ws 7

*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, 23 Nov 2010 18:46:25 +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/23/t12905378826xof9dbomza62ea.htm/, Retrieved Tue, 23 Nov 2010 19:44:46 +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/23/t12905378826xof9dbomza62ea.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

9 26 24 14 11 12 24 9 23 25 11 7 8 25 9 25 17 6 17 8 30 9 23 18 12 10 8 19 9 19 18 8 12 9 22 10 29 16 10 12 7 22 10 25 20 10 11 4 25 10 21 16 11 11 11 23 10 22 18 16 12 7 17 10 25 17 11 13 7 21 10 24 23 13 14 12 19 10 18 30 12 16 10 19 10 22 23 8 11 10 15 10 15 18 12 10 8 16 10 22 15 11 11 8 23 10 28 12 4 15 4 27 10 20 21 9 9 9 22 10 12 15 8 11 8 14 10 24 20 8 17 7 22 10 20 31 14 17 11 23 10 21 27 15 11 9 23 10 20 34 16 18 11 21 10 21 21 9 14 13 19 10 23 31 14 10 8 18 10 28 19 11 11 8 20 10 24 16 8 15 9 23 10 24 20 9 15 6 25 10 24 21 9 13 9 19 10 23 22 9 16 9 24 10 23 17 9 13 6 22 10 29 24 10 9 6 25 10 24 25 16 18 16 26 10 18 26 11 18 5 29 10 25 25 8 12 7 32 10 21 17 9 17 9 25 10 26 32 16 9 6 29 10 22 33 11 9 6 28 10 22 13 16 12 5 17 10 22 32 12 18 12 28 10 23 25 12 12 7 29 10 30 29 14 18 10 26 10 23 22 9 14 9 25 10 17 18 10 15 8 14 10 23 17 9 16 5 25 10 23 20 10 10 8 26 10 25 15 12 11 8 20 10 24 20 14 14 10 18 10 24 33 14 9 6 32 10 23 29 10 12 8 25 10 21 23 14 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 8 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation Parameter[t] = + 6.67822358754462 + 1.09089428266741Variable[t] -0.0608903034875088S.D.[t] + 0.214416815593605`T-STAT`[t] -0.142213186036547`2-tail`[t] -0.24081553440865`1-tail`[t] + 0.399817197705633MultipleLinearRegression[t] -0.0160680246338639t + 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) 6.67822358754462 16.640062 0.4013 0.688742 0.344371 Variable 1.09089428266741 1.669545 0.6534 0.514487 0.257243 S.D. -0.0608903034875088 0.062235 -0.9784 0.329444 0.164722 `T-STAT` 0.214416815593605 0.11107 1.9305 0.055423 0.027711 `2-tail` -0.142213186036547 0.103898 -1.3688 0.173102 0.086551 `1-tail` -0.24081553440865 0.129923 -1.8535 0.065759 0.03288 MultipleLinearRegression 0.399817197705633 0.075551 5.292 0 0 t -0.0160680246338639 0.006317 -2.5438 0.011971 0.005986 Multiple Linear Regression - Regression Statistics Multiple R 0.504343958942387 R-squared 0.25436282892168 Adjusted R-squared 0.219796867348513 F-TEST (value) 7.3587661776242 F-TEST (DF numerator) 7 F-TEST (DF denominator) 151 p-value 1.34744991164837e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.44924263771775 Sum Squared Residuals 1796.48849085137 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 26 23.1621535271571 2.83784647284294 2 23 24.3738768317413 -1.3738768317413 3 25 24.3498012852022 0.650198714797821 4 23 22.1568469781363 0.843153021863694 5 19 21.9573213777632 -2.95732137776317 6 29 24.0643929427763 4.93560705722375 7 25 25.8688750865717 -0.86887508657174 8 21 23.8254419552097 -2.82544195520971 9 22 23.1818231669331 -1.18182316693311 10 25 23.6116169726047 1.38838302739529 11 24 21.5131155047419 2.48688449525806 12 18 21.0536032368461 -3.05360323684612 13 22 19.7178972136106 2.28210278638941 14 15 21.8876094213482 -6.88760942134818 15 22 24.4963026894861 -2.49630268948612 16 28 25.1556660504705 2.84433394952951 17 20 23.3137848280649 -3.31378482806494 18 12 20.206493389453 -8.20649338945301 19 24 22.472047847216 1.52795215278396 20 20 22.5092424378522 -2.50924243785224 21 21 24.2860626277986 -3.2860626277986 22 20 21.7814215278614 -1.78142152786138 23 21 20.3435970193275 0.656402980672482 24 23 22.1638232562704 0.836176743729601 25 28 22.8926096360805 5.10739036391946 26 24 22.8057453896905 1.19425461030955 27 24 24.2826139653374 -0.282613965337373 28 24 21.3687322198293 2.63126778017065 29 23 22.8642203221265 0.135779677873502 30 23 23.5020555808545 -0.502055580854503 31 29 25.0424765846648 3.95752341533523 32 24 22.9637623293952 1.03623767060476 33 18 25.6631423949179 -7.66314239491789 34 25 26.6358138675096 -1.6358138675096 35 21 23.3298677034299 -2.32986770342994 36 26 27.3607837179795 -1.36078371797954 37 22 25.8119241141845 -3.81192411418451 38 22 23.5019330388059 -1.5019330388059 39 22 23.3302833032171 -1.33028330321707 40 23 26.1976213889639 -3.19762138896394 41 30 23.5916484690051 6.40835153099488 42 23 23.339579571665 -0.339579571664994 43 17 19.4821027501849 -2.48210275018491 44 23 24.2907308053963 -1.29073080539632 45 23 24.8370583965925 -1.8370583965925 46 25 23.013159148313 1.98684085168696 47 24 21.4135682150906 2.58643178490936 48 24 27.8776950808154 -3.87769508081536 49 23 23.5405299968907 -0.540529996890733 50 21 24.2772206597823 -3.27722065978226 51 24 26.1366857961263 -2.13668579612633 52 24 22.3484336549356 1.6515663450644 53 28 22.0251846412147 5.97481535878531 54 16 21.5169173509197 -5.5169173509197 55 20 20.4789198645736 -0.478919864573648 56 29 23.8541579839914 5.1458420160086 57 27 24.238035121938 2.76196487806198 58 22 23.4951552848874 -1.49515528488743 59 28 24.2466109377594 3.75338906224063 60 16 20.8090179954004 -4.80901799540038 61 25 23.2233477954266 1.77665220457342 62 24 23.7583687896257 0.241631210374307 63 28 23.9098862827089 4.09011371729114 64 24 24.5407734245581 -0.540773424558093 65 23 22.9061139720403 0.0938860279597222 66 30 27.029779741278 2.97022025872196 67 24 21.6434529082386 2.3565470917614 68 21 24.2871449575035 -3.28714495750352 69 25 23.447380275401 1.55261972459896 70 25 24.1077442125973 0.892255787402678 71 22 21.0608196731265 0.93918032687349 72 23 22.6336379512891 0.366362048710895 73 26 23.0117695894899 2.98823041051014 74 23 21.8355533441557 1.16444665584434 75 25 23.1460069619869 1.85399303801315 76 21 21.4729491641733 -0.472949164173296 77 25 23.6626865172753 1.33731348272467 78 24 22.2658198419973 1.73418015800268 79 29 23.5810179005989 5.41898209940106 80 22 23.6571462351028 -1.65714623510282 81 27 23.6255180370527 3.37448196294728 82 26 19.7660868643529 6.23391313564712 83 22 21.3690568461563 0.630943153843704 84 24 22.0468444219424 1.95315557805762 85 27 23.0774863545094 3.92251364549055 86 24 21.3204291306657 2.67957086933426 87 24 24.6815444756721 -0.681544475672105 88 29 24.251013710068 4.74898628993204 89 22 22.1734213910241 -0.173421391024074 90 21 20.532921974541 0.467078025459013 91 24 20.4230471813872 3.57695281861276 92 24 21.5860172526589 2.41398274734108 93 23 21.7900762536225 1.20992374637753 94 20 22.0992409303702 -2.09924093037018 95 27 21.2572004094112 5.74279959058881 96 26 23.2190918041 2.78090819589998 97 25 21.8094744037476 3.1905255962524 98 21 19.9806371919358 1.0193628080642 99 21 20.5737101349482 0.426289865051761 100 19 20.2063592950003 -1.20635929500026 101 21 21.3624295145167 -0.362429514516656 102 21 20.9808663759238 0.0191336240762447 103 16 19.5302432228548 -3.53024322285476 104 22 20.3902089314541 1.60979106854587 105 29 21.5252258293849 7.47477417061509 106 15 21.3920032767024 -6.39200327670238 107 17 20.3933948873818 -3.3933948873818 108 15 19.6598038042491 -4.65980380424906 109 