WS7

*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Tue, 30 Nov 2010 16:59:28 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/30/t1291136305y7zueqkzyi4955e.htm/, Retrieved Tue, 30 Nov 2010 17:58:35 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Nov/30/t1291136305y7zueqkzyi4955e.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 24 14 11 12 24 26 1 25 11 7 8 25 23 1 17 6 17 8 30 25 1 18 12 10 8 19 23 1 18 8 12 9 22 19 1 16 10 12 7 22 29 1 20 10 11 4 25 25 1 16 11 11 11 23 21 1 18 16 12 7 17 22 2 17 11 13 7 21 25 2 23 13 14 12 19 24 2 30 12 16 10 19 18 2 23 8 11 10 15 22 2 18 12 10 8 16 15 2 15 11 11 8 23 22 2 12 4 15 4 27 28 2 21 9 9 9 22 20 2 15 8 11 8 14 12 2 20 8 17 7 22 24 3 31 14 17 11 23 20 3 27 15 11 9 23 21 3 34 16 18 11 21 20 3 21 9 14 13 19 21 3 31 14 10 8 18 23 3 19 11 11 8 20 28 3 16 8 15 9 23 24 3 20 9 15 6 25 24 3 21 9 13 9 19 24 3 22 9 16 9 24 23 3 17 9 13 6 22 23 3 24 10 9 6 25 29 3 25 16 18 16 26 24 3 26 11 18 5 29 18 3 25 8 12 7 32 25 3 17 9 17 9 25 21 3 32 16 9 6 29 26 3 33 11 9 6 28 22 3 13 16 12 5 17 22 3 32 12 18 12 28 22 3 25 12 12 7 29 23 3 29 14 18 10 26 30 3 22 9 14 9 25 23 3 18 10 15 8 14 17 3 17 9 16 5 25 23 3 20 10 10 8 26 23 3 15 12 11 8 20 25 3 20 14 14 10 18 24 3 33 14 9 6 32 24 3 29 10 12 8 25 23 3 23 14 17 7 25 21 3 26 16 5 4 23 24 3 18 9 12 8 21 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 10 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation PStandards[t] = + 8.7962501281589 -0.351026313258320Week[t] + 0.332860819537130Consern[t] -0.359233719372248Doubts[t] + 0.192857556338692PExpect[t] + 0.0149952339047633PCritisism[t] + 0.386464059692393Organisation[t] + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 8.7962501281589 2.589994 3.3962 0.000872 0.000436 Week -0.351026313258320 0.338223 -1.0379 0.300986 0.150493 Consern 0.332860819537130 0.055715 5.9744 0 0 Doubts -0.359233719372248 0.107145 -3.3528 0.00101 0.000505 PExpect 0.192857556338692 0.101296 1.9039 0.058813 0.029406 PCritisism 0.0149952339047633 0.128842 0.1164 0.907501 0.453751 Organisation 0.386464059692393 0.073159 5.2825 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.609523247377143 R-squared 0.371518589093177 Adjusted R-squared 0.346710112346855 F-TEST (value) 14.9754695901778 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 2.02726724296554e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.40841376090285 Sum Squared Residuals 1765.82722355781 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 23.7540528911651 0.245947108834937 2 25 23.1738115287681 1.82618847123193 3 30 25.0085972521040 4.99140274789605 4 19 21.0631247416520 -2.06312474165197 5 22 21.3549137269535 0.645086273046456 6 22 23.8053747782492 -1.80537477824919 7 25 23.3531185595752 1.64688144042483 8 23 20.2215519606182 2.77844803938184 9 17 19.6104456832432 -2.61044568324321 10 21 22.0749768827249 -1.07497688272487 11 19 23.2350440273733 -4.23504402737327 12 19 23.9612437702189 -4.96124377021892 13 15 23.6497213680241 -8.64972136802412 14 16 17.6203859508545 -1.62038595085451 15 23 19.8791431858008 3.12085681419919 16 27 24.4254304106852 2.57456958931477 17 22 21.4511275436107 0.548872456389319 18 14 17.0922037469936 -3.09220374699363 19 22 24.5362266651154 -2.53622666511538 20 23 24.2053917473815 -1.20539174738148 21 23 21.7140430037114 1.28595699628857 22 21 24.6783643235871 -3.67836432358706 23 19 22.5108340073573 -3.51083400735726 24 18 23.9697953303735 -5.96979533037352 25 20 23.1783445088454 -3.17834450884536 26 23 22.4980324288407 0.501967571159322 27 25 23.4252562859027 1.57474371409734 28 19 23.4173876944767 -4.41738769447670 29 24 23.9423571233375 0.0576428766624917 30 22 21.6544946549215 0.345505345078505 31 25 25.1726408051087 -0.172640805108744 32 26 23.3034493560463 2.69655064395372 33 29 22.9487468413379 6.0512531586621 34 32 25.2716807275416 6.72831927245836 35 25 