CaseStatistiek - Multipele Regressie met maandelijkse dummy’s en trend

*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Wed, 30 Dec 2009 11:53:45 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/30/t1262199512rgw2tch2tmrevdv.htm/, Retrieved Wed, 30 Dec 2009 19:58:46 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Dec/30/t1262199512rgw2tch2tmrevdv.htm/}, year = {2009}, } @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 = {2009}, 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:

CaseStatistiek - Multipele Regressie met maandelijkse dummy’s en trend

Dataseries X:

» Textbox « » Textfile « » CSV «

15 2.1 14.4 2.1 13.5 2.6 12.8 2.6 12.3 2.7 12.2 2.5 14.5 2.4 17.2 1.9 18 2.2 18.1 1.9 18 2 18.3 2.2 18.7 2.5 18.6 2.5 18.3 2.7 17.9 2.6 17.4 2.3 17.4 2 20.1 2.3 23.2 2.9 24.2 2.5 24.2 2.5 23.9 2.3 23.8 2.5 23.8 2.3 23.3 2.4 22.4 2.2 21.5 2.4 20.5 2.6 19.9 2.8 22 2.8 24.9 2.5 25.7 2.5 25.3 2.2 24.4 2.1 23.8 1.9 23.5 1.9 23 1.7 22.2 1.7 21.4 1.6 20.3 1.4 19.5 1.1 21.7 0.8 24.7 0.9 25.3 1 24.9 1 24.1 1.1 23.4 1.3 23.1 1.4 22.4 1.4 21.3 1.6 20.3 2 19.3 2.1 18.7 1.9 21 1.5 24 1.2 24.8 1.5 24.2 2.2 23.3 2.1 22.7 2.1 22.3 2.1 21.8 1.9 21.2 1.3 20.5 1.1 19.7 1.4 19.2 1.6 21.2 1.9 23.9 1.7 24.8 1.6 24.2 1.2 23 1.3 22.2 0.9 21.8 0.5 21.2 0.8 20.5 1 19.7 1.3 19 1.3 18.4 1.2 20.7 1.2 24.5 1 26 0.8 25.2 0.7 24.1 0.6 23.7 0.7 23.5 1 23.1 1 22.7 1.3 22.5 1.1 21.7 0.8 20.5 0.7 21.9 0.7 22.9 0.9 21.5 1.3 19 1.4 17 1.6 16.1 2.1 15.9 0.3 15.7 2.1 15.1 2.5 14.8 2.3 14.3 2.4 14.5 3 18.9 1.7 21.6 3.5 20.4 4 17.9 3.7 15.7 3.7 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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y(Werkloosheid)[t] = + 22.3119272633899 -0.845157726243135`X(inflatie)`[t] -0.468052257632672M1[t] -0.676589278536247M2[t] -1.24014382457792M3[t] -1.66097439588356M4[t] -2.42280847221682M5[t] -2.63589692983462M6[t] + 0.551946789395343M7[t] + 2.41265713972108M8[t] + 2.42304528561004M9[t] + 1.40995682799224M10[t] + 0.350739892750045M11[t] -0.00311212062499351t + 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) 22.3119272633899 0.771389 28.9243 0 0 `X(inflatie)` -0.845157726243135 0.169364 -4.9902 1e-06 1e-06 M1 -0.468052257632672 0.879524 -0.5322 0.595202 0.297601 M2 -0.676589278536247 0.879261 -0.7695 0.442506 0.221253 M3 -1.24014382457792 0.879228 -1.4105 0.159948 0.079974 M4 -1.66097439588356 0.879203 -1.8892 0.060315 0.030157 M5 -2.42280847221682 0.879191 -2.7557 0.006397 0.003199 M6 -2.63589692983462 0.879227 -2.998 0.003062 0.001531 M7 0.551946789395343 0.879655 0.6275 0.531075 0.265537 M8 2.41265713972108 0.879297 2.7438 0.006625 0.003312 M9 2.42304528561004 0.879354 2.7555 0.006402 0.003201 M10 1.40995682799224 0.879529 1.6031 0.110495 0.055247 M11 0.350739892750045 0.891661 0.3934 0.694476 0.347238 t -0.00311212062499351 0.002888 -1.0776 0.2825 0.14125 Multiple Linear Regression - Regression Statistics Multiple R 0.600826655444131 R-squared 0.360992669892181 Adjusted R-squared 0.319457193435173 F-TEST (value) 8.69118885071248 F-TEST (DF numerator) 13 F-TEST (DF denominator) 200 p-value 5.9841021027296e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.59960122520741 Sum Squared Residuals 1351.58530601997 