Workshop 7 mini-tutorial Concern over mistakes - Linear trend

*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Sun, 21 Nov 2010 12:21:55 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/21/t1290342179exxqtjcy3k25adp.htm/, Retrieved Sun, 21 Nov 2010 13:23:02 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Nov/21/t1290342179exxqtjcy3k25adp.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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9 24 14 11 12 24 26 9 25 11 7 8 25 23 9 17 6 17 8 30 25 9 18 12 10 8 19 23 9 18 8 12 9 22 19 9 16 10 12 7 22 29 10 20 10 11 4 25 25 10 16 11 11 11 23 21 10 18 16 12 7 17 22 10 17 11 13 7 21 25 10 23 13 14 12 19 24 10 30 12 16 10 19 18 10 23 8 11 10 15 22 10 18 12 10 8 16 15 10 15 11 11 8 23 22 10 12 4 15 4 27 28 10 21 9 9 9 22 20 10 15 8 11 8 14 12 10 20 8 17 7 22 24 10 31 14 17 11 23 20 10 27 15 11 9 23 21 10 34 16 18 11 21 20 10 21 9 14 13 19 21 10 31 14 10 8 18 23 10 19 11 11 8 20 28 10 16 8 15 9 23 24 10 20 9 15 6 25 24 10 21 9 13 9 19 24 10 22 9 16 9 24 23 10 17 9 13 6 22 23 10 24 10 9 6 25 29 10 25 16 18 16 26 24 10 26 11 18 5 29 18 10 25 8 12 7 32 25 10 17 9 17 9 25 21 10 32 16 9 6 29 26 10 33 11 9 6 28 22 10 13 16 12 5 17 22 10 32 12 18 12 28 22 10 25 12 12 7 29 23 10 29 14 18 10 26 30 10 22 9 14 9 25 23 10 18 10 15 8 14 17 10 17 9 16 5 25 23 10 20 10 10 8 26 23 10 15 12 11 8 20 25 10 20 14 14 10 18 24 10 33 14 9 6 32 24 10 29 10 12 8 25 23 10 23 14 17 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 9 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation Concernovermistakes[t] = -18.3591714482501 + 1.58838471475259Month[t] + 0.798757118515112Doubtsaboutactions[t] + 0.233450466257556Parentalexpectations[t] + 0.207082749570131Parentalcritism[t] + 0.571862761699043Personalstandards[t] -0.0999815995143377Organization[t] + 0.00354783249216936t + 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) -18.3591714482501 19.993412 -0.9183 0.359947 0.179973 Month 1.58838471475259 2.002175 0.7933 0.428831 0.214415 Doubtsaboutactions 0.798757118515112 0.131148 6.0905 0 0 Parentalexpectations 0.233450466257556 0.134333 1.7379 0.084276 0.042138 Parentalcritism 0.207082749570131 0.170009 1.2181 0.225097 0.112548 Personalstandards 0.571862761699043 0.096247 5.9416 0 0 Organization -0.0999815995143377 0.105485 -0.9478 0.344732 0.172366 t 0.00354783249216936 0.008438 0.4205 0.674741 0.33737 Multiple Linear Regression - Regression Statistics Multiple R 0.641530498673369 R-squared 0.411561380728101 Adjusted R-squared 0.384282769238676 F-TEST (value) 15.087328799255 F-TEST (DF numerator) 7 F-TEST (DF denominator) 151 p-value 7.32747196252603e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.49056162493448 Sum Squared Residuals 3044.93669980746 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 23.3005712933059 0.699428706694143 2 25 20.017522467184 4.98247753281596 3 17 21.0211399791428 -4.02113997914275 4 18 18.0925500792619 -0.0925500792619017 5 18 17.6905678029333 0.309432197066654 6 16 17.8776483781721 -1.8776483781721 7 20 20.7303968936034 -0.73039689360339 8 16 22.2384819662609 -6.23848196626085 9 18 22.109776689597 -4.10977668959702 10 17 20.3404956440243 -3.34049564402434 11 23 22.1666780037712 0.833321996228798 12 30 22.0240937482091 7.97590625179086 13 23 14.9779833304996 8.02201666950045 14 18 18.8006776299538 -0.800677629953756 15 15 21.5420869454813 -6.54208694548131 16 12 17.7473672648275 -5.74736726482754 17 21 19.3199506278201 1.68004937217993 18 15 15.0095102272645 -0.00951022726446701 19 20 19.5818010071521 0.418198992847862 20 31 26.1780117087719 4.8219882912281 21 27 25.0654667635792 1.93453323642076 22 34 26.8723465536459 7.12765344635406 23 21 19.5212510677299 1.47874893227007 24 31 20.7775429191891 10.2224570808109 25 19 19.2620873882198 -0.262087388219846 26 16 20.1257631629215 -4.12576316292152 27 20 21.4505453886165 -1.45054538861649 28 21 