*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, 21 Dec 2010 14:02:45 +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/21/t12929400686xevlkcblcw67y0.htm/, Retrieved Tue, 21 Dec 2010 15:01:08 +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/21/t12929400686xevlkcblcw67y0.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 14 41 38 13 12 1 1 18 39 32 16 11 1 1 11 30 35 19 15 1 0 12 31 33 15 6 1 1 16 34 37 14 13 1 1 18 35 29 13 10 1 1 14 39 31 19 12 1 1 14 34 36 15 14 1 1 15 36 35 14 12 1 1 15 37 38 15 9 1 0 17 38 31 16 10 1 1 19 36 34 16 12 1 0 10 38 35 16 12 1 1 16 39 38 16 11 1 1 18 33 37 17 15 1 0 14 32 33 15 12 1 0 14 36 32 15 10 1 1 17 38 38 20 12 1 0 14 39 38 18 11 1 1 16 32 32 16 12 1 0 18 32 33 16 11 1 1 11 31 31 16 12 1 1 14 39 38 19 13 1 1 12 37 39 16 11 1 0 17 39 32 17 12 1 1 9 41 32 17 13 1 0 16 36 35 16 10 1 1 14 33 37 15 14 1 1 15 33 33 16 12 1 0 11 34 33 14 10 1 1 16 31 31 15 12 1 0 13 27 32 12 8 1 1 17 37 31 14 10 1 1 15 34 37 16 12 1 0 14 34 30 14 12 1 0 16 32 33 10 7 1 0 9 29 31 10 9 1 0 15 36 33 14 12 1 1 17 29 31 16 10 1 0 13 35 33 16 10 1 0 15 37 32 16 10 1 1 16 34 33 14 12 1 0 16 38 32 20 15 1 0 12 35 33 14 10 1 1 15 38 28 14 10 1 1 11 37 35 11 12 1 1 15 38 39 14 13 1 1 15 33 34 15 11 1 1 17 36 38 16 11 1 0 13 38 32 14 12 1 1 16 32 38 16 14 1 0 14 32 3 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 13 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Separate[t] = + 14.7798585054866 -0.0486161950838779Populatie[t] + 0.700533423699235Geslacht[t] -0.0308352531395231Happiness[t] + 0.460644654108866Connected[t] + 0.169100541942854Learning[t] + 0.0831719663977894Software[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) 14.7798585054866 1.980048 7.4644 0 0 Populatie -0.0486161950838779 0.435544 -0.1116 0.911203 0.455601 Geslacht 0.700533423699235 0.404009 1.734 0.084023 0.042012 Happiness -0.0308352531395231 0.08281 -0.3724 0.709905 0.354953 Connected 0.460644654108866 0.050387 9.1421 0 0 Learning 0.169100541942854 0.102808 1.6448 0.101126 0.050563 Software 0.0831719663977894 0.110126 0.7552 0.450736 0.225368 Multiple Linear Regression - Regression Statistics Multiple R 0.553216177627319 R-squared 0.306048139188582 Adjusted R-squared 0.291230661733534 F-TEST (value) 20.6545371921127 F-TEST (DF numerator) 6 F-TEST (DF denominator) 281 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.28868462732981 Sum Squared Residuals 3039.14048842796 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 38 37.0828836506427 0.917116349357299 2 32 36.4623829892977 -4.46238298929768 3 35 33.3724173657143 1.62758263428573 4 33 31.6767434776329 1.32325652236714 5 37 34.0489730739423 2.95102692605774 6 29 34.0293307806359 -5.02933078063587 7 31 37.1761975940821 -6.17619759408213 8 36 34.3629160885620 1.63708391143804 9 35 34.9179256689017 0.082074331098265 10 38 35.2981549657601 2.70184503423991 11 31 35.2488681982313 -4.24886819823132 12 34 35.1327857402294 -1.13278574022935 13 35 35.6310589030036 -0.631058903003556 14 38 36.5240534955767 1.47594650442327 15 37 34.2003034721785 2.7996965278215 16 33 32.5747494238494 0.425250576150586 17 32 34.2509841074893 -2.2509841074893 18 38 36.7921477224975 1.20785227750245 19 38 36.2233916620422 1.77660833795775 20 32 33.3827128832125 -1.38271288321246 21 33 32.5373369868364 0.462663013163614 22 31 33.0762444948012 -2.07624449480121 23 38 37.2593695604799 0.740630439520082 24 39 35.7261051999171 3.27389480008291 25 32 36.0449573270786 -4.04495732707861 26 32 37.9966340505096 -5.99663405050956 27 35 