MR Paper (monthly dummies)

*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, 17 Dec 2010 16:35:58 +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/17/t1292603812yc05dpn58qnw2e6.htm/, Retrieved Fri, 17 Dec 2010 17:36:55 +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/17/t1292603812yc05dpn58qnw2e6.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 «

15 10 12 16 6 2 0 0 12 9 7 12 6 1 1 2 9 12 11 11 4 1 2 1 10 12 11 12 6 0 0 0 13 9 14 14 6 0 0 0 16 11 16 16 7 1 0 0 14 12 13 13 6 0 0 0 16 11 13 14 7 1 1 0 10 12 5 13 6 0 0 0 8 12 8 13 4 2 0 1 12 11 14 13 5 1 0 0 15 11 15 15 8 0 0 0 14 12 8 14 4 0 1 0 14 6 13 12 6 1 1 2 12 13 12 12 6 1 2 1 12 11 11 12 5 0 0 0 10 12 8 11 4 0 0 0 4 10 4 10 2 0 0 0 14 11 15 15 8 0 1 0 15 12 12 16 7 0 0 0 16 12 14 14 6 0 0 0 12 12 9 13 4 0 1 0 12 11 16 13 4 0 0 0 12 12 10 13 4 0 0 1 12 12 8 13 5 1 0 1 12 12 14 14 4 0 0 0 11 6 6 9 4 3 2 1 11 5 16 14 6 1 0 0 11 12 11 12 6 1 1 0 11 14 7 13 6 1 1 0 11 12 13 11 4 3 1 1 11 9 7 13 2 0 0 0 15 11 14 15 7 0 0 0 15 11 17 16 6 0 0 0 9 11 15 15 7 0 0 0 16 12 8 14 4 0 0 0 13 10 8 8 4 0 2 1 9 12 11 11 4 1 0 0 16 11 16 15 6 0 0 0 12 12 10 15 6 0 0 0 15 9 5 11 3 0 0 2 5 15 8 12 3 0 0 0 11 11 8 12 6 2 2 0 17 11 15 14 5 2 2 0 9 15 6 8 4 0 1 1 13 12 16 16 6 0 0 0 16 9 16 16 6 0 0 0 16 12 16 14 6 0 0 0 14 9 19 12 6 2 0 2 16 11 14 15 6 1 0 0 11 12 15 1 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 6 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation Popularity[t] = + 0.100276382934112 + 0.157263405271108FindingFriends[t] + 0.236372152928434KnowingPeople[t] + 0.323351350417035Liked[t] + 0.666471137832579Celebrity[t] -0.0593960178122206B[t] + 0.20312779537524`2B`[t] + 0.500771877991365`3B`[t] -0.104817868555572M1[t] -0.531890927774699M2[t] -0.906326361891386M3[t] -0.42086638214816M4[t] + 0.265856736325493M5[t] -1.09338003746871M6[t] -1.29051116073166M7[t] + 0.50770470226122M8[t] -0.960871026350095M9[t] -0.397549712140203M10[t] -0.768379620810554M11[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) 0.100276382934112 1.575466 0.0636 0.949343 0.474671 FindingFriends 0.157263405271108 0.101728 1.5459 0.124431 0.062216 KnowingPeople 0.236372152928434 0.06331 3.7336 0.000276 0.000138 Liked 0.323351350417035 0.101942 3.1719 0.001869 0.000935 Celebrity 0.666471137832579 0.164994 4.0394 8.9e-05 4.4e-05 B -0.0593960178122206 0.22941 -0.2589 0.796095 0.398048 `2B` 0.20312779537524 0.281529 0.7215 0.471822 0.235911 `3B` 0.500771877991365 0.340941 1.4688 0.144181 0.072091 M1 -0.104817868555572 0.842703 -0.1244 0.901194 0.450597 M2 -0.531890927774699 0.837472 -0.6351 0.526413 0.263207 M3 -0.906326361891386 0.841743 -1.0767 0.283495 0.141747 M4 -0.42086638214816 0.847106 -0.4968 0.620106 0.310053 M5 0.265856736325493 0.831778 0.3196 0.74974 0.37487 M6 -1.09338003746871 0.836023 -1.3078 0.193119 0.09656 M7 -1.29051116073166 0.850436 -1.5175 0.131452 0.065726 M8 0.50770470226122 0.853539 0.5948 0.552943 0.276471 M9 -0.960871026350095 0.843937 -1.1386 0.256875 0.128437 M10 -0.397549712140203 0.835074 -0.4761 0.634786 0.317393 M11 -0.768379620810554 0.838042 -0.9169 0.360819 0.18041 Multiple Linear Regression - Regression Statistics Multiple R 0.738146206087162 R-squared 0.544859821560871 Adjusted R-squared 0.485060382057919 F-TEST (value) 9.1114536539089 F-TEST (DF numerator) 18 F-TEST (DF denominator) 137 p-value 6.66133814775094e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.10730300856287 Sum Squared Residuals 608.379457876042 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 15 13.4582148002744 1.54178519972559 2 12 11.6626797386441 0.337320261355937 3 9 10.7515854233561 -1.75158542335612 4 10 12.0457075782519 -2.04570757825191 5 13 13.6164596405316 -0.616459640531612 6 16 14.2982718039909 