*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: Wed, 24 Nov 2010 08:59:08 +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/24/t1290589194v6qn89wnz6t5jyo.htm/, Retrieved Wed, 24 Nov 2010 10:00:06 +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/24/t1290589194v6qn89wnz6t5jyo.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 «

13 13 14 13 12 12 8 13 15 10 12 16 12 9 7 12 10 10 10 11 12 12 7 12 15 13 16 18 9 12 11 11 12 12 14 14 11 6 6 9 11 5 16 14 11 12 11 12 15 11 16 11 7 14 12 12 11 14 7 13 11 12 13 11 10 12 11 12 14 11 15 16 10 11 7 9 6 7 9 11 11 9 7 13 15 11 14 15 11 11 15 10 12 12 7 11 14 12 15 13 15 11 17 16 9 11 15 15 13 8 14 14 13 9 14 14 16 12 8 14 13 10 8 8 12 10 14 13 14 12 14 15 11 8 8 13 9 12 11 11 16 11 16 15 12 12 10 15 10 7 8 9 13 11 14 13 16 11 16 16 14 12 13 13 15 9 5 11 5 15 8 12 8 11 10 12 11 11 8 12 16 11 13 14 17 11 15 14 9 15 6 8 9 11 12 13 13 12 16 16 10 12 5 13 6 9 15 11 12 12 12 14 8 12 8 13 14 13 13 13 12 11 14 13 11 9 12 12 16 9 16 16 8 11 10 15 15 11 15 15 7 12 8 12 16 12 16 14 14 9 19 12 16 11 14 15 9 9 6 12 14 12 13 13 11 12 15 12 13 12 7 12 15 12 13 13 5 14 4 5 15 11 14 13 13 12 13 13 11 11 11 14 11 6 14 17 12 10 12 13 12 12 15 13 12 13 14 12 12 8 13 13 14 12 8 14 6 12 6 11 7 12 7 12 14 6 13 12 14 11 13 16 10 10 11 12 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 popularity[t] = + 0.630092326762164 + 0.0911674453868626finding[t] + 0.341648642438405knowing[t] + 0.48873661315285liked[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) 0.630092326762164 1.492032 0.4223 0.673399 0.3367 finding 0.0911674453868626 0.100623 0.906 0.366354 0.183177 knowing 0.341648642438405 0.059082 5.7827 0 0 liked 0.48873661315285 0.094366 5.1792 1e-06 0 Multiple Linear Regression - Regression Statistics Multiple R 0.667556284783105 R-squared 0.445631393353423 Adjusted R-squared 0.434689907695924 F-TEST (value) 40.7286000551516 F-TEST (DF numerator) 3 F-TEST (DF denominator) 152 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.20796509448368 Sum Squared Residuals 741.016698485668 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 12.9519260819160 0.0480739180839669 2 12 10.8108667818988 1.1891332181012 3 15 13.4613363003372 1.53866369966277 4 12 9.70697919014695 2.29302080985305 5 10 10.3343559496962 -0.334355949696189 6 12 9.98048152630755 2.01951847369245 7 15 16.0789064325572 -1.07890643255715 8 9 10.8583394829083 -1.85833948290832 9 12 13.3494952496821 -1.34949524968208 10 11 7.62561837208942 3.37438162791058 11 11 13.3946204168509 -2.39462041685085 12 11 11.3470760960612 -0.347076096061168 13 15 12.4754152497135 2.52458475028652 14 7 11.8710596292733 -4.8710596292733 15 11 10.6515530302341 0.348446969765875 16 11 11.5416367677851 -0.541636767785127 17 10 11.3470760960612 -1.34707609606117 18 14 14.5774496730393 -0.577449673039323 19 10 8.42310424146214 1.57689575853786 20 6 9.7192049710972 -3.7192049710972 21 11 10.1957158032998 0.804284196700187 22 15 13.7470644174481 1.25293558255193 23 11 11.6450299941222 -0.645029994122223 24 12 9.4917449131547 2.5082550868453 25 14 13.2024072789676 0.797592721032365 26 15 15.2607469579161 -0.260746957916132 27 9 14.0887130598865 -5.08871305988647 28 13 12.9848254681346 0.0151745318653686 29 13 13.0759929135215 -0.0759929135214936 30 16 11.2996033950517 4.70039660494834 31 13 8.18484882536083 4.81515117463917 32 12 12.6784237457555 -0.678423745755506 33 14 13.8382318628349 0.161768137165069 34 11 10.4461970003514 0.553802999648645 35 9 10.8583394829083 -1.85833948290832 36 16 14.4303617023249 1.56963829767512 37 12 12.4716372930813 -0.471637293081313 38 10 8.4000831023531 1.59991689764691 39 13 12.7695911911424 0.230408808857631 40 16 14.9190983154777 1.08090168452227 41 14 12.5191099940908 1.48089000590917 42 15 8.5349452921173 