*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: Sun, 05 Dec 2010 20:18:32 +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/05/t1291580231e5hcwygpxfop3zx.htm/, Retrieved Sun, 05 Dec 2010 21:17:23 +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/05/t1291580231e5hcwygpxfop3zx.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 41 38 13 12 14 1 1 39 32 16 11 18 1 1 30 35 19 15 11 1 0 31 33 15 6 12 1 1 34 37 14 13 16 1 1 35 29 13 10 18 1 1 39 31 19 12 14 1 1 34 36 15 14 14 1 1 36 35 14 12 15 1 1 37 38 15 9 15 1 0 38 31 16 10 17 1 1 36 34 16 12 19 1 0 38 35 16 12 10 1 1 39 38 16 11 16 1 1 33 37 17 15 18 1 0 32 33 15 12 14 1 0 36 32 15 10 14 1 1 38 38 20 12 17 1 0 39 38 18 11 14 1 1 32 32 16 12 16 1 0 32 33 16 11 18 1 1 31 31 16 12 11 1 1 39 38 19 13 14 1 1 37 39 16 11 12 1 0 39 32 17 12 17 1 1 41 32 17 13 9 1 0 36 35 16 10 16 1 1 33 37 15 14 14 1 1 33 33 16 12 15 1 0 34 33 14 10 11 1 1 31 31 15 12 16 1 0 27 32 12 8 13 1 1 37 31 14 10 17 1 1 34 37 16 12 15 1 0 34 30 14 12 14 1 0 32 33 10 7 16 1 0 29 31 10 9 9 1 0 36 33 14 12 15 1 1 29 31 16 10 17 1 0 35 33 16 10 13 1 0 37 32 16 10 15 1 1 34 33 14 12 16 1 0 38 32 20 15 16 1 0 35 33 14 10 12 1 1 38 28 14 10 15 1 1 37 35 11 12 11 1 1 38 39 14 13 15 1 1 33 34 15 11 15 1 1 36 38 16 11 17 1 0 38 32 14 12 13 1 1 32 38 16 14 16 1 0 32 30 1 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 17 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Happiness[t] = + 10.5667844818342 + 0.998144277551916Pop[t] + 0.790351801127384Gender[t] + 0.0273029937954519Connected[t] -0.0159940655898807Separate[t] + 0.118947366727600Learning[t] -0.0160951875172021Software[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) 10.5667844818342 1.428095 7.3992 0 0 Pop 0.998144277551916 0.307984 3.2409 0.001335 0.000667 Gender 0.790351801127384 0.288697 2.7377 0.006583 0.003291 Connected 0.0273029937954519 0.041303 0.661 0.509127 0.254563 Separate -0.0159940655898807 0.042953 -0.3724 0.709905 0.354953 Learning 0.118947366727600 0.074059 1.6061 0.109373 0.054687 Software -0.0160951875172021 0.079388 -0.2027 0.839484 0.419742 Multiple Linear Regression - Regression Statistics Multiple R 0.341681220105783 R-squared 0.116746056172977 Adjusted R-squared 0.0978865413581648 F-TEST (value) 6.19030008562503 F-TEST (DF numerator) 6 F-TEST (DF denominator) 281 p-value 4.06812294373449e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.36852463154137 Sum Squared Residuals 1576.38440939131 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14 14.2201023309641 -0.220102330964103 2 18 14.6343980246124 3.3656019753876 3 11 14.6331502337977 -3.63315023379767 4 12 13.5711567783899 -1.57115677838991 5 16 14.1478276191961 1.85217238080388 6 18 14.2324213335346 3.76757866646538 7 14 14.9911390028679 -0.991139002867864 8 14 14.2666738639964 -0.266673863996394 9 15 14.2505169254840 0.749483074516018 10 15 14.397070651789 0.602929348211001 11 17 13.8488324827966 3.15116751720337 12 19 14.5044057245291 4.49559427547094 13 10 13.7526658454027 -3.7526658454027 14 16 14.5384336310731 1.4615663689269 15 18 14.4451763505491 3.55482364945094 16 14 13.5018886470822 0.498111352917848 17 14 13.6592850628882 0.340714937111756 18 17 14.9708249166708 2.02917508332915 19 14 13.9859765634009 0.0140234365990846 20 16 14.4271818805270 1.57281811947298 21 18 13.6369312013270 4.36306879867305 22 11 14.4158729523214 -3.41587295232145 23 14 14.8630853562215 -0.863085356221496 24 12 14.4678335778923 -2.46783357789231 25 17 13.9468984026954 3.05310159730460 26 9 14.7757610038965 -5.77576100389648 