18.1772639671097 2.82273603289032 29 22 21.8404586063841 0.159541393615926 30 17 19.3786812679951 -2.37868126799509 31 24 20.3628830419833 3.63711695801675 32 25 30.4026260368562 -5.40262603685615 33 26 26.4499559136845 -0.44995591368447 34 25 24.086412180723 0.913587819277008 35 17 22.8670220283224 -5.86702202832237 36 32 27.760560760874 4.23943923912604 37 33 23.5983866371489 9.40161336285112 38 13 21.7984983327297 -8.79849833272967 39 32 27.7477901143871 4.25220988561288 40 25 25.787102563668 -0.787102563668003 41 29 26.9946561977486 2.00534380225136 42 22 21.9915422579662 0.00845774203379339 43 18 17.1296141440575 0.870385855942537 44 17 21.6372078571851 -4.63720785718513 45 20 22.2319210210565 -2.23192102105651 46 15 20.4352937876135 -5.43529378761353 47 20 22.1071288311651 -2.10712883116511 48 33 28.1211719978756 4.87882800212443 49 29 22.1411505218413 6.85884947815874 50 23 26.4998596091402 -3.49985960914021 51 26 23.2345975129204 2.76540248707957 52 18 18.9656042544921 -0.965604254492144 53 20 18.796120045743 1.20387995425697 54 11 11.7160709940257 -0.716070994025723 55 28 29.0105804767345 -1.01058047673453 56 26 23.3905043460467 2.60949565395329 57 22 22.3414695454203 -0.341469545420308 58 17 20.1564210484307 -3.1564210484307 59 12 15.5692778789805 -3.56927787898049 60 14 20.8167935559991 -6.81679355599913 61 17 20.8202241820746 -3.82022418207459 62 21 21.3347129501434 -0.334712950143374 63 19 22.9763818374361 -3.9763818374361 64 18 23.1920758880957 -5.19207588809566 65 10 17.9120405565538 -7.91204055655376 66 29 24.4099265188341 4.59007348116592 67 31 18.5584769188011 12.4415230811989 68 19 22.9869414093617 -3.98694140936168 69 9 20.0961723263517 -11.0961723263517 70 20 22.5809984574057 -2.5809984574057 71 28 17.6552736410877 10.3447263589123 72 19 18.2291083555071 0.770891644492931 73 30 23.1787562563361 6.82124374366391 74 29 27.1018574495787 1.8981425504213 75 26 21.5208597487263 4.47914025127372 76 23 19.5775913896633 3.42240861033671 77 13 22.7673890269749 -9.7673890269749 78 21 22.6999656986182 -1.69996569861817 79 19 21.6345836806373 -2.63458368063734 80 28 22.9691570142453 5.03084298575475 81 23 25.6973992029916 -2.6973992029916 82 18 13.9549031616295 4.04509683837052 83 21 20.7615465591829 0.238453440817123 84 20 21.9157961866931 -1.91579618669311 85 23 20.0777478836276 2.92225211637242 86 21 20.8386011500172 0.161398849982821 87 21 21.8931506037604 -0.89315060376045 88 15 23.0305779438395 -8.03057794383953 89 28 27.3005835439217 0.699416456078303 90 19 17.7045900098864 1.2954099901136 91 26 21.2772051999812 4.72279480001875 92 10 13.4207961925499 -3.42079619254989 93 16 17.1995105289364 -1.19951052893641 94 22 21.1713453970672 0.828654602932829 95 19 18.9989312859951 0.00106871400488016 96 31 28.940378376922 2.05962162307796 97 31 25.2905586288165 5.70944137118354 98 29 24.8528116175613 4.14718838243874 99 19 17.5096261454999 1.49037385450014 100 22 18.9524275113635 3.0475724886365 101 23 22.4963923849776 0.503607615022413 102 15 16.287535418075 -1.28753541807505 103 20 21.4228525089516 -1.4228525089516 104 18 19.6658145225114 -1.66581452251145 105 23 22.2563692427647 0.743630757235343 106 25 20.9086574355098 4.09134256449023 107 21 16.6722771524643 4.32772284753566 108 24 19.5680077116824 4.4319922883176 109 25 25.3550235068465 -0.35502350684648 110 17 19.619766860822 -2.61976686082202 111 13 14.6659551691233 -1.66595516912328 112 28 18.4262616637208 9.57373833627919 113 21 20.4196764510916 0.580323548908431 114 25 28.3159565386191 -3.31595653861912 115 9 21.1551764227403 -12.1551764227403 116 16 18.006110633023 -2.00611063302303 117 19 21.2544613841651 -2.25446138416515 118 17 19.6108037739653 -2.61080377396526 119 25 24.6763915340849 0.323608465915102 120 20 15.5671337387445 4.4328662612555 121 29 21.8716126114376 7.12838738856236 122 14 19.1167857657226 -5.11678576572262 123 22 27.0867941796051 -5.0867941796051 