6.4650547078827 43 5 10.5956325049065 -5.59563250490654 44 8 10.9142600082359 -2.9142600082359 45 11 10.2309627233591 0.769037276640908 46 16 12.9166791618568 3.08332083814319 47 17 13.5999764467336 3.40002355326638 48 9 7.95738876741833 1.04261123258167 49 9 12.0862939062656 -3.08629390626556 50 13 15.0102657608646 -2.01026576086459 51 10 9.7859208545836 0.214079145416408 52 6 11.9514317165013 -5.95143171650135 53 12 12.6661979648053 -0.666197964805272 54 8 10.8108667818988 -2.81086678189880 55 14 12.6102774394777 1.38972256052231 56 12 12.7695911911424 -0.769591191142369 57 11 11.4152224023390 -0.415222402338985 58 16 14.736763424704 1.26323657529600 59 8 12.3804698476945 -4.38046984769445 60 15 14.0887130598865 0.911286940113527 61 7 10.3221301687460 -3.32213016874595 62 16 14.0327925345589 1.96720746544111 63 14 13.8067628994078 0.193237100592184 64 16 13.7470644174481 2.25293558255193 65 9 9.36533054770856 -0.365330547708559 66 14 12.5191099940908 1.48089000590917 67 11 12.7136706658148 -1.71367066581479 68 13 9.98048152630755 3.01951847369245 69 15 12.5191099940908 2.48089000590917 70 5 5.71671419769611 -0.716714197696112 71 15 12.7695911911424 2.23040880885763 72 13 12.5191099940908 0.480890005909173 73 11 12.23338187698 -1.23338187698001 74 11 14.2687004168195 -3.26870041681946 75 12 11.9951264608787 0.00487353912130259 76 12 13.2024072789676 -1.20240727896764 77 12 12.4631894687632 -0.463189468763243 78 12 12.1544402125434 -0.154440212543377 79 14 11.2996033950517 2.70039660494835 80 6 9.1500962707163 -3.15009627071630 81 7 9.98048152630755 -2.98048152630755 82 14 11.4833687086168 2.5166312913832 83 14 13.8941523881625 0.105847611837486 84 10 11.1647412052874 -1.16474120528744 85 13 9.29718424143074 3.70281575856926 86 12 11.7798921838864 0.220107816113565 87 9 9.2534894970534 -0.253489497053393 88 12 12.3574487085854 -0.357448708585405 89 16 13.7470644174481 2.25293558255193 90 10 10.5726113657975 -0.572611365797496 91 14 12.8692064608473 1.1307935391527 92 10 13.4054157750097 -3.40541577500966 93 16 15.0102657608646 0.98973423913541 94 15 13.3617210306323 1.63827896936768 95 12 11.2559086506743 0.744091349325694 96 10 9.8333935555931 0.166606444406895 97 8 8.98843498521087 -0.988434985210874 98 8 9.09417574538871 -1.09417574538871 99 11 13.4735620812875 -2.47356208128748 100 13 11.8358127092140 1.16418729078598 101 16 15.2607469579161 0.739253042083868 102 16 14.1798805052733 1.82011949472666 103 14 16.5117225203824 -2.51172252038242 104 11 9.60358596380987 1.39641403619013 105 4 7.79572748191291 -3.79572748191291 106 14 13.0515413516210 0.948458648378974 107 9 11.6534778184403 -2.65347781844029 108 14 14.0887130598865 -0.088713059886473 109 8 11.8005657891547 -3.80056578915474 110 8 11.6741514237086 -3.6741514237086 111 11 12.4838630740315 -1.48386307403155 112 12 12.8377374974202 -0.837737497420186 113 11 10.4692181394604 0.5307818605396 114 14 13.4965832203965 0.503416779603474 115 15 13.6436711911110 1.35632880888903 116 16 13.2583278042952 2.74167219570478 117 16 13.3494952496821 2.65050475031792 118 11 12.2770766213574 -1.27707662135735 119 14 13.6911438921205 0.308856107879515 120 14 11.5975572931127 2.40244270688729 121 12 12.1774613516524 -0.177461351652422 122 14 12.9641518628663 1.03584813713367 123 8 10.5726113657975 -2.57261136579750 124 13 13.7823113375073 -0.782311337507348 125 16 13.6911438921205 2.30885610787951 126 12 10.6163061101748 1.38369388982515 127 16 14.3269684759878 1.67303152401222 128 12 13.2024072789676 -1.20240727896764 129 11 11.6182308983810 -0.618230898381014 130 4 5.3642701970989 -1.36427019709890 131 16 14.3269684759878 1.67303152401222 132 15 12.0862939062656 2.91370609373444 133 10 12.2770766213574 -2.27707662135735 134 13 12.9044533809066 0.09554661909342 135 15 