*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Tue, 23 Nov 2010 12:35:22 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/23/t1290515683ae3gbs0fr3y3kdv.htm/, Retrieved Tue, 23 Nov 2010 13:34:53 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Nov/23/t1290515683ae3gbs0fr3y3kdv.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 «

22.5 20 12 0 0 1 3 0 2 2 3 0 3 0 4 4.8 0 0 0.9 12 0 0 4 5 6 0 0 22.5 28 18 0 3 6 12 0 2 6 0 7 30 2 6 24 0 1 1 0 0 3 0 0 22.4 0 9 4 0 0 1.6 2 1 12 0 1 24 2 20 0 8 9 0 0 6 22.5 0 11 18 17 18 2.2 0 3 33 0 5 2.5 3 10 4 0 2 75 6 7 1.2 0 0 18 0 8 1.6 0 5 4 0 9 3 0 4 2 0 0 16.8 7 0 90 5 1 19.2 4 0 6 2 6 4.2 15 9 2 0 5 42.5 15 38 7.5 0 10 0 0 3 3.9 0 8 4 8 28 30 2 20 0 0 0 8 0 10 15 3 8 4 0 10 0 2 8 6 4 8 4.4 0 8 20 6 6 0 7 32 0 0 3 0 0 15 0 1 12 0 0 5 0 4 8 0 8 14 7 0 2 6 4 19 18 8 22 9 0 9 18 1 24 15 0 18 4.5 1 1 12 10 0 0 0 0 32 0 20 5 0 19 0 0 20 0 0 1 3 0 0 15 0 57 15 2 28 42 0 0 18 12 6 24 8 20 18 12 4 30 1 0 0 15 4 6 3 10 4.5 0 6 0 0 1 21 0 13 3.6 0 3 1.2 0 5 0 0 3 24 0 0 19.2 0 4 22.5 0 5 0 0 0 10.4 0 46 6 0 0 28 4 24 2.5 0 0 20 0 0 32 9 53 6 0 38 0 0 0 8 10 5 18 0 7 9 0 5 2 4 1 20 30 16 0 0 1 26 7 31 0 0 4 0 0 0 0 0 1 0 0 0 12 2 9 12 25 30 32 0 4 6 2 8 0 0 11 0 0 16 4 0 0 12.6 11 1 25.5 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 8 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation Sport[t] = + 8.93855171769656 + 0.417448994564574Event[t] + 0.134345700937438`Tv `[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) 8.93855171769656 1.421807 6.2868 0 0 Event 0.417448994564574 0.202148 2.0651 0.040561 0.020281 `Tv ` 0.134345700937438 0.101792 1.3198 0.18882 0.09441 Multiple Linear Regression - Regression Statistics Multiple R 0.22521342086788 R-squared 0.0507210849390127 Adjusted R-squared 0.0386283599063887 F-TEST (value) 4.19434699806505 F-TEST (DF numerator) 2 F-TEST (DF denominator) 157 p-value 0.0168041294646729 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 13.6370072181489 Sum Squared Residuals 29196.9706412519 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 22.5 18.8996800202373 3.60031997976274 2 0 9.072897418634 -9.072897418634 3 3 9.20724311957143 -6.20724311957143 4 2 10.1908987013903 -8.19089870139028 5 3 9.4759345214463 -6.47593452144631 6 4.8 8.93855171769656 -4.13855171769656 7 0.9 13.9479396524714 -13.0479396524714 8 0 11.280076200642 -11.280076200642 9 6 8.93855171769656 -2.93855171769656 10 22.5 23.0453461823785 -0.545346182378491 11 0 10.9969729070149 -10.9969729070149 12 12 9.20724311957143 2.79275688042857 13 6 9.87897162425862 -3.87897162425862 14 30 10.5795239124503 19.4204760875497 15 24 9.072897418634 14.927102581366 16 1 8.93855171769656 -7.93855171769656 17 3 8.93855171769656 -5.93855171769656 18 22.4 10.1476630261335 12.2523369738665 19 4 8.93855171769656 -4.93855171769656 20 1.6 9.90779540776314 -8.30779540776314 21 12 9.072897418634 2.92710258136601 22 24 12.4603637255745 11.5396362744255 23 0 13.4872549826501 -13.4872549826501 24 0 9.74462592332118 -9.74462592332118 25 22.5 10.4163544280084 12.0836455719916 26 18 18.4534072421682 -0.453407242168186 27 2.2 9.34158882050887 -7.14158882050887 28 33 9.61028022238374 23.3897197776163 29 2.5 11.5343557107647 -9.03435571076466 30 4 9.20724311957143 -5.20724311957143 31 75 12.3836655916461 62.616334408354 32 1.2 8.93855171769656 -7.73855171769656 33 18 10.0133173251961 7.98668267480394 34 1.6 9.61028022238374 -8.01028022238375 35 4 10.1476630261335 -6.1476630261335 36 3 9.4759345214463 -6.47593452144631 37 2 8.93855171769656 -6.93855171769656 38 16.8 11.8606946796486 4.93930532035143 39 90 