minitutorial ws 4

*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Fri, 03 Dec 2010 15:46:44 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/03/t1291391107q52a8oa3vfn4ufn.htm/, Retrieved Fri, 03 Dec 2010 16:45:17 +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/Dec/03/t1291391107q52a8oa3vfn4ufn.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 «

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 10 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation ConcernoverMistakes[t] = -18.3591714482512 + 1.58838471475270month[t] + 0.79875711851511Doubtsaboutactions[t] + 0.233450466257558ParentalExpectations[t] + 0.207082749570129ParentalCriticism[t] + 0.571862761699044PersonalStandards[t] -0.0999815995143383Organization[t] + 0.00354783249216934t + 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) -18.3591714482512 19.993412 -0.9183 0.359947 0.179973 month 1.58838471475270 2.002175 0.7933 0.428831 0.214415 Doubtsaboutactions 0.79875711851511 0.131148 6.0905 0 0 ParentalExpectations 0.233450466257558 0.134333 1.7379 0.084276 0.042138 ParentalCriticism 0.207082749570129 0.170009 1.2181 0.225097 0.112548 PersonalStandards 0.571862761699044 0.096247 5.9416 0 0 Organization -0.0999815995143383 0.105485 -0.9478 0.344732 0.172366 t 0.00354783249216934 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 23.3005712933063 0.699428706693719 2 25 20.0175224671839 4.98247753281608 3 17 21.0211399791426 -4.02113997914265 4 18 18.0925500792618 -0.0925500792618023 5 18 17.6905678029332 0.309432197066762 6 16 17.877648378172 -1.87764837817201 7 20 20.7303968936034 -0.7303968936034 8 16 22.2384819662608 -6.23848196626085 9 18 22.1097766895970 -4.10977668959702 10 17 20.3404956440243 -3.34049564402435 11 23 22.1666780037712 0.833321996228807 12 30 22.0240937482091 7.97590625179086 13 23 14.9779833304995 8.02201666950045 14 18 18.8006776299538 -0.800677629953757 15 15 21.5420869454813 -6.54208694548131 16 12 17.7473672648276 -5.74736726482756 17 21 19.3199506278201 1.68004937217993 18 15 15.0095102272645 -0.00951022726447562 19 20 19.5818010071522 0.41819899284785 20 31 26.1780117087719 4.8219882912281 21 27 25.0654667635792 1.93453323642076 22 34 26.8723465536459 7.12765344635407 23 21 19.5212510677299 1.47874893227008 24 31 20.7775429191891 10.2224570808109 25 19 19.2620873882198 -0.262087388219842 26 16 20.1257631629215 -4.12576316292152 27 20 21.4505453886165 -1.45054538861650 28 21 18.1772639671097 2.82273603289032 29 22 21.8404586063841 0.15954139361592 30 17 19.3786812679951 -2.37868126799510 31 24 20.3628830419833 3.63711695801675 32 25 30.4026260368561 -5.40262603685613 33 26 26.4499559136845 -0.449955913684488 34 25 24.086412180723 0.913587819277002 35 17 22.8670220283224 -5.86702202832238 36 32 27.7605607608740 4.23943923912604 37 33 23.5983866371489 9.40161336285112 38 13 21.7984983327297 -8.79849833272967 39 32 27.7477901143871 4.25220988561288 40 25 25.787102563668 -0.787102563668005 41 29 26.9946561977486 2.00534380225137 42 22 21.9915422579662 0.00845774203379076 43 18 17.1296141440575 0.87038585594253 44 17 21.6372078571851 -4.63720785718515 45 20 22.2319210210565 -2.23192102105651 46 15 20.4352937876135 -5.43529378761353 47 20 22.1071288311651 -2.1071288311651 48 33 28.1211719978756 4.87882800212443 49 29 22.1411505218413 6.85884947815874 50 23 26.4998596091402 -3.49985960914021 51 26 23.2345975129204 2.76540248707958 52 18 18.9656042544921 -0.965604254492147 53 20 18.7961200457430 1.20387995425697 