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 15 20.0659316600211 -5.06593166002109 2 14.4 19.8542825184930 -5.45428251849305 3 13.5 18.8650369887048 -5.3650369887048 4 12.8 18.4410942967742 -5.64109429677418 5 12.3 17.5916323271916 -5.2916323271916 6 12.2 17.5444632941974 -5.34446329419744 7 14.5 20.8137106654267 -6.31371066542673 8 17.2 23.0938877582490 -5.89388775824903 9 18 22.8476164656401 -4.84761646564005 10 18.1 22.0849632052702 -3.98496320527021 11 18 20.9381183767787 -2.93811837677872 12 18.3 20.4152348181550 -2.11523481815504 13 18.7 19.6905231220244 -0.990523122024437 14 18.6 19.4788739804959 -0.878873980495865 15 18.3 18.7431757685806 -0.443175768580572 16 17.9 18.4037488492743 -0.503748849274256 17 17.4 17.8923499701889 -0.49234997018894 18 17.4 17.9296967098191 -0.52969670981909 19 20.1 20.8608809905511 -0.760880990551116 20 23.2 22.2113845845060 0.988615415494023 21 24.2 22.5567237002672 1.64327629973281 22 24.2 21.5405231220244 2.65947687797559 23 23.9 20.6472256114058 3.25277438859415 24 23.8 20.1243420527822 3.67565794721782 25 23.8 19.8222092197731 3.97779078022686 26 23.3 19.5260443056203 3.77395569437974 27 22.4 19.1284091842022 3.27159081579778 28 21.5 18.5354349470230 2.96456505297704 29 20.5 17.6014572048161 2.89854279518392 30 19.9 17.2162250813247 2.68377491867534 31 22 20.4009566799296 1.59904332007037 32 24.9 22.5121022275033 2.38789777249669 33 25.7 22.5193782527673 3.18062174723273 34 25.3 21.7567249923974 3.54327500760257 35 24.4 20.7789117091545 3.62108829084545 36 23.8 20.5940912410281 3.20590875897186 37 23.5 20.1229268627705 3.37707313722953 38 23 20.0803092664905 2.91969073350947 39 22.2 19.5136425998239 2.68635740017614 40 21.4 19.1742156805175 2.22578431948245 41 20.3 18.5783010288079 1.72169897119209 42 19.5 18.6156477684381 0.884352231561935 43 21.7 22.0539266849160 -0.353926684915975 44 24.7 23.8270091419924 0.872990858007598 45 25.3 23.7497693946321 1.55023060536795 46 24.9 22.7335688163893 2.16643118361073 47 24.1 21.5867239878978 2.51327601210224 48 23.4 21.0638404292741 2.33615957072590 49 23.1 20.5081602783921 2.59183972160788 50 22.4 20.2965111368635 2.10348886313645 51 21.3 19.5608129249483 1.73918707505175 52 20.3 18.7988071425204 1.50119285747963 53 19.3 17.9493451729378 1.35065482706220 54 18.7 17.9021761399436 0.797823860056363 55 21 21.4249708290459 -0.424970829045858 56 24 23.5361163766195 0.463883623380462 57 24.8 23.2898450840106 1.51015491598944 58 24.2 21.6820340973976 2.51796590260242 59 23.3 20.7042208141547 2.59577918584530 60 22.7 20.3503688007797 2.34963119922033 61 22.3 19.879204422522 2.420795577478 62 21.8 19.8365868262421 1.96341317375794 63 21.2 19.7770147953213 1.42298520467873 64 20.5 19.5221036486393 0.977896351360733 65 19.7 18.5036101338081 1.19638986619193 66 19.2 18.1183780103167 1.08162198968335 67 21.2 21.0495622910487 0.150437708951317 68 23.9 23.0761920659981 0.82380793400195 69 24.8 23.1679838638863 1.63201613611367 70 24.2 22.4898463761408 1.71015362385921 71 23 21.3430015476493 1.65699845235071 72 22.2 21.3272126247715 0.872787375228494 73 21.8 21.1941113370111 0.605888662988908 74 21.2 20.7289148776096 0.471085122390416 75 20.5 19.9932166656943 0.506783334305709 76 19.7 19.3157266558907 