Workshop 7 - Populatievariabele

*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, 19 Nov 2010 14:57:03 +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/19/t1290178556dbum4b5534lsbj4.htm/, Retrieved Fri, 19 Nov 2010 15:56:08 +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/19/t1290178556dbum4b5534lsbj4.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 «

1 26 24 14 11 12 24 1 23 25 11 7 8 25 0 25 17 6 17 8 30 1 23 18 12 10 8 19 1 19 18 8 12 9 22 0 29 16 10 12 7 22 1 25 20 10 11 4 25 1 21 16 11 11 11 23 1 22 18 16 12 7 17 1 25 17 11 13 7 21 1 24 23 13 14 12 19 1 18 30 12 16 10 19 1 22 23 8 11 10 15 1 15 18 12 10 8 16 1 22 15 11 11 8 23 1 28 12 4 15 4 27 1 20 21 9 9 9 22 1 12 15 8 11 8 14 1 24 20 8 17 7 22 1 20 31 14 17 11 23 1 21 27 15 11 9 23 1 20 34 16 18 11 21 1 21 21 9 14 13 19 1 23 31 14 10 8 18 1 28 19 11 11 8 20 1 24 16 8 15 9 23 1 24 20 9 15 6 25 1 24 21 9 13 9 19 1 23 22 9 16 9 24 1 23 17 9 13 6 22 1 29 24 10 9 6 25 1 24 25 16 18 16 26 1 18 26 11 18 5 29 1 25 25 8 12 7 32 1 21 17 9 17 9 25 1 26 32 16 9 6 29 1 22 33 11 9 6 28 1 22 13 16 12 5 17 0 22 32 12 18 12 28 1 23 25 12 12 7 29 1 30 29 14 18 10 26 1 23 22 9 14 9 25 1 17 18 10 15 8 14 1 23 17 9 16 5 25 1 23 20 10 10 8 26 1 25 15 12 11 8 20 1 24 20 14 14 10 18 1 24 33 14 9 6 32 1 23 29 10 12 8 25 1 21 23 14 17 7 25 1 24 26 16 5 4 23 1 24 18 9 12 8 2 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 20 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Organization[t] = + 16.1354931228066 -0.00122026371875766Pop[t] -0.0706717971761332concernmistakes[t] + 0.218172682267896doubtactions[t] -0.148958357244339parentalexp[t] -0.255147679267417parentalcrit[t] + 0.422750826496799personalstandards[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) 16.1354931228066 2.180404 7.4002 0 0 Pop -0.00122026371875766 0.931511 -0.0013 0.998957 0.499478 concernmistakes -0.0706717971761332 0.063193 -1.1184 0.26518 0.13259 doubtactions 0.218172682267896 0.112994 1.9308 0.055365 0.027683 parentalexp -0.148958357244339 0.104676 -1.423 0.156773 0.078387 parentalcrit -0.255147679267417 0.131267 -1.9437 0.053775 0.026888 personalstandards 0.422750826496799 0.076009 5.5619 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.471563537683633 R-squared 0.222372170072703 Adjusted R-squared 0.191676334680836 F-TEST (value) 7.24437589770311 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 8.12359079893632e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.51085220908301 Sum Squared Residuals 1873.5646515715 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 26 22.9382730336376 3.06172696636235 2 23 24.2522581622017 -1.25225816220167 3 25 24.3521599520306 0.647840047969375 4 23 21.9817533939887 1.01824660601130 5 19 21.8242507506514 -2.82425075065142 6 29 22.9134553317931 6.08654466820693 7 25 24.8122017539068 0.187798246093245 8 21 22.6815262170137 -1.68152621701367 9 22 21.9661734348454 0.0338265651545764 10 25 22.4880267694249 2.51197323057507 11 24 20.2301429443289 3.76985705567110 12 18 19.7296463258742 -1.72964632587423 13 22 18.4054466572701 3.59455334272992 14 15 20.7135009144983 -5.7135009144983 15 22 23.5176410519921 -1.51764105199206 16 28 24.3182082617247 3.68179173827531 17 20 22.2772831131239 -2.27728311312393 18 12 19.0583655667172 -7.05836556671718 19 24 21.4484107286123 2.55158927138771 20 20 21.3822171627093 -1.38221716270933 21 21 23.2871225356826 -2.28712253568263 22 20 20.6120871254788 -0.612087125478788 23 21 19.2436481303422 1.75635186965783 24 23 21.0766145687380 1.92338543126204 25 28 21.9667013837971 6.03329861620287 26 24 21.9414700997675 2.05852990023254 27 24 23.4879002841267 0.512099715873324 28 24 20.4131972046562 3.58680279534382 29 23 22.009404468231 0.990595531768979 30 23 22.7295799106534 0.270420089346643 31 29 24.3171359211561 4.68286407884393 32 24 22.0861490362109 1.91385096378911 33 18 24.9994907791273 -6.99949077912727 34 25 26.0673517939213 -1.06735179392131 35 21 22.6365559233641 -1.63655592336415 36 26 26.7518009433416 -0.751800943341579 37 22 25.1675149083292 -3.16751490832917 38 22 22.8298277792609 -0.829827779260923 39 22 22.5860683606884 -0.586068360688403 40 23 25.6717900435025 -2.67179004350249 41 30 22.8980025585751 7.10199744142493 42 23 22.7300720092165 0.269927990783503 43 17 18.6868621107472 -1.68686211074722 44 23 23.8061049976782 -0.806104997678154 45 23 24.3633202205782 -1.36332022057823 46 25 22.4675612547696 2.53243874523044 47 24 20.7478755501632 3.25212444983676 48 24 27.5130362611200 -3.51303626112005 49 23 23.0066065050076 -0.00660650500755594 50 21 23.8136839101817 -2.81368391018166 51 24 25.7454555549298 -1.74545555492978 52 24 21.8748202856899 2.12517971431007 53 28 21.5288985471088 6.47110145289124 54 16 21.0928407206741 -5.09284072067408 55 20 19.9054146319908 0.094585368009180 56 29 23.4503891168428 5.54961088315715 57 27 23.9240599117373 3.07594008826271 58 22 23.2079505241347 -1.20795052413472 59 28 24.0506390339991 3.9493609660009 60 16 20.3583294252799 -4.35832942527991 61 25 22.9585968830890 2.04140311691096 62 24 23.5105670572103 0.489432942789682 63 28 23.6853702433054 4.31462975669462 64 24 24.3564492439618 -0.356449243961849 65 23 22.7272670874199 0.272732912580117 66 30 26.9736022557915 3.02639774420849 67 24 21.3096234238734 2.69037657612656 68 21 24.1916950902503 -3.19169509025025 69 25 23.3462676093766 1.65373239062337 70 25 24.0110039828237 0.988996017176252 71 22 20.7823264844313 1.21767351556868 72 23 22.5061712395142 0.49382876048577 73 26 22.8612409275567 3.13875907244331 74 23 21.5927750820852 1.40722491791485 75 25 23.0638695010699 1.93613049893012 76 21 21.3168831555804 -0.316883155580361 77 25 23.6803796842006 1.31962031579943 78 24 22.1870093737059 1.81299062629408 79 29 23.6020849027998 5.39791509720024 80 22 23.6567879857421 -1.65678798574208 81 27 23.6440743013568 3.35592569864323 82 26 19.6794775538621 6.32052244613786 83 22 21.3228629307273 0.677137069272718 84 24 22.1001785275448 1.89982147245523 85 27 23.1293197886535 3.87068021134649 86 24 21.3357136824906 2.66428631750942 87 24 24.90913310396 -0.90913310396001 88 29 24.4700758132844 4.52992418671557 89 22 22.2324058151312 -0.232405815131221 90 21 20.5876858077807 0.412314192219327 91 24 20.4113892991445 3.58861070085553 92 24 21.828131068546 2.171868931454 93 23 21.9750443118448 1.02495568815518 94 20 22.2964768925519 -2.29647689255191 95 27 21.4428114872233 5.5571885127767 96 26 23.4633027638642 2.53669723613584 97 25 21.9302313045194 3.06976869548062 98 21 20.0557803852883 0.944219614711652 99 21 20.7910436882908 0.208956311709183 100 19 20.3930949425186 -1.39309494251856 101 21 21.6279652048029 -0.627965204802907 102 21 21.3152840182238 -0.315284018223772 103 16 19.7577220055957 -3.75772200559566 104 22 20.6994771731542 1.30052282684582 105 29 21.8282368833615 7.17176311663855 106 15 21.6955994695746 -6.69559946957463 107 17 20.7294441261593 -3.72944412615933 108 15 19.9460341338604 -4.94603413386036 109 21 21.681413833758 -0.681413833758009 110 21 21.0113661574783 -0.0113661574783428 111 19 19.3058984830925 -0.305898483092524 112 24 18.0652530061233 5.93474699387672 113 20 22.3943167253148 -2.39431672531480 114 17 25.2043109943269 -8.20431099432686 115 23 25.0687454166209 -2.06874541662094 116 24 22.4144758783322 1.58552412166779 117 14 22.0958419614756 -8.09584196147561 118 19 22.9162570511729 -3.91625705117291 119 24 22.1917091922928 1.80829080770716 120 13 20.4042395899461 -7.40423958994609 121 22 25.4129125170636 -3.41291251706361 122 16 21.1579972122105 -5.15799721221048 123 19 23.3118603257399 -4.3118603257399 124 25 22.8499576704545 2.1500423295455 125 25 24.2095274487118 0.790472551288172 126 23 21.4250302696518 1.57496973034824 127 24 23.6111415167243 0.388858483275664 128 26 23.5870328926082 