Multiple Regression 4

*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, 29 Dec 2009 04:08:12 -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/29/t126208500330p1w5t28nm4rkh.htm/, Retrieved Tue, 29 Dec 2009 12:10:16 +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/29/t126208500330p1w5t28nm4rkh.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:

Met Seasonal Dummies Met Lineair trend Met 4lags

Dataseries X:

» Textbox « » Textfile « » CSV «

4.3 10.8 4.4 4.4 4.5 4.6 4.1 10.4 4.3 4.4 4.4 4.5 3.9 10.1 4.1 4.3 4.4 4.4 3.7 9.8 3.9 4.1 4.3 4.4 3.6 9.7 3.7 3.9 4.1 4.3 3.9 10.3 3.6 3.7 3.9 4.1 4.2 10.9 3.9 3.6 3.7 3.9 4.2 10.8 4.2 3.9 3.6 3.7 4.1 10.6 4.2 4.2 3.9 3.6 4.1 10.4 4.1 4.2 4.2 3.9 4.1 10.3 4.1 4.1 4.2 4.2 4.1 10.2 4.1 4.1 4.1 4.2 4.1 10 4.1 4.1 4.1 4.1 4 9.7 4.1 4.1 4.1 4.1 3.9 9.4 4 4.1 4.1 4.1 3.8 9.2 3.9 4 4.1 4.1 3.8 9.1 3.8 3.9 4 4.1 4 9.6 3.8 3.8 3.9 4 4.4 10.2 4 3.8 3.8 3.9 4.6 10.2 4.4 4 3.8 3.8 4.6 10 4.6 4.4 4 3.8 4.6 9.9 4.6 4.6 4.4 4 4.7 9.9 4.6 4.6 4.6 4.4 4.8 9.9 4.7 4.6 4.6 4.6 4.8 9.7 4.8 4.7 4.6 4.6 4.7 9.5 4.8 4.8 4.7 4.6 4.7 9.4 4.7 4.8 4.8 4.7 4.7 9.3 4.7 4.7 4.8 4.8 4.6 9.3 4.7 4.7 4.7 4.8 5 9.9 4.6 4.7 4.7 4.7 5.4 10.5 5 4.6 4.7 4.7 5.5 10.6 5.4 5 4.6 4.7 5.6 10.6 5.5 5.4 5 4.6 5.6 10.5 5.6 5.5 5.4 5 5.8 10.6 5.6 5.6 5.5 5.4 6 10.8 5.8 5.6 5.6 5.5 6.1 10.8 6 5.8 5.6 5.6 6.1 10.7 6.1 6 5.8 5.6 6 10.6 6.1 6.1 6 5.8 6 10.6 6 6.1 6.1 6 6.1 10.8 6 6 6.1 6.1 6.5 11.4 6.1 6 6 6.1 7.1 12 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 9 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 0.0335157175898164 + 0.0317667969328308X[t] + 1.49494432782640Y1[t] -0.669453640778338Y2[t] -0.126862020467570Y3[t] + 0.246168085780859Y4[t] -0.169060236440471M1[t] -0.143500017446115M2[t] -0.101294922082687M3[t] -0.179767159035877M4[t] -0.185797235933362M5[t] + 0.26915662315277M6[t] -0.114909765968540M7[t] -0.171035776651497M8[t] -0.00890299086717574M9[t] -0.068787914595903M10[t] + 0.0463262564646009M11[t] + 0.000843338901157726t + 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) 0.0335157175898164 0.132317 0.2533 0.800276 0.400138 X 0.0317667969328308 0.019135 1.6601 0.098329 0.049165 Y1 1.49494432782640 0.066947 22.3303 0 0 Y2 -0.669453640778338 0.121043 -5.5307 0 0 Y3 -0.126862020467570 0.121326 -1.0456 0.296889 0.148445 Y4 0.246168085780859 0.06621 3.718 0.000255 0.000128 M1 -0.169060236440471 0.057317 -2.9496 0.003529 0.001765 M2 -0.143500017446115 0.058663 -2.4462 0.01523 0.007615 M3 -0.101294922082687 0.058463 -1.7326 0.084576 0.042288 M4 -0.179767159035877 0.058673 -3.0639 0.00246 0.00123 M5 -0.185797235933362 0.059449 -3.1253 0.002018 0.001009 M6 0.26915662315277 0.058842 4.5742 8e-06 4e-06 M7 -0.114909765968540 0.060531 -1.8984 0.058968 0.029484 M8 -0.171035776651497 0.065159 -2.6249 0.00928 0.00464 M9 -0.00890299086717574 0.061737 -0.1442 0.885469 0.442734 M10 -0.068787914595903 0.058749 -1.1709 0.242924 0.121462 M11 0.0463262564646009 0.057902 0.8001 0.424533 0.212266 t 0.000843338901157726 0.000519 1.6259 0.105408 0.052704 Multiple Linear Regression - Regression Statistics Multiple R 0.989982053773046 R-squared 0.980064466792699 Adjusted R-squared 0.97850986099213 F-TEST (value) 630.426354020904 F-TEST (DF numerator) 