11.1601423914569 78.8398576085431 40 19.2 10.6083476959548 8.59165230404515 41 6 10.5795239124503 -4.57952391245033 42 4.2 16.4093979446021 -12.2093979446021 43 2 9.61028022238375 -7.61028022238375 44 42.5 20.3054232717878 22.1945767282122 45 7.5 10.2820087270709 -2.78200872707093 46 0 9.34158882050887 -9.34158882050887 47 3.9 10.0133173251961 -6.11331732519606 48 4 16.0398233004614 -12.0398233004614 49 30 12.4603637255745 17.5396362744255 50 0 8.93855171769656 -8.93855171769656 51 8 10.2820087270709 -2.28200872707093 52 15 11.2656643088898 3.73433569111022 53 4 10.2820087270709 -6.28200872707094 54 0 10.8482153143252 -10.8482153143252 55 6 11.6831133034544 -5.68311330345435 56 4.4 10.0133173251961 -5.61331732519606 57 20 12.2493198907086 7.75068010929138 58 0 16.1597571096466 -16.1597571096466 59 0 9.34158882050887 -9.34158882050887 60 0 10.9537372317581 -10.9537372317581 61 0 10.9681491235104 -10.9681491235104 62 0 9.61028022238375 -9.61028022238375 63 0 11.6831133034544 -11.6831133034544 64 0 14.1589834873373 -14.1589834873373 65 7 9.20724311957143 -2.20724311957143 66 6 13.1609160137662 -7.16091601376617 67 18 15.2337490948368 2.76625090516322 68 9 10.1476630261335 -1.1476630261335 69 18 12.5802975347596 5.41970246524036 70 15 11.3567743345704 3.64322566542956 71 4.5 9.49034641319857 -4.99034641319857 72 12 13.1130416633423 -1.11304166334229 73 0 8.93855171769656 -8.93855171769656 74 32 11.6254657364453 20.3745342635547 75 5 11.4911200355079 -6.49112003550788 76 0 11.6254657364453 -11.6254657364453 77 0 9.072897418634 -9.072897418634 78 3 8.93855171769656 -5.93855171769656 79 15 16.5962566711305 -1.59625667113051 80 15 13.535129333074 1.46487066692604 81 42 8.93855171769655 33.0614482823034 82 18 14.7540138580961 3.24598614190394 83 24 14.9650576929619 9.0349423070381 84 18 14.4853224562212 3.51467754377881 85 30 9.35600071226114 20.6439992877389 86 0 15.7376694399149 -15.7376694399149 87 6 11.5343557107647 -5.53435571076465 88 4.5 9.74462592332118 -5.24462592332118 89 0 9.072897418634 -9.072897418634 90 21 10.6850458298832 10.3149541701168 91 3.6 9.34158882050887 -5.74158882050887 92 1.2 9.61028022238375 -8.41028022238375 93 0 9.34158882050887 -9.34158882050887 94 24 8.93855171769656 15.0614482823034 95 19.2 9.4759345214463 9.72406547855369 96 22.5 9.61028022238375 12.8897197776163 97 0 8.93855171769656 -8.93855171769656 98 10.4 15.1184539608187 -4.7184539608187 99 6 8.93855171769656 -2.93855171769656 100 28 13.8326445184534 14.1673554815466 101 2.5 8.93855171769656 -6.43855171769656 102 20 8.93855171769656 11.0614482823034 103 32 19.8159148184619 12.1840851815381 104 6 14.0436883533192 -8.0436883533192 105 0 8.93855171769656 -8.93855171769656 106 8 13.7847701680295 -5.78477016802948 107 18 9.87897162425862 8.12102837574138 108 9 9.61028022238375 -0.610280222383746 109 2 10.7426933968923 -8.74269339689229 110 20 23.6115527696328 -3.61155276963276 111 0 9.072897418634 -9.072897418634 112 26 16.0254114087091 9.97458859129086 113 0 9.4759345214463 -9.4759345214463 114 0 8.93855171769656 -8.93855171769656 115 0 9.072897418634 -9.072897418634 116 0 8.93855171769656 -8.93855171769656 117 12 10.9825610152626 1.01743898473736 118 12 23.405147609934 -11.405147609934 119 32 9.4759345214463 22.5240654785537 120 6 10.8482153143252 -4.84821531432521 121 0 10.4163544280084 -10.4163544280084 122 0 11.0880829326956 -11.0880829326956 123 4 8.93855171769656 -4.93855171769656 124 12.6 13.6648363588443 -1.0648363588443 125 25.5 11.3711862263227 14.1288137736773 126 4.8 8.93855171769656 -4.13855171769656 127 4.5 12.1005622980189 -7.60056229801893 128 4.8 9.61028022238375 -4.81028022238375 129 16 9.89338351601088 6.10661648398912 130 3 12.8155264779629 -9.8155264779629 131 7 12.9642840706526 -5.96428407065259 132 0 11.831870896144 -11.831870896144 133 20 19.8977474938084 0.102252506191618 134 4.8 9.34158882050887 -4.54158882050887 135 0 9.4759345214463 -9.4759345214463 136 4.8 10.1620749178858 -5.36207491788576 137 0 9.87897162425862 -9.87897162425862 138 3.2 9.61028022238375 -6.41028022238375 139 29.9 9.61028022238374 20.2897197776163 140 24 9.7734497068257 14.2265502931743 141 35.2 12.2349079989564 22.9650920010436 142 30 10.6850458298833 19.3149541701167 143 26 8.93855171769655 17.0614482823034 144 58.8 11.4144219015795 47.3855780984205 145 15 14.0102258946476 0.989774105352425 146 14 9.4759345214463 4.52406547855369 147 4.8 23.3953743933489 -18.5953743933489 148 30 8.93855171769655 21.0614482823034 149 14.4 8.93855171769656 5.46144828230344 150 10 9.072897418634 0.927102581366006 151 9.6 10.1476630261335 -0.547663026133497 152 0 11.3567743345704 -11.3567743345704 153 26 15.3104472287652 10.6895527712348 154 0 11.6254657364453 -11.6254657364453 155 31.5 15.2625728783413 16.2374271216587 156 0 8.93855171769656 -8.93855171769656 157 1 10.7426933968923 -9.74269339689229 158 24 9.4759345214463 14.5240654785537 159 3.6 9.34158882050887 -5.74158882050887 160 3 11.0880829326956 -8.08808293269556 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.00771258105736868 0.0154251621147374 0.992287418942631 7 0.00460442155047244 0.00920884310094487 0.995395578449528 8 0.00685439146081054 0.0137087829216211 0.99314560853919 9 0.00451075221220117 0.00902150442440234 0.995489247787799 10 0.00160247450199213 0.00320494900398425 0.998397525498008 11 0.00112826163729211 0.00225652327458421 0.998871738362708 12 0.00196860553760566 0.00393721107521132 0.998031394462394 13 0.000694122419658647 0.00138824483931729 0.999305877580341 14 0.0258442954385563 0.0516885908771126 0.974155704561444 15 0.0716896443629561 0.143379288725912 0.928310355637044 16 0.0469532094181939 0.0939064188363877 0.953046790581806 17 0.0286819864747701 0.0573639729495401 0.97131801352523 18 0.0209893795869841 0.0419787591739682 0.979010620413016 19 0.0122142900582269 0.0244285801164539 0.987785709941773 20 0.0073860034860802 0.0147720069721604 0.99261399651392 21 0.00504795433260083 0.0100959086652017 0.9949520456674 22 0.00324756961105656 0.00649513922211311 0.996752430388943 23 0.00478147224757064 0.0095629444951413 0.99521852775243 24 0.0045466050923104 0.0090932101846208 0.99545339490769 25 0.00332704321923509 0.00665408643847018 0.996672956780765 26 0.00200446774894238 0.00400893549788476 0.997995532251058 27 0.00127962413983881 0.00255924827967762 0.99872037586016 28 0.0076572988901766 0.0153145977803532 0.992342701109823 29 0.00815159095408625 0.0163031819081725 0.991848409045914 30 0.00526215871479054 0.0105243174295811 0.99473784128521 31 0.810036958681249 0.379926082637502 0.189963041318751 32 0.775126323572307 0.449747352855386 0.224873676427693 33 0.735283583473943 0.529432833052114 0.264716416526057 34 0.708722773139961 0.582554453720078 0.291277226860039 35 0.6853671654564 0.629265669087201 0.3146328345436 36 0.64563360738284 0.708732785234321 0.354366392617161 37 0.598652331139194 0.802695337721613 0.401347668860806 38 0.571457602379166 0.857084795241668 0.428542397620834 39 0.999976228567795 4.75428644107706e-05 2.37714322053853e-05 40 0.999966333637662 6.73327246768317e-05 3.36663623384158e-05 41 0.999947576948687 0.000104846102626738 5.24230513133688e-05 42 0.999943182317756 0.000113635364488732 5.68176822443661e-05 43 0.999920380651172 