*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 13:45:53 +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/t1291124856ydnzobkecmm18un.htm/, Retrieved Tue, 30 Nov 2010 14:47:52 +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/t1291124856ydnzobkecmm18un.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 11 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation y[t] = + 12.9137999388331 + 0.323663672507733x[t] + 0.934728575797638M1[t] -0.516961686524345M2[t] -1.87410454366720M3[t] -0.636699995630935M4[t] + 0.91160974204709M5[t] + 1.22044286151192M6[t] -0.898179717499406M7[t] -1.10405174269112M8[t] -1.92307692307692M9[t] -0.71720489788521M10[t] -1.87328251192189M11[t] + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 12.9137999388331 1.212086 10.6542 0 0 x 0.323663672507733 0.506173 0.6394 0.523523 0.261762 M1 0.934728575797638 1.192474 0.7839 0.434368 0.217184 M2 -0.516961686524345 1.191166 -0.434 0.664919 0.332459 M3 -1.87410454366720 1.191166 -1.5733 0.117762 0.058881 M4 -0.636699995630935 1.192474 -0.5339 0.594184 0.297092 M5 0.91160974204709 1.191166 0.7653 0.445298 0.222649 M6 1.22044286151192 1.192474 1.0235 0.307752 0.153876 M7 -0.898179717499406 1.213381 -0.7402 0.460326 0.230163 M8 -1.10405174269112 1.215254 -0.9085 0.365084 0.182542 M9 -1.92307692307692 1.212756 -1.5857 0.114926 0.057463 M10 -0.71720489788521 1.213381 -0.5911 0.555363 0.277681 M11 -1.87328251192189 1.215254 -1.5415 0.125323 0.062661 Multiple Linear Regression - Regression Statistics Multiple R 0.342663940796646 R-squared 0.117418576322287 Adjusted R-squared 0.0463381932073034 F-TEST (value) 1.65191254150029 F-TEST (DF numerator) 12 F-TEST (DF denominator) 149 p-value 0.083263726308721 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.09193395483857 Sum Squared Residuals 1424.44828158147 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 12 14.4958558596462 -2.49585585964622 2 11 13.0441655973242 -2.04416559732419 3 14 11.6870227401813 2.31297725981866 4 12 12.6007636157099 -0.600763615709873 5 21 14.4727370258956 6.52726297410438 6 12 14.7815701453605 -2.78157014536045 7 22 12.6629475663491 9.33705243365087 8 11 12.4570755411574 -1.4570755411574 9 10 11.6380503607716 -1.63805036077161 10 13 12.8439223859633 0.156077614036677 11 10 11.3641810994189 -1.36418109941890 12 8 13.5611272838485 -5.56112728384854 13 15 14.1721921871384 0.827807812861563 14 14 13.0441655973242 0.955834402675809 15 10 11.6870227401813 -1.68702274018133 16 14 12.6007636157099 1.39923638429013 17 14 14.1490733533879 -0.14907335338789 18 11 14.7815701453605 -3.78157014536046 19 10 12.3392838938414 -2.33928389384139 20 13 12.4570755411574 0.542924458842584 21 7 11.3143866882639 -4.31438668826388 22 14 12.8439223859633 1.15607761403668 23 12 11.6878447719266 0.312155228073354 24 14 13.5611272838485 0.438872716151467 25 11 14.1721921871384 -3.17219218713844 26 9 13.0441655973242 -4.04416559732419 27 11 11.3633590676736 -0.3633590676736 28 15 12.9244272882176 2.0755727117824 29 14 14.4727370258956 -0.472737025895624 30 13 14.4579064728527 -1.45790647285272 31 9 12.6629475663491 -3.66294756634912 32 15 12.1334118686497 2.86658813135032 33 10 11.6380503607716 -1.63805036077161 34 11 12.8439223859633 -1.84392238596332 35 13 11.3641810994189 1.63581890058109 36 8 13.2374636113408 -5.2374636113408 37 20 14.1721921871384 5.82780781286156 38 12 12.7205019248165 -0.720501924816458 39 10 11.6870227401813 -1.68702274018133 40 10 12.6007636157099 -2.60076361570987 41 9 14.1490733533879 -5.14907335338789 42 14 14.7815701453605 -0.781570145360455 43 8 12.3392838938414 -4.33928389384139 44 14 12.1334118686497 