0.384273344109281 77 19 18.5507804589325 0.449219541067539 78 18.4 18.419095653314 -0.0190956533139872 79 20.7 21.6038272519190 -0.903827251918955 80 24.5 23.6304570268683 0.869542973131679 81 26 23.8067645973809 2.19323540261909 82 25.2 22.8750797917624 2.32492020823756 83 24.1 21.8972665085196 2.20273349148044 84 23.7 21.4588987225202 2.24110127747979 85 23.5 20.7341870263896 2.76581297361040 86 23.1 20.5225378848610 2.57746211513897 87 22.7 19.7023239003214 2.99767609967857 88 22.5 19.4474127536394 3.05258724636058 89 21.7 18.9360138745541 2.76398612544589 90 20.5 18.8043290689356 1.69567093106437 91 21.9 21.9890606675406 -0.0890606675406008 92 22.9 23.6776273519927 -0.777627351992713 93 21.5 23.3468402867594 -1.84684028675942 94 19 22.2461239358923 -3.24612393589232 95 17 21.0147633347765 -4.01476333477651 96 16.1 20.2383324582799 -4.1383324582799 97 15.9 21.2884519872599 -5.38845198725988 98 15.7 19.5555189384937 -3.85551893849367 99 15.1 18.6507891813297 -3.55078918132974 100 14.8 18.3958780346477 -3.59587803464774 101 14.3 17.5464160650652 -3.24641606506517 102 14.5 16.8231208510765 -2.3231208510765 103 18.9 21.1065574937975 -2.20655749379754 104 21.6 21.4428718162606 0.157128183739361 105 20.4 21.0275689784030 -0.62756897840304 106 17.9 20.2649157180332 -2.36491571803319 107 15.7 19.202586662166 -3.502586662166 108 14.5 19.4403450571612 -4.94034505716116 109 14 19.2227279967764 -5.22272799677643 110 13.9 19.1801104004965 -5.28011040049649 111 14.4 18.8669910517028 -4.46699105170276 112 15.8 17.8514379514019 -2.05143795140194 113 15.6 16.9174602091951 -1.31746020919505 114 14.7 16.7857754035766 -2.08577540357658 115 16.7 20.1395385474302 -3.43953854743017 116 17.9 22.2506840950039 -4.35068409500385 117 18.7 22.7650547560137 -4.0650547560137 118 20.1 21.7488541777709 -1.64885417777091 119 19.5 20.7710408945280 -1.27104089452804 120 19.4 20.2481573359044 -0.84815733590437 121 18.6 19.2698983219008 -0.669898321900821 122 17.8 19.1427649529966 -1.34276495299657 123 17.1 18.5760982863299 -1.4760982863299 124 16.5 18.9127975480181 -2.41279754801809 125 15.5 18.3168828963085 -2.81688289630846 126 14.9 18.6077769538116 -3.70777695381155 127 18.6 21.5389612345436 -2.93896123454358 128 19.1 23.2275279189957 -4.12752791899569 129 18.8 23.3193197168840 -4.51931971688397 130 18.2 22.2186033660169 -4.01860336601687 131 18 21.3253058553983 -3.32530585539831 132 19 20.8024222967746 -1.80242229677464 133 20.7 20.4157736911413 0.284226308858711 134 21.2 19.8660614591155 1.33393854088453 135 20.7 19.2148790198245 1.48512098017551 136 19.6 18.9599678731425 0.64003212685752 137 18.6 18.7021163119301 -0.102116311930104 138 18.7 17.9788210979414 0.721178902058564 139 23.8 21.2480684691707 2.55193153082928 140 24.9 22.9366351536228 1.96336484637717 141 24.8 22.8593954062625 1.94060459373752 142 23.8 22.0967421458926 1.70325785410737 143 22.3 20.6963499995282 1.60365000047181 144 21.7 20.4270137587775 1.27298624122253 145 20.7 20.2093966983927 0.490603301607260 146 19.7 20.1667791021128 -0.466779102112798 147 18.4 19.7691439806948 -1.36914398069476 148 17.4 18.7535908803939 -1.35359088039393 149 17 17.3970342750655 -0.397034275065482 150 18 17.5188967873199 0.481103212680054 