1.70172819600908 7 14 11.9721584559423 2.02784154405769 8 16 14.7466651794767 1.25333482052328 9 10 10.4108213668964 -0.410821366896409 10 8 10.7322967065934 -2.73229670659337 11 12 11.8475315878759 0.152468412124053 12 15 15.557795493759 -0.557795493758962 13 14 11.1695278536034 2.83047214639665 14 14 12.6091224404013 1.39087755959866 15 12 12.8015146076379 -0.801514607637853 16 12 11.2219730351482 0.778026964851774 17 10 10.3670206118581 -0.367020611858071 18 4 6.09147478972572 -2.09147478972572 19 14 14.4704121284025 -0.47041212840254 20 15 15.1705273550904 -0.170527355090445 21 16 12.8615220936694 3.13847790633065 22 12 10.7898168125301 1.21018318746988 23 12 11.7132007737125 0.286799226287543 24 12 11.7213827602149 0.27861723978512 25 12 11.7508957058228 0.249104294177201 26 12 11.9575599165796 0.0424400834204132 27 11 7.86064949062879 3.13935050937121 28 11 12.7140311890182 -1.71403118901817 29 11 12.8761624742886 -1.87616247428859 30 11 11.2093152497399 -0.209315249739901 31 11 10.518225099373 0.481774900626972 32 11 9.21446663422095 1.78553336577905 33 15 13.6940811766479 1.30591882335215 34 15 14.6233991622275 0.376600837772497 35 9 14.1229447351158 -5.12294473511583 36 16 11.0712179267837 4.92878207321632 37 13 9.61879261392553 3.38120738607447 38 9 10.218993388731 -1.21899338873096 39 16 13.5548990091309 2.44510099086915 40 12 12.7793894765746 -0.779389476574584 41 15 9.5211865554096 5.47881344459041 42 5 9.13645426646165 -4.13645426646165 43 11 10.597146490738 0.402853509261961 44 17 14.0301989872315 2.96980101276855 45 9 8.87318438125444 0.126815618745559 46 13 14.5442904145702 -1.54429041457018 47 16 13.7016702900865 2.2983297099135 48 16 14.2951374258763 1.70486257412369 49 14 14.6636948198169 -0.663694819816935 50 16 13.3971941195785 2.60280588042155 51 11 12.5057362102224 -1.50573621022242 52 11 11.8686757359823 -0.868675735982295 53 11 14.1147234759694 -3.11472347596939 54 12 11.6183906157346 0.381609384265384 55 12 13.0894064173536 -1.08940641735356 56 12 13.1741873888851 -1.17418738888512 57 14 13.1145892363039 0.885410763696123 58 10 10.9692342642606 -0.969234264260633 59 9 9.25842508978436 -0.258425089784361 60 12 12.4846117254544 -0.484611725454421 61 10 10.3988061050514 -0.398806105051366 62 14 12.834452876094 1.16554712390603 63 8 9.44267685207114 -1.44267685207114 64 16 14.5683253612371 1.43167463876289 65 14 16.3459025095284 -2.34590250952838 66 14 10.1193603949235 3.88063960507647 67 12 10.4028440273487 1.59715597265128 68 14 14.3498105521258 -0.349810552125769 69 7 10.6235374819635 -3.62353748196349 70 19 13.9845669112247 5.01543308877529 71 15 12.3677739243778 2.6322260756222 72 8 11.7376890646163 -3.73768906461626 73 10 14.7490889706227 -4.74908897062267 74 13 13.0036142685323 -0.00361426853231367 75 13 10.7505653994844 2.24943460051561 76 10 10.5049861265316 -0.504986126531649 77 12 9.7875286715141 2.21247132848591 78 15 16.6892681443786 -1.68926814437861 79 7 10.3346234696617 -3.33462346966168 80 14 15.0559092707721 -1.05590927077206 81 10 8.09995459014887 1.90004540985113 82 6 9.76305267609099 -3.76305267609099 83 11 11.0544536717411 -0.0544536717410568 84 12 9.86479172260414 2.13520827739586 85 14 14.632139809958 -0.632139809958001 86 12 13.3190951691181 -1.31909516911807 87 14 13.9058892463777 0.094110753622328 88 11 9.9854101282601 1.01458987173991 89 10 10.0418478826802 -0.0418478826801826 90 13 12.749170204854 0.250829795146043 91 8 9.4494849658037 -1.44948496580371 92 9 12.7102676229031 -3.71026762290307 93 6 11.6560499795334 -5.65604997953335 94 12 13.2277757023603 -1.2277757023603 95 14 11.985082263302 2.01491773669805 96 11 10.89821362185 0.101786378149977 97 8 10.7136658937449 -2.71366589374489 98 7 9.22615316034233 -2.22615316034233 