54 11 11.7160709940257 -0.716070994025735 55 28 29.0105804767345 -1.01058047673453 56 26 23.3905043460467 2.60949565395329 57 22 22.3414695454203 -0.341469545420307 58 17 20.1564210484307 -3.15642104843071 59 12 15.5692778789805 -3.56927787898050 60 14 20.8167935559991 -6.81679355599913 61 17 20.8202241820746 -3.82022418207459 62 21 21.3347129501434 -0.334712950143380 63 19 22.9763818374361 -3.97638183743611 64 18 23.1920758880957 -5.19207588809565 65 10 17.9120405565538 -7.91204055655377 66 29 24.4099265188341 4.59007348116592 67 31 18.5584769188011 12.4415230811989 68 19 22.9869414093617 -3.98694140936169 69 9 20.0961723263517 -11.0961723263517 70 20 22.5809984574057 -2.58099845740569 71 28 17.6552736410878 10.3447263589122 72 19 18.2291083555071 0.770891644492931 73 30 23.1787562563361 6.82124374366391 74 29 27.1018574495787 1.89814255042130 75 26 21.5208597487263 4.47914025127371 76 23 19.5775913896633 3.42240861033671 77 13 22.7673890269749 -9.7673890269749 78 21 22.6999656986182 -1.69996569861817 79 19 21.6345836806373 -2.63458368063733 80 28 22.9691570142453 5.03084298575474 81 23 25.6973992029916 -2.69739920299159 82 18 13.9549031616295 4.04509683837052 83 21 20.7615465591829 0.238453440817124 84 20 21.9157961866931 -1.91579618669312 85 23 20.0777478836276 2.92225211637243 86 21 20.8386011500172 0.161398849982816 87 21 21.8931506037605 -0.893150603760456 88 15 23.0305779438395 -8.03057794383952 89 28 27.3005835439217 0.699416456078311 90 19 17.7045900098864 1.29540999011360 91 26 21.2772051999812 4.72279480001875 92 10 13.4207961925499 -3.4207961925499 93 16 17.1995105289364 -1.19951052893642 94 22 21.1713453970672 0.82865460293282 95 19 18.9989312859951 0.00106871400488703 96 31 28.9403783769220 2.05962162307796 97 31 25.2905586288165 5.70944137118355 98 29 24.8528116175613 4.14718838243874 99 19 17.5096261454999 1.49037385450014 100 22 18.9524275113635 3.04757248863650 101 23 22.4963923849776 0.503607615022413 102 15 16.2875354180751 -1.28753541807506 103 20 21.4228525089516 -1.42285250895161 104 18 19.6658145225114 -1.66581452251145 105 23 22.2563692427646 0.743630757235358 106 25 20.9086574355098 4.09134256449023 107 21 16.6722771524643 4.32772284753566 108 24 19.5680077116824 4.4319922883176 109 25 25.3550235068465 -0.355023506846472 110 17 19.619766860822 -2.61976686082202 111 13 14.6659551691233 -1.66595516912329 112 28 18.4262616637208 9.57373833627919 113 21 20.4196764510916 0.580323548908437 114 25 28.3159565386191 -3.31595653861913 115 9 21.1551764227403 -12.1551764227403 116 16 18.0061106330230 -2.00611063302304 117 19 21.2544613841652 -2.25446138416516 118 17 19.6108037739653 -2.61080377396526 119 25 24.6763915340849 0.323608465915107 120 20 15.5671337387445 4.43286626125549 121 29 21.8716126114376 7.12838738856236 122 14 19.1167857657226 -5.11678576572263 123 22 27.0867941796051 -5.08679417960509 124 15 15.9355784175142 -0.935578417514242 125 19 25.6263325925739 -6.62633259257395 126 20 22.0928920267450 -2.09289202674503 127 15 17.7095654037931 -2.70956540379315 128 20 22.1149283807381 -2.11492838073813 129 18 20.5115649579609 -2.51156495796086 130 33 25.7620025241802 7.23799747581977 131 22 24.0135738555549 -2.01357385555485 132 16 16.6900618439135 -0.690061843913491 133 17 19.3420422957593 -2.34204229575933 134 16 15.3134803176989 0.68651968230106 135 21 17.2994992608764 3.70050073912357 136 26 27.7996968946194 -1.79969689461943 137 18 21.304233865906 -3.30423386590599 138 18 23.2073200148495 -5.20732001484945 139 17 18.6825913123659 -1.68259131236590 140 22 24.9799528930422 -2.97995289304222 141 30 24.9254198082097 5.0745801917903 142 30 27.5705627248667 2.42943727513332 143 24 29.9683835869881 -5.96838358698809 144 21 22.2960469748642 -1.29604697486422 145 21 25.6227704527493 -4.62277045274928 146 29 27.6739609431583 1.32603905684171 147 31 23.464342466474 7.53565753352598 148 20 19.2655893559701 0.734410644029932 149 16 14.3261339717709 1.67386602822906 150 22 19.2236647882233 2.77633521177669 151 20 20.7522347250232 -0.752234725023154 152 28 27.5610774834422 0.438922516557781 153 38 26.890415116 11.1095848840000 154 22 19.4362722728422 2.56372772715775 155 20 25.9470773992814 -5.9470773992814 156 17 18.31008307594 -1.31008307593998 157 28 24.8140500775851 3.18594992241494 158 22 24.4230458313632 -2.42304583136319 159 31 26.3398127723852 4.66018722761484 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.482919301614959 0.965838603229918 0.517080698385041 12 0.554073239343645 0.89185352131271 0.445926760656355 13 0.778571207452893 0.442857585094213 0.221428792547107 14 0.804401377897167 0.391197244205666 0.195598622102833 15 0.744773564280576 0.510452871438847 0.255226435719424 16 0.66423254463189 0.67153491073622 0.33576745536811 17 0.623527767746131 0.752944464507739 0.376472232253869 18 0.581415909333898 0.837168181332203 0.418584090666102 19 0.541563815283281 0.916872369433438 0.458436184716719 20 0.562150479533601 0.875699040932797 0.437849520466399 21 0.485348761129402 0.970697522258804 0.514651238870598 22 0.455924906437963 0.911849812875926 0.544075093562037 23 0.418029313423604 0.836058626847208 0.581970686576396 24 0.525131871059443 0.949736257881114 0.474868128940557 25 0.496594569472841 0.993189138945682 0.503405430527159 26 0.528430312047999 0.943139375904001 0.471569687952001 27 0.462456469163947 0.924912938327894 0.537543530836053 28 0.399432869722768 0.798865739445536 0.600567130277232 29 0.337499119939794 0.674998239879589 0.662500880060206 30 0.303449426252635 0.606898852505269 0.696550573747365 31 0.292068810897149 0.584137621794297 0.707931189102851 32 0.427890514331057 0.855781028662114 0.572109485668943 33 0.367770972580548 0.735541945161096 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 0.761514402351724 0.476971195296551 0.238485597648276 39 0.748042922363758 0.503914155272483 0.251957077636242 40 0.711410768934749 0.577178462130503 0.288589231065251 41 0.676447198133766 0.647105603732469 0.323552801866234 42 0.62816507684451 0.74366984631098 0.37183492315549 43 0.576422723698907 0.847154552602186 0.423577276301093 44 0.564043835542671 0.871912328914659 0.435956164457329 45 0.547145831190928 0.905708337618143 0.452854168809072 46 0.579192685522074 0.841614628955852 0.420807314477926 47 0.535476535517343 0.929046928965313 0.464523464482657 48 0.525984911848510 0.948030176302979 0.474015088151489 49 0.5862103539833 0.8275792920334 0.4137896460167 50 0.5573213315437 0.8853573369126 0.4426786684563 51 0.526419736329641 0.947160527340718 0.473580263670359 52 0.476679027266429 0.953358054532857 0.523320972733571 53 0.433008721292444 0.866017442584889 0.566991278707556 54 0.388214689123759 0.776429378247518 0.611785310876241 55 0.347336244766196 0.694672489532392 0.652663755233804 56 0.318722802009980 0.637445604019959 0.68127719799002 57 0.275855712367904 0.551711424735809 0.724144287632096 58 0.247829977005935 0.495659954011869 0.752170022994066 59 0.229544224760974 0.459088449521947 