*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: Thu, 02 Dec 2010 16:58:13 +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/02/t1291309251oi8x0vqgpp1qtlp.htm/, Retrieved Thu, 02 Dec 2010 18:00:51 +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/02/t1291309251oi8x0vqgpp1qtlp.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

1 1 4 4 3 1 21 2 4 1 3 3 1 1 21 1 5 2 2 3 2 1 24 1 2 1 4 5 4 2 21 1 1 1 3 4 1 2 21 2 1 1 5 4 2 22 2 2 1 3 5 3 2 22 1 1 1 5 5 1 1 20 2 1 1 3 3 1 1 21 1 1 1 4 4 3 21 2 3 2 5 5 5 2 21 1 1 1 3 3 3 1 22 2 1 1 3 4 1 1 22 1 1 1 4 4 2 1 23 2 2 1 4 4 2 1 23 2 4 2 4 4 5 2 21 2 1 1 3 5 2 2 24 1 1 1 5 3 2 1 23 1 1 1 4 5 2 2 21 1 2 1 3 3 2 1 23 1 3 1 3 4 3 2 32 2 1 1 3 4 3 1 21 2 1 2 3 4 3 2 21 1 1 1 4 3 1 2 21 1 1 2 5 5 1 1 21 2 1 1 4 4 4 2 21 2 2 4 5 5 1 1 20 2 1 1 3 2 3 1 24 2 1 1 4 5 2 1 22 2 1 1 2 4 1 2 22 2 1 1 5 5 2 2 21 1 1 1 2 4 1 2 21 1 1 1 3 5 2 1 21 2 1 1 3 3 1 2 21 1 1 1 3 3 1 1 23 2 1 1 3 4 1 1 23 2 1 1 4 4 1 2 21 2 1 1 3 5 3 1 20 1 1 1 5 5 3 2 21 2 1 1 2 3 1 1 20 1 1 1 3 5 3 2 21 1 1 1 3 5 1 1 22 2 4 1 4 4 2 2 21 1 1 1 5 5 3 1 22 2 1 1 3 3 2 1 22 2 4 3 3 4 1 2 22 1 2 2 3 5 1 1 22 1 2 1 3 3 1 1 21 2 1 1 3 5 1 1 21 2 1 1 3 4 1 2 21 1 2 2 3 3 3 1 23 2 1 1 4 5 2 2 23 2 1 1 3 4 2 2 23 1 1 1 2 5 2 1 22 1 1 1 3 3 4 1 24 2 1 1 3 5 3 1 23 2 1 1 3 4 3 2 21 2 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 8 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 R Framework error message Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Multiple Linear Regression - Estimated Regression Equation X1[t] = + 31.7133444903618 -0.888380446729087X2[t] -0.911256916123055X3[t] -0.934267347790764X4[t] -0.857698947974369X5[t] -0.73976811275555X6[t] -0.825774142894657X7[t] -0.206548035295779X8[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) 31.7133444903618 1.394929 22.7347 0 0 X2 -0.888380446729087 0.096796 -9.1779 0 0 X3 -0.911256916123055 0.097993 -9.2992 0 0 X4 -0.934267347790764 0.092033 -10.1514 0 0 X5 -0.857698947974369 0.045692 -18.7712 0 0 X6 -0.73976811275555 0.112197 -6.5935 0 0 X7 -0.825774142894657 0.091381 -9.0367 0 0 X8 -0.206548035295779 0.482639 -0.428 0.669289 0.334645 Multiple Linear Regression - Regression Statistics Multiple R 0.883180283143714 R-squared 0.780007412533811 Adjusted R-squared 0.769876174953131 F-TEST (value) 76.9903386750383 F-TEST (DF numerator) 7 F-TEST (DF denominator) 152 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.78385098401767 Sum Squared Residuals 2176.26429692623 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1 2.37564895991937 -1.37564895991937 2 4 6.14311915507773 -2.14311915507773 3 5 2.83097424781336 2.16902575218664 4 2 0.0504625866944826 1.94953741330552 5 1 4.26253565923562 -3.26253565923562 6 1 2.47666933890264 -1.47666933890264 7 1 2.66649797142566 -1.66649797142566 8 1 4.26973280413983 -3.26973280413983 9 1 7.95501355998322 -6.95501355998322 10 1 -0.669639636667459 1.66963963666746 11 5 1.06285478211181 3.93714521788819 12 3 3.99892979487694 -0.998929794876938 13 3 5.67283129314951 -2.67283129314951 14 4 2.33833317340188 1.66166682659812 15 4 0.480236852316786 3.51976314768321 16 4 1.21146711608535 2.78853288391465 17 3 1.22352868655787 1.77647131344213 18 5 4.79225587578117 0.207744124218827 19 4 2.97085138758632 1.02914861241368 20 3 3.14070758999186 -0.140707589991859 21 3 -6.4007074793866 9.4007074793866 22 3 