1.86658813135032 45 11 11.6380503607716 -0.63805036077161 46 13 12.8439223859633 0.156077614036678 47 9 11.6878447719266 -2.68784477192664 48 11 13.5611272838485 -2.56112728384853 49 15 14.4958558596462 0.504144140353831 50 11 12.7205019248165 -1.72050192481646 51 10 11.6870227401813 -1.68702274018133 52 14 12.6007636157099 1.39923638429013 53 18 14.1490733533879 3.85092664661211 54 14 14.7815701453605 -0.781570145360455 55 11 12.3392838938414 -1.33928389384139 56 12 12.4570755411574 -0.457075541157416 57 13 11.6380503607716 1.36194963922839 58 9 12.8439223859633 -3.84392238596332 59 10 11.3641810994189 -1.36418109941891 60 15 13.5611272838485 1.43887271615147 61 20 14.1721921871384 5.82780781286156 62 12 12.7205019248165 -0.720501924816458 63 12 11.6870227401813 0.312977259818668 64 14 12.9244272882176 1.07557271178240 65 13 14.4727370258956 -1.47273702589562 66 11 14.4579064728527 -3.45790647285272 67 17 12.6629475663491 4.33705243365087 68 12 12.1334118686497 -0.133411868649683 69 13 11.6380503607716 1.36194963922839 70 14 12.5202587134556 1.47974128654441 71 13 11.3641810994189 1.63581890058109 72 15 13.5611272838485 1.43887271615147 73 13 14.4958558596462 -1.49585585964617 74 10 12.7205019248165 -2.72050192481646 75 11 11.3633590676736 -0.3633590676736 76 19 12.9244272882176 6.0755727117824 77 13 14.4727370258956 -1.47273702589562 78 17 14.7815701453605 2.21842985463954 79 13 12.3392838938414 0.660716106158607 80 9 12.1334118686497 -3.13341186864968 81 11 11.3143866882639 -0.314386688263877 82 10 12.5202587134556 -2.52025871345559 83 9 11.6878447719266 -2.68784477192664 84 12 13.2374636113408 -1.2374636113408 85 12 14.4958558596462 -2.49585585964617 86 13 13.0441655973242 -0.0441655973241913 87 13 11.3633590676736 1.63664093232640 88 12 12.9244272882176 -0.924427288217599 89 15 14.4727370258956 0.527262974104376 90 22 14.7815701453605 7.21842985463954 91 13 12.6629475663491 0.337052433650874 92 15 12.4570755411574 2.54292445884258 93 13 11.6380503607716 1.36194963922839 94 15 12.8439223859633 2.15607761403668 95 10 11.6878447719266 -1.68784477192665 96 11 13.5611272838485 -2.56112728384853 97 16 14.4958558596462 1.50414414035383 98 11 13.0441655973242 -2.04416559732419 99 11 11.3633590676736 -0.3633590676736 100 10 12.6007636157099 -2.60076361570987 101 10 14.4727370258956 -4.47273702589563 102 16 14.4579064728527 1.54209352714728 103 12 12.6629475663491 -0.662947566349126 104 11 12.1334118686497 -1.13341186864968 105 16 11.6380503607716 4.36194963922839 106 19 12.5202587134556 6.47974128654441 107 11 11.6878447719266 -0.687844771926646 108 16 13.2374636113408 2.7625363886592 109 15 14.1721921871384 0.827807812861564 110 24 13.0441655973242 10.9558344026758 111 14 11.6870227401813 2.31297725981867 112 15 12.9244272882176 2.0755727117824 113 11 14.4727370258956 -3.47273702589562 114 15 14.4579064728527 0.542093527147277 115 12 12.6629475663491 -0.662947566349126 116 10 12.1334118686497 -2.13341186864968 117 14 11.6380503607716 2.36194963922839 118 13 12.8439223859633 0.156077614036678 119 9 11.6878447719266 -2.68784477192664 120 15 13.5611272838485 1.43887271615147 121 15 14.4958558596462 0.504144140353831 122 14 13.0441655973242 0.955834402675809 123 11 11.6870227401813 -0.687022740181332 124 8 12.9244272882176 -4.9244272882176 125 11 14.4727370258956 -3.47273702589562 126 11 14.7815701453605 -3.78157014536046 127 8 12.3392838938414 -4.33928389384139 128 10 12.4570755411574 -2.45707554115742 129 11 11.6380503607716 -0.63805036077161 130 13 12.8439223859633 0.156077614036678 131 11 11.3641810994189 -0.364181099418912 132 20 13.2374636113408 6.7625363886592 133 