124 15 15.9355784175142 -0.935578417514243 125 19 25.626332592574 -6.62633259257396 126 20 22.092892026745 -2.09289202674502 127 15 17.7095654037931 -2.70956540379314 128 20 22.1149283807381 -2.11492838073814 129 18 20.5115649579609 -2.51156495796087 130 33 25.7620025241802 7.23799747581976 131 22 24.0135738555549 -2.01357385555486 132 16 16.6900618439135 -0.69006184391349 133 17 19.3420422957593 -2.34204229575932 134 16 15.3134803176989 0.686519682301067 135 21 17.2994992608764 3.70050073912356 136 26 27.7996968946194 -1.79969689461943 137 18 21.304233865906 -3.30423386590599 138 18 23.2073200148495 -5.20732001484945 139 17 18.6825913123659 -1.6825913123659 140 22 24.9799528930422 -2.97995289304224 141 30 24.9254198082097 5.07458019179029 142 30 27.5705627248667 2.42943727513332 143 24 29.9683835869881 -5.9683835869881 144 21 22.2960469748642 -1.29604697486422 145 21 25.6227704527493 -4.62277045274929 146 29 27.6739609431583 1.32603905684171 147 31 23.464342466474 7.53565753352599 148 20 19.2655893559701 0.734410644029934 149 16 14.3261339717709 1.67386602822906 150 22 19.2236647882233 2.77633521177669 151 20 20.7522347250232 -0.752234725023152 152 28 27.5610774834422 0.438922516557777 153 38 26.890415116 11.109584884 154 22 19.4362722728422 2.56372772715776 155 20 25.9470773992814 -5.9470773992814 156 17 18.31008307594 -1.31008307593998 157 28 24.8140500775851 3.18594992241494 158 22 24.4230458313632 -2.4230458313632 159 31 26.3398127723852 4.66018722761482 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.482919301614958 0.965838603229916 0.517080698385042 12 0.55407323934365 0.8918535213127 0.44592676065635 13 0.778571207452893 0.442857585094215 0.221428792547107 14 0.804401377897167 0.391197244205667 0.195598622102833 15 0.744773564280577 0.510452871438847 0.255226435719423 16 0.66423254463189 0.671534910736221 0.33576745536811 17 0.623527767746131 0.752944464507738 0.376472232253869 18 0.581415909333899 0.837168181332202 0.418584090666101 19 0.541563815283281 0.916872369433437 0.458436184716719 20 0.562150479533601 0.875699040932797 0.437849520466399 21 0.485348761129403 0.970697522258805 0.514651238870597 22 0.455924906437964 0.911849812875927 0.544075093562036 23 0.418029313423603 0.836058626847207 0.581970686576397 24 0.525131871059443 0.949736257881115 0.474868128940557 25 0.496594569472841 0.993189138945682 0.503405430527159 26 0.528430312047999 0.943139375904002 0.471569687952001 27 0.462456469163947 0.924912938327894 0.537543530836053 28 0.399432869722767 0.798865739445533 0.600567130277233 29 0.337499119939794 0.674998239879588 0.662500880060206 30 0.303449426252635 0.606898852505269 0.696550573747365 31 0.292068810897148 0.584137621794295 0.707931189102852 32 0.427890514331056 0.855781028662112 0.572109485668944 33 0.367770972580548 0.735541945161097 0.632229027419452 34 0.338921624250193 0.677843248500386 0.661078375749807 35 0.389911976046697 0.779823952093394 0.610088023953303 36 0.35418446066544 0.70836892133088 0.64581553933456 37 0.465426892273875 0.93085378454775 0.534573107726125 38 0.761514402351725 0.476971195296551 0.238485597648275 39 0.748042922363758 0.503914155272485 0.251957077636242 40 0.711410768934748 0.577178462130505 0.288589231065252 41 0.676447198133765 0.647105603732471 0.323552801866236 42 0.62816507684451 0.74366984631098 0.37183492315549 43 0.576422723698905 0.84715455260219 0.423577276301095 44 0.564043835542673 0.871912328914655 0.435956164457327 45 0.547145831190928 0.905708337618144 0.452854168809072 46 0.579192685522073 0.841614628955854 0.420807314477927 47 0.535476535517342 0.929046928965316 0.464523464482658 48 0.525984911848509 0.948030176302981 0.474015088151491 49 0.586210353983298 0.827579292033405 0.413789646016702 50 0.557321331543701 0.885357336912599 0.442678668456299 51 0.526419736329641 0.947160527340718 0.473580263670359 52 0.476679027266428 0.953358054532855 