27 16 13.7302502328462 2.26974976715380 28 14 14.2233768046111 -0.223376804611061 29 15 14.4384908087326 0.561509191267411 30 11 13.4697376429799 -2.46973764297986 31 16 14.2969255855938 1.70307441440615 32 13 13.0889063935808 -0.0889063935807798 33 17 14.3739865566734 2.62601344332664 34 15 14.4018175401685 0.598182459831482 35 14 13.4855294647151 0.514470535284903 36 16 12.9876277510302 3.01237224896984 37 9 12.9055165257892 -3.90551652578916 38 15 13.4921532555364 1.50784674446364 39 17 14.3934573397649 2.60654266023505 40 13 13.7349353702305 -0.734935370230512 41 15 13.8055354234113 1.19446457658870 42 16 14.2278990690728 1.77210093092716 43 16 14.2281519465311 1.77184805346886 44 12 13.4970406367753 -1.49704063677531 45 15 14.4492717472385 0.550728252761545 46 11 13.9209778190966 -2.92097781909663 47 15 14.2250514631982 0.774948536801839 48 15 14.3196445639323 0.68035543606769 49 17 14.4565246496867 2.54347535031326 50 13 13.5627533087171 -0.562753308717143 51 16 14.2990271119533 1.70097288804667 52 14 13.4631138521586 0.536886147841402 53 11 13.1450465468994 -2.14504654689935 54 12 14.3697282870614 -2.36972828706143 55 12 12.9168648249268 -0.916864824926845 56 15 14.3743910443826 0.625608955617353 57 16 14.5863147059154 1.41368529408458 58 15 14.3132847679609 0.6867152320391 59 12 13.6065166068070 -1.60651660680697 60 12 14.5092931057680 -2.50929310576802 61 8 13.2508868248439 -5.25088682484386 62 13 13.7686599109926 -0.768659910992583 63 11 14.4016152963139 -3.40161529631387 64 14 14.1300971440239 -0.130097144023925 65 15 14.4977819337078 0.502218066292198 66 10 13.7416209120470 -3.74162091204698 67 11 14.6941160173600 -3.69411601735998 68 12 13.9161843407305 -1.91618434073054 69 15 14.0145608454657 0.985439154534266 70 15 13.6387687328366 1.36123126716341 71 14 13.0873683295160 0.912631670483972 72 16 14.0821149472543 1.91788505274572 73 15 14.5755337674096 0.424466232590447 74 15 13.8624058102842 1.13759418971578 75 13 13.7714063949399 -0.77140639493994 76 12 14.8175238975541 -2.81752389755415 77 17 14.4676313340377 2.53236866596233 78 13 14.513877121225 -1.51387712122500 79 15 13.1867700696249 1.81322993037510 80 13 13.8533153763263 -0.853315376326296 81 15 13.6001568108356 1.39984318916444 82 15 14.4291205339640 0.57087946603603 83 16 13.6384036160594 2.36159638394059 84 15 14.2923415701369 0.707658429863142 85 14 14.5026693149468 -0.502669314946754 86 15 13.4990804121396 1.50091958786041 87 14 14.4224967431427 -0.422496743142708 88 13 14.3452728991407 -1.34527289914066 89 7 14.319543442005 -7.31954344200499 90 17 13.9083987200132 3.09160127998675 91 13 14.6070556598848 -1.60705565988482 92 15 14.3651442716044 0.634855728395553 93 14 14.3722107761589 -0.372210776158940 94 13 14.0204189301376 -1.02041893013762 95 16 14.5865169497701 1.41348305022994 96 12 14.4996194652174 -2.49961946521743 97 14 14.5733704900549 -0.57337049005486 98 17 13.7413569171971 3.25864308280287 99 15 13.3671494586193 1.63285054138069 100 17 14.4948332059058 2.5051667940942 101 12 13.7414580391245 -1.74145803912445 102 16 14.8839274321182 1.11607256788178 103 11 13.5979541625488 -2.59795416254876 104 15 14.3586216027105 0.641378397289493 105 9 13.4984119295804 -4.49841192958045 106 16 14.6619650132577 1.33803498674231 107 15 13.7705985644295 1.22940143557046 108 10 13.714155045329 -3.714155045329 109 10 14.1722606270538 -4.17226062705379 110 15 14.3405877617564 0.659412238243648 111 11 14.3516944461073 -3.35169444610728 112 13 14.4182778444629 -1.41827784446289 113 18 14.0881096264485 3.91189037355148 114 16 