151 23.8 20.6191126133006 3.1808873866994 152 25.5 22.5612266156257 2.93877338437435 153 25.6 22.7375341861382 2.86246581386175 154 23.7 20.9606916542766 2.73930834572336 155 22 20.2364256889067 1.76357431109330 156 21.3 20.2206367660289 1.07936323397108 157 20.7 19.6649566151469 1.03504338485306 158 20.4 19.1997601557454 1.20023984425457 159 20.3 18.2105146259572 2.08948537404281 160 20.4 18.1246350245238 2.27536497547618 161 19.8 17.4442046001899 2.35579539981013 162 19.5 16.8899409314498 2.61005906855017 163 23.1 20.0746725300548 3.0253274699452 164 23.5 21.7632392145069 1.73676078549309 165 23.5 21.6859994671466 1.81400053285344 166 22.9 21.3459250698983 1.55407493010172 167 21.9 20.1990802414068 1.70091975859322 168 21.5 19.4226493649102 2.07735063508983 169 20.5 18.9514849866525 1.54851501334749 170 20.2 18.7398358451239 1.46016415487606 171 19.4 18.6802638142032 0.719736185796846 172 19.2 17.9182580317753 1.28174196822473 173 18.8 16.9842802895684 1.81571971043162 174 18.8 17.0216270291985 1.77837297080147 175 22.6 20.2908744004278 2.30912559957219 176 23.3 22.2329884027529 1.06701159724713 177 23 22.5783275185141 0.421672481485911 178 21.4 21.7311584855199 -0.331158485519928 179 19.9 20.4152821117798 -0.5152821117798 180 18.8 19.9769143257804 -1.17691432578044 181 18.6 19.8438130380200 -1.24381303802003 182 18.4 19.5476481238672 -1.14764812386715 183 18.6 18.9809814572005 -0.380981457200483 184 19.9 18.5570387652699 1.34296123473015 185 19.2 18.2146714314332 0.985328568566837 186 18.4 17.9984708531904 0.401529146809626 187 21.1 21.1832024517953 -0.0832024517953405 188 20.5 23.1253164541204 -2.62531645412039 189 19.1 22.9635609341357 -3.86356093413573 190 18.1 21.2712341748984 -3.17123417489844 191 17 19.6172947106611 -2.61729471066106 192 17.1 19.0944111520374 -1.99441115203739 193 17.4 18.2851836832825 -0.885183683282472 194 16.8 17.9890187691296 -1.18901876912959 195 15.3 16.7462259214684 -1.44622592146841 196 14.3 16.5758305474107 -2.27583054741072 197 13.4 14.9657266242093 -1.56572662420933 198 15.3 14.1579156375963 1.14208436240365 199 22.1 17.258131463577 4.841868536423 200 23.7 19.5383085563993 4.16169144360069 201 22.2 19.4610688090390 2.73893119096104 202 19.5 19.0364786391664 0.463521360833633 203 16.6 19.3264019452882 -2.72640194528819 204 17.3 19.3951287950347 -2.09512879503472 205 19.8 19.4310590525229 0.368940947477065 206 21.2 19.388441456243 1.81155854375701 207 21.5 19.9204798336924 1.5795201663076 208 20.6 19.4120213691375 1.18797863086255 209 19.1 19.407717125798 -0.307717125798018 210 19.6 19.8676427285497 -0.267642728549737 211 23.5 23.6439847355249 -0.143984735524900 212 24 24.6564252389825 -0.656425238982506 213 23.2 24.9172485821194 -1.71724858211941 214 21.2 23.8165322312523 -2.61653223125231 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.00219386553496994 0.00438773106993987 0.99780613446503 18 0.000262292061780181 0.000524584123560361 0.99973770793822 19 0.000148920626777027 0.000297841253554054 0.999851079373223 20 0.000889480066704738 0.00177896013340948 0.999110519933295 21 0.000532553359143747 0.00106510671828749 0.999467446640856 22 0.000209935689878497 0.000419871379756994 0.999790064310122 23 6.76130474790721e-05 