3.76170026082644 -0.761700260826441 23 3 3.77374906108701 -0.773749061087005 24 4 6.27809530476642 -2.27809530476642 25 5 4.90238168163924 0.097618318360758 26 4 0.677305783426405 3.32269421657359 27 5 5.76008062961361 -0.760080629613611 28 3 3.17191234565729 -0.171912345657287 29 4 3.13342581754182 0.86657418245818 30 2 3.9987958326032 -1.9987958326032 31 5 3.79662553048097 1.20337446951903 32 2 5.59626289333312 -3.59626289333312 33 3 3.99112476551619 -0.991124765516188 34 3 6.4846433400622 -3.4846433400622 35 3 4.96374467914868 -1.96374467914868 36 3 4.07536423241959 -1.07536423241959 37 4 4.85649478057757 -0.856494780577566 38 3 4.67733491012305 -1.67733491012305 39 5 2.14560050160237 2.85439949839763 40 2 8.27660963582733 -6.27660963582733 41 3 2.88536861435792 0.114631385642081 42 3 1.56736030498090 1.43263969501910 43 4 4.68500597721006 -0.68500597721006 44 5 2.22216890141876 2.77783109858124 45 3 2.01976821172446 0.980231788275538 46 3 3.70624176716831 -0.706241767168311 47 3 3.95867670352577 -0.958676703525767 48 3 6.67914257509741 -3.67914257509741 49 3 4.90238168163924 -1.90238168163924 50 3 4.56394071514268 -1.56394071514268 51 3 3.14123084690257 -0.141230846902569 52 4 1.34145952177669 2.65854047822331 53 3 2.96960808126132 0.0303919187386763 54 2 3.87319393029737 -1.87319393029737 55 3 1.37227498280515 1.62772501719485 56 3 1.36446995344440 1.63553004655560 57 3 2.2082068054368 0.791793194563202 58 4 2.96193701417431 1.03806298582569 59 2 4.73856394535875 -2.73856394535875 60 5 2.88536861435792 2.11463138564208 61 4 4.60982761620436 -0.609827616204356 62 2 5.64214979439479 -3.64214979439479 63 2 4.77048875043846 -2.77048875043846 64 3 3.28275820092964 -0.282758200929639 65 4 2.17628200035709 1.82371799964291 66 5 1.28790155362800 3.712098446372 67 3 4.93306318039396 -1.93306318039396 68 3 5.73543759698394 -2.73543759698394 69 4 3.02140889116018 0.978591108839819 70 3 4.05248776302562 -1.05248776302562 71 4 4.70788244660403 -0.707882446604029 72 3 2.93906054478035 0.0609394552196528 73 3 2.05835116513827 0.941648834861732 74 4 4.87950521224528 -0.879505212245275 75 2 3.95743339720077 -1.95743339720077 76 2 3.95743339720077 -1.95743339720077 77 4 3.04250602710649 0.957493972893511 78 2 3.94523786445451 -1.94523786445451 79 4 6.5612117398786 -2.5612117398786 80 3 4.00017310120193 -1.00017310120193 81 5 3.81963596214868 1.18036403785132 82 3 5.79076212836833 -2.79076212836833 83 3 5.56133762367858 -2.56133762367858 84 4 4.93306318039396 -0.933063180393961 85 3 3.08753891648014 -0.0875389164801413 86 3 4.76157437702646 -1.76157437702646 87 4 3.99112476551619 0.00887523448381165 88 3 4.93306318039396 -1.93306318039396 89 3 2.55775531699476 0.442244683005242 90 3 5.79076212836833 -2.79076212836833 91 2 7.5675230218265 -5.5675230218265 92 4 2.02766966638355 1.97233033361645 93 3 2.73237854721083 0.267621452789174 94 5 1.28790155362800 3.712098446372 95 3 2.28477520525319 0.715224794746806 96 5 2.16861093327008 2.83138906672992 97 4 1.4047858750254 2.5952141249746 98 3 3.91469032797353 -0.914690327973533 99 3 6.53053024112388 -3.53053024112388 100 5 4.90238168163924 0.097618318360758 101 4 1.23257702224361 2.76742297775639 102 3 1.89769003090417 1.10230996909583 103 5 0.157524545037891 4.84247545496211 104 4 -0.373804411898308 4.37380441189831 105 2 4.68500597721006 -2.68500597721006 106 5 3.96811433384848 1.03188566615152 107 4 