13.9951445943149 2.00485540568511 115 14 14.0725424286310 -0.0725424286310211 116 14 14.1803213600125 -0.180321360012484 117 14 14.0657557648872 -0.0657557648872282 118 14 14.5270235809402 -0.527023580940206 119 12 13.2434158325801 -1.24341583258008 120 14 14.4637540271638 -0.463754027163767 121 15 14.1221992839878 0.877800716012237 122 15 14.4355420809306 0.564457919069411 123 15 14.4173453670539 0.582654632946097 124 13 14.3355992585901 -1.33559925859008 125 17 13.7411940442746 3.2588059557254 126 17 14.7779019011881 2.22209809881192 127 19 14.3198468077870 4.68015319221305 128 15 14.0334025169303 0.966597483069707 129 13 13.6530263888442 -0.653026388844156 130 9 12.8300290913694 -3.83002909136942 131 15 14.6300162530100 0.369983746989962 132 15 13.0726089622089 1.92739103779107 133 15 13.4394859213824 1.56051407861759 134 16 14.3562167105691 1.64378328943094 135 11 13.3790022224854 -2.37900222248544 136 14 13.5406016910105 0.459398308989503 137 11 13.7620472375629 -2.76204723756287 138 15 14.0656940138920 0.934305986107981 139 13 13.0150936177481 -0.0150936177481430 140 15 14.4595744994161 0.540425500583935 141 16 13.4315919596833 2.56840804031667 142 14 14.3952555003425 -0.395255500342466 143 15 13.7695688634303 1.23043113656969 144 16 14.0122964461837 1.98770355381628 145 16 14.7289517544144 1.27104824558558 146 11 13.3252236920391 -2.32522369203912 147 12 13.6528241449895 -1.65282414498951 148 9 13.4101825231548 -4.41018252315479 149 16 13.8458331213910 2.15416687860903 150 13 14.4851989362873 -1.48519893628733 151 16 13.6437572360029 2.35624276399714 152 12 14.4937035278874 -2.49370352788742 153 9 14.3854977287336 -5.38549772873358 154 13 13.8211754896156 -0.821175489615556 155 14 14.0869405774980 -0.0869405774980255 156 19 14.3198468077870 4.68015319221305 157 13 14.4978830556351 -1.49788305563512 158 12 13.9198087701461 -1.91980877014614 159 10 12.2734835012613 -2.27348350126134 160 14 12.2959384847500 1.70406151525005 161 16 12.8732666907237 3.12673330927626 162 10 13.2849281397436 -3.28492813974364 163 11 11.8029465323671 -0.802946532367067 164 14 12.3462862027289 1.65371379727107 165 12 12.7824412656936 -0.782441265693551 166 9 13.0308370968439 -4.03083709684392 167 9 12.4222005049211 -3.42220050492105 168 11 12.4280716821249 -1.42807168212487 169 16 13.4582792502075 2.54172074979250 170 9 12.3928314573611 -3.39283145736114 171 13 12.7069314512107 0.293068548789283 172 16 13.1264363736060 2.87356362639397 173 13 12.4878514258677 0.512148574132325 174 9 13.1381497895209 -4.13814978952089 175 12 12.1885640410778 -0.188564041077778 176 16 13.2120243163487 2.78797568365127 177 11 13.0853813334396 -2.08538133343961 178 14 13.4742733157974 0.525726684202615 179 13 12.2544172058790 0.745582794120957 180 15 12.8559630833239 2.14403691667606 181 14 12.6835563978928 1.31644360210717 182 16 12.2684049935593 3.7315950064407 183 13 13.3650613406156 -0.365061340615577 184 14 12.8509522000946 1.14904779990544 185 15 13.2408390958088 1.75916090419125 186 13 12.0791891929734 0.920810807026561 187 11 12.0926390184706 -1.09263901847061 188 11 13.1271666071604 -2.12716660716038 189 14 13.4649030410288 0.535096958971234 190 15 13.0821107581296 1.91788924187036 191 11 13.4470714439293 -2.44707144392925 192 15 13.1043858778267 1.89561412217330 193 12 12.5602890105581 -0.560289010558091 194 14 13.5479232187075 0.452076781292509 195 14 13.3763702688211 0.623629731178851 196 8 12.4603855591497 -4.46038555914969 197 9 12.6160679454366 -3.61606794543657 198 15 12.2465456242431 2.75345437575693 199 17 