21.6979824626058 3.30201753739423 36 29 24.5207328660951 4.47926713390488 37 28 25.1039060437239 2.89609395627608 38 17 17.2140984912314 -0.21409849123139 39 28 26.2375009152913 1.76249908470866 40 29 23.0618177306679 5.93818226933214 41 26 27.5821730276651 -1.58217302766507 42 25 23.5566420106601 1.44335798933988 43 14 19.7250429774189 -5.72504297741893 44 25 22.2180720900328 2.78192790996719 45 26 21.7452611929541 4.25473880704591 46 20 20.3282753322474 -0.328275332247418 47 18 21.4962110683218 -3.49621106832178 48 32 24.7991330049920 7.20086699500804 49 25 25.1267236814656 -0.12672368146564 50 25 21.8689883151578 3.13101168484222 51 23 20.9492191363233 2.05078086367674 52 21 22.2109524456219 -1.21095244562185 53 20 24.0632966040934 -4.06329660409343 54 15 16.6497891157883 -1.64978911578835 55 30 26.8471716045173 3.15282839548272 56 24 25.3692244228919 -1.36922442289186 57 26 24.3425541834753 1.6574458165247 58 24 21.8201218709400 2.17987812905996 59 22 21.4538424886006 0.546157511399372 60 14 15.8252519300394 -1.82525193003939 61 24 22.2795509196819 1.72044908031812 62 24 23.0131682733902 0.986831726609842 63 24 23.3826882245844 0.617311775415574 64 24 20.0175825766829 3.98241742331714 65 19 18.5645248522072 0.43547514779281 66 31 26.8491800092098 4.15081999079023 67 22 26.7045192626381 -4.70451926263810 68 27 21.5772786424205 5.4227213575795 69 19 17.7490286715042 1.25097132849583 70 25 22.3518131493053 2.64818685069468 71 20 25.1108710070759 -5.11087100707585 72 21 21.5637813025458 -0.563781302545751 73 27 27.5717783023730 -0.571778302373033 74 23 24.5326861243508 -1.53268612435084 75 25 25.8088852628178 -0.808885262817832 76 20 22.3566306448581 -2.35663064485807 77 21 19.2998108992965 1.70018910070348 78 22 22.5325440926986 -0.532544092698643 79 23 23.0127172928268 -0.0127172928268160 80 25 24.2110321713930 0.788967828606965 81 25 23.4613281496717 1.53867185032834 82 17 23.8687241667847 -6.86872416678469 83 19 21.5517631830704 -2.55176318307040 84 25 24.0373284972327 0.962671502767348 85 19 22.0710378851961 -3.07103788519606 86 20 22.8964761436804 -2.89647614368043 87 26 22.2614316135497 3.73856838645031 88 23 20.4189227063368 2.58107729366322 89 27 24.1993066790166 2.80069332098336 90 17 20.6591658195465 -3.65916581954647 91 17 23.1123592044767 -6.11235920447671 92 19 19.8325537603912 -0.83255376039119 93 17 19.465714624122 -2.46571462412202 94 22 21.8348616535768 0.165138346423220 95 21 23.1893120424487 -2.18931204244867 96 32 28.396510129026 3.60348987097397 97 21 24.459655157015 -3.45965515701502 98 21 24.142194364357 -3.14219436435699 99 18 21.0183995389187 -3.01839953891872 100 18 21.0926729490165 -3.09267294901653 101 23 22.6141674684254 0.385832531574645 102 19 20.3904284656099 -1.39042846560993 103 20 20.8139286560790 -0.813928656079017 104 21 22.0547948691766 -1.05479486917659 105 20 23.4975148431207 -3.49751484312073 106 17 18.6777634769777 -1.67776347697769 107 18 20.1117835459183 -2.11178354591827 108 19 20.601762536503 -1.60176253650299 109 22 21.8579494639154 0.142050536084615 110 15 18.5415140690785 -3.54151406907845 111 14 18.6075402216834 -4.60754022168340 112 18 26.3791792080809 -8.3791792080809 113 24 21.1382991042758 2.86170089572419 114 35 23.4053019297676 11.5946980702324 115 29 18.8289713313132 10.1710286686868 116 21 21.7013100672859 -0.70131006728592 117 25 20.3701352947869 4.62986470521306 118 20 18.2677144387943 1.73228556120566 119 22 22.9873511751830 -0.987351175183036 120 13 16.7246645151032 -3.72466451510316 121 26 23.0057308718302 2.99426912816983 122 17 16.7033077040266 0.296692295973389 123 25 19.8935813295805 5.10641867041948 124 20 20.4199056469751 -0.419905646975105 125 19 17.8412546392388 1.15874536076121 126 21 22.3850040546944 -1.38500405469436 127 22 20.7748813448280 1.22511865517205 128 24 22.3872508957394 1.61274910426061 129 21 22.6743308789582 -1.67433087895821 130 26 25.2502763319129 0.749723668087063 131 24 20.3919608716662 3.60803912833382 132 16 20.0348123142121 -4.03481231421209 133 23 22.0621501741582 0.937849825841796 134 18 20.528420548334 -2.52842054833400 135 16 22.1128108119103 -6.11281081191028 136 26 23.8858006103059 2.11419938969415 137 19 18.8471445482954 0.152855451704559 138 21 16.7389731078739 4.26102689212608 139 21 21.9012942661034 -0.901294266103412 140 22 18.3512341653153 3.64876583468466 141 23 19.6298693379126 3.37013066208739 142 29 24.6121898261332 4.38781017386684 143 21 19.1446590999530 1.85534090004697 144 21 19.6938327913337 1.30616720866632 145 23 21.6579190775089 1.34208092249111 146 27 22.783911087518 4.216088912482 147 25 25.2340795034825 -0.234079503482477 148 21 20.7719387424248 0.228061257575235 149 10 16.9580950705777 -6.95809507057771 150 20 22.4204524716016 -2.42045247160164 151 26 22.2933247683636 3.70667523163643 152 24 23.4453285174839 0.554671482516143 153 29 31.4517181559671 -2.45171815596705 154 19 18.9095253390712 0.0904746609288042 155 24 21.8791607141571 2.12083928584293 156 19 20.5305402222784 -1.53054022227839 157 24 23.1995081745349 0.800491825465104 158 22 21.5900695504639 0.409930449536128 159 17 23.5965892775799 -6.59658927757986 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.298766895345018 0.597533790690036 0.701233104654982 11 0.292862818035912 0.585725636071823 0.707137181964088 12 0.234114081060344 0.468228162120689 0.765885918939656 13 0.51772804289695 0.9645439142061 0.48227195710305 14 0.48971989470148 0.97943978940296 0.51028010529852 15 0.633425989491412 0.733148021017176 0.366574010508588 16 0.546410363223741 0.907179273552517 0.453589636776259 17 0.498585270931847 0.997170541863694 0.501414729068153 18 0.48037632514435 0.96075265028870 0.51962367485565 19 0.401651942004692 0.803303884009384 0.598348057995308 20 0.521648956117027 0.956702087765946 0.478351043882973 21 0.566160777422926 0.867678445154149 0.433839222577074 22 0.501766443035757 0.996467113928485 0.498233556964243 23 0.443905785589936 0.887811571179871 0.556094214410064 24 0.460750349781693 0.921500699563387 0.539249650218307 25 0.410480247936476 0.820960495872953 0.589519752063524 26 0.360173161990325 0.72034632398065 0.639826838009675 27 0.33394100315796 0.66788200631592 0.66605899684204 28 0.321498747507456 0.642997495014912 0.678501252492544 29 0.279524598645847 0.559049197291694 0.720475401354153 30 0.229642022622237 0.459284045244474 0.770357977377763 31 0.191881958068730 0.383763916137461 0.80811804193127 32 0.233284439109624 0.466568878219248 0.766715560890376 33 0.394010360457278 0.788020720914557 0.605989639542722 34 0.647691059806609 0.704617880386782 0.352308940193391 35 0.627073224937105 0.74585355012579 0.372926775062895 36 0.68835450387327 0.623290992253461 0.311645496126730 37 0.677272694405501 0.645454611188998 0.322727305594499 38 0.630205167803926 0.739589664392147 0.369794832196074 39 0.595967274848936 0.808065450302129 0.404032725151064 40 0.676213981586087 0.647572036827826 0.323786018413913 41 0.64675041995129 0.70649916009742 0.35324958004871 42 0.601785129466713 0.796429741066573 0.398214870533287 43 0.688023823593658 0.623952352812684 0.311976176406342 44 0.6570904664246 0.685819067150801 0.342909533575400 45 0.679845867147657 0.640308265704685 0.320154132852343 46 0.63190849000037 0.736183019999261 0.368091509999630 47 0.626302703421533 0.747394593156933 0.373697296578467 48 0.723918060904944 0.552163878190111 0.276081939095056 49 0.683397002545757 0.633205994908487 0.316602997454243 50 0.66739393748844 0.665212125023119 0.332606062511560 51 0.626374802675746 0.747250394648508 0.373625197324254 52 0.585190577518528 0.829618844962944 0.414809422481472 53 0.61855538936217 0.762889221275659 0.381444610637829 54 0.58325714154869 0.83348571690262 0.41674285845131 55 0.635601577465287 