2.37025797848159 1.62974202151841 108 2 6.53053024112388 -4.53053024112388 109 2 6.53833527048463 -4.53833527048463 110 5 5.4744466209335 -0.474446620933496 111 4 1.85216146356150 2.14783853643850 112 4 5.29858008439244 -1.29858008439244 113 2 6.54649863356439 -4.54649863356439 114 5 4.43635667075881 0.56364332924119 115 4 3.77753469099322 0.222465309006783 116 4 19.7286004117406 -15.7286004117406 117 1 -0.956094422810319 1.95609442281032 118 3 5.56128901813658 -2.56128901813658 119 1 5.21108328739417 -4.21108328739417 120 1 2.82793626805588 -1.82793626805588 121 1 20.6557608275857 -19.6557608275857 122 1 -1.27997627784836 2.27997627784836 123 1 0.900465231076488 0.0995347689235117 124 1 4.56257664818728 -3.56257664818728 125 1 1.67268140582246 -0.672681405822456 126 2 19.843094768985 -17.843094768985 127 21 18.7343381532519 2.26566184674808 128 23 20.4942456816636 2.5057543183364 129 21 18.7022793858985 2.29772061410153 130 21 14.5509214966682 6.44907850333182 131 20 16.1089266475051 3.89107335249488 132 21 17.2260115495097 3.77398845049033 133 24 22.2663359726096 1.73366402739041 134 23 16.2375290143858 6.76247098561423 135 22 18.8107725907946 3.18922740920543 136 21 19.7129684010199 1.28703159898007 137 22 21.5572493586088 0.442750641391246 138 21 21.4501334223114 -0.450133422311382 139 21 16.3339734190213 4.66602658097869 140 21 17.3662955972117 3.63370440278825 141 22 18.2775525133348 3.7224474866652 142 20 18.9287034260134 1.07129657398661 143 21 17.1904290606707 3.80957093932931 144 21 19.0173206260904 1.98267937390965 145 22 17.9210021052548 4.0789978947452 146 21 19.6810435959402 1.31895640405978 147 23 20.5249271804183 2.47507281958168 148 23 19.7532342625831 3.24676573741694 149 24 19.5829887655406 4.41701123445945 150 32 20.7867997470985 11.2132002529015 151 22 18.9956874630214 3.00431253697862 152 22 20.7409128460368 1.25908715396319 153 20 19.0714018511497 0.928598148850251 154 21 20.7867997470985 0.213200252901513 155 23 19.6684715387689 3.33152846123106 156 21 20.5249271804183 0.475072819581682 157 21 23.2726472545575 -2.27264725455749 158 23 18.9948334513334 4.00516654866664 159 24 20.7634000207938 3.23659997920619 160 22 19.0173206260904 2.98267937390965 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.155463951381050 0.310927902762099 0.84453604861895 12 0.110912895532763 0.221825791065526 0.889087104467237 13 0.0495861563442277 0.0991723126884555 0.950413843655772 14 0.0208404862951032 0.0416809725902064 0.979159513704897 15 0.0107952234971223 0.0215904469942445 0.989204776502878 16 0.00419709120179888 0.00839418240359775 0.995802908798201 17 0.00154023636164184 0.00308047272328367 0.998459763638358 18 0.000725266382143797 0.00145053276428759 0.999274733617856 19 0.000392765643960546 0.000785531287921091 0.99960723435604 20 0.000266550299969111 0.000533100599938223 0.99973344970003 21 0.000143201583343966 0.000286403166687933 0.999856798416656 22 5.15532690979813e-05 0.000103106538195963 0.999948446730902 23 1.89879780348999e-05 3.79759560697997e-05 0.999981012021965 24 1.27962791659137e-05 2.55925583318273e-05 0.999987203720834 25 6.17040342322235e-06 1.23408068464447e-05 0.999993829596577 26 6.91560578102104e-06 1.38312115620421e-05 0.999993084394219 27 3.02233855638431e-06 6.04467711276863e-06 0.999996977661444 28 1.10529244638445e-06 2.21058489276891e-06 0.999998894707554 29 3.68633496957395e-07 