12.1628345839421 4.8371654160579 200 13 12.2175023225282 0.782497677471782 201 15 13.369785848932 1.630214151068 202 15 13.3168151489961 1.68318485100392 203 14 13.4470714439293 0.552928556070745 204 16 12.6566185208745 3.34338147912545 205 13 12.1693572528360 0.830642747163955 206 16 12.5905407321555 3.40945926784446 207 9 12.9918600580657 -3.99186005806572 208 16 12.2166944920178 3.78330550798219 209 11 12.4238751635082 -1.42387516350815 210 10 12.5295131975980 -2.52951319759802 211 11 13.4629643875918 -2.46296438759181 212 15 12.4357279273743 2.56427207262572 213 17 13.5434009542457 3.45659904575429 214 14 13.3824660699427 0.617533930057294 215 8 12.4074542301459 -4.40745423014589 216 15 13.3073437523001 1.69265624769986 217 11 12.3477586174614 -1.34775861746139 218 16 12.5328231438401 3.46717685615989 219 10 13.3373932300430 -3.33739323004295 220 15 12.1838789036935 2.81612109630653 221 16 12.5100535318980 3.48994646810201 222 19 12.4056784496315 6.59432155036853 223 12 12.4443914935598 -0.444391493559812 224 8 12.1308464527623 -4.13084645276234 225 11 12.2178056883102 -1.21780568831018 226 14 13.2553607466662 0.744639253333823 227 9 11.8885305767727 -2.88853057677268 228 15 12.7032687957712 2.29673120422883 229 13 13.8644748399651 -0.864474839965083 230 16 13.1589918654176 2.84100813458239 231 11 12.2013453840158 -1.20134538401581 232 12 11.4763916263767 0.523608373623256 233 13 12.4710260047961 0.528973995203875 234 10 13.3631226871786 -3.36312268717862 235 11 12.1739806392251 -1.17398063922514 236 12 12.0907621160289 -0.0907621160288627 237 8 12.2129183070712 -4.21291830707123 238 12 12.0246225763146 -0.0246225763146469 239 12 12.4443297425646 -0.444329742564602 240 11 12.0973859068501 -1.09738590685012 241 13 12.4010944341745 0.598905565825521 242 14 12.8728509403429 1.12714905965709 243 10 12.8386246882813 -2.83862468828132 244 12 12.8931295539449 -0.893129553944902 245 15 12.0651337808205 2.93486621917949 246 13 12.0327805328636 0.967219467136424 247 13 13.1270431051700 -0.127043105169957 248 13 13.5046261593222 -0.504626159322158 249 12 12.3156076133591 -0.315607613359097 250 12 12.4554981779107 -0.45549817791074 251 9 12.6406244552847 -3.64062445528467 252 9 13.2282206257933 -4.22822062579326 253 15 13.192817528107 1.807182471893 254 10 12.2604230024648 -2.26042300246483 255 14 13.2216585859672 0.778341414032796 256 15 12.0025905622613 2.99740943773867 257 7 12.2788725937998 -5.27887259379982 258 14 12.3671676495578 1.63283235044223 259 8 12.6515682667131 -4.65156826671306 260 10 13.2941355415897 -3.29413554158973 261 13 12.0775762853815 0.922423714618452 262 13 12.2175416934603 0.78245830653967 263 13 13.4741104428749 -0.474110442874854 264 8 12.1017059274573 -4.10170592745726 265 12 12.3962464238676 -0.396246423867639 266 13 13.1619405932196 -0.161940593219607 267 12 13.5544458876014 -1.55444588760143 268 10 12.3048660457853 -2.30486604578534 269 13 13.4469703220019 -0.446970322001933 270 12 12.6451073488143 -0.645107348814335 271 9 12.1314138133942 -3.13141381339416 272 15 12.530367618095 2.469632381905 273 13 12.6820839831604 0.317916016839630 274 13 12.0535719751566 0.94642802484336 275 13 12.6729159522464 0.327084047753606 276 15 11.2635617658352 3.73643823416484 277 15 12.327017663492 2.67298233650801 278 14 12.6177426040237 1.38225739597633 279 15 13.1864577321356 1.81354226786441 280 11 12.1647732373791 -1.16477323737906 281 15 12.8184978302103 2.18150216978969 282 14 13.3489044021032 0.651095597896834 283 13 12.1226491252813 0.877350874718697 284 12 12.0592278159739 -0.0592278159738843 