0.728796845069425 0.364398422534713 56 0.60225319633977 0.795493607320459 0.397746803660229 57 0.561523322400797 0.876953355198407 0.438476677599203 58 0.527493091749708 0.945013816500583 0.472506908250292 59 0.479240186677494 0.958480373354988 0.520759813322506 60 0.441976257343637 0.883952514687274 0.558023742656363 61 0.408603809675575 0.81720761935115 0.591396190324425 62 0.365370182278464 0.730740364556928 0.634629817721536 63 0.322185484647086 0.644370969294171 0.677814515352914 64 0.355533778227218 0.711067556454436 0.644466221772782 65 0.312412143239998 0.624824286479996 0.687587856760002 66 0.323445736422026 0.646891472844052 0.676554263577974 67 0.386380227359454 0.772760454718908 0.613619772640546 68 0.460998806599389 0.921997613198778 0.539001193400611 69 0.422443161013477 0.844886322026954 0.577556838986523 70 0.407859671974091 0.815719343948181 0.592140328025909 71 0.471201033094374 0.942402066188747 0.528798966905626 72 0.425358324718032 0.850716649436063 0.574641675281968 73 0.383752335876975 0.767504671753951 0.616247664123025 74 0.347675070003015 0.69535014000603 0.652324929996985 75 0.315138385761927 0.630276771523853 0.684861614238073 76 0.290915525912683 0.581831051825365 0.709084474087317 77 0.268111710248665 0.53622342049733 0.731888289751335 78 0.231980314090994 0.463960628181987 0.768019685909006 79 0.200018428048624 0.400036856097248 0.799981571951376 80 0.177156260768199 0.354312521536398 0.8228437392318 81 0.165992825962023 0.331985651924045 0.834007174037977 82 0.241216446238205 0.482432892476409 0.758783553761795 83 0.225020397231971 0.450040794463942 0.774979602768029 84 0.193184778802020 0.386369557604041 0.80681522119798 85 0.190249078361090 0.380498156722181 0.80975092163891 86 0.180429490739649 0.360858981479298 0.819570509260351 87 0.191464508436194 0.382929016872387 0.808535491563806 88 0.181138320822322 0.362276641644645 0.818861679177678 89 0.172034328451083 0.344068656902167 0.827965671548917 90 0.173203378427212 0.346406756854425 0.826796621572788 91 0.240378428879544 0.480756857759089 0.759621571120455 92 0.205708652468982 0.411417304937964 0.794291347531018 93 0.185305240636398 0.370610481272796 0.814694759363602 94 0.156230068865860 0.312460137731719 0.84376993113414 95 0.139489366493743 0.278978732987485 0.860510633506257 96 0.145634974846141 0.291269949692283 0.854365025153859 97 0.143365004764136 0.286730009528272 0.856634995235864 98 0.136277002286913 0.272554004573827 0.863722997713087 99 0.125731393211147 0.251462786422294 0.874268606788853 100 0.117562891664697 0.235125783329394 0.882437108335303 101 0.0965543002104032 0.193108600420806 0.903445699789597 102 0.0785538312647814 0.157107662529563 0.921446168735219 103 0.0624788198764325 0.124957639752865 0.937521180123568 104 0.049705494594523 0.099410989189046 0.950294505405477 105 0.0508641611755694 0.101728322351139 0.94913583882443 106 0.0406411850626796 0.0812823701253592 0.95935881493732 107 0.0349212450848357 0.0698424901696713 0.965078754915164 108 0.0301907790219146 0.0603815580438293 0.969809220978085 109 0.0230347323549735 0.0460694647099469 0.976965267645027 110 0.0216185277370544 0.0432370554741087 0.978381472262946 111 0.0261466210496592 0.0522932420993183 0.97385337895034 112 0.114911107255718 0.229822214511436 0.885088892744282 113 0.111059427664653 0.222118855329305 0.888940572335347 114 0.52504665069777 0.94990669860446 0.47495334930223 115 0.845434393773354 0.309131212453292 0.154565606226646 116 0.810530639338856 0.378938721322288 0.189469360661144 117 0.868966110477751 0.262067779044499 0.131033889522249 118 0.844471636852604 0.311056726294792 0.155528363147396 119 0.815063462239049 0.369873075521902 0.184936537760951 120 0.847764684975945 0.304470630048111 0.152235315024055 121 0.825462935115577 0.349074129768846 0.174537064884423 122 0.784933490285733 0.430133019428534 0.215066509714267 123 