0.523320972733572 53 0.433008721292444 0.866017442584887 0.566991278707556 54 0.388214689123759 0.776429378247518 0.611785310876241 55 0.347336244766195 0.69467248953239 0.652663755233805 56 0.318722802009979 0.637445604019959 0.68127719799002 57 0.275855712367904 0.551711424735809 0.724144287632095 58 0.247829977005935 0.49565995401187 0.752170022994065 59 0.229544224760973 0.459088449521947 0.770455775239027 60 0.264607003917429 0.529214007834858 0.735392996082571 61 0.24812764027652 0.496255280553041 0.75187235972348 62 0.2141301810355 0.428260362071 0.7858698189645 63 0.196907532926841 0.393815065853682 0.803092467073159 64 0.217946681722194 0.435893363444389 0.782053318277806 65 0.266979412065807 0.533958824131614 0.733020587934193 66 0.27592912725405 0.5518582545081 0.72407087274595 67 0.63776942013587 0.72446115972826 0.36223057986413 68 0.62191817253088 0.756163654938239 0.37808182746912 69 0.795195289203808 0.409609421592385 0.204804710796192 70 0.767814750635936 0.464370498728128 0.232185249364064 71 0.912753156491534 0.174493687016931 0.0872468435084657 72 0.893727121804518 0.212545756390964 0.106272878195482 73 0.924292609592878 0.151414780814245 0.0757073904071225 74 0.912497020729957 0.175005958540086 0.087502979270043 75 0.916330968011296 0.167338063977408 0.0836690319887039 76 0.910662472173307 0.178675055653386 0.089337527826693 77 0.962094085816428 0.0758118283671447 0.0379059141835724 78 0.952685243442334 0.0946295131153326 0.0473147565576663 79 0.94347392980676 0.11305214038648 0.0565260701932399 80 0.947942852549188 0.104114294901625 0.0520571474508123 81 0.938265238808533 0.123469522382935 0.0617347611914673 82 0.937582724026703 0.124834551946594 0.062417275973297 83 0.922053336251284 0.155893327497431 0.0779466637487156 84 0.906574250002528 0.186851499994943 0.0934257499974717 85 0.896763278206496 0.206473443587007 0.103236721793504 86 0.878080050015044 0.243839899969911 0.121919949984956 87 0.853375575666524 0.293248848666952 0.146624424333476 88 0.905330192016902 0.189339615966196 0.0946698079830978 89 0.886155588871522 0.227688822256956 0.113844411128478 90 0.863647711730098 0.272704576539803 0.136352288269902 91 0.865827478842622 0.268345042314757 0.134172521157378 92 0.854384780881698 0.291230438236603 0.145615219118302 93 0.829831700773176 0.340336598453648 0.170168299226824 94 0.79955374740597 0.400892505188061 0.200446252594031 95 0.763688446644035 0.472623106711929 0.236311553355965 96 0.731055574998138 0.537888850003724 0.268944425001862 97 0.75174192733153 0.496516145336941 0.24825807266847 98 0.749346506853056 0.501306986293889 0.250653493146944 99 0.712234696431953 0.575530607136094 0.287765303568047 100 0.689744864923867 0.620510270152265 0.310255135076133 101 0.649434922236285 0.70113015552743 0.350565077763715 102 0.606634845790477 0.786730308419046 0.393365154209523 103 0.56324421674873 0.873511566502539 0.43675578325127 104 0.518654156668534 0.962691686662931 0.481345843331466 105 0.475880650474406 0.951761300948813 0.524119349525594 106 0.46361214111995 0.9272242822399 0.53638785888005 107 0.47077904927371 0.94155809854742 0.52922095072629 108 0.509532807449636 0.980934385100727 0.490467192550364 109 0.470971756762878 0.941943513525756 0.529028243237122 110 0.428611691000273 0.857223382000546 0.571388308999727 111 0.381451505416846 0.762903010833693 0.618548494583154 112 0.711288640363238 0.577422719273525 0.288711359636762 113 0.747397544448189 0.505204911103622 0.252602455551811 114 0.720032266639849 0.559935466720303 0.279967733360151 115 0.854652166059168 0.290695667881664 0.145347833940832 116 0.822716200104192 0.354567599791616 0.177283799895808 117 0.789598373374736 0.420803253250528 0.210401626625264 118 0.752405016530783 0.495189966938434 0.247594983469217 119 0.721776844050078 0.556446311899843 0.278223155949921 120 0.773892573829068 0.452214852341863 0.226107426170932 121 