285 16 12.7453535369368 3.25464646306319 286 16 12.018522876856 3.98147712314400 287 9 13.407084330786 -4.40708433078601 288 14 13.1205428163391 0.879457183660885 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.358930196295522 0.717860392591045 0.641069803704478 11 0.448739687685556 0.897479375371111 0.551260312314444 12 0.67636286593515 0.6472742681297 0.32363713406485 13 0.695973486708303 0.608053026583394 0.304026513291697 14 0.634185005926937 0.731629988146125 0.365814994073063 15 0.830223062758358 0.339553874483284 0.169776937241642 16 0.773806530494603 0.452386939010794 0.226193469505397 17 0.698329453303015 0.60334109339397 0.301670546696985 18 0.719153717146188 0.561692565707623 0.280846282853812 19 0.666002681418097 0.667994637163807 0.333997318581903 20 0.590426773349644 0.819146453300711 0.409573226650356 21 0.754601418823555 0.49079716235289 0.245398581176445 22 0.865231165434462 0.269537669131076 0.134768834565538 23 0.831599359835247 0.336801280329506 0.168400640164753 24 0.837855342736272 0.324289314527457 0.162144657263728 25 0.816859721919534 0.366280556160931 0.183140278080466 26 0.96855152065946 0.0628969586810801 0.0314484793405401 27 0.960833662426217 0.078332675147565 0.0391663375737825 28 0.946724172078724 0.106551655842551 0.0532758279212756 29 0.928408865678607 0.143182268642786 0.0715911343213932 30 0.943827177430067 0.112345645139866 0.0561728225699328 31 0.929133303498318 0.141733393003363 0.0708666965016816 32 0.912499326319414 0.175001347361172 0.087500673680586 33 0.898222083035655 0.20355583392869 0.101777916964345 34 0.872017694756547 0.255964610486906 0.127982305243453 35 0.841622014320701 0.316755971358598 0.158377985679299 36 0.821588660764654 0.356822678470692 0.178411339235346 37 0.90046270337563 0.199074593248741 0.0995372966243703 38 0.881846042009328 0.236307915981343 0.118153957990672 39 0.873400220374846 0.253199559250308 0.126599779625154 40 0.850471625090035 0.299056749819929 0.149528374909965 41 0.82199782158256 0.356004356834879 0.178002178417440 42 0.795749483792181 0.408501032415639 0.204250516207819 43 0.77857048060181 0.44285903879638 0.22142951939819 44 0.763546596815127 0.472906806369746 0.236453403184873 45 0.731269373918708 0.537461252162583 0.268730626081292 46 0.753713692655872 0.492572614688256 0.246286307344128 47 0.720857626127907 0.558284747744186 0.279142373872093 48 0.68027912297603 0.63944175404794 0.31972087702397 49 0.672525446687354 0.654949106625292 0.327474553312646 50 0.631815281032201 0.736369437935598 0.368184718967799 51 0.607940363510572 0.784119272978856 0.392059636489428 52 0.563595352742508 0.872809294514985 0.436404647257492 53 0.544456589452996 0.911086821094008 0.455543410547004 54 0.549536976339049 0.900926047321902 0.450463023660951 55 0.515449988133838 0.969100023732324 0.484550011866162 56 0.47404603803922 0.94809207607844 0.52595396196078 57 0.437202668411020 0.874405336822041 0.56279733158898 58 0.394917634196166 0.789835268392331 0.605082365803834 59 0.369221851788613 0.738443703577226 0.630778148211387 60 0.404474447256193 0.808948894512386 0.595525552743807 61 0.575627766681700 0.848744466636599 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0.688338442162554 252 0.345844720915972 0.691689441831944 0.654155279084028 253 0.326053608498063 0.652107216996125 0.673946391501937 254 0.302928382928226 0.605856765856453 0.697071617071773 255 0.259366807571524 0.518733615143049 0.740633192428475 256 0.24980207058659 0.49960414117318 0.75019792941341 257 0.441994183547034 0.883988367094067 