21 21.3291392407309 -0.329139240730865 110 21 20.6321904902105 0.367809509789468 111 19 18.9325500538508 0.0674499461492113 112 24 17.8294658515374 6.17053414846261 113 20 21.8748409742144 -1.87484097421436 114 17 24.5188654204699 -7.5188654204699 115 23 24.2858541101742 -1.28585411017424 116 24 21.8076772869391 2.19232271306087 117 14 21.4880741641059 -7.48807416410592 118 19 22.2861213929966 -3.28612139299661 119 24 21.6500900632095 2.34990993679047 120 13 19.8964383041808 -6.89643830418078 121 22 24.6721943043691 -2.67219430436911 122 16 20.5376135192885 -4.53761351928849 123 19 22.6285225854727 -3.62852258547274 124 25 22.0948829634973 2.90511703650273 125 25 23.4831964078493 1.51680359215074 126 23 20.7553869260591 2.24461307394087 127 24 22.7590916096781 1.24090839032194 128 26 22.7759815861276 3.22401841387242 129 26 20.8003706672399 5.19962933276006 130 25 23.3951564337143 1.60484356628568 131 18 21.5991239299519 -3.59912392995193 132 21 19.1856863026733 1.81431369732666 133 26 22.7721081477539 3.2278918522461 134 23 21.1286695289675 1.87133047103249 135 23 19.0474475269278 3.95255247307219 136 22 21.7490138515839 0.250986148416128 137 20 21.5223154968376 -1.52231549683762 138 13 21.2268052627589 -8.22680526275892 139 24 20.5561734652747 3.44382653472531 140 15 20.7442930612423 -5.74429306124235 141 14 22.2452383177519 -8.2452383177519 142 22 23.1051451975367 -1.10514519753668 143 10 16.9966410249546 -6.99664102495459 144 24 23.4075179051279 0.592482094872088 145 22 20.8952255779007 1.10477442209927 146 24 24.6919111512327 -0.691911151232678 147 19 20.6777846956121 -1.67778469561206 148 20 21.0671514035548 -1.06715140355484 149 13 16.2728111632552 -3.27281116325521 150 20 19.1499145726773 0.850085427322731 151 22 22.1075686181769 -0.107568618176906 152 24 22.2642447148001 1.73575528519993 153 29 22.0960251700772 6.90397482992283 154 12 19.8635042296644 -7.86350422966438 155 20 19.8581485746411 0.141851425358917 156 21 20.2780328838708 0.72196711612925 157 24 22.4661368906263 1.53386310937373 158 22 20.7508756629491 1.2491243370509 159 20 16.8172134145822 3.18278658541778 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.354919788605345 0.70983957721069 0.645080211394655 12 0.471916456698002 0.943832913396005 0.528083543301998 13 0.407737227362213 0.815474454724427 0.592262772637786 14 0.303674340651241 0.607348681302482 0.696325659348759 15 0.500835723595075 0.99832855280985 0.499164276404925 16 0.600440248575707 0.799119502848586 0.399559751424293 17 0.506189591311772 0.987620817376456 0.493810408688228 18 0.595563491827328 0.808873016345345 0.404436508172672 19 0.590404733432486 0.819190533135028 0.409595266567514 20 0.509164409381669 0.981671181236662 0.490835590618331 21 0.450081358015264 0.900162716030528 0.549918641984736 22 0.374747174117746 0.749494348235491 0.625252825882254 23 0.387038999847178 0.774077999694356 0.612961000152822 24 0.487274808402721 0.974549616805441 0.512725191597279 25 0.700172667718112 0.599654664563776 0.299827332281888 26 0.639033131861522 0.721933736276956 0.360966868138478 27 0.573639752876311 0.852720494247379 0.426360247123689 28 0.557957298944464 0.884085402111073 0.442042701055536 29 0.491851753114906 0.983703506229812 0.508148246885094 30 0.427096774395021 0.854193548790041 0.572903225604979 31 0.426368422041866 0.852736844083731 0.573631577958134 32 0.36357490224991 0.72714980449982 0.63642509775009 33 0.618536706351568 0.762926587296864 0.381463293648432 34 0.58139197705194 0.83721604589612 