0.000159238697655282 7.9619348827641e-05 44 0.999939445235578 0.000121109528845029 6.05547644225144e-05 45 0.999906760855483 0.000186478289034364 9.32391445171821e-05 46 0.999878559280035 0.000242881439930981 0.00012144071996549 47 0.999828680596862 0.000342638806276612 0.000171319403138306 48 0.999848025897821 0.000303948204357833 0.000151974102178916 49 0.999865107064704 0.000269785870591151 0.000134892935295576 50 0.99981994258098 0.000360114838039219 0.000180057419019609 51 0.999725140836867 0.000549718326265663 0.000274859163132831 52 0.999585963085547 0.000828073828905328 0.000414036914452664 53 0.999434260465987 0.00113147906802508 0.000565739534012538 54 0.999346290625807 0.0013074187483868 0.000653709374193398 55 0.999091526345916 0.00181694730816878 0.000908473654084388 56 0.998747284923193 0.00250543015361346 0.00125271507680673 57 0.998366896895841 0.00326620620831717 0.00163310310415859 58 0.998726829200493 0.00254634159901405 0.00127317079950702 59 0.99842430141388 0.00315139717223885 0.00157569858611942 60 0.998185104175864 0.00362979164827182 0.00181489582413591 61 0.997908456813474 0.00418308637305238 0.00209154318652619 62 0.997467529243841 0.00506494151231727 0.00253247075615864 63 0.99719661236914 0.00560677526171957 0.00280338763085978 64 0.997260221195228 0.00547955760954329 0.00273977880477164 65 0.996156783265614 0.00768643346877127 0.00384321673438563 66 0.995054209959281 0.00989158008143727 0.00494579004071864 67 0.993238408804941 0.0135231823901177 0.00676159119505885 68 0.990770102295917 0.018459795408166 0.00922989770408298 69 0.988152843119376 0.0236943137612481 0.0118471568806241 70 0.984473299711715 0.0310534005765695 0.0155267002882848 71 0.980169764143244 0.039660471713513 0.0198302358567565 72 0.97402273504824 0.0519545299035182 0.0259772649517591 73 0.96984868531976 0.0603026293604818 0.0301513146802409 74 0.977934166257394 0.0441316674852125 0.0220658337426063 75 0.973010790796972 0.0539784184060554 0.0269892092030277 76 0.971297092380403 0.0574058152391934 0.0287029076195967 77 0.967037795534268 0.065924408931463 0.0329622044657315 78 0.95985288057116 0.0802942388576805 0.0401471194288403 79 0.949206454375076 0.101587091249847 0.0507935456249237 80 0.936159541651567 0.127680916696866 0.0638404583484329 81 0.981496943561552 0.0370061128768962 0.0185030564384481 82 0.976048453832348 0.0479030923353039 0.0239515461676519 83 0.972232515654203 0.0555349686915931 0.0277674843457965 84 0.964816479676069 0.070367040647862 0.035183520323931 85 0.975220505830636 0.0495589883387273 0.0247794941693637 86 0.977173699179314 0.045652601641372 0.022826300820686 87 0.971459384273317 0.0570812314533663 0.0285406157266831 88 0.9645239697526 0.0709520604947995 0.0354760302473997 89 0.959587544278822 0.080824911442355 0.0404124557211775 90 0.9548964851772 0.090207029645602 0.045103514822801 91 0.945347567443142 0.109304865113716 0.0546524325568582 92 0.937545554506028 0.124908890987945 0.0624544454939723 93 0.930601706853464 0.138796586293072 0.0693982931465362 94 0.933449609954172 0.133100780091657 0.0665503900458284 95 0.925231332843126 0.149537334313748 0.0747686671568738 96 0.923156414812943 0.153687170374114 0.0768435851870568 97 0.913792135980236 0.172415728039528 0.086207864019764 98 0.896568388091272 0.206863223817457 0.103431611908728 99 0.875001806822558 0.249996386354883 0.124998193177442 100 0.877037964802974 0.245924070394052 0.122962035197026 101 0.858108968772467 0.283782062455066 0.141891031227533 102 0.847577857543528 0.304844284912944 0.152422142456472 103 0.850049887122318 0.299900225755364 0.149950112877682 