17 F-TEST (DF denominator) 218 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.175250034029212 Sum Squared Residuals 6.69534122513832 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4.3 4.40203335242442 -0.102033352424419 2 4.1 4.25430515223282 -0.154305152232818 3 3.9 4.03116323735205 -0.131163237352046 4 3.7 3.7915923648573 -0.0915923648573 5 3.6 3.61888640527351 -0.0188864052735082 6 3.9 4.05427876373087 -0.154278763730867 7 4.2 4.18168324103351 0.0183167589664943 8 4.2 4.33432368056343 -0.134323680563429 9 4.1 4.22743493891048 -0.127434938910483 10 4.1 4.04833738150769 0.0516626184923065 11 4.1 4.30191400158816 -0.201914001588164 12 4.1 4.26594060637819 -0.165940606378193 13 4.1 4.06675354087423 0.0332464591257717 14 4 4.08362705968989 -0.0836270596898938 15 3.9 3.96765102209199 -0.0676510220919917 16 3.8 3.80111969594859 -0.00111969594858663 17 3.8 3.72289341160093 0.0771065883990729 18 4 4.24958876560114 -0.249588765601138 19 4.4 4.17248405257463 0.227515947425368 20 4.6 4.55667157518964 0.0433284248103599 21 4.6 4.71912934564898 -0.119129345648983 22 4.6 4.52150916194161 0.0784908380583934 23 4.7 4.7105615021221 -0.0105615021220973 24 4.8 4.86380663449747 -0.0638066344974667 25 4.8 4.77178544627639 0.0282145537236084 26 4.7 4.71220407866075 -0.0122040786607490 27 4.7 4.61451200698074 0.0854879930192584 28 4.7 4.62526860189135 0.0747313981086547 29 4.6 4.63276806594178 -0.0327680659417752 30 5 4.93351410072804 0.0664858992719626 31 5.4 5.23427422387598 0.165725776124024 32 5.5 5.52505070865344 -0.0250507086534416 33 5.6 5.49437819304511 0.105621806954890 34 5.6 5.56243142335438 0.0375685766456217 35 5.8 5.70040128119708 0.099598718802924 36 6 5.97219119511681 0.0278088048831929 37 6.1 5.99368924356519 0.106310756434808 38 6.1 6.00714742230088 0.0928525776991196 39 6 6.003935025857 -0.00393502585700686 40 6 5.81335911013175 0.186640889868250 41 6.1 5.90608790417791 0.193912095822092 42 6.5 6.54312581515429 -0.0431258151542925 43 7.1 6.69173176095504 0.408268239044956 44 7.4 7.25930138689756 0.140698613102444 45 7.4 7.44296062585501 -0.0429606258550102 46 7.5 7.20225629113246 0.297743708867543 47 7.6 7.58052715889829 0.0194728411017143 48 7.8 7.69462041546719 0.105379584532811 49 7.8 7.74576081736856 0.0542391826314357 50 7.7 7.64702757394646 0.0529724260535435 51 7.6 7.53664930021969 0.0633506997803081 52 7.5 7.42252827092574 0.0774717290742593 53 7.3 7.34430198657808 -0.0443019865780823 54 7.6 7.57200847501301 0.0279915249869868 55 8 7.77828892292482 0.221711077075184 56 8 8.12725684494207 -0.127256844942070 57 7.9 7.9288059306332 -0.0288059306332038 58 7.8 7.73384549149038 0.0661545085096245 59 7.7 7.86254448736629 -0.162544487366291 60 7.8 7.74402202345152 0.0559779765484836 61 7.7 7.77713763654806 -0.0771376365480636 62 7.5 7.56881743166521 -0.0688174316652107 63 7.3 7.33298931473766 -0.0329893147376583 64 7.1 7.12438861020757 -0.0243886102075737 65 7 6.95168265062378 0.0483173493762211 66 7.3 7.38707500908114 -0.0870750090811387 67 7.8 7.51765616607706 0.282343833922938 68 7.9 7.97881551025211 -0.078815510252111 69 7.9 7.89070715291942 0.00929284708057888 70 7.8 7.76560958043464 0.0343904195653585 71 7.8 7.83929381876405 -0.0392938187640516 72 