10 14.4958558596462 -4.49585585964617 134 15 12.7205019248165 2.27949807518354 135 12 11.3633590676736 0.636640932326403 136 14 12.9244272882176 1.07557271178240 137 23 14.1490733533879 8.85092664661211 138 14 14.4579064728527 -0.457906472852723 139 16 12.6629475663491 3.33705243365087 140 11 12.4570755411574 -1.45707554115742 141 12 11.3143866882639 0.685613311736124 142 10 12.8439223859633 -2.84392238596332 143 14 11.3641810994189 2.63581890058109 144 12 13.5611272838485 -1.56112728384853 145 12 14.1721921871384 -2.17219218713844 146 11 13.0441655973242 -2.04416559732419 147 12 11.6870227401813 0.312977259818668 148 13 12.6007636157099 0.399236384290135 149 11 14.1490733533879 -3.14907335338789 150 19 14.4579064728527 4.54209352714728 151 12 12.6629475663491 -0.662947566349126 152 17 12.4570755411574 4.54292445884258 153 9 11.3143866882639 -2.31438668826387 154 12 12.8439223859633 -0.843922385963322 155 19 11.6878447719266 7.31215522807335 156 18 13.5611272838485 4.43887271615147 157 15 14.4958558596462 0.504144140353831 158 14 13.0441655973242 0.955834402675809 159 11 11.6870227401813 -0.687022740181332 160 9 12.9244272882176 -3.9244272882176 161 18 14.4727370258956 3.52726297410438 162 16 14.7815701453605 1.21842985463954 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.337780831063268 0.675561662126535 0.662219168936732 17 0.62871856748692 0.74256286502616 0.37128143251308 18 0.501671424645815 0.99665715070837 0.498328575354185 19 0.752944753543612 0.494110492912775 0.247055246456388 20 0.672512519562935 0.654974960874131 0.327487480437065 21 0.603387153859492 0.793225692281015 0.396612846140508 22 0.507317869080162 0.985364261839677 0.492682130919838 23 0.439215174965781 0.878430349931563 0.560784825034219 24 0.515451878497094 0.969096243005812 0.484548121502906 25 0.436090667770313 0.872181335540626 0.563909332229687 26 0.435920502878543 0.871841005757086 0.564079497121457 27 0.401071275502698 0.802142551005397 0.598928724497302 28 0.339331006960693 0.678662013921385 0.660668993039307 29 0.395189622998765 0.790379245997529 0.604810377001235 30 0.407251498438798 0.814502996877597 0.592748501561202 31 0.626573265129218 0.746853469741564 0.373426734870782 32 0.64292360858431 0.71415278283138 0.35707639141569 33 0.584473513993787 0.831052972012425 0.415526486006213 34 0.544496424205012 0.911007151589976 0.455503575794988 35 0.506074297447569 0.987851405104863 0.493925702552431 36 0.49326477539186 0.98652955078372 0.50673522460814 37 0.698793966125103 0.602412067749794 0.301206033874897 38 0.652654435734238 0.694691128531525 0.347345564265762 39 0.610922794894886 0.778154410210229 0.389077205105114 40 0.600828646299587 0.798342707400826 0.399171353700413 41 0.716586435175849 0.566827129648302 0.283413564824151 42 0.674486142063232 0.651027715873535 0.325513857936768 43 0.710558424199965 0.578883151600071 0.289441575800035 44 0.677048432075357 0.645903135849287 0.322951567924643 45 0.63336346907416 0.73327306185168 0.36663653092584 46 0.578901861736057 0.842196276527886 0.421098138263943 47 0.576113968813167 0.847772062373665 0.423886031186833 48 0.542456327709479 0.915087344581042 0.457543672290521 49 0.488628772445794 0.977257544891588 0.511371227554206 50 0.444423572995858 0.888847145991715 0.555576427004142 51 0.404163395562237 0.808326791124474 0.595836604437763 52 0.362973954767578 0.725947909535156 0.637026045232422 53 0.390604287065507 0.781208574131015 0.609395712934493 54 0.349241291218775 0.69848258243755 0.650758708781225 55 0.3058962993593 0.6117925987186 0.6941037006407 56 0.269859473362723 0.539718946725446 0.730140526637277 57 0.255202718282265 