7.3726699391479e-07 0.999999631366503 30 3.0121984190711e-07 6.0243968381422e-07 0.999999698780158 31 1.81429955987243e-07 3.62859911974486e-07 0.999999818570044 32 1.43003224228268e-07 2.86006448456536e-07 0.999999856996776 33 7.04116255306589e-08 1.40823251061318e-07 0.999999929588374 34 2.39830634811741e-08 4.79661269623483e-08 0.999999976016936 35 9.1127957400767e-09 1.82255914801534e-08 0.999999990887204 36 3.54808022550136e-09 7.09616045100272e-09 0.99999999645192 37 1.47668488418799e-09 2.95336976837597e-09 0.999999998523315 38 7.3700595096255e-10 1.4740119019251e-09 0.999999999262994 39 5.17398374010846e-10 1.03479674802169e-09 0.999999999482602 40 3.68018105661827e-10 7.36036211323654e-10 0.999999999631982 41 1.48381760372402e-10 2.96763520744803e-10 0.999999999851618 42 6.51923087821082e-11 1.30384617564216e-10 0.999999999934808 43 2.46061006394588e-11 4.92122012789176e-11 0.999999999975394 44 1.22872381096429e-11 2.45744762192859e-11 0.999999999987713 45 3.86012132249383e-12 7.72024264498766e-12 0.99999999999614 46 1.21831008163146e-12 2.43662016326291e-12 0.999999999998782 47 5.24936227917484e-13 1.04987245583497e-12 0.999999999999475 48 1.98319984199235e-13 3.96639968398469e-13 0.999999999999802 49 7.90931989288633e-14 1.58186397857727e-13 0.99999999999992 50 2.34353607295710e-14 4.68707214591419e-14 0.999999999999977 51 7.63046900492085e-15 1.52609380098417e-14 0.999999999999992 52 2.42759349231032e-15 4.85518698462063e-15 0.999999999999998 53 7.40934870769284e-16 1.48186974153857e-15 1 54 1.00412145078997e-15 2.00824290157994e-15 1 55 3.06840316468986e-16 6.13680632937972e-16 1 56 1.11866139961425e-16 2.23732279922850e-16 1 57 3.27413330754563e-17 6.54826661509127e-17 1 58 1.04731399008913e-17 2.09462798017825e-17 1 59 5.517589434278e-18 1.1035178868556e-17 1 60 4.66157955337024e-18 9.32315910674048e-18 1 61 1.48318597733071e-18 2.96637195466143e-18 1 62 1.48449770582779e-18 2.96899541165558e-18 1 63 7.11670164579306e-19 1.42334032915861e-18 1 64 2.23543556722614e-19 4.47087113445227e-19 1 65 7.64658781243808e-20 1.52931756248762e-19 1 66 5.34775044247164e-20 1.06955008849433e-19 1 67 1.71461233651706e-20 3.42922467303412e-20 1 68 4.53300427593439e-21 9.06600855186879e-21 1 69 1.45665275687773e-21 2.91330551375546e-21 1 70 4.45971830417149e-22 8.91943660834298e-22 1 71 1.47471749569893e-22 2.94943499139785e-22 1 72 5.41033635344792e-23 1.08206727068958e-22 1 73 1.64897805869278e-23 3.29795611738555e-23 1 74 5.3593302638376e-24 1.07186605276752e-23 1 75 3.03453001264190e-24 6.06906002528381e-24 1 76 1.59785301529071e-24 3.19570603058141e-24 1 77 7.14020622664366e-25 1.42804124532873e-24 1 78 4.3276392162937e-25 8.6552784325874e-25 1 79 1.75651896493056e-25 3.51303792986113e-25 1 80 5.4266878613196e-26 1.08533757226392e-25 1 81 3.35040923086611e-26 6.70081846173221e-26 1 82 1.11104193468001e-26 2.22208386936003e-26 1 83 3.95423287638295e-27 7.9084657527659e-27 1 84 1.50541602382247e-27 3.01083204764494e-27 1 85 4.16409304432627e-28 8.32818608865254e-28 1 86 1.09752245291131e-28 2.19504490582262e-28 1 87 2.81426876966845e-29 5.62853753933689e-29 1 88 9.3538254970244e-30 1.87076509940488e-29 1 89 2.65851745962428e-30 5.31703491924856e-30 1 90 9.89962008969118e-31 1.97992401793824e-30 1 91 1.26997242195615e-30 2.53994484391231e-30 1 92 3.81353175232462e-31 7.62706350464924e-31 1 93 1.00921317444842e-31 2.01842634889683e-31 