148095 -2.83690731480952 129 11 12.0251257542995 -1.02512575429955 130 13 13.2346195894292 -0.234619589429174 131 11 11.7910964022639 -0.791096402263907 132 20 13.6716225340616 6.32837746593838 133 10 14.9274351667173 -4.92743516671733 134 15 13.2025278703086 1.79747212969143 135 12 11.8453850131657 0.154614986834288 136 14 13.3560065952888 0.643993404711236 137 23 14.63109929888 8.36890070112 138 14 14.9365693091168 -0.936569309116773 139 16 13.1467918082590 2.85320819174095 140 11 12.9372979731294 -1.93729797312942 141 12 11.8489362693046 0.151063730695401 142 10 13.3350102477491 -3.33501024774907 143 14 11.8914870605838 2.10851293941619 144 12 14.0485933356964 -2.04859333569637 145 12 14.7512456817224 -2.75124568172238 146 11 13.5794986719433 -2.57949867194332 147 12 12.2223558148005 -0.222355814800459 148 13 13.1798171102938 -0.179817110293815 149 11 14.7314899571999 -3.7314899571999 150 19 15.0369599674367 3.96304003256333 151 12 13.2471824665789 -1.24718246657895 152 17 13.0376886314493 3.96231136855068 153 9 11.9493269276245 -2.9493269276245 154 12 13.4354009060690 -1.43540090606897 155 19 12.2684578622185 6.73154213778145 156 18 14.1489839940163 3.85101600598373 157 15 15.1282164833571 -0.128216483357129 158 14 13.6798893302632 0.320110669736786 159 11 12.3227464731204 -1.32274647312036 160 9 13.5567879119286 -4.55678791192856 161 18 15.1084607588346 2.89153924116536 162 16 15.4139307690714 0.586069230928583 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.772706073702215 0.454587852595571 0.227293926297785 18 0.649158397435939 0.701683205128122 0.350841602564061 19 0.843001669042847 0.313996661914306 0.156998330957153 20 0.771593391410703 0.456813217178594 0.228406608589297 21 0.703689296751179 0.592621406497642 0.296310703248821 22 0.608358573831227 0.783282852337546 0.391641426168773 23 0.544324958500197 0.911350082999606 0.455675041499803 24 0.606538955554221 0.786922088891558 0.393461044445779 25 0.52526961284687 0.94946077430626 0.47473038715313 26 0.520456406570525 0.95908718685895 0.479543593429475 27 0.484528181923587 0.969056363847174 0.515471818076413 28 0.4171109876693 0.8342219753386 0.5828890123307 29 0.438214930851976 0.876429861703953 0.561785069148024 30 0.470796702973717 0.941593405947435 0.529203297026283 31 0.615410334589867 0.769179330820266 0.384589665410133 32 0.667663639637575 0.66467272072485 0.332336360362425 33 0.618268035912747 0.763463928174506 0.381731964087253 34 0.561504538913159 0.876990922173682 0.438495461086841 35 0.541711298297106 0.916577403405788 0.458288701702894 36 0.514860984628764 0.970278030742473 0.485139015371236 37 0.752327709564741 0.495344580870517 0.247672290435259 38 0.708324419115886 0.583351161768227 0.291675580884114 39 0.664584064165432 0.670831871669135 0.335415935834568 40 0.644091744964574 0.711816510070851 0.355908255035426 41 0.730073911159692 0.539852177680616 0.269926088840308 42 0.69734882887394 0.605302342252121 0.302651171126060 43 0.71452904418432 0.57094191163136 0.28547095581568 44 0.690362091659311 0.619275816681377 0.309637908340689 45 0.65414245694913 0.69171508610174 0.34585754305087 46 0.602394153794903 0.795211692410194 0.397605846205097 47 0.580039442067356 0.839921115865288 0.419960557932644 48 0.547243475472912 0.905513049054176 0.452756524527088 49 0.49303555418454 0.98607110836908 0.50696444581546 50 0.449954877593947 0.899909755187894 0.550045122406053 51 0.401831926879422 0.803663853758845 0.598168073120578 52 0.368785212274218 0.737570424548436 0.631214787725782 53 0.410733681496324 0.821467362992649 0.589266318503676 54 0.369752451849031 0.739504903698062 0.630247548150969 55 0.323282845998495 