0.770455775239026 60 0.264607003917427 0.529214007834855 0.735392996082573 61 0.24812764027652 0.49625528055304 0.75187235972348 62 0.214130181035499 0.428260362070998 0.785869818964501 63 0.196907532926841 0.393815065853682 0.803092467073159 64 0.217946681722193 0.435893363444386 0.782053318277807 65 0.266979412065807 0.533958824131614 0.733020587934193 66 0.275929127254054 0.551858254508108 0.724070872745946 67 0.63776942013587 0.72446115972826 0.36223057986413 68 0.621918172530883 0.756163654938234 0.378081827469117 69 0.795195289203809 0.409609421592383 0.204804710796191 70 0.767814750635933 0.464370498728134 0.232185249364067 71 0.912753156491534 0.174493687016932 0.0872468435084658 72 0.893727121804516 0.212545756390967 0.106272878195484 73 0.924292609592878 0.151414780814245 0.0757073904071223 74 0.912497020729957 0.175005958540086 0.0875029792700431 75 0.916330968011296 0.167338063977408 0.0836690319887039 76 0.910662472173308 0.178675055653384 0.089337527826692 77 0.962094085816427 0.0758118283671457 0.0379059141835728 78 0.952685243442333 0.0946295131153332 0.0473147565576666 79 0.94347392980676 0.113052140386480 0.0565260701932398 80 0.947942852549188 0.104114294901625 0.0520571474508123 81 0.938265238808533 0.123469522382935 0.0617347611914673 82 0.937582724026703 0.124834551946594 0.0624172759732972 83 0.922053336251284 0.155893327497433 0.0779466637487164 84 0.906574250002529 0.186851499994942 0.0934257499974709 85 0.896763278206496 0.206473443587007 0.103236721793503 86 0.878080050015044 0.243839899969911 0.121919949984956 87 0.853375575666524 0.293248848666953 0.146624424333476 88 0.905330192016902 0.189339615966196 0.0946698079830979 89 0.886155588871522 0.227688822256956 0.113844411128478 90 0.863647711730098 0.272704576539804 0.136352288269902 91 0.865827478842622 0.268345042314756 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 0.47262310671193 0.236311553355965 96 0.731055574998138 0.537888850003723 0.268944425001862 97 0.75174192733153 0.49651614533694 0.24825807266847 98 0.749346506853056 0.501306986293889 0.250653493146944 99 0.712234696431953 0.575530607136093 0.287765303568047 100 0.689744864923868 0.620510270152265 0.310255135076132 101 0.649434922236285 0.70113015552743 0.350565077763715 102 0.606634845790477 0.786730308419046 0.393365154209523 103 0.56324421674873 0.873511566502539 0.436755783251269 104 0.518654156668534 0.962691686662932 0.481345843331466 105 0.475880650474408 0.951761300948816 0.524119349525592 106 0.463612141119946 0.927224282239892 0.536387858880054 107 0.470779049273711 0.941558098547422 0.529220950726289 108 0.509532807449635 0.98093438510073 0.490467192550365 109 0.47097175676288 0.94194351352576 0.52902824323712 110 0.428611691000273 0.857223382000546 0.571388308999727 111 0.381451505416848 0.762903010833696 0.618548494583152 112 0.711288640363238 0.577422719273525 0.288711359636762 113 0.747397544448189 0.505204911103622 0.252602455551811 114 0.720032266639849 0.559935466720302 0.279967733360151 115 0.854652166059168 0.290695667881664 0.145347833940832 116 0.822716200104193 0.354567599791615 0.177283799895807 117 0.789598373374736 0.420803253250528 0.210401626625264 118 0.752405016530784 0.495189966938432 0.247594983469216 119 0.721776844050078 0.556446311899844 0.278223155949922 120 0.773892573829069 0.452214852341862 0.226107426170931 121 0.86094268064034 0.278114638719321 0.139057319359660 122 0.83849371344511 0.323012573109779 0.161506286554890 123 