99 9 10.1471529489625 -1.14715294896246 100 14 12.259667856444 1.74033214355596 101 13 11.1204709471793 1.87952905282075 102 15 12.1692895792053 2.83071042079473 103 5 4.90664053546203 0.0933594645379717 104 15 13.2079516706985 1.79204832930148 105 13 11.8384552478665 1.16154475213346 106 12 11.5695951456168 0.430404854383241 107 6 7.46770165538778 -1.46770165538778 108 7 10.1881430730212 -3.18814307302118 109 13 8.94410976077616 4.05589023922384 110 16 14.9332641906188 1.06673580938115 111 10 12.8457825503456 -2.84578255034555 112 16 15.1874448823948 0.812555117605199 113 15 13.9231160012426 1.07688399875745 114 8 7.93885260215693 0.0611473978430705 115 11 11.5597085507878 -0.559708550787802 116 13 14.4077852771954 -1.40778527719541 117 16 14.667152968038 1.33284703196203 118 11 8.66020245706635 2.33979754293365 119 14 14.2454332692655 -0.245433269265491 120 9 10.560320846528 -1.56032084652795 121 8 10.4581464157102 -2.45814641571018 122 8 10.7541093361781 -2.75410933617805 123 11 11.343532468272 -0.343532468271953 124 12 13.3519650571308 -1.35196505713083 125 11 11.87270936418 -0.872709364179983 126 14 14.0206638313973 -0.0206638313973066 127 11 11.844687502302 -0.844687502302047 128 14 13.3324048841998 0.667595115800225 129 13 14.3410371676024 -1.34103716760242 130 12 10.8673950466192 1.13260495338081 131 4 5.96752687486148 -1.96752687486148 132 15 13.4541416962166 1.5458583037834 133 10 11.6131027590622 -1.61310275906218 134 13 13.9096319400772 -0.909631940077212 135 15 13.8249701387454 1.17502986125463 136 12 13.2681602404261 -1.26816024042611 137 13 14.0882498563449 -1.08824985634494 138 8 7.54924458129335 0.450755418706653 139 10 9.88328044923307 0.116719550766925 140 15 14.6455787228664 0.354421277133577 141 16 14.0450714138947 1.95492858610533 142 16 14.9743893994743 1.02561060052568 143 14 12.5900937332268 1.40990626677316 144 14 13.6629306694687 0.337069330531349 145 12 10.8298144916315 1.17018550836847 146 15 13.1741294551048 1.82587054489521 147 13 12.2650456547654 0.734954345234571 148 16 13.2442633326002 2.75573666739982 149 14 14.3246220092734 -0.324622009273371 150 8 9.41024393613823 -1.41024393613823 151 16 12.9713819075915 3.02861809240854 152 16 16.9542464543343 -0.954246454334277 153 12 12.7745428961807 -0.774542896180748 154 11 12.2939853013656 -1.29398530136558 155 16 15.6781621312625 0.321837868737497 156 9 10.5036239736069 -1.50362397360694 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 22 0.323786208970121 0.647572417940241 0.67621379102988 23 0.198177397469349 0.396354794938699 0.80182260253065 24 0.149863051390141 0.299726102780283 0.850136948609859 25 0.0961110260149067 0.192222052029813 0.903888973985093 26 0.195961037724433 0.391922075448866 0.804038962275567 27 0.336483767954478 0.672967535908955 0.663516232045522 28 0.379681503157996 0.759363006315991 0.620318496842004 29 0.380717951546443 0.761435903092886 0.619282048453557 30 0.296831171299768 0.593662342599537 0.703168828700232 31 0.229199644117799 0.458399288235597 0.770800355882201 32 0.178552350860857 0.357104701721715 0.821447649139143 33 0.13065102605307 0.26130205210614 0.86934897394693 34 0.0915350425122398 0.18307008502448 0.90846495748776 35 0.20053174405398 0.401063488107961 0.79946825594602 36 0.394900035811142 0.789800071622283 0.605099964188858 37 0.361869018688302 0.723738037376604 0.638130981311698 38 0.342066949724391 0.684133899448782 0.657933050275609 39 0.38607005002474 0.77214010004948 0.61392994997526 40 0.333397101271001 0.666794202542001 0.666602898728999 41 0.621330333419953 0.757339333160095 0.378669666580047 42 0.740339915761034 0.519320168477932 0.259660084238966 43 0.687405978808893 0.625188042382215 0.312594021191107 44 0.680095001737681 0.639809996524638 