0.86094268064034 0.27811463871932 0.13905731935966 122 0.83849371344511 0.323012573109779 0.161506286554889 123 0.8144281484347 0.3711437031306 0.1855718515653 124 0.771549295854049 0.456901408291903 0.228450704145951 125 0.77469827761769 0.450603444764621 0.225301722382311 126 0.725912210291747 0.548175579416506 0.274087789708253 127 0.690676886270889 0.618646227458222 0.309323113729111 128 0.639778003698588 0.720443992602823 0.360221996301412 129 0.590736886156087 0.818526227687826 0.409263113843913 130 0.718503215808757 0.562993568382487 0.281496784191243 131 0.660323778713815 0.67935244257237 0.339676221286185 132 0.595126930986174 0.809746138027651 0.404873069013826 133 0.553718763961046 0.892562472077908 0.446281236038954 134 0.481445774757763 0.962891549515526 0.518554225242237 135 0.50489983869972 0.99020032260056 0.49510016130028 136 0.432400563387952 0.864801126775904 0.567599436612048 137 0.38385109062999 0.76770218125998 0.61614890937001 138 0.39624875461526 0.792497509230519 0.60375124538474 139 0.323763162155536 0.647526324311071 0.676236837844465 140 0.254403000965545 0.50880600193109 0.745596999034455 141 0.344047179913995 0.688094359827989 0.655952820086005 142 0.294575906829285 0.58915181365857 0.705424093170715 143 0.226445586897251 0.452891173794503 0.773554413102749 144 0.159698858380338 0.319397716760677 0.840301141619662 145 0.239930077553041 0.479860155106083 0.760069922446959 146 0.169348307271413 0.338696614542826 0.830651692728587 147 0.160521283906014 0.321042567812029 0.839478716093986 148 0.087308090660505 0.17461618132101 0.912691909339495 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 2 0.0144927536231884 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290342179exxqtjcy3k25adp/10fgfq1290342102.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290342179exxqtjcy3k25adp/10fgfq1290342102.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290342179exxqtjcy3k25adp/1rxie1290342102.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290342179exxqtjcy3k25adp/1rxie1290342102.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290342179exxqtjcy3k25adp/2rxie1290342102.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290342179exxqtjcy3k25adp/2rxie1290342102.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290342179exxqtjcy3k25adp/3jozh1290342102.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290342179exxqtjcy3k25adp/3jozh1290342102.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290342179exxqtjcy3k25adp/4jozh1290342102.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290342179exxqtjcy3k25adp/4jozh1290342102.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290342179exxqtjcy3k25adp/5ufgk1290342102.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290342179exxqtjcy3k25adp/5ufgk1290342102.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290342179exxqtjcy3k25adp/6ufgk1290342102.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290342179exxqtjcy3k25adp/6ufgk1290342102.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290342179exxqtjcy3k25adp/75oyn1290342102.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290342179exxqtjcy3k25adp/75oyn1290342102.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290342179exxqtjcy3k25adp/85oyn1290342102.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290342179exxqtjcy3k25adp/85oyn1290342102.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290342179exxqtjcy3k25adp/95oyn1290342102.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/21/t1290342179exxqtjcy3k25adp/95oyn1290342102.ps (open in new window)

Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

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

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

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Software written by Ed van Stee & Patrick Wessa

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