2.41296710739181 129 26 21.5399285742017 4.46007142579827 130 25 24.1683192291157 0.831680770884255 131 18 22.382329545965 -4.38232954596500 132 21 19.9024097475582 1.0975902524418 133 26 23.7053951309063 2.29460486909375 134 23 21.9972045070866 1.00279549291341 135 23 19.7672234439454 3.23277655605457 136 22 22.5939285533469 -0.593928553346898 137 20 22.4123047203027 -2.41230472030275 138 13 22.1252322959819 -9.12523229598186 139 24 21.4721717213307 2.52782827866925 140 15 21.6118362562167 -6.6118362562167 141 14 23.154851176375 -9.154851176375 142 22 24.1073332118053 -2.10733321180532 143 10 17.6923804758315 -7.69238047583154 144 24 24.4820758117929 -0.482075811792852 145 22 21.8707624522028 0.129237547797233 146 24 25.8203979673877 -1.82039796738770 147 19 21.6471507628983 -2.64715076289828 148 20 22.1388029915682 -2.13880299156818 149 13 17.11075710931 -4.11075710930999 150 20 20.1429975151972 -0.142997515197190 151 22 23.3046961372628 -1.30469613726279 152 24 23.3677301403169 0.632269859683088 153 29 23.1942587827458 5.80574121725418 154 12 20.9590100880380 -8.95901008803795 155 20 20.9706692810721 -0.970669281072056 156 21 21.4613274311630 -0.46132743116296 157 24 23.6761765620028 0.323823437997186 158 22 21.9304042222859 0.0695957777140708 159 20 17.7084024574386 2.29159754256143 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.434874568012066 0.869749136024133 0.565125431987934 11 0.29001724939983 0.58003449879966 0.70998275060017 12 0.297358081075688 0.594716162151376 0.702641918924312 13 0.26708743316352 0.53417486632704 0.73291256683648 14 0.619368477451672 0.761263045096655 0.380631522548328 15 0.514624949569935 0.97075010086013 0.485375050430065 16 0.59205883795555 0.815882324088899 0.407941162044449 17 0.522320473536046 0.955359052927908 0.477679526463954 18 0.658322042279512 0.683355915440975 0.341677957720488 19 0.589093050653621 0.821813898692758 0.410906949346379 20 0.582919154275846 0.834161691448308 0.417080845724154 21 0.535596172415712 0.928807655168576 0.464403827584288 22 0.46453348045751 0.92906696091502 0.53546651954249 23 0.408743226737791 0.817486453475582 0.591256773262209 24 0.389990793819939 0.779981587639878 0.610009206180061 25 0.544321199971513 0.911357600056973 0.455678800028487 26 0.486015658161594 0.972031316323189 0.513984341838406 27 0.417595348139769 0.835190696279538 0.582404651860231 28 0.412286313568451 0.824572627136902 0.587713686431549 29 0.348736843823599 0.697473687647198 0.651263156176401 30 0.289438779509337 0.578877559018674 0.710561220490663 31 0.31729568291391 0.63459136582782 0.68270431708609 32 0.269967532547655 0.53993506509531 0.730032467452345 33 0.470437123635462 0.940874247270923 0.529562876364538 34 0.417389781165895 0.83477956233179 0.582610218834105 35 0.373384633395211 0.746769266790421 0.626615366604789 36 0.318385613454205 0.63677122690841 0.681614386545795 37 0.297798863300276 0.595597726600552 0.702201136699724 38 0.249668735545484 0.499337471090968 0.750331264454516 39 0.229007451947749 0.458014903895498 0.770992548052251 40 0.202569559028598 0.405139118057196 0.797430440971402 41 0.368166824053903 0.736333648107807 0.631833175946097 42 0.316677642880745 0.633355285761489 0.683322357119255 43 0.284539351615209 0.569078703230418 0.71546064838479 44 0.240898601141232 0.481797202282465 0.759101398858768 45 0.206456407710322 0.412912815420644 0.793543592289678 46 0.184935171741685 0.369870343483369 0.815064828258315 47 0.172106876700983 0.344213753401966 0.827893123299017 48 0.158517498014174 0.317034996028349 0.841482501985826 49 0.129248430079564 0.258496860159129 0.870751569920436 50 0.118395377199675 0.23679075439935 0.881604622800325 51 0.0976518596117569 0.195303719223514 0.902348140388243 52 0.0827641258947307 0.165528251789461 0.917235874105269 53 0.139165645905757 0.278331291811515 0.860834354094243 54 0.173931038643452 0.347862077286904 