13.0078466072437 1.99215339275632 136 12 11.1525154243372 0.847484575662791 137 14 13.5999764467336 0.400023553266377 138 7 12.0303733809380 -5.03037338093798 139 19 14.1798805052733 4.82011949472666 140 12 13.1671603589084 -1.16716035890836 141 12 13.4528884760192 -1.45288847601918 142 13 13.3494952496821 -0.349495249682081 143 15 14.3269684759878 0.673031524012219 144 8 7.89067288393194 0.109327116068061 145 12 11.4941640667756 0.505835933224387 146 10 9.53543965753205 0.464560342467951 147 8 11.2996033950517 -3.29960339505165 148 10 14.4533828414339 -4.45338284143392 149 15 13.9416250891720 1.05837491082797 150 16 13.1549345779581 2.84506542204188 151 13 12.0862939062656 0.91370609373444 152 16 14.6686171184262 1.33138288157381 153 9 10.5726113657975 -1.57261136579750 154 14 12.9725996871844 1.02740031281560 155 14 12.2808545779895 1.71914542201048 156 12 12.23338187698 -0.233381876980005 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.086201880935124 0.172403761870248 0.913798119064876 8 0.0833522204081176 0.166704440816235 0.916647779591882 9 0.0360808192587593 0.0721616385175186 0.96391918074124 10 0.0219291507697497 0.0438583015394995 0.97807084923025 11 0.020940230221166 0.041880460442332 0.979059769778834 12 0.00880623720360763 0.0176124744072153 0.991193762796392 13 0.198379266507272 0.396758533014543 0.801620733492728 14 0.526411535169698 0.947176929660603 0.473588464830302 15 0.434357733359196 0.868715466718391 0.565642266640804 16 0.348412761424439 0.696825522848877 0.651587238575561 17 0.293882402179742 0.587764804359484 0.706117597820258 18 0.226225051465612 0.452450102931224 0.773774948534388 19 0.174172417301069 0.348344834602138 0.825827582698931 20 0.437433438164969 0.874866876329939 0.56256656183503 21 0.365951007473965 0.73190201494793 0.634048992526035 22 0.348472024037108 0.696944048074216 0.651527975962892 23 0.287922798627498 0.575845597254996 0.712077201372502 24 0.272788762242382 0.545577524484764 0.727211237757618 25 0.248950671465902 0.497901342931805 0.751049328534098 26 0.203478639842294 0.406957279684587 0.796521360157706 27 0.390186419496689 0.780372838993378 0.609813580503311 28 0.333347992813808 0.666695985627616 0.666652007186192 29 0.279610034577421 0.559220069154842 0.720389965422579 30 0.416709864125572 0.833419728251145 0.583290135874428 31 0.566320954354563 0.867358091290874 0.433679045645437 32 0.507952219671794 0.984095560656412 0.492047780328206 33 0.455369951046781 0.910739902093563 0.544630048953219 34 0.404162576788001 0.808325153576003 0.595837423211999 35 0.399941413116693 0.799882826233385 0.600058586883307 36 0.417194699123449 0.834389398246899 0.582805300876551 37 0.371859735161688 0.743719470323377 0.628140264838312 38 0.332054934625048 0.664109869250095 0.667945065374952 39 0.286999458544914 0.573998917089828 0.713000541455086 40 0.274363034773185 0.54872606954637 0.725636965226815 41 0.254531737551611 0.509063475103223 0.745468262448389 42 0.50573444837906 0.98853110324188 0.49426555162094 43 0.818823224136912 0.362353551726177 0.181176775863088 44 0.853132498553995 0.293735002892010 0.146867501446005 45 0.824967582815225 0.35006483436955 0.175032417184775 46 0.85908501442819 0.281829971143619 0.140914985571809 47 0.903785606999456 0.192428786001088 0.096214393000544 48 0.884828655839032 0.230342688321935 0.115171344160968 49 0.907437340266227 0.185125319467546 0.0925626597337728 50 0.900298501156844 0.199402997686312 0.099701498843156 51 0.88183370410319 0.236332591793621 0.118166295896811 52 0.97014316906413 0.0597136618717391 0.0298568309358696 53 0.961760656356331 0.0764786872873383 0.0382393436436691 54 0.970880407675343 0.0582391846493136 0.0291195923246568 55 0.967606540734937 0.0647869185301267 0.0323934592650633 56 0.958906173288762 0.0821876534224754 