7.9 7.88854975354981 0.0114502464501885 73 7.8 7.87933681114661 -0.0793368111466127 74 7.6 7.65515372452372 -0.0551537245237173 75 7.4 7.44711909586753 -0.0471190958675341 76 7.2 7.23216503195088 -0.0321650319508847 77 6.9 7.0562823926738 -0.156282392673806 78 7.1 7.18633252617932 -0.0863325261793207 79 7.5 7.30130997854827 0.198690021451729 80 7.6 7.69893929872546 -0.0989392987254639 81 7.4 7.63169885128134 -0.231698851281342 82 7.3 7.19250512700667 0.107494872993328 83 7.2 7.37546328491366 -0.175463284913664 84 7.3 7.29424383162373 0.00575616837626721 85 7.2 7.29956595644891 -0.0995659564489112 86 7.1 7.09124575156606 0.00875424843394182 87 7 7.00808874711443 -0.00808874711442774 88 6.9 6.87886043159587 0.0211395684041336 89 6.8 6.7791940183634 0.0208059816365949 90 7.2 7.15957161927426 0.0404283807257425 91 7.6 7.45157781558415 0.148422184415849 92 7.7 7.71773749178353 -0.0177374917835284 93 7.6 7.68071161678863 -0.0807116167886335 94 7.5 7.44342262214606 0.0565773778539448 95 7.5 7.55943541597521 -0.0594354159752149 96 7.6 7.61820087311445 -0.0182008731144489 97 7.6 7.58437112213316 0.0156288778668375 98 7.6 7.51603582767947 0.0839641723205256 99 7.5 7.53686802081745 -0.0368680208174539 100 7.3 7.3280081391743 -0.0280081391743017 101 7.2 7.08760121999724 0.112398780002755 102 7.4 7.55318763417745 -0.153187634177453 103 8 7.55571448727554 0.444285512724460 104 8.2 8.2269602689245 -0.0269602689244969 105 8 8.22138046357024 -0.221380463570235 106 7.7 7.68669229143094 0.0133077085690649 107 7.7 7.60403231918878 0.0959676808112202 108 7.8 7.83081483541524 -0.0308148354152411 109 7.8 7.79774067994938 0.00225932005061674 110 7.7 7.67381840895296 0.0261815910470431 111 7.5 7.5451561693083 -0.0451561693082975 112 7.3 7.25374721896034 0.0462527810396612 113 7.1 7.09297186590787 0.0070281340921267 114 7.1 7.39713324077411 -0.297133240774112 115 7.2 7.1366464244201 0.0633535755798995 116 6.8 7.19746693327844 -0.397466933278436 117 6.6 6.6367563065195 -0.0367563065195005 118 6.4 6.5211143916181 -0.121114391618097 119 6.4 6.53780534185541 -0.137805341855413 120 6.5 6.53723492376239 -0.0372349237623927 121 6.3 6.47876784747665 -0.178767847476646 122 5.9 6.08047351949303 -0.180473519493025 123 5.5 5.65310210812253 -0.15310210812253 124 5.2 5.28891278853631 -0.0889127885363065 125 4.9 5.10135871984097 -0.201358719840969 126 5.4 5.28402304344151 0.115976956558492 127 5.8 5.8045830196624 -0.00458301966239773 128 5.7 5.97040607964144 -0.270406079641435 129 5.6 5.57564819957161 0.0243518004283855 130 5.5 5.49369006196951 0.00630993803049341 131 5.4 5.62554522081233 -0.225545220812331 132 5.4 5.46652254985306 -0.0665225498530555 133 5.4 5.34061369108711 0.0593863089128854 134 5.5 5.34873328306473 0.151266716935266 135 5.8 5.52301270092044 0.276987299079560 136 5.7 5.82374505744521 -0.123745057445209 137 5.4 5.44601155330613 -0.0460115533061346 138 5.6 5.516359058541 0.0836409414589957 139 5.8 5.72902763298049 0.0709723670195055 140 6.2 5.86499161494363 0.335008385056375 141 6.8 6.4150686706292 0.384931329370794 142 6.7 7.0090734392488 -0.309073439248796 143 6.7 6.58505985970309 0.114940140296909 144 6.4 6.63840236732913 -0.238402367329132 145 6.3 6.17891254526389 0.121087454736111 146 