0.51040543656453 0.744797281717735 58 0.27283509128384 0.54567018256768 0.72716490871616 59 0.235339798158879 0.470679596317758 0.764660201841121 60 0.243889276406892 0.487778552813784 0.756110723593108 61 0.355962970263177 0.711925940526354 0.644037029736823 62 0.317377692494738 0.634755384989477 0.682622307505262 63 0.274969806040954 0.549939612081908 0.725030193959046 64 0.236667811214553 0.473335622429105 0.763332188785448 65 0.217845020614632 0.435690041229264 0.782154979385368 66 0.214505168711306 0.429010337422612 0.785494831288694 67 0.247545835642865 0.495091671285729 0.752454164357135 68 0.209980974259345 0.419961948518689 0.790019025740655 69 0.189068272236464 0.378136544472927 0.810931727763536 70 0.175781322997055 0.35156264599411 0.824218677002945 71 0.158807938792301 0.317615877584602 0.841192061207699 72 0.151280769263382 0.302561538526764 0.848719230736618 73 0.139343871174369 0.278687742348738 0.860656128825631 74 0.132252763773357 0.264505527546713 0.867747236226643 75 0.108722955403645 0.217445910807289 0.891277044596355 76 0.180619337073986 0.361238674147973 0.819380662926014 77 0.160666066246838 0.321332132493676 0.839333933753162 78 0.159869274349017 0.319738548698033 0.840130725650983 79 0.133419300521172 0.266838601042344 0.866580699478828 80 0.133633642628767 0.267267285257535 0.866366357371233 81 0.113071117459237 0.226142234918474 0.886928882540763 82 0.105701182184106 0.211402364368211 0.894298817815894 83 0.102956524518073 0.205913049036145 0.897043475481927 84 0.093538745127504 0.187077490255008 0.906461254872496 85 0.0904650156483978 0.180930031296796 0.909534984351602 86 0.0757091102280865 0.151418220456173 0.924290889771914 87 0.0653086823089265 0.130617364617853 0.934691317691073 88 0.0555025489973315 0.111005097994663 0.944497451002668 89 0.0436330002530659 0.0872660005061317 0.956366999746934 90 0.130303434625050 0.260606869250101 0.86969656537495 91 0.107427291397107 0.214854582794213 0.892572708602893 92 0.101480580545939 0.202961161091878 0.898519419454061 93 0.0853912150184802 0.170782430036960 0.91460878498152 94 0.0755270412448336 0.151054082489667 0.924472958755166 95 0.0652115013261324 0.130423002652265 0.934788498673868 96 0.068089645214674 0.136179290429348 0.931910354785326 97 0.0586370017494233 0.117274003498847 0.941362998250577 98 0.058457359281055 0.11691471856211 0.941542640718945 99 0.0464228148208487 0.0928456296416974 0.953577185179151 100 0.0430237722189214 0.0860475444378427 0.956976227781079 101 0.0565345540050087 0.113069108010017 0.943465445994991 102 0.0468682982208290 0.0937365964416581 0.953131701779171 103 0.0364538707599023 0.0729077415198047 0.963546129240098 104 0.0286516086787033 0.0573032173574066 0.971348391321297 105 0.0380125622788413 0.0760251245576826 0.961987437721159 106 0.08179538238886 0.16359076477772 0.91820461761114 107 0.0676503915196008 0.135300783039202 0.9323496084804 108 0.0642001252248345 0.128400250449669 0.935799874775165 109 0.0517673382719902 0.103534676543980 0.94823266172801 110 0.352429390357195 0.70485878071439 0.647570609642805 111 0.328714954261349 0.657429908522699 0.671285045738651 112 0.328084144451477 0.656168288902954 0.671915855548523 113 0.352576844393672 0.705153688787344 0.647423155606328 114 0.304255974334159 0.608511948668317 0.695744025665841 115 0.258914421790944 0.517828843581889 0.741085578209056 116 0.242136398700441 0.484272797400881 0.75786360129956 117 0.237649890819895 0.47529978163979 0.762350109180105 118 0.199827520034223 0.399655040068446 0.800172479965777 119 0.225315825556131 0.450631651112262 0.77468417444387 120 0.194834720864086 0.389669441728171 