0.558005816452966 258 0.416713847212537 0.833427694425075 0.583286152787463 259 0.664036945463862 0.671926109072275 0.335963054536138 260 0.680622976006884 0.638754047986232 0.319377023993116 261 0.628777366245814 0.742445267508372 0.371222633754186 262 0.567835484776264 0.864329030447472 0.432164515223736 263 0.504734081322237 0.990531837355526 0.495265918677763 264 0.784774694932994 0.430450610134013 0.215225305067006 265 0.736835198304998 0.526329603390004 0.263164801695002 266 0.689318394456549 0.621363211086902 0.310681605543451 267 0.709240244785966 0.581519510428067 0.290759755214033 268 0.711042223685127 0.577915552629745 0.288957776314873 269 0.633611661023615 0.73277667795277 0.366388338976385 270 0.555492113341331 0.889015773317338 0.444507886658669 271 0.661196146686769 0.677607706626462 0.338803853313231 272 0.573449671900275 0.85310065619945 0.426550328099725 273 0.502886746855429 0.994226506289141 0.497113253144571 274 0.407128362169368 0.814256724338736 0.592871637830632 275 0.35147399158198 0.70294798316396 0.64852600841802 276 0.264096783655839 0.528193567311678 0.735903216344161 277 0.189739391442570 0.379478782885141 0.81026060855743 278 0.112030095359088 0.224060190718177 0.887969904640912 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 0 0 OK 10% type I error level 2 0.00743494423791822 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/05/t1291580231e5hcwygpxfop3zx/10mozo1291580294.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t1291580231e5hcwygpxfop3zx/10mozo1291580294.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t1291580231e5hcwygpxfop3zx/1f52d1291580294.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t1291580231e5hcwygpxfop3zx/1f52d1291580294.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t1291580231e5hcwygpxfop3zx/2f52d1291580294.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t1291580231e5hcwygpxfop3zx/2f52d1291580294.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t1291580231e5hcwygpxfop3zx/38ejx1291580294.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t1291580231e5hcwygpxfop3zx/38ejx1291580294.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t1291580231e5hcwygpxfop3zx/48ejx1291580294.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t1291580231e5hcwygpxfop3zx/48ejx1291580294.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t1291580231e5hcwygpxfop3zx/58ejx1291580294.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t1291580231e5hcwygpxfop3zx/58ejx1291580294.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t1291580231e5hcwygpxfop3zx/6jn0j1291580294.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t1291580231e5hcwygpxfop3zx/6jn0j1291580294.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t1291580231e5hcwygpxfop3zx/7bfi41291580294.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t1291580231e5hcwygpxfop3zx/7bfi41291580294.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t1291580231e5hcwygpxfop3zx/8bfi41291580294.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t1291580231e5hcwygpxfop3zx/8bfi41291580294.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t1291580231e5hcwygpxfop3zx/9bfi41291580294.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/05/t1291580231e5hcwygpxfop3zx/9bfi41291580294.ps (open in new window)

Parameters (Session):

par1 = 3 ; par2 = equal ; par3 = 2 ; par4 = no ;

Parameters (R input):

par1 = 7 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = no ;

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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