0.0410938267112377 57 0.947734755858905 0.104530488282190 0.0522652441410948 58 0.939887384998697 0.120225230002607 0.0601126150013035 59 0.974062637622457 0.0518747247550859 0.0259373623775429 60 0.968568209337054 0.0628635813258914 0.0314317906629457 61 0.978669772123905 0.0426604557521899 0.0213302278760949 62 0.979127931114817 0.0417441377703654 0.0208720688851827 63 0.973037272586346 0.0539254548273081 0.0269627274136541 64 0.97379276946177 0.0524144610764606 0.0262072305382303 65 0.967735288354832 0.0645294232903366 0.0322647116451683 66 0.963197136820467 0.0736057263590658 0.0368028631795329 67 0.959512290013635 0.0809754199727297 0.0404877099863649 68 0.968010771469781 0.0639784570604377 0.0319892285302189 69 0.970552088242013 0.0588958235159738 0.0294479117579869 70 0.962901950788636 0.0741960984227287 0.0370980492113644 71 0.963466298217235 0.0730674035655295 0.0365337017827647 72 0.953737438816679 0.0925251223666425 0.0462625611833212 73 0.945610146749026 0.108779706501948 0.0543898532509738 74 0.960652083615915 0.0786958327681696 0.0393479163840848 75 0.949645850327103 0.100708299345794 0.0503541496728972 76 0.941199441695723 0.117601116608553 0.0588005583042766 77 0.927444103107724 0.145111793784552 0.0725558968922762 78 0.91002853352596 0.179942932948081 0.0899714664740406 79 0.921637935733515 0.156724128532970 0.0783620642664848 80 0.937127041202154 0.125745917595693 0.0628729587978463 81 0.947463344495757 0.105073311008486 0.0525366555042432 82 0.954946685838749 0.0901066283225025 0.0450533141612513 83 0.942699416416632 0.114601167166736 0.0573005835833679 84 0.931777089740177 0.136445820519646 0.0682229102598231 85 0.960978398724827 0.0780432025503467 0.0390216012751733 86 0.950105792355086 0.0997884152898288 0.0498942076449144 87 0.937286606846272 0.125426786307456 0.0627133931537278 88 0.922737257177036 0.154525485645928 0.0772627428229642 89 0.923948093360448 0.152103813279104 0.0760519066395522 90 0.906467519723498 0.187064960553004 0.0935324802765019 91 0.893323471854008 0.213353056291984 0.106676528145992 92 0.922977802782124 0.154044394435751 0.0770221972178756 93 0.907810945108188 0.184378109783624 0.0921890548918118 94 0.898255421667261 0.203489156665479 0.101744578332739 95 0.87894578465289 0.242108430694217 0.121054215347109 96 0.85399738855818 0.292005222883639 0.146002611441820 97 0.836055360115174 0.327889279769652 0.163944639884826 98 0.810798512523365 0.378402974953269 0.189201487476635 99 0.813216376429652 0.373567247140695 0.186783623570348 100 0.789748538887547 0.420502922224905 0.210251461112453 101 0.755731789070371 0.488536421859258 0.244268210929629 102 0.73813188542655 0.523736229146899 0.261868114573449 103 0.789239075131679 0.421521849736642 0.210760924868321 104 0.799981778337964 0.400036443324073 0.200018221662036 105 0.827291963653987 0.345416072692026 0.172708036346013 106 0.799273159693544 0.401453680612912 0.200726840306456 107 0.807495188954656 0.385009622090688 0.192504811045344 108 0.772248961466905 0.455502077066191 0.227751038533095 109 0.833235847269117 0.333528305461765 0.166764152730883 110 0.890305744683313 0.219388510633374 0.109694255316687 111 0.885873914094556 0.228252171810888 0.114126085905444 112 0.886247944045492 0.227504111909015 0.113752055954508 113 0.865821099854971 0.268357800290057 0.134178900145029 114 0.834878590877945 0.330242818244111 0.165121409122055 115 0.807071744737087 0.385856510525826 0.192928255262913 116 0.809362125542888 0.381275748914225 0.190637874457112 117 0.820635233142559 0.358729533714882 0.179364766857441 118 0.796367607281125 0.407264785437749 0.203632392718875 119 0.75388772424975 0.492224551500501 0.246112275750251 120 0.765319316053459 0.469361367893082 0.234680683946541 121 0.71818222149935 0.5636355570013 0.28181777850065 