0.805165279135914 121 0.172945297275848 0.345890594551695 0.827054702724152 122 0.139599721892354 0.279199443784708 0.860400278107646 123 0.109859561514941 0.219719123029881 0.89014043848506 124 0.125522865758427 0.251045731516855 0.874477134241573 125 0.172505656588698 0.345011313177396 0.827494343411302 126 0.216355271733591 0.432710543467183 0.783644728266409 127 0.274977310018662 0.549954620037324 0.725022689981338 128 0.27435851067944 0.54871702135888 0.72564148932056 129 0.223419497947999 0.446838995895998 0.776580502052001 130 0.185576964848226 0.371153929696451 0.814423035151774 131 0.224563687144847 0.449127374289694 0.775436312855153 132 0.287238779291542 0.574477558583083 0.712761220708458 133 0.290100153562408 0.580200307124816 0.709899846437592 134 0.263814863007056 0.527629726014112 0.736185136992944 135 0.211169720250086 0.422339440500172 0.788830279749914 136 0.175554912968105 0.351109825936209 0.824445087031895 137 0.52550700193366 0.94898599613268 0.47449299806634 138 0.474475385802294 0.948950771604588 0.525524614197706 139 0.459848412813028 0.919696825626056 0.540151587186972 140 0.533088769546092 0.933822460907817 0.466911230453909 141 0.475037316836013 0.950074633672026 0.524962683163987 142 0.392621215211266 0.785242430422533 0.607378784788734 143 0.360157140849169 0.720314281698339 0.639842859150831 144 0.445009733676195 0.89001946735239 0.554990266323805 145 0.352703310900012 0.705406621800025 0.647296689099988 146 0.266671988712201 0.533343977424401 0.7333280112878 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 7 0.0534351145038168 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/30/t1291124856ydnzobkecmm18un/1076je1291124741.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291124856ydnzobkecmm18un/1076je1291124741.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291124856ydnzobkecmm18un/10n4k1291124741.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291124856ydnzobkecmm18un/10n4k1291124741.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291124856ydnzobkecmm18un/20n4k1291124741.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291124856ydnzobkecmm18un/20n4k1291124741.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291124856ydnzobkecmm18un/3seln1291124741.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291124856ydnzobkecmm18un/3seln1291124741.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291124856ydnzobkecmm18un/4seln1291124741.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291124856ydnzobkecmm18un/4seln1291124741.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291124856ydnzobkecmm18un/5seln1291124741.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291124856ydnzobkecmm18un/5seln1291124741.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291124856ydnzobkecmm18un/63nk81291124741.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291124856ydnzobkecmm18un/63nk81291124741.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291124856ydnzobkecmm18un/73nk81291124741.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291124856ydnzobkecmm18un/73nk81291124741.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291124856ydnzobkecmm18un/8ee1s1291124741.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291124856ydnzobkecmm18un/8ee1s1291124741.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291124856ydnzobkecmm18un/9ee1s1291124741.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291124856ydnzobkecmm18un/9ee1s1291124741.ps (open in new window)

Parameters (Session):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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