6.3 6.21933423525905 0.0806657647409535 147 6.4 6.34514988188876 0.0548501181112442 148 6.3 6.3494978335453 -0.0494978335452978 149 6 6.10643116980369 -0.106431169803692 150 6.3 6.2124777471801 0.0875222528198968 151 6.3 6.52223045755278 -0.222230457552780 152 6.6 6.2732001317131 0.326799868286901 153 7.5 6.75686712440555 0.743132875594448 154 7.8 7.90675972904265 -0.106759729042649 155 7.9 7.83698701389802 0.0630129861019814 156 7.8 7.71254376297029 0.0874562370297083 157 7.6 7.51455641932629 0.0854435806737116 158 7.5 7.35737398064873 0.142626019351275 159 7.6 7.40623832244477 0.193761677555232 160 7.5 7.53627477768879 -0.0362747776887867 161 7.3 7.27810082772257 0.0218991722774283 162 7.6 7.50267166991697 0.0973283300830303 163 7.5 7.7486556959051 -0.248655695905095 164 7.6 7.34379809462258 0.256201905377416 165 7.9 7.62639175379224 0.273608246207757 166 7.9 8.0322480513225 -0.132248051322492 167 8.1 7.91959649750566 0.180403502494341 168 8.2 8.178720726105 0.0212792738949928 169 8 8.09678127923364 -0.0967812792336396 170 7.5 7.71599480492611 -0.215994804926113 171 6.8 7.15024242160975 -0.350242421609751 172 6.5 6.40133848806016 0.09866151193984 173 6.6 6.44636679180478 0.153633208195221 174 7.6 7.27857080041746 0.321429199582542 175 8 8.21132441789252 -0.211324417892520 176 8.1 7.99167584929536 0.108324150704639 177 7.7 7.90552962132311 -0.205529621323112 178 7.5 7.35157478133472 0.148425218665283 179 7.6 7.52210591430802 0.0778940856919793 180 7.8 7.84489981352785 -0.0448998135278474 181 7.8 7.83880826695043 -0.0388082669504336 182 7.8 7.66622459779407 0.133775402205931 183 7.5 7.6958107177701 -0.195810717770094 184 7.5 7.21257877913975 0.287421220860252 185 7.1 7.4114048130702 -0.311404813070205 186 7.5 7.34222636269332 0.157773637306680 187 7.5 7.75726543356737 -0.257265433567370 188 7.6 7.48176943396798 0.118230566032019 189 7.7 7.62596787077703 0.0740321292229708 190 7.7 7.73523587019348 -0.0352358701934781 191 7.9 7.77473849372383 0.125261506276169 192 8.1 8.04335172795028 0.0566482720497196 193 8.2 8.06484977639866 0.135150223601336 194 8.2 8.07513127544107 0.12486872455893 195 8.2 8.06874219930391 0.131257800696086 196 7.9 8.0276607163613 -0.127660716361295 197 7.3 7.59860748859514 -0.298607488595136 198 6.9 7.38368761966635 -0.483687619666351 199 6.6 6.84857098830948 -0.248570988309482 200 6.7 6.60849990165082 0.0915000983491846 201 6.9 7.00896710960453 -0.108967109604534 202 7 7.11203035901249 -0.112030359012489 203 7.1 7.1570549458201 -0.0570549458201079 204 7.2 7.19654218113932 0.00345781886067522 205 7.1 7.14742176741423 -0.0474217674142335 206 6.9 6.9693161349806 -0.0693161349806013 207 7 6.79542835398235 0.204571646017645 208 6.8 7.02578090872034 -0.22578090872034 209 6.4 6.63953213812991 -0.239532138129911 210 6.7 6.57249919363267 0.127500806367334 211 6.6 6.94600007166352 -0.346000071663518 212 6.4 6.5291913471233 -0.129191347123301 213 6.3 6.32995148925529 -0.0299514892552874 214 6.2 6.34184282758176 -0.141842827581759 215 6.5 6.37918354404733 0.120816455952673 216 6.8 6.80940519410694 -0.00940519410693876 217 6.8 6.86737485707086 -0.0673748570708648 218 6.4 6.6143835095481 -0.214383509548105 219 6.1 6.08571599319627 0.0142840068037293 220 5.8 