0.64656569199699 0.676717154001505 56 0.282364269078399 0.564728538156798 0.717635730921601 57 0.272698375636523 0.545396751273045 0.727301624363477 58 0.282757617873879 0.565515235747758 0.717242382126121 59 0.243369783361029 0.486739566722059 0.75663021663897 60 0.257596536704583 0.515193073409167 0.742403463295417 61 0.373303887501909 0.746607775003818 0.626696112498091 62 0.331508726582845 0.663017453165689 0.668491273417155 63 0.286969959997719 0.573939919995437 0.713030040002281 64 0.248377089332414 0.496754178664828 0.751622910667586 65 0.230402896814893 0.460805793629787 0.769597103185107 66 0.224766721302993 0.449533442605987 0.775233278697007 67 0.2562974519774 0.5125949039548 0.7437025480226 68 0.218291417736106 0.436582835472212 0.781708582263894 69 0.194100042429507 0.388200084859013 0.805899957570493 70 0.177587702011799 0.355175404023598 0.822412297988201 71 0.157751112061017 0.315502224122033 0.842248887938983 72 0.143910076304354 0.287820152608709 0.856089923695646 73 0.139322243856158 0.278644487712316 0.860677756143842 74 0.131598462192143 0.263196924384287 0.868401537807857 75 0.107347494712763 0.214694989425526 0.892652505287237 76 0.173197555844339 0.346395111688678 0.826802444155661 77 0.158374329563243 0.316748659126486 0.841625670436757 78 0.150879699801539 0.301759399603078 0.849120300198461 79 0.125577276047144 0.251154552094289 0.874422723952856 80 0.128757964036592 0.257515928073184 0.871242035963408 81 0.106524198488204 0.213048396976408 0.893475801511796 82 0.0991017243751591 0.198203448750318 0.900898275624841 83 0.0990559919700648 0.198111983940130 0.900944008029935 84 0.08878450387995 0.1775690077599 0.91121549612005 85 0.0890812747698955 0.178162549539791 0.910918725230104 86 0.0740610782928778 0.148122156585756 0.925938921707122 87 0.0623867554248579 0.124773510849716 0.937613244575142 88 0.0540795238412011 0.108159047682402 0.945920476158799 89 0.0423183081411922 0.0846366162823844 0.957681691858808 90 0.119854443789268 0.239708887578535 0.880145556210732 91 0.0995603888274496 0.199120777654899 0.90043961117255 92 0.0941814615566146 0.188362923113229 0.905818538443385 93 0.0779893672950644 0.155978734590129 0.922010632704936 94 0.068005978981824 0.136011957963648 0.931994021018176 95 0.058273574538688 0.116547149077376 0.941726425461312 96 0.0592272750268874 0.118454550053775 0.940772724973113 97 0.0517325625041054 0.103465125008211 0.948267437495895 98 0.0504732970383355 0.100946594076671 0.949526702961665 99 0.0395118890367896 0.0790237780735792 0.96048811096321 100 0.0378463176304778 0.0756926352609556 0.962153682369522 101 0.0524274323877837 0.104854864775567 0.947572567612216 102 0.0423967092843835 0.084793418568767 0.957603290715616 103 0.0331102014048612 0.0662204028097224 0.966889798595139 104 0.0262514394443578 0.0525028788887156 0.973748560555642 105 0.0332334218744025 0.066466843748805 0.966766578125598 106 0.0702385606619857 0.140477121323971 0.929761439338014 107 0.0569482636546898 0.113896527309380 0.94305173634531 108 0.0512737965989401 0.102547593197880 0.94872620340106 109 0.0414153359821755 0.0828306719643509 0.958584664017824 110 0.325645001970921 0.651290003941842 0.674354998029079 111 0.31751285659448 0.63502571318896 0.68248714340552 112 0.35842581279516 0.71685162559032 0.64157418720484 113 0.361156498409635 0.72231299681927 0.638843501590365 114 0.315239912376169 0.630479824752338 0.684760087623831 115 0.277100663403380 0.554201326806759 0.72289933659662 116 0.250117058001976 0.500234116003952 0.749882941998024 117 0.274298024961551 0.548596049923102 0.725701975038449 118 0.251599999163036 0.503199998326071 0.748400000836964 119 0.249846293906230 