34.3584141431531 0.641585856846894 28 37 33.9022714344531 3.09772856554691 29 33 33.8741927904608 -0.874192790460846 30 33 33.2531000167473 -0.253100016747282 31 31 32.7529676871607 -1.75296768716074 32 32 29.4623719150249 2.53762808497511 33 31 35.150555883936 -4.15055588393598 34 37 34.3348374445697 2.66516255543029 35 30 33.3269381901243 -3.32693819012429 36 33 31.2517163758672 1.74828362413285 37 31 30.2519731183128 0.748026881687208 38 33 34.2173922452025 -1.2173922452025 39 31 31.8035997349508 -0.803599734950756 40 33 33.9902752484628 -0.99027524846281 41 32 34.8498940504015 -2.84989405040150 42 33 33.9658011075445 -0.96580110754448 43 32 36.3719654511312 -4.3719654511312 44 33 33.6829094177166 -0.682909417716625 45 28 35.6728710443239 -7.67287104432389 46 35 34.9946097097401 0.00539029025986888 47 39 35.9223869435173 3.07761305648274 48 34 33.6219202821202 0.378079717879798 49 38 35.1112842801106 2.88871571988939 50 32 35.2003520596993 -3.20035205969928 51 38 33.549056816008 4.45094318399196 52 30 32.239304949111 -2.23930494911098 53 33 32.1599535574394 0.84004644256058 54 38 34.5105151703861 3.48948482961393 55 32 31.0396129136868 0.960387086313191 56 35 34.8795385246239 0.120461475376136 57 34 36.6072254619745 -2.60722546197452 58 34 32.0316141740254 1.96838582597462 59 36 34.856471234275 1.143528765725 60 34 34.7216439253016 -0.721643925301568 61 28 30.9153101766513 -2.91531017665131 62 34 35.538553143585 -1.53855314358499 63 35 34.6245223899234 0.375477610076617 64 35 32.5623656850991 2.43763431490086 65 31 34.3348374445697 -3.33483744456971 66 37 34.5013974490176 2.4986025509824 67 35 35.8840127820268 -0.884012782026823 68 27 32.1392602813415 -5.1392602813415 69 40 35.9616585473426 4.03834145265737 70 37 34.0949486749793 2.90505132502066 71 36 34.1604267731972 1.83957322680282 72 38 32.5006951788201 5.49930482117991 73 39 34.839382461251 4.160617538749 74 41 35.9814276539872 5.01857234601277 75 27 33.6959745271495 -6.69597452714952 76 30 36.6501511172821 -6.6501511172821 77 37 35.7382728670151 1.26172713298495 78 31 34.313335984451 -3.31333598445097 79 31 30.3631344703887 0.636865529611282 80 27 35.0779084894761 -8.07790848947612 81 36 33.1736593667616 2.82634063323839 82 37 34.7954820986786 2.20451790132142 83 33 34.8163021881147 -1.81630218811470 84 34 33.1612756280113 0.838724371988664 85 31 33.7386841108048 -2.73868411080479 86 39 34.8891656542269 4.11083434577313 87 34 33.9050280436004 0.0949719563996314 88 32 32.0932846803044 -0.0932846803044281 89 33 33.9517742736342 -0.951774273634176 90 36 31.9653149089993 4.03468509100072 91 32 35.7364137002027 -3.73641370020271 92 41 34.7954820986786 6.20451790132142 93 28 33.2752828475487 -5.27528284754865 94 30 31.5859830544759 -1.58598305447586 95 36 36.4408815291789 -0.440881529178940 96 35 35.8924491327127 -0.892449132712668 97 31 34.5768014526247 -3.57680145262473 98 34 34.954567476918 -0.954567476918028 99 36 32.2084696959715 3.79153030402854 100 36 36.2820894875217 -0.282089487521708 101 35 35.0255717762179 -0.0255717762178542 102 37 36.1512095666127 0.848790433387295 103 28 32.5840832168702 -4.58408321687020 104 39 33.7910208240631 5.20897917593694 105 32 36.0758818385322 -4.07588183853225 106 35 36.3156813498085 -1.31568134980851 107 39 36.8588165996325 2.14118340036746 108 35 34.626597628388 0.373402371611966 109 42 37.5425535974868 4.45744640251324 110 34 32.4922588281342 1.50774117186575 111 33 33.2425884275968 -0.242588427596785 112 41 33.5611472181761 7.43885278182391 113 34 34.7815195469107 -0.781519546910745 