1 94 6.12268790970224e-32 1.22453758194045e-31 1 95 1.79345096663399e-32 3.58690193326799e-32 1 96 6.05303839435888e-33 1.21060767887178e-32 1 97 4.63161064696674e-33 9.26322129393349e-33 1 98 1.87582738675623e-33 3.75165477351246e-33 1 99 4.22793814228283e-34 8.45587628456566e-34 1 100 3.11270941433688e-34 6.22541882867376e-34 1 101 1.32953161950206e-34 2.65906323900412e-34 1 102 5.05185468252413e-35 1.01037093650483e-34 1 103 3.66185528842847e-35 7.32371057685693e-35 1 104 8.2497565979814e-36 1.64995131959628e-35 1 105 3.79435166114653e-36 7.58870332229307e-36 1 106 3.21236919651021e-36 6.42473839302043e-36 1 107 8.9274092961232e-37 1.78548185922464e-36 1 108 4.10109031187917e-37 8.20218062375834e-37 1 109 9.70524758501e-38 1.941049517002e-37 1 110 1.21508271972970e-37 2.43016543945940e-37 1 111 1.04190643431426e-37 2.08381286862852e-37 1 112 2.96229609787904e-38 5.92459219575807e-38 1 113 1.08278835334840e-38 2.16557670669681e-38 1 114 1.23635198924795e-38 2.47270397849591e-38 1 115 1.36257660419212e-38 2.72515320838424e-38 1 116 2.10202111180223e-38 4.20404222360445e-38 1 117 5.91740691012132e-38 1.18348138202426e-37 1 118 2.33536847214855e-38 4.67073694429709e-38 1 119 1.69987175204676e-38 3.39974350409352e-38 1 120 3.4662425336193e-39 6.9324850672386e-39 1 121 5.46170252921793e-31 1.09234050584359e-30 1 122 4.07105411588352e-28 8.14210823176704e-28 1 123 1.68196470622117e-28 3.36392941244234e-28 1 124 5.59561503083533e-29 1.11912300616707e-28 1 125 1.9276568801026e-29 3.8553137602052e-29 1 126 6.1598099702658e-09 1.23196199405316e-08 0.99999999384019 127 0.140912842385290 0.281825684770580 0.85908715761471 128 0.630912761262145 0.73817447747571 0.369087238737855 129 0.796861597487209 0.406276805025583 0.203138402512791 130 0.88029037801928 0.239419243961441 0.119709621980721 131 0.9017249307098 0.196550138580398 0.0982750692901991 132 0.916480832795925 0.167038334408151 0.0835191672040753 133 0.918418046024984 0.163163907950032 0.0815819539750162 134 0.939543392298916 0.120913215402168 0.0604566077010838 135 0.926754511354593 0.146490977290814 0.073245488645407 136 0.90851137584874 0.182977248302519 0.0914886241512593 137 0.877214378004845 0.245571243990309 0.122785621995155 138 0.841697489368913 0.316605021262173 0.158302510631087 139 0.804223307700478 0.391553384599045 0.195776692299522 140 0.757147203360091 0.485705593279818 0.242852796639909 141 0.696061432677943 0.607877134644114 0.303938567322057 142 0.751896868781145 0.49620626243771 0.248103131218855 143 0.679792370333806 0.640415259332388 0.320207629666194 144 0.587204807667148 0.825590384665703 0.412795192332852 145 0.506854862779615 0.98629027444077 0.493145137220385 146 0.402226173873165 0.80445234774633 0.597773826126835 147 0.30559654114493 0.61119308228986 0.69440345885507 148 0.202535681877286 0.405071363754572 0.797464318122714 149 0.166239403534038 0.332478807068076 0.833760596465962 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 111 0.798561151079137 NOK 5% type I error level 113 0.81294964028777 NOK 10% type I error level 114 0.820143884892086 NOK

Charts produced by software:

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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') }

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Software written by Ed van Stee & Patrick Wessa

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