0.81884772019526 0.36230455960948 0.18115227980474 124 0.775736548666179 0.448526902667643 0.224263451333821 125 0.736948954016555 0.52610209196689 0.263051045983445 126 0.687213315889905 0.62557336822019 0.312786684110095 127 0.65056692040333 0.698866159193339 0.349433079596669 128 0.608879043132354 0.782241913735293 0.391120956867646 129 0.548980198719546 0.902039602560909 0.451019801280454 130 0.486133536580089 0.972267073160179 0.513866463419911 131 0.48512864833697 0.97025729667394 0.51487135166303 132 0.481496070194777 0.962992140389555 0.518503929805223 133 0.431232964581146 0.862465929162292 0.568767035418854 134 0.382007378077292 0.764014756154584 0.617992621922708 135 0.527320709199474 0.945358581601052 0.472679290800526 136 0.489078932601186 0.978157865202373 0.510921067398814 137 0.415828116272502 0.831656232545004 0.584171883727498 138 0.426741655609868 0.853483311219736 0.573258344390132 139 0.354949247980126 0.709898495960253 0.645050752019874 140 0.319580930313584 0.639161860627168 0.680419069686416 141 0.285765681679147 0.571531363358294 0.714234318320853 142 0.337286385084011 0.674572770168021 0.66271361491599 143 0.47898331862229 0.95796663724458 0.52101668137771 144 0.402102523662042 0.804205047324084 0.597897476337958 145 0.321048768939353 0.642097537878705 0.678951231060647 146 0.309641523073978 0.619283046147956 0.690358476926022 147 0.256131855465172 0.512263710930344 0.743868144534828 148 0.160109246321649 0.320218492643297 0.839890753678351 149 0.304811284883757 0.609622569767514 0.695188715116243 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 2 0.0142857142857143 OK 10% type I error level 7 0.05 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/30/t1291136305y7zueqkzyi4955e/1077ly1291136357.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291136305y7zueqkzyi4955e/1077ly1291136357.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291136305y7zueqkzyi4955e/1i6641291136357.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291136305y7zueqkzyi4955e/1i6641291136357.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291136305y7zueqkzyi4955e/2i6641291136357.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291136305y7zueqkzyi4955e/2i6641291136357.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291136305y7zueqkzyi4955e/3tf5p1291136357.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291136305y7zueqkzyi4955e/3tf5p1291136357.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291136305y7zueqkzyi4955e/4tf5p1291136357.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291136305y7zueqkzyi4955e/4tf5p1291136357.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291136305y7zueqkzyi4955e/5tf5p1291136357.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291136305y7zueqkzyi4955e/5tf5p1291136357.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291136305y7zueqkzyi4955e/6l74s1291136357.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291136305y7zueqkzyi4955e/6l74s1291136357.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291136305y7zueqkzyi4955e/7wyld1291136357.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291136305y7zueqkzyi4955e/7wyld1291136357.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291136305y7zueqkzyi4955e/8wyld1291136357.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291136305y7zueqkzyi4955e/8wyld1291136357.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291136305y7zueqkzyi4955e/9wyld1291136357.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291136305y7zueqkzyi4955e/9wyld1291136357.ps (open in new window)

Parameters (Session):

par1 = 6 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 6 ; 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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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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