0.41860802294806 35 0.544726822311973 0.910546355376054 0.455273177688027 36 0.488700881720025 0.97740176344005 0.511299118279975 37 0.473974073410279 0.947948146820558 0.526025926589721 38 0.422661113659191 0.845322227318383 0.577338886340809 39 0.37253860621463 0.74507721242926 0.62746139378537 40 0.347706064692881 0.695412129385762 0.652293935307119 41 0.52449684086587 0.95100631826826 0.47550315913413 42 0.469843656948027 0.939687313896055 0.530156343051973 43 0.436007891245913 0.872015782491827 0.563992108754087 44 0.38778305441189 0.775566108823781 0.61221694558811 45 0.347261726035618 0.694523452071236 0.652738273964382 46 0.323095827094318 0.646191654188637 0.676904172905682 47 0.301448151242985 0.60289630248597 0.698551848757015 48 0.296878814039141 0.593757628078281 0.703121185960859 49 0.259055512992683 0.518111025985366 0.740944487007317 50 0.25662403390584 0.513248067811679 0.74337596609416 51 0.236112890427242 0.472225780854484 0.763887109572758 52 0.20639170624035 0.412783412480699 0.79360829375965 53 0.277768768455564 0.555537536911127 0.722231231544436 54 0.355967741394077 0.711935482788154 0.644032258605923 55 0.339436207686297 0.678872415372593 0.660563792313703 56 0.401634448221715 0.80326889644343 0.598365551778285 57 0.377971364465172 0.755942728930345 0.622028635534828 58 0.346554906663464 0.693109813326929 0.653445093336536 59 0.346166462769419 0.692332925538838 0.653833537230581 60 0.423439817522322 0.846879635044644 0.576560182477678 61 0.379191710505945 0.75838342101189 0.620808289494055 62 0.336952134466272 0.673904268932544 0.663047865533728 63 0.339445417533124 0.678890835066247 0.660554582466876 64 0.305288310534378 0.610576621068755 0.694711689465622 65 0.265987342467539 0.531974684935078 0.734012657532461 66 0.249527994697487 0.499055989394974 0.750472005302513 67 0.221389367646431 0.442778735292862 0.778610632353569 68 0.243638209215618 0.487276418431236 0.756361790784382 69 0.21015576796126 0.42031153592252 0.78984423203874 70 0.177471690697582 0.354943381395164 0.822528309302418 71 0.14877690114677 0.29755380229354 0.85122309885323 72 0.123683108282613 0.247366216565226 0.876316891717387 73 0.107657988989492 0.215315977978983 0.892342011010508 74 0.0875428904657323 0.175085780931465 0.912457109534268 75 0.0712485454452062 0.142497090890412 0.928751454554794 76 0.0595115531753172 0.119023106350634 0.940488446824683 77 0.0471412507791543 0.0942825015583086 0.952858749220846 78 0.0367301186332553 0.0734602372665105 0.963269881366745 79 0.0417420020136818 0.0834840040273636 0.958257997986318 80 0.0382410118168572 0.0764820236337143 0.961758988183143 81 0.0320173348063511 0.0640346696127023 0.967982665193649 82 0.0422328403359398 0.0844656806718796 0.95776715966406 83 0.0329524518656971 0.0659049037313943 0.967047548134303 84 0.0257589105813041 0.0515178211626082 0.974241089418696 85 0.0235650947291348 0.0471301894582696 0.976434905270865 86 0.0185940566397446 0.0371881132794893 0.981405943360255 87 0.015121099807183 0.0302421996143661 0.984878900192817 88 0.0154803270183072 0.0309606540366145 0.984519672981693 89 0.012987881970014 0.025975763940028 0.987012118029986 90 0.00980225192331642 0.0196045038466328 0.990197748076684 91 0.00833281719119404 0.0166656343823881 0.991667182808806 92 0.00678435126045641 0.0135687025209128 0.993215648739544 93 0.0049857069969585 0.009971413993917 0.995014293003041 94 0.00473501134319891 0.00947002268639782 0.9952649886568 95 0.00701762230194559 0.0140352446038912 