0.826068961356548 55 0.159575878156311 0.319151756312621 0.84042412184369 56 0.215218305593620 0.430436611187241 0.78478169440638 57 0.207489330429576 0.414978660859152 0.792510669570424 58 0.176953056703907 0.353906113407814 0.823046943296093 59 0.187517198195841 0.375034396391683 0.812482801804159 60 0.217191090225374 0.434382180450748 0.782808909774626 61 0.191206171839512 0.382412343679023 0.808793828160488 62 0.160350647477010 0.320701294954020 0.83964935252299 63 0.159547827536068 0.319095655072137 0.840452172463932 64 0.133194770459558 0.266389540919116 0.866805229540442 65 0.108806347002456 0.217612694004913 0.891193652997544 66 0.106178531024338 0.212357062048676 0.893821468975662 67 0.0960491004241851 0.192098200848370 0.903950899575815 68 0.094458022395619 0.188916044791238 0.905541977604381 69 0.0796449352593425 0.159289870518685 0.920355064740658 70 0.067251752351868 0.134503504703736 0.932748247648132 71 0.0541105459451245 0.108221091890249 0.945889454054875 72 0.0423281880983922 0.0846563761967843 0.957671811901608 73 0.0399777178930837 0.0799554357861674 0.960022282106916 74 0.0319331520959022 0.0638663041918045 0.968066847904098 75 0.0264991330134145 0.0529982660268289 0.973500866986586 76 0.0201882923363140 0.0403765846726281 0.979811707663686 77 0.0158263539820185 0.0316527079640369 0.984173646017982 78 0.0126080753474495 0.0252161506948990 0.98739192465255 79 0.0191819053060338 0.0383638106120675 0.980818094693966 80 0.0152053792399013 0.0304107584798026 0.984794620760099 81 0.0149391379386452 0.0298782758772905 0.985060862061355 82 0.0244879563955224 0.0489759127910449 0.975512043604478 83 0.0186149625728466 0.0372299251456931 0.981385037427153 84 0.0154411691048128 0.0308823382096257 0.984558830895187 85 0.0161356491991315 0.0322712983982629 0.983864350800869 86 0.0142360821103373 0.0284721642206747 0.985763917889663 87 0.0106468889528112 0.0212937779056224 0.98935311104719 88 0.0139131760542329 0.0278263521084658 0.986086823945767 89 0.0107297304011554 0.0214594608023108 0.989270269598845 90 0.00951800969050194 0.0190360193810039 0.990481990309498 91 0.00968002956714122 0.0193600591342824 0.990319970432859 92 0.00836363445204981 0.0167272689040996 0.99163636554795 93 0.00776427121630875 0.0155285424326175 0.992235728783691 94 0.0064677600798349 0.0129355201596698 0.993532239920165 95 0.0122826071796537 0.0245652143593073 0.987717392820346 96 0.0107858677703109 0.0215717355406219 0.98921413222969 97 0.0102082214628374 0.0204164429256748 0.989791778537163 98 0.0077761519128095 0.015552303825619 0.99222384808719 99 0.00568500929668349 0.0113700185933670 0.994314990703317 100 0.00431173178332286 0.00862346356664571 0.995688268216677 101 0.00314473791890114 0.00628947583780229 0.996855262081099 102 0.00220251733011943 0.00440503466023886 0.99779748266988 103 0.0023888435640736 0.0047776871281472 0.997611156435926 104 0.00184255702859343 0.00368511405718685 0.998157442971407 105 0.0082031774322939 0.0164063548645878 0.991796822567706 106 0.0182908333969044 0.0365816667938089 0.981709166603095 107 0.0179985849880857 0.0359971699761715 0.982001415011914 108 0.0225944114364476 0.0451888228728953 0.977405588563552 109 0.0173327381191765 0.0346654762383529 0.982667261880824 110 0.0137607771357787 0.0275215542715574 0.986239222864221 111 0.00998363511700458 0.0199672702340092 0.990016364882995 112 0.0253419473691905 0.050683894738381 0.97465805263081 113 0.0227611743117899 0.0455223486235797 0.97723882568821 114 0.0598812694695286 0.119762538939057 0.940118730530471 115 0.0505354214776951 0.101070842955390 0.949464578522305 116 0.0408348571971748 0.0816697143943496 0.959165142802825 117 0.125670110991191 0.251340221982381 0.874329889008809 118 0.122007793296485 0.244015586592969 0.877992206703515 119 0.108078685838032 0.216157371676064 0.891921314161968 120 0.181914326417674 0.363828652835349 0.818085673582326 