0.8144281484347 0.3711437031306 0.1855718515653 124 0.77154929585405 0.456901408291901 0.228450704145950 125 0.77469827761769 0.450603444764621 0.225301722382310 126 0.725912210291747 0.548175579416506 0.274087789708253 127 0.69067688627089 0.618646227458221 0.309323113729111 128 0.639778003698588 0.720443992602823 0.360221996301412 129 0.590736886156087 0.818526227687827 0.409263113843913 130 0.718503215808757 0.562993568382487 0.281496784191244 131 0.660323778713816 0.679352442572369 0.339676221286184 132 0.595126930986174 0.809746138027651 0.404873069013826 133 0.553718763961046 0.892562472077909 0.446281236038954 134 0.481445774757762 0.962891549515525 0.518554225242238 135 0.504899838699719 0.990200322600562 0.495100161300281 136 0.432400563387952 0.864801126775904 0.567599436612048 137 0.383851090629990 0.767702181259979 0.61614890937001 138 0.396248754615259 0.792497509230519 0.603751245384741 139 0.323763162155535 0.64752632431107 0.676236837844465 140 0.254403000965545 0.50880600193109 0.745596999034455 141 0.344047179913995 0.68809435982799 0.655952820086005 142 0.294575906829285 0.58915181365857 0.705424093170715 143 0.226445586897251 0.452891173794503 0.773554413102749 144 0.159698858380339 0.319397716760677 0.840301141619661 145 0.239930077553042 0.479860155106083 0.760069922446958 146 0.169348307271413 0.338696614542827 0.830651692728587 147 0.160521283906014 0.321042567812028 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/Dec/03/t1291391107q52a8oa3vfn4ufn/1035me1291391192.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291391107q52a8oa3vfn4ufn/1035me1291391192.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291391107q52a8oa3vfn4ufn/1wm7l1291391192.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291391107q52a8oa3vfn4ufn/1wm7l1291391192.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291391107q52a8oa3vfn4ufn/2pwoo1291391192.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291391107q52a8oa3vfn4ufn/2pwoo1291391192.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291391107q52a8oa3vfn4ufn/3pwoo1291391192.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291391107q52a8oa3vfn4ufn/3pwoo1291391192.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291391107q52a8oa3vfn4ufn/4pwoo1291391192.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291391107q52a8oa3vfn4ufn/4pwoo1291391192.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291391107q52a8oa3vfn4ufn/5z5681291391192.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291391107q52a8oa3vfn4ufn/5z5681291391192.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291391107q52a8oa3vfn4ufn/6z5681291391192.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291391107q52a8oa3vfn4ufn/6z5681291391192.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291391107q52a8oa3vfn4ufn/7aenu1291391192.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291391107q52a8oa3vfn4ufn/7aenu1291391192.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291391107q52a8oa3vfn4ufn/8aenu1291391192.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291391107q52a8oa3vfn4ufn/8aenu1291391192.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291391107q52a8oa3vfn4ufn/935me1291391192.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t1291391107q52a8oa3vfn4ufn/935me1291391192.ps (open in new window)

Parameters (Session):

par1 = 0 ; par2 = 36 ;

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') }

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