114 32 35.4067757803411 -3.40677578034105 115 40 33.6499989261125 6.35000107388755 116 40 33.6947837482324 6.30521625176763 117 35 33.314554451374 1.68544554862598 118 36 36.2082513141447 -0.208251314144699 119 37 32.6756915339538 4.32430846604617 120 27 33.0669107017804 -6.06691070178043 121 39 35.6701144351766 3.32988556482339 122 38 35.8831153396919 2.11688466030811 123 31 35.1701981772424 -4.17019817724238 124 33 33.2640898877155 -0.264089887715528 125 32 35.5404123103973 -3.54041231039733 126 39 38.9655420549244 0.0344579450756088 127 36 33.3322353367665 2.66776466323347 128 33 34.0359079645094 -1.03590796450937 129 33 32.6083412861362 0.391658713863788 130 32 29.9576723969995 2.04232760300050 131 37 36.7660175036318 0.23398249636825 132 30 29.6502173079392 0.349782692060791 133 38 34.6780368993114 3.32196310068863 134 29 33.2136123412696 -4.2136123412696 135 22 30.2369595837534 -8.23695958375344 136 35 33.4128667656694 1.58713323433064 137 35 31.6037531981825 3.39624680181751 138 34 33.786392065316 0.213607934683997 139 35 31.2190219559153 3.78097804408471 140 34 33.0808602707608 0.919139729239178 141 37 31.3422737101593 5.65772628984073 142 35 32.94171052241 2.05828947759001 143 23 32.1691980921461 -9.16919809214609 144 31 35.7205789988351 -4.7205789988351 145 27 33.8040859334960 -6.80408593349595 146 36 34.1716327158177 1.82836728418226 147 31 32.8055204720713 -1.80552047207131 148 32 33.5231426687945 -1.52314266879455 149 39 34.7161177242196 4.28388227578042 150 37 37.9957366081746 -0.995736608174622 151 38 33.3539528685376 4.64604713146241 152 39 34.3889560597104 4.61104394028959 153 34 35.6915386303655 -1.69153863036545 154 31 32.5885721794916 -1.58857217949161 155 37 32.4380499652762 4.56195003472379 156 36 33.3322353367665 2.66776466323347 157 32 34.313335984451 -2.31333598445097 158 38 32.496963862408 5.50303613759202 159 26 29.9389383442658 -3.93893834426577 160 26 31.3227314734047 -5.32273147340471 161 33 35.8301080539887 -2.83010805398873 162 39 34.2021854306128 4.79781456938723 163 30 27.8525235701755 2.14747642982449 164 33 31.4498038023749 1.55019619762508 165 25 29.9452994564870 -4.94529945648696 166 38 34.0611635326622 3.93883646733783 167 37 30.6434191560294 6.35658084397057 168 31 33.9295892582831 -2.9295892582831 169 37 35.2739076947318 1.7260923052682 170 35 36.2496982129866 -1.24969821298656 171 25 30.5423372497994 -5.54233724979938 172 28 34.5975055269604 -6.59750552696038 173 35 32.571028905675 2.42897109432497 174 33 34.9413090874548 -1.94130908745475 175 30 31.0069292919727 -1.00692929197268 176 31 32.4661394075062 -1.46613940750618 177 37 35.4234552016824 1.57654479831764 178 36 35.3355782010108 0.664421798989156 179 30 32.8607008682413 -2.86070086824126 180 36 33.0578037786497 2.94219622135031 181 32 35.3872335435865 -3.38723354358649 182 28 27.4720782016648 0.527921798335158 183 36 33.5238348377149 2.47616516228510 184 34 34.7209733528567 -0.720973352856674 185 31 35.5944149104376 -4.59441491043756 186 28 29.719360255877 -1.71936025587699 187 36 31.4572654457959 4.54273455420408 188 36 33.2473042601082 2.75269573989176 189 40 36.2568675092286 3.74313249077142 190 33 32.0372144660843 0.962785533915664 191 37 34.8842673399228 2.11573266007724 192 32 32.7885187728117 -0.788518772811717 193 38 34.9882593957567 3.01174060424333 194 31 34.1647729935997 -3.16477299359974 195 37 33.9536442386842 3.04635576131575 196 33 32.8504053507431 0.149594649256926 197 30 32.025353118356 -2.02535311835603 198 30 28.5719286581844 1.42807134181559 199 31 