121 0.17719198977613 0.35438397955226 0.82280801022387 122 0.211836401735673 0.423672803471346 0.788163598264327 123 0.198754972937049 0.397509945874099 0.80124502706295 124 0.193871684089692 0.387743368179384 0.806128315910308 125 0.177529373559175 0.355058747118351 0.822470626440825 126 0.144708962640183 0.289417925280366 0.855291037359817 127 0.114727282096881 0.229454564193762 0.885272717903119 128 0.116280047275404 0.232560094550808 0.883719952724596 129 0.164553153251405 0.329106306502810 0.835446846748595 130 0.140635516878917 0.281271033757833 0.859364483121083 131 0.123611185647210 0.247222371294419 0.87638881435279 132 0.10713660391431 0.21427320782862 0.89286339608569 133 0.0974755281142478 0.194951056228496 0.902524471885752 134 0.0793738430315658 0.158747686063132 0.920626156968434 135 0.107972369258030 0.215944738516061 0.89202763074197 136 0.0801787199472224 0.160357439894445 0.919821280052778 137 0.0585128419740382 0.117025683948076 0.941487158025962 138 0.149755405236693 0.299510810473386 0.850244594763307 139 0.209641176305557 0.419282352611115 0.790358823694443 140 0.190479830365639 0.380959660731278 0.809520169634361 141 0.424807529122923 0.849615058245846 0.575192470877077 142 0.35929351226585 0.7185870245317 0.64070648773415 143 0.671530929246601 0.656938141506797 0.328469070753399 144 0.615294098951965 0.76941180209607 0.384705901048035 145 0.50484919126439 0.99030161747122 0.49515080873561 146 0.429177174381381 0.858354348762762 0.570822825618619 147 0.437382041964606 0.874764083929212 0.562617958035394 148 0.305353605634068 0.610707211268136 0.694646394365932 149 0.212991087878009 0.425982175756018 0.787008912121991 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 5 0.0357142857142857 NOK 5% type I error level 37 0.264285714285714 NOK 10% type I error level 43 0.307142857142857 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/19/t1290178556dbum4b5534lsbj4/10no241290178602.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290178556dbum4b5534lsbj4/10no241290178602.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290178556dbum4b5534lsbj4/1y55s1290178602.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290178556dbum4b5534lsbj4/1y55s1290178602.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290178556dbum4b5534lsbj4/2y55s1290178602.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290178556dbum4b5534lsbj4/2y55s1290178602.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290178556dbum4b5534lsbj4/3re4d1290178602.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290178556dbum4b5534lsbj4/3re4d1290178602.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290178556dbum4b5534lsbj4/4re4d1290178602.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290178556dbum4b5534lsbj4/4re4d1290178602.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290178556dbum4b5534lsbj4/5re4d1290178602.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290178556dbum4b5534lsbj4/5re4d1290178602.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290178556dbum4b5534lsbj4/61nmg1290178602.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290178556dbum4b5534lsbj4/61nmg1290178602.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290178556dbum4b5534lsbj4/7cflj1290178602.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290178556dbum4b5534lsbj4/7cflj1290178602.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290178556dbum4b5534lsbj4/8cflj1290178602.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290178556dbum4b5534lsbj4/8cflj1290178602.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290178556dbum4b5534lsbj4/9cflj1290178602.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/19/t1290178556dbum4b5534lsbj4/9cflj1290178602.ps (open in new window)

Parameters (Session):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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