104 0.827973424515649 0.344053150968702 0.172026575484351 105 0.81255506822152 0.374889863556961 0.187444931778481 106 0.784523688692708 0.430952622614584 0.215476311307292 107 0.75936942143722 0.481261157125559 0.24063057856278 108 0.71952567758142 0.56094864483716 0.28047432241858 109 0.697559110345157 0.604881779309686 0.302440889654843 110 0.655341865761602 0.689316268476796 0.344658134238398 111 0.634780620166471 0.730438759667059 0.365219379833529 112 0.62477568825615 0.7504486234877 0.37522431174385 113 0.605257332774683 0.789485334450634 0.394742667225317 114 0.586911632909873 0.826176734180253 0.413088367090127 115 0.57013153630535 0.8597369273893 0.42986846369465 116 0.555594076680621 0.888811846638758 0.444405923319379 117 0.503873988218792 0.992252023562416 0.496126011781208 118 0.472374756857971 0.944749513715942 0.527625243142029 119 0.54275691628081 0.91448616743838 0.45724308371919 120 0.499019466592667 0.998038933185334 0.500980533407333 121 0.480399470145306 0.960798940290612 0.519600529854694 122 0.463810916444917 0.927621832889833 0.536189083555084 123 0.427770593191103 0.855541186382206 0.572229406808897 124 0.377815961472382 0.755631922944765 0.622184038527618 125 0.375675623171959 0.751351246343917 0.624324376828042 126 0.338075166876164 0.676150333752328 0.661924833123836 127 0.31028291760124 0.620565835202479 0.68971708239876 128 0.275361101445332 0.550722202890665 0.724638898554668 129 0.232251633371565 0.464503266743129 0.767748366628435 130 0.226392155294985 0.452784310589971 0.773607844705015 131 0.209706964796461 0.419413929592923 0.790293035203539 132 0.222962418884022 0.445924837768044 0.777037581115978 133 0.270802815632073 0.541605631264146 0.729197184367927 134 0.241177638613979 0.482355277227958 0.75882236138602 135 0.239842652936742 0.479685305873483 0.760157347063258 136 0.219009356399572 0.438018712799143 0.780990643600428 137 0.216513360123559 0.433026720247119 0.78348663987644 138 0.204501531089631 0.409003062179262 0.795498468910369 139 0.212654817684385 0.42530963536877 0.787345182315615 140 0.173691952691313 0.347383905382626 0.826308047308687 141 0.177093585251496 0.354187170502991 0.822906414748504 142 0.220390821308124 0.440781642616248 0.779609178691876 143 0.198724349179707 0.397448698359414 0.801275650820293 144 0.804816465673544 0.390367068652911 0.195183534326456 145 0.737527690838991 0.524944618322019 0.262472309161009 146 0.661643853883449 0.676712292233102 0.338356146116551 147 0.720901972850326 0.558196054299348 0.279098027149674 148 0.881393099213445 0.237213801573111 0.118606900786555 149 0.858482658610053 0.283034682779893 0.141517341389947 150 0.802918577471422 0.394162845057156 0.197081422528578 151 0.71946451672875 0.561070966542501 0.28053548327125 152 0.63917702868535 0.721645942629301 0.360822971314651 153 0.531342652898841 0.937314694202317 0.468657347101159 154 0.422110253017568 0.844220506035136 0.577889746982432 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 40 0.268456375838926 NOK 5% type I error level 59 0.395973154362416 NOK 10% type I error level 74 0.496644295302013 NOK

Charts produced by software:

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Parameters (Session):

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

Parameters (R input):

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

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

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

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Software written by Ed van Stee & Patrick Wessa

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