0.319904998262319 45 0.622781026795824 0.754437946408351 0.377218973204175 46 0.59141748857988 0.81716502284024 0.40858251142012 47 0.594084544590765 0.811830910818469 0.405915455409235 48 0.548737836029669 0.902524327940662 0.451262163970331 49 0.519180899919437 0.961638200161127 0.480819100080563 50 0.561312739682893 0.877374520634215 0.438687260317108 51 0.515894147560252 0.968211704879496 0.484105852439748 52 0.469586952950472 0.939173905900945 0.530413047049528 53 0.710443374086939 0.579113251826123 0.289556625913061 54 0.67923499827972 0.641530003440561 0.320765001720281 55 0.648880044245457 0.702239911509086 0.351119955754543 56 0.608676855808446 0.782646288383107 0.391323144191554 57 0.570615405681939 0.858769188636122 0.429384594318061 58 0.526509114058141 0.946981771883718 0.473490885941859 59 0.474102407439848 0.948204814879696 0.525897592560152 60 0.510421893827865 0.97915621234427 0.489578106172135 61 0.480446035485245 0.96089207097049 0.519553964514755 62 0.439403451722482 0.878806903444964 0.560596548277518 63 0.401920933884559 0.803841867769118 0.598079066115441 64 0.399032709060042 0.798065418120083 0.600967290939958 65 0.429050361096252 0.858100722192503 0.570949638903748 66 0.5549283365334 0.890143326933201 0.445071663466601 67 0.523609840280777 0.952780319438446 0.476390159719223 68 0.472987052619486 0.945974105238973 0.527012947380514 69 0.654607773620145 0.69078445275971 0.345392226379855 70 0.823908630916631 0.352182738166738 0.176091369083369 71 0.835886132041156 0.328227735917688 0.164113867958844 72 0.896528124400598 0.206943751198805 0.103471875599402 73 0.967267822148519 0.0654643557029626 0.0327321778514813 74 0.956531634055944 0.0869367318881115 0.0434683659440557 75 0.953791026213446 0.0924179475731086 0.0462089737865543 76 0.941879999945265 0.11624000010947 0.0581200000547348 77 0.944198805898018 0.111602388203964 0.0558011941019821 78 0.941781513592634 0.116436972814732 0.0582184864073662 79 0.965742578495343 0.0685148430093132 0.0342574215046566 80 0.957493799151066 0.0850124016978676 0.0425062008489338 81 0.9617364261034 0.0765271477931981 0.0382635738965991 82 0.984655822673408 0.0306883546531838 0.0153441773265919 83 0.979598767899615 0.0408024642007709 0.0204012321003854 84 0.982230332428989 0.0355393351420223 0.0177696675710111 85 0.977078983804692 0.0458420323906168 0.0229210161953084 86 0.972338743576207 0.055322512847587 0.0276612564237935 87 0.96307419146394 0.0738516170721186 0.0369258085360593 88 0.957132415764648 0.0857351684707041 0.042867584235352 89 0.95229660547926 0.0954067890414813 0.0477033945207406 90 0.937710250321273 0.124579499357455 0.0622897496787274 91 0.928252920939812 0.143494158120376 0.0717470790601879 92 0.949666456406607 0.100667087186785 0.0503335435933926 93 0.993098667797613 0.0138026644047735 0.00690133220238673 94 0.992537120371463 0.0149257592570737 0.00746287962853684 95 0.991380026397147 0.0172399472057061 0.00861997360285305 96 0.988940670402795 0.0221186591944098 0.0110593295972049 97 0.992269810918166 0.0154603781636682 0.00773018908183411 98 0.991610291485868 0.0167794170282634 0.00838970851413171 99 0.988966881784174 0.0220662364316526 0.0110331182158263 100 0.985705647743316 0.0285887045133674 0.0142943522566837 101 0.990727092538387 0.0185458149232253 0.00927290746161265 102 0.991572259887247 0.0168554802255069 0.00842774011275347 103 0.988604291002227 0.0227914179955469 0.0113957089977735 104 0.987023136191883 0.0259537276162336 0.0129768638081168 105 0.984184437498218 0.0316311250035646 0.0158155625017823 106 0.978283414954385 0.0434331700912301 0.021716585045615 107 0.970961546161185 0.0580769076776291 0.0290384538388145 108 0.977099354499593 0.0458012910008136 0.0229006455004068 109 0.996053221047057 