0.499692587812461 0.75015370609377 120 0.208089153872756 0.416178307745511 0.791910846127244 121 0.216333371333278 0.432666742666556 0.783666628666722 122 0.193618746849053 0.387237493698106 0.806381253150947 123 0.163517092116601 0.327034184233202 0.836482907883399 124 0.164819452630627 0.329638905261254 0.835180547369373 125 0.173495857271167 0.346991714542333 0.826504142728833 126 0.186935534478665 0.37387106895733 0.813064465521335 127 0.238143043839517 0.476286087679033 0.761856956160483 128 0.234463071391394 0.468926142782789 0.765536928608606 129 0.187945535084898 0.375891070169797 0.812054464915102 130 0.155720756134684 0.311441512269368 0.844279243865316 131 0.185904548488573 0.371809096977146 0.814095451511427 132 0.236088671918261 0.472177343836521 0.76391132808174 133 0.249921166705361 0.499842333410721 0.75007883329464 134 0.219582402694018 0.439164805388036 0.780417597305982 135 0.169647980863842 0.339295961727685 0.830352019136158 136 0.133825850746976 0.267651701493953 0.866174149253024 137 0.517739967905579 0.964520064188842 0.482260032094421 138 0.43418534099144 0.86837068198288 0.56581465900856 139 0.49278851392728 0.98557702785456 0.50721148607272 140 0.479680236664301 0.959360473328603 0.520319763335699 141 0.501674668010802 0.996650663978396 0.498325331989198 142 0.393252189670307 0.786504379340614 0.606747810329693 143 0.355521522239329 0.711043044478658 0.644478477760671 144 0.322715534659962 0.645431069319924 0.677284465340038 145 0.230014010146478 0.460028020292957 0.769985989853522 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 8 0.062015503875969 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/30/t12911263790iwwqa5ss1qm5nj/10xr3f1291126451.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911263790iwwqa5ss1qm5nj/10xr3f1291126451.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911263790iwwqa5ss1qm5nj/188om1291126451.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911263790iwwqa5ss1qm5nj/188om1291126451.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911263790iwwqa5ss1qm5nj/288om1291126451.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911263790iwwqa5ss1qm5nj/288om1291126451.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911263790iwwqa5ss1qm5nj/3jz671291126451.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911263790iwwqa5ss1qm5nj/3jz671291126451.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911263790iwwqa5ss1qm5nj/4jz671291126451.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911263790iwwqa5ss1qm5nj/4jz671291126451.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911263790iwwqa5ss1qm5nj/5jz671291126451.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911263790iwwqa5ss1qm5nj/5jz671291126451.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911263790iwwqa5ss1qm5nj/6bq5s1291126451.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911263790iwwqa5ss1qm5nj/6bq5s1291126451.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911263790iwwqa5ss1qm5nj/7bq5s1291126451.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911263790iwwqa5ss1qm5nj/7bq5s1291126451.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911263790iwwqa5ss1qm5nj/84i4d1291126451.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911263790iwwqa5ss1qm5nj/84i4d1291126451.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911263790iwwqa5ss1qm5nj/94i4d1291126451.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t12911263790iwwqa5ss1qm5nj/94i4d1291126451.ps (open in new window)

Parameters (Session):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; par2 = Include Monthly 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