0.000135226094958144 0.999932386952521 24 1.68725427920608e-05 3.37450855841216e-05 0.999983127457208 25 7.18281920765376e-06 1.43656384153075e-05 0.999992817180792 26 3.17846768625148e-06 6.35693537250296e-06 0.999996821532314 27 1.06482587399752e-06 2.12965174799503e-06 0.999998935174126 28 5.96962800974273e-07 1.19392560194855e-06 0.9999994030372 29 1.0922851680909e-06 2.1845703361818e-06 0.999998907714832 30 5.80531455384039e-06 1.16106291076808e-05 0.999994194685446 31 1.58903467917798e-05 3.17806935835597e-05 0.999984109653208 32 2.18058446282902e-05 4.36116892565804e-05 0.999978194155372 33 2.64561926591471e-05 5.29123853182942e-05 0.99997354380734 34 4.11126025800664e-05 8.22252051601329e-05 0.99995888739742 35 0.000100595252152664 0.000201190504305328 0.999899404747847 36 0.000222472407315671 0.000444944814631342 0.999777527592684 37 0.000418969783080435 0.00083793956616087 0.99958103021692 38 0.000392111800603987 0.000784223601207975 0.999607888199396 39 0.000265564264374385 0.000531128528748769 0.999734435735626 40 0.000153227733830093 0.000306455467660187 0.99984677226617 41 8.19901506453517e-05 0.000163980301290703 0.999918009849355 42 4.19692865074351e-05 8.39385730148703e-05 0.999958030713493 43 2.12390306667535e-05 4.24780613335069e-05 0.999978760969333 44 1.01406202045212e-05 2.02812404090424e-05 0.999989859379795 45 5.2398481765334e-06 1.04796963530668e-05 0.999994760151824 46 3.81632221579245e-06 7.6326444315849e-06 0.999996183677784 47 4.7554673199533e-06 9.5109346399066e-06 0.99999524453268 48 1.19311500342561e-05 2.38623000685122e-05 0.999988068849966 49 4.03406459633968e-05 8.06812919267936e-05 0.999959659354037 50 0.000117467077176759 0.000234934154353519 0.999882532922823 51 0.000374152089337856 0.000748304178675712 0.999625847910662 52 0.00230274442753217 0.00460548885506434 0.997697255572468 53 0.00981774001140582 0.0196354800228116 0.990182259988594 54 0.0242114241166965 0.048422848233393 0.975788575883303 55 0.0330917814701884 0.0661835629403768 0.966908218529812 56 0.0343238678138944 0.0686477356277887 0.965676132186106 57 0.0414421301539309 0.0828842603078617 0.95855786984607 58 0.0904064073293604 0.180812814658721 0.90959359267064 59 0.154060637736731 0.308121275473462 0.845939362263269 60 0.222857283141036 0.445714566282071 0.777142716858964 61 0.275492676234387 0.550985352468773 0.724507323765613 62 0.306618628909731 0.613237257819462 0.693381371090269 63 0.301252229787959 0.602504459575919 0.698747770212041 64 0.282659796020917 0.565319592041834 0.717340203979083 65 0.269458865120474 0.538917730240949 0.730541134879526 66 0.262411590939579 0.524823181879158 0.737588409060421 67 0.265231513554858 0.530463027109717 0.734768486445142 68 0.269005930254623 0.538011860509246 0.730994069745377 69 0.271987377054885 0.543974754109771 0.728012622945115 70 0.277996087496112 0.555992174992225 0.722003912503888 71 0.301824106440183 0.603648212880367 0.698175893559817 72 0.315988426615308 0.631976853230617 0.684011573384692 73 0.30513711316392 0.61027422632784 0.69486288683608 74 0.298472348400744 0.596944696801489 0.701527651599256 75 0.291538940847304 0.583077881694607 0.708461059152696 76 0.287876924800365 0.575753849600731 