122 0.674304466635128 0.651391066729745 0.325695533364872 123 0.684414808519145 0.63117038296171 0.315585191480855 124 0.634315333055595 0.73136933388881 0.365684666944405 125 0.631874304977187 0.736251390045627 0.368125695022813 126 0.609068476976629 0.781863046046741 0.390931523023370 127 0.568248168962381 0.863503662075238 0.431751831037619 128 0.523833537227549 0.952332925544901 0.476166462772451 129 0.527793870692623 0.944412258614753 0.472206129307377 130 0.476249175923816 0.952498351847633 0.523750824076184 131 0.43089222550058 0.86178445100116 0.56910777449942 132 0.457070589332974 0.914141178665949 0.542929410667026 133 0.487302341380377 0.974604682760754 0.512697658619623 134 0.420088764016329 0.840177528032657 0.579911235983671 135 0.41306173325581 0.82612346651162 0.58693826674419 136 0.364971408744657 0.729942817489314 0.635028591255343 137 0.296606070051064 0.593212140102128 0.703393929948936 138 0.502775285713216 0.994449428573568 0.497224714286784 139 0.805469354418959 0.389061291162082 0.194530645581041 140 0.829249127753443 0.341501744493114 0.170750872246557 141 0.82786786808849 0.344264263823021 0.172132131911510 142 0.758957973033748 0.482084053932503 0.241042026966252 143 0.674687264658509 0.650625470682983 0.325312735341491 144 0.573507106201103 0.852985787597794 0.426492893798897 145 0.48517114090760 0.97034228181520 0.5148288590924 146 0.731009514682407 0.537980970635187 0.268990485317593 147 0.662541212845265 0.674917574309471 0.337458787154735 148 0.856244589250297 0.287510821499406 0.143755410749703 149 0.767132523061463 0.465734953877073 0.232867476938537 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 5 0.0349650349650350 OK 10% type I error level 27 0.188811188811189 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290589194v6qn89wnz6t5jyo/10rrb01290589137.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290589194v6qn89wnz6t5jyo/10rrb01290589137.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290589194v6qn89wnz6t5jyo/1l8e71290589137.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290589194v6qn89wnz6t5jyo/1l8e71290589137.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290589194v6qn89wnz6t5jyo/2l8e71290589137.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290589194v6qn89wnz6t5jyo/2l8e71290589137.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290589194v6qn89wnz6t5jyo/3dhdr1290589137.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290589194v6qn89wnz6t5jyo/3dhdr1290589137.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290589194v6qn89wnz6t5jyo/4dhdr1290589137.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290589194v6qn89wnz6t5jyo/4dhdr1290589137.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290589194v6qn89wnz6t5jyo/5dhdr1290589137.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290589194v6qn89wnz6t5jyo/5dhdr1290589137.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290589194v6qn89wnz6t5jyo/66ruu1290589137.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290589194v6qn89wnz6t5jyo/66ruu1290589137.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290589194v6qn89wnz6t5jyo/7y0ux1290589137.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290589194v6qn89wnz6t5jyo/7y0ux1290589137.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290589194v6qn89wnz6t5jyo/8y0ux1290589137.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290589194v6qn89wnz6t5jyo/8y0ux1290589137.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290589194v6qn89wnz6t5jyo/9y0ux1290589137.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290589194v6qn89wnz6t5jyo/9y0ux1290589137.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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') }

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