32.5262311007677 -1.52623110076767 200 32 33.068188554462 -1.06818855446198 201 34 33.4210205780107 0.578979421989288 202 36 34.1311811313129 1.86881886868705 203 37 34.7917615805042 2.20823841949581 204 36 34.1127296169237 1.88727038307630 205 33 33.6540333879413 -0.654033387941283 206 33 33.3166404880764 -0.316640488076399 207 33 33.8920629907193 -0.892062990719312 208 44 36.2001953738055 7.79980462619453 209 39 32.6326994119541 6.36730058804593 210 32 31.4927294576825 0.507270542317505 211 35 34.9674393063205 0.0325606936794515 212 25 30.4145072746199 -5.41450727461987 213 35 33.9470670548107 1.05293294518926 214 34 36.2129671466562 -2.21296714665616 215 35 33.980066804729 1.01993319527097 216 39 35.1356424059285 3.86435759407153 217 33 33.7596042567927 -0.75960425679275 218 36 34.990118562569 1.00988143743099 219 32 33.9078847092995 -1.90788470929949 220 32 31.375068186663 0.624931813337028 221 36 31.5794929443668 4.42050705563324 222 32 31.6731002243884 0.326899775611623 223 34 32.727064338185 1.27293566181502 224 33 32.8037483790234 0.196251620976623 225 35 32.8803431615477 2.11965683845234 226 30 33.4079554685778 -3.40795546857781 227 38 32.2263398962299 5.77366010377008 228 34 32.2625991093499 1.73740089065011 229 33 38.174181741376 -5.17418174137598 230 32 33.6789728278899 -1.67897282788993 231 31 33.7157038942203 -2.71570389422033 232 30 32.6291216359985 -2.62912163599854 233 27 34.1585784046226 -7.15857840462257 234 31 32.2344066348069 -1.23440663480688 235 30 33.757732107193 -3.75773210719297 236 32 29.5418233632483 2.45817663675171 237 35 33.5998375078707 1.40016249212932 238 28 29.2484071014825 -1.2484071014825 239 33 33.2297372052665 -0.229737205266491 240 35 30.4939479246055 4.50605207539446 241 35 32.2355844309366 2.76441556906341 242 32 34.0714590501603 -2.07145905016035 243 21 26.6188700603556 -5.61887006035564 244 20 27.5616608286921 -7.56166082869212 245 34 31.0396237119245 2.96037628807546 246 32 31.8534829844785 0.146517015521537 247 34 34.1909794879922 -0.190979487992215 248 32 33.7349635926304 -1.7349635926304 249 33 34.3146138371325 -1.31461383713253 250 33 33.3540529250894 -0.354052925089426 251 37 34.3285763889004 2.67142361109964 252 32 32.5156422466873 -0.515642246687265 253 34 35.1749140097538 -1.17491400975384 254 30 32.2205203585657 -2.22052035856572 255 30 30.9375038056904 -0.937503805690408 256 38 32.8374175062401 5.16258249375992 257 36 35.4321076240205 0.567892375979483 258 32 30.8228152154705 1.17718478452953 259 34 35.5722450624236 -1.57224506242363 260 33 33.8667409558743 -0.86674095587434 261 27 27.1657366265918 -0.165736626591792 262 32 33.4876894551457 -1.48768945514570 263 34 35.9522582876297 -1.95225828762967 264 29 30.8779977961901 -1.87799779619012 265 35 33.3129091716643 1.68709082833572 266 27 31.7625560380775 -4.76255603807745 267 33 35.2309047744943 -2.23090477449431 268 38 32.9971069902323 5.00289300976775 269 36 34.9057688000415 1.09423119995850 270 33 33.9417699081685 -0.941769908168503 271 39 31.8543804268134 7.1456195731866 272 29 31.9018723096723 -2.9018723096723 273 32 33.2007741017267 -1.20077410172675 274 34 28.234485220508 5.765514779492 275 38 33.9557194771489 4.0442805228511 276 17 25.0831294444403 -8.08312944444032 277 35 34.599580765425 0.400419234574966 278 32 33.9221276148621 -1.9221276148621 279 34 33.584607901659 0.415392098340985 280 36 34.0931765819314 1.90682341806859 281 31 35.5254988323898 -4.52549883238982 282 35 34.0788444180547 0.92115558194532 283 29 29.5941600765066 -0.594160076506555 284 22 23.9943184072973 -1.99431840729729 285 41 36.2496089546724 4.75039104532755 286 36 33.3092551201821 2.69074487981793 287 42 38.1676938158166 3.83230618418341 288 33 32.2335091924719 0.766490807528059 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.671718757526935 0.656562484946131 0.328281242473066 11 0.563349762383776 0.873300475232448 0.436650237616224 12 0.547351250060871 0.905297499878258 0.452648749939129 13 0.425183589912217 0.850367179824434 0.574816410087783 14 0.473818923705128 0.947637847410256 0.526181076294872 15 0.504815940556559 0.990368118886882 0.495184059443441 16 0.40447909128555 0.8089581825711 0.59552090871445 17 0.319736707859930 0.639473415719859 0.68026329214007 18 0.387007917495816 0.774015834991631 0.612992082504184 19 0.432235832793337 0.864471665586674 0.567764167206663 20 0.380673117179054 0.761346234358108 0.619326882820946 21 0.31520902528575 0.6304180505715 0.68479097471425 22 0.325407007441643 0.650814014883287 0.674592992558357 23 0.269055764020157 0.538111528040315 0.730944235979843 24 0.275123266966606 0.550246533933211 0.724876733033394 25 0.257133800945069 0.514267601890138 0.742866199054931 26 0.391916916105875 0.78383383221175 0.608083083894125 27 0.342979523491196 0.685959046982392 0.657020476508804 28 0.311731858418219 0.623463716836438 0.688268141581781 29 0.266465970149786 0.532931940299572 0.733534029850214 30 0.2160100160217 0.4320200320434 0.7839899839783 31 0.202634050168455 0.40526810033691 0.797365949831545 32 0.166879054274460 0.333758108548920 0.83312094572554 33 0.167201167570534 0.334402335141068 0.832798832429466 34 0.15684846512852 0.31369693025704 0.84315153487148 35 0.161593681588789 0.323187363177578 0.838406318411211 36 0.140262998926150 0.280525997852301 0.85973700107385 37 0.111984545465530 0.223969090931060 0.88801545453447 38 0.0874902147810894 0.174980429562179 0.91250978521891 39 0.0742316366902544 0.148463273380509 0.925768363309746 40 0.0567670188774914 0.113534037754983 0.943232981122509 41 0.0465813705993475 0.093162741198695 0.953418629400652 42 0.035715029678433 0.071430059356866 0.964284970321567 43 0.0344698230507218 0.0689396461014437 0.965530176949278 44 0.0254248944754902 0.0508497889509803 0.97457510552451 45 0.0719903107352156 0.143980621470431 0.928009689264784 46 0.0562993042291649 0.112598608458330 0.943700695770835 47 0.0680769375264316 0.136153875052863 0.931923062473568 48 0.0529930870394549 0.105986174078910 0.947006912960545 49 0.0599768285143458 0.119953657028692 0.940023171485654 50 0.0521089409055009 0.104217881811002 0.9478910590945 51 0.0572510915195748 0.114502183039150 0.942748908480425 52 0.0508364305940312 0.101672861188062 0.949163569405969 53 0.0395472577595547 0.0790945155191095 0.960452742240445 54 0.0388817486123361 0.0777634972246722 0.961118251387664 55 0.0314038674684381 0.0628077349368763 0.968596132531562 56 0.0252542304002179 0.0505084608004358 0.974745769599782 57 0.0205788380748516 0.0411576761497032 0.979421161925148 58 0.0156853202110292 0.0313706404220584 0.98431467978897 59 0.0140489693458500 0.0280979386916999 0.98595103065415 60 0.0106318752966104 0.0212637505932207 0.98936812470339 61 0.0120338260582495 0.0240676521164991 0.98796617394175 62 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0.527266394932909 252 0.419503568526987 0.839007137053975 0.580496431473013 253 0.370542877566241 0.741085755132483 0.629457122433759 254 0.350450214926165 0.70090042985233 0.649549785073835 255 0.299726196201852 0.599452392403704 0.700273803798148 256 0.409256787075011 0.818513574150022 