0.712123075199635 77 0.278997682419674 0.557995364839349 0.721002317580326 78 0.268535181079892 0.537070362159783 0.731464818920108 79 0.255761514945842 0.511523029891683 0.744238485054158 80 0.234208610384854 0.468417220769709 0.765791389615146 81 0.228746874638317 0.457493749276635 0.771253125361683 82 0.235752509268745 0.47150501853749 0.764247490731255 83 0.250718717628978 0.501437435257955 0.749281282371022 84 0.271468939306588 0.542937878613176 0.728531060693412 85 0.300928286018024 0.601856572036049 0.699071713981976 86 0.327686543262931 0.655373086525861 0.67231345673707 87 0.369973260419879 0.739946520839758 0.630026739580121 88 0.41845655412865 0.8369131082573 0.58154344587135 89 0.471732197656206 0.943464395312413 0.528267802343794 90 0.488347036679414 0.976694073358827 0.511652963320586 91 0.459962844222814 0.919925688445629 0.540037155777186 92 0.483145915061967 0.966291830123934 0.516854084938033 93 0.608840179980754 0.782319640038492 0.391159820019246 94 0.794804371044196 0.410391257911609 0.205195628955804 95 0.922932627011357 0.154134745977286 0.0770673729886428 96 0.972122223670917 0.0557555526581658 0.0278777763290829 97 0.989926547718292 0.0201469045634156 0.0100734522817078 98 0.994470813058114 0.0110583738837712 0.00552918694188558 99 0.996008367811531 0.00798326437693697 0.00399163218846849 100 0.996713829191385 0.00657234161722937 0.00328617080861468 101 0.996789666889474 0.0064206662210527 0.00321033311052635 102 0.995995533218378 0.00800893356324488 0.00400446678162244 103 0.995134568710738 0.00973086257852304 0.00486543128926152 104 0.993925754801861 0.0121484903962775 0.00607424519813875 105 0.99197800590591 0.0160439881881791 0.00802199409408954 106 0.9901201462846 0.0197597074308006 0.00987985371540031 107 0.989612351066014 0.0207752978679715 0.0103876489339857 108 0.992828383582282 0.0143432328354352 0.00717161641771761 109 0.995763819691072 0.00847236061785646 0.00423618030892823 110 0.997804367268336 0.00439126546332749 0.00219563273166374 111 0.99852432491977 0.00295135016046247 0.00147567508023123 112 0.99812848487551 0.00374303024897927 0.00187151512448964 113 0.997510247556279 0.00497950488744263 0.00248975244372131 114 0.997090417181772 0.00581916563645693 0.00290958281822847 115 0.998247924953603 0.00350415009279378 0.00175207504639689 116 0.999095308796953 0.00180938240609491 0.000904691203047453 117 0.999443784374333 0.00111243125133453 0.000556215625667266 118 0.999250401016231 0.00149919796753755 0.000749598983768773 119 0.998944892442454 0.00211021511509246 0.00105510755754623 120 0.998499598760884 0.00300080247823227 0.00150040123911613 121 0.99805730177734 0.00388539644532143 0.00194269822266071 122 0.997645748328523 0.00470850334295375 0.00235425167147687 123 0.99723287357963 0.00553425284074185 0.00276712642037092 124 0.99724666942535 0.00550666114929832 0.00275333057464916 125 0.997609633411185 0.00478073317762978 0.00239036658881489 126 0.998802793115442 0.00239441376911694 0.00119720688455847 127 0.9995631803826 0.000873639234798842 0.000436819617399421 128 0.999917337633673 0.000165324732654103 8.26623663270513e-05 129 0.999990700864012 1.85982719756708e-05 9.29913598783538e-06 130 0.99999854737987 2.90524026192165e-06 