0.992982377698054 96 0.00570568070229898 0.011411361404598 0.994294319297701 97 0.00485829763138739 0.00971659526277478 0.995141702368613 98 0.00370982406489184 0.00741964812978368 0.996290175935108 99 0.00279243516048258 0.00558487032096516 0.997207564839517 100 0.00231229150212311 0.00462458300424622 0.997687708497877 101 0.00181201691437998 0.00362403382875997 0.99818798308562 102 0.00132547390397147 0.00265094780794293 0.998674526096029 103 0.001611385652426 0.003222771304852 0.998388614347574 104 0.00125266947585097 0.00250533895170195 0.998747330524149 105 0.00549530781737634 0.0109906156347527 0.994504692182624 106 0.0131215320632558 0.0262430641265116 0.986878467936744 107 0.0137420253251101 0.0274840506502203 0.98625797467489 108 0.0185735697640731 0.0371471395281461 0.981426430235927 109 0.0143844689314593 0.0287689378629186 0.98561553106854 110 0.0103918414164169 0.0207836828328339 0.989608158583583 111 0.00747423951515114 0.0149484790303023 0.992525760484849 112 0.0218603042549021 0.0437206085098042 0.978139695745098 113 0.0219589601411374 0.0439179202822747 0.978041039858863 114 0.05467608497893 0.10935216995786 0.94532391502107 115 0.0468892658509956 0.0937785317019912 0.953110734149004 116 0.0393580569194593 0.0787161138389186 0.96064194308054 117 0.102523948514166 0.205047897028331 0.897476051485834 118 0.09632814567137 0.19265629134274 0.90367185432863 119 0.0860205876962028 0.172041175392406 0.913979412303797 120 0.149104401189881 0.298208802379761 0.85089559881012 121 0.146065449219174 0.292130898438348 0.853934550780826 122 0.185090803488405 0.37018160697681 0.814909196511595 123 0.184133922154256 0.368267844308513 0.815866077845744 124 0.174401104619242 0.348802209238484 0.825598895380758 125 0.150958814572763 0.301917629145526 0.849041185427237 126 0.121150887699949 0.242301775399899 0.878849112300051 127 0.0947742915519478 0.189548583103896 0.905225708448052 128 0.0924262901788662 0.184852580357732 0.907573709821134 129 0.130226845149647 0.260453690299295 0.869773154850352 130 0.112616517090961 0.225233034181922 0.887383482909039 131 0.0941978249292126 0.188395649858425 0.905802175070787 132 0.083618781928756 0.167237563857512 0.916381218071244 133 0.0819450988731645 0.163890197746329 0.918054901126836 134 0.072953350247881 0.145906700495762 0.92704664975212 135 0.171512038868158 0.343024077736317 0.828487961131842 136 0.136628566990416 0.273257133980833 0.863371433009584 137 0.114239841788962 0.228479683577923 0.885760158211038 138 0.160955313934111 0.321910627868221 0.83904468606589 139 0.39195445821844 0.78390891643688 0.60804554178156 140 0.337750603767425 0.67550120753485 0.662249396232575 141 0.481408140548728 0.962816281097457 0.518591859451272 142 0.39028321313202 0.78056642626404 0.60971678686798 143 0.553431960036677 0.893136079926645 0.446568039963323 144 0.499741685279347 0.999483370558693 0.500258314720653 145 0.403076750935162 0.806153501870323 0.596923249064838 146 0.298613380818743 0.597226761637487 0.701386619181257 147 0.290180448483953 0.580360896967906 0.709819551516047 148 0.172902385860862 0.345804771721724 0.827097614139138 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 10 0.072463768115942 NOK 5% type I error level 29 0.210144927536232 NOK 10% type I error level 39 0.282608695652174 NOK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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Software written by Ed van Stee & Patrick Wessa

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