0.00789355790588693 0.00394677895294347 110 0.994850677856218 0.0102986442875637 0.00514932214378185 111 0.998032013693346 0.0039359726133082 0.0019679863066541 112 0.99674425131662 0.00651149736675871 0.00325574868337935 113 0.995998354945618 0.00800329010876354 0.00400164505438177 114 0.993237243750193 0.0135255124996137 0.00676275624980684 115 0.9899651489014 0.0200697021972018 0.0100348510986009 116 0.984385831565707 0.0312283368685855 0.0156141684342927 117 0.979967684727494 0.0400646305450116 0.0200323152725058 118 0.986632285117811 0.0267354297643771 0.0133677148821886 119 0.97958092075763 0.0408381584847393 0.0204190792423697 120 0.969442057697838 0.061115884604324 0.030557942302162 121 0.969029055492585 0.0619418890148293 0.0309709445074146 122 0.95671267376444 0.0865746524711214 0.0432873262355607 123 0.943033813267005 0.113932373465989 0.0569661867329947 124 0.967809026146156 0.0643819477076885 0.0321909738538443 125 0.95642240861324 0.0871551827735214 0.0435775913867607 126 0.928827684892496 0.142344630215008 0.0711723151075038 127 0.903779695915307 0.192440608169386 0.096220304084693 128 0.862879597584109 0.274240804831783 0.137120402415891 129 0.827821751134548 0.344356497730905 0.172178248865452 130 0.851672376148246 0.296655247703508 0.148327623851754 131 0.785788146275578 0.428423707448844 0.214211853724422 132 0.750035187748658 0.499929624502684 0.249964812251342 133 0.982769413527077 0.0344611729458458 0.0172305864729229 134 0.973379412686258 0.0532411746274847 0.0266205873137423 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 4 0.0353982300884956 NOK 5% type I error level 31 0.274336283185841 NOK 10% type I error level 48 0.424778761061947 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292603812yc05dpn58qnw2e6/105gu21292603748.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292603812yc05dpn58qnw2e6/105gu21292603748.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292603812yc05dpn58qnw2e6/1gfx91292603748.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292603812yc05dpn58qnw2e6/1gfx91292603748.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292603812yc05dpn58qnw2e6/2qowt1292603748.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292603812yc05dpn58qnw2e6/2qowt1292603748.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292603812yc05dpn58qnw2e6/3qowt1292603748.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292603812yc05dpn58qnw2e6/3qowt1292603748.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292603812yc05dpn58qnw2e6/4qowt1292603748.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292603812yc05dpn58qnw2e6/4qowt1292603748.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292603812yc05dpn58qnw2e6/5qowt1292603748.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292603812yc05dpn58qnw2e6/5qowt1292603748.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292603812yc05dpn58qnw2e6/61ydw1292603748.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292603812yc05dpn58qnw2e6/61ydw1292603748.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292603812yc05dpn58qnw2e6/7upvh1292603748.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292603812yc05dpn58qnw2e6/7upvh1292603748.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292603812yc05dpn58qnw2e6/8upvh1292603748.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292603812yc05dpn58qnw2e6/8upvh1292603748.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292603812yc05dpn58qnw2e6/9upvh1292603748.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292603812yc05dpn58qnw2e6/9upvh1292603748.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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') }

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