1.45262013096083e-06 131 0.999999498276827 1.00344634582624e-06 5.01723172913118e-07 132 0.99999954160491 9.16790177528964e-07 4.58395088764482e-07 133 0.999999267183315 1.46563336912039e-06 7.32816684560197e-07 134 0.999998893422106 2.21315578741017e-06 1.10657789370508e-06 135 0.999998353933178 3.29213364403409e-06 1.64606682201705e-06 136 0.99999746899791 5.0620041790483e-06 2.53100208952415e-06 137 0.999996406724257 7.18655148540499e-06 3.59327574270250e-06 138 0.999995414159882 9.17168023620021e-06 4.58584011810011e-06 139 0.9999951791603 9.64167940222912e-06 4.82083970111456e-06 140 0.99999351285026 1.2974299479486e-05 6.487149739743e-06 141 0.999990708317525 1.85833649498292e-05 9.2916824749146e-06 142 0.999986132853557 2.77342928857259e-05 1.38671464428630e-05 143 0.999980990040237 3.80199195266957e-05 1.90099597633479e-05 144 0.999971522191179 5.69556176424205e-05 2.84778088212103e-05 145 0.999954427784431 9.1144431138557e-05 4.55722155692785e-05 146 0.999940041572164 0.000119916855671819 5.99584278359095e-05 147 0.99994882124935 0.000102357501300850 5.11787506504249e-05 148 0.999969313126324 6.13737473514143e-05 3.06868736757071e-05 149 0.999974537847932 5.0924304135998e-05 2.5462152067999e-05 150 0.999975651943583 4.86961128347798e-05 2.43480564173899e-05 151 0.999973613953467 5.27720930660061e-05 2.63860465330030e-05 152 0.999965661042064 6.86779158716536e-05 3.43389579358268e-05 153 0.999958117642822 8.37647143558455e-05 4.18823571779227e-05 154 0.999955649918508 8.87001629839255e-05 4.43500814919628e-05 155 0.99994377156762 0.000112456864761517 5.62284323807587e-05 156 0.999911666433119 0.000176667133761904 8.83335668809518e-05 157 0.999855536500098 0.000288926999804997 0.000144463499902498 158 0.999770875031995 0.000458249936010301 0.000229124968005151 159 0.999673443465515 0.000653113068969613 0.000326556534484806 160 0.999534326402862 0.000931347194275593 0.000465673597137796 161 0.999357242375214 0.00128551524957244 0.000642757624786218 162 0.999114361404 0.00177127719200020 0.000885638596000102 163 0.998811466913793 0.00237706617241481 0.00118853308620741 164 0.998217102350895 0.00356579529821074 0.00178289764910537 165 0.997512622116249 0.00497475576750278 0.00248737788375139 166 0.997029323670137 0.00594135265972604 0.00297067632986302 167 0.99762094381455 0.00475811237090032 0.00237905618545016 168 0.99834185545209 0.00331628909581796 0.00165814454790898 169 0.997897303815984 0.00420539236803124 0.00210269618401562 170 0.997071772829872 0.00585645434025575 0.00292822717012787 171 0.995480594460797 0.0090388110784059 0.00451940553920295 172 0.99342447134352 0.0131510573129605 0.00657552865648026 173 0.992100769965803 0.0157984600683947 0.00789923003419737 174 0.989355999558421 0.0212880008831581 0.0106440004415790 175 0.984984941874531 0.0300301162509376 0.0150150581254688 176 0.978695467692007 0.0426090646159852 0.0213045323079926 177 0.974000185143546 0.0519996297129071 0.0259998148564535 178 0.971583498925738 0.0568330021485243 0.0284165010742621 179 0.976669511583996 0.0466609768320077 0.0233304884160038 180 0.973243364965172 0.0535132700696567 0.0267566350348283 181 0.960615396195616 0.0787692076087689 0.0393846038043844 182 