0.590743212924989 257 0.378175377272245 0.75635075454449 0.621824622727755 258 0.331803575111651 0.663607150223302 0.668196424888349 259 0.335398462794848 0.670796925589697 0.664601537205152 260 0.319577633214043 0.639155266428086 0.680422366785957 261 0.30449648189931 0.60899296379862 0.69550351810069 262 0.285677035805828 0.571354071611655 0.714322964194172 263 0.297596488828074 0.595192977656148 0.702403511171926 264 0.345705453060086 0.691410906120173 0.654294546939914 265 0.296437823569151 0.592875647138303 0.703562176430849 266 0.438765984047917 0.877531968095835 0.561234015952083 267 0.679157350705324 0.641685298589353 0.320842649294676 268 0.611103371322369 0.777793257355263 0.388896628677631 269 0.534277392685341 0.931445214629318 0.465722607314659 270 0.466167053050828 0.932334106101656 0.533832946949172 271 0.427434530529717 0.854869061059434 0.572565469470283 272 0.703457459477989 0.593085081044022 0.296542540522011 273 0.606001739919587 0.787996520160826 0.393998260080413 274 0.530337366355995 0.93932526728801 0.469662633644005 275 0.445618159039543 0.891236318079087 0.554381840960457 276 0.629150952195323 0.741698095609353 0.370849047804677 277 0.547323093204622 0.905353813590756 0.452676906795378 278 0.392519142572311 0.785038285144622 0.607480857427689 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 1 0.00371747211895911 OK 5% type I error level 17 0.0631970260223048 NOK 10% type I error level 26 0.0966542750929368 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929400686xevlkcblcw67y0/10qhgb1292940096.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929400686xevlkcblcw67y0/10qhgb1292940096.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929400686xevlkcblcw67y0/1r6z51292940095.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929400686xevlkcblcw67y0/1r6z51292940095.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929400686xevlkcblcw67y0/2cpjl1292940096.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929400686xevlkcblcw67y0/2cpjl1292940096.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929400686xevlkcblcw67y0/3cpjl1292940096.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929400686xevlkcblcw67y0/3cpjl1292940096.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929400686xevlkcblcw67y0/4cpjl1292940096.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929400686xevlkcblcw67y0/4cpjl1292940096.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929400686xevlkcblcw67y0/5nyin1292940096.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929400686xevlkcblcw67y0/5nyin1292940096.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929400686xevlkcblcw67y0/6nyin1292940096.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929400686xevlkcblcw67y0/6nyin1292940096.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929400686xevlkcblcw67y0/7yqz91292940096.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929400686xevlkcblcw67y0/7yqz91292940096.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929400686xevlkcblcw67y0/8yqz91292940096.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929400686xevlkcblcw67y0/8yqz91292940096.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929400686xevlkcblcw67y0/9qhgb1292940096.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929400686xevlkcblcw67y0/9qhgb1292940096.ps (open in new window)

Parameters (Session):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 5 ; 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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