0.941860472338219 0.116279055323563 0.0581395276617813 183 0.920137056253163 0.159725887493675 0.0798629437468374 184 0.939420153405118 0.121159693189764 0.0605798465948822 185 0.97513611428762 0.0497277714247613 0.0248638857123807 186 0.983517232879284 0.0329655342414321 0.0164827671207161 187 0.975066558116042 0.0498668837679157 0.0249334418839578 188 0.958793247028146 0.0824135059437086 0.0412067529718543 189 0.937175682060427 0.125648635879147 0.0628243179395735 190 0.906932919975442 0.186134160049115 0.0930670800245575 191 0.912713057834673 0.174573884330655 0.0872869421653273 192 0.94852481725868 0.102950365482639 0.0514751827413194 193 0.95864402114871 0.0827119577025808 0.0413559788512904 194 0.960755398992611 0.0784892020147779 0.0392446010073890 195 0.917473141817943 0.165053716364115 0.0825268581820573 196 0.83816563477557 0.323668730448858 0.161834365224429 197 0.884788576510282 0.230422846979435 0.115211423489718 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 104 0.574585635359116 NOK 5% type I error level 122 0.674033149171271 NOK 10% type I error level 133 0.734806629834254 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/30/t1262199512rgw2tch2tmrevdv/10hm0r1262199215.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262199512rgw2tch2tmrevdv/10hm0r1262199215.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262199512rgw2tch2tmrevdv/1e4zo1262199215.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262199512rgw2tch2tmrevdv/1e4zo1262199215.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262199512rgw2tch2tmrevdv/2n59y1262199215.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262199512rgw2tch2tmrevdv/2n59y1262199215.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262199512rgw2tch2tmrevdv/3dqo31262199215.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262199512rgw2tch2tmrevdv/3dqo31262199215.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262199512rgw2tch2tmrevdv/4ozuu1262199215.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262199512rgw2tch2tmrevdv/4ozuu1262199215.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262199512rgw2tch2tmrevdv/5g1811262199215.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262199512rgw2tch2tmrevdv/5g1811262199215.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262199512rgw2tch2tmrevdv/6qx0v1262199215.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262199512rgw2tch2tmrevdv/6qx0v1262199215.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262199512rgw2tch2tmrevdv/7r8df1262199215.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262199512rgw2tch2tmrevdv/7r8df1262199215.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262199512rgw2tch2tmrevdv/86g7j1262199215.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262199512rgw2tch2tmrevdv/86g7j1262199215.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262199512rgw2tch2tmrevdv/97nyo1262199215.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262199512rgw2tch2tmrevdv/97nyo1262199215.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

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

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

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