5.89170563976206 -0.0917056397620612 221 6.1 5.70232322261148 0.397676777388523 222 7.2 6.7883280190208 0.411671980979206 223 7.3 7.8287992160486 -0.528799216048607 224 6.9 7.06199622154561 -0.161996221545613 225 6.1 6.4816447354695 -0.381644735469499 226 5.8 5.7398211182312 0.0601788817687991 227 6.2 6.02774989831258 0.172250101687423 228 7.1 6.79998658464132 0.300013415358676 229 7.7 7.5537389430433 0.146261056956702 230 7.9 7.7436522276263 0.156347772373705 231 7.7 7.65242536041427 0.047574639585727 232 7.4 7.27146753509711 0.128532464902892 233 7.5 7.07719335397681 0.422806646023186 234 8 7.9833405357762 0.0166594642238047 235 8.1 8.28217599314864 -0.182175993148639 236 8 7.95194762628601 0.0480523737139876 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.00644265830184751 0.0128853166036950 0.993557341698152 22 0.000910979207215807 0.00182195841443161 0.999089020792784 23 0.000209077950404875 0.000418155900809749 0.999790922049595 24 0.000576163139611566 0.00115232627922313 0.999423836860388 25 0.000656373446697832 0.00131274689339566 0.999343626553302 26 0.000348516947587257 0.000697033895174514 0.999651483052413 27 8.96399266819688e-05 0.000179279853363938 0.999910360073318 28 2.19963601556938e-05 4.39927203113876e-05 0.999978003639844 29 1.90620351699062e-05 3.81240703398124e-05 0.99998093796483 30 1.05721725709989e-05 2.11443451419979e-05 0.99998942782743 31 5.3936416795443e-06 1.07872833590886e-05 0.99999460635832 32 2.33416672105400e-06 4.66833344210801e-06 0.999997665833279 33 8.23652789176766e-07 1.64730557835353e-06 0.99999917634721 34 3.74829896684443e-07 7.49659793368886e-07 0.999999625170103 35 2.47940732551697e-07 4.95881465103394e-07 0.999999752059267 36 1.19818998548701e-07 2.39637997097402e-07 0.999999880181001 37 4.02971109759671e-08 8.05942219519341e-08 0.999999959702889 38 1.08805663802705e-08 2.17611327605411e-08 0.999999989119434 39 1.48298202169896e-08 2.96596404339791e-08 0.99999998517018 40 5.5706228643657e-09 1.11412457287314e-08 0.999999994429377 41 1.60029280362787e-09 3.20058560725574e-09 0.999999998399707 42 4.36967195772226e-10 8.73934391544452e-10 0.999999999563033 43 1.38418523647804e-09 2.76837047295608e-09 0.999999998615815 44 1.04401022361943e-09 2.08802044723886e-09 0.99999999895599 45 4.8726843748224e-10 9.7453687496448e-10 0.999999999512732 46 1.79902142067903e-10 3.59804284135806e-10 0.999999999820098 47 2.39484405261704e-10 4.78968810523407e-10 0.999999999760516 48 7.37724730767207e-11 1.47544946153441e-10 0.999999999926227 49 1.42318908806446e-10 2.84637817612891e-10 0.999999999857681 50 1.71891674028303e-10 3.43783348056606e-10 0.999999999828108 51 1.76019130221396e-10 3.52038260442793e-10 0.99999999982398 52 1.1643601186109e-10 2.3287202372218e-10 0.999999999883564 53 6.4358788732335e-10 1.2871757746467e-09 0.999999999356412 54 2.28364562113425e-10 4.56729124226851e-10 0.999999999771635 55 1.03645872998783e-10 2.07291745997565e-10 0.999999999896354 56 7.24603842663935e-11 1.44920768532787e-10 0.99999999992754 57 3.69552030193347e-11 7.39104060386694e-11 0.999999999963045 58 1.99240930861477e-11 3.98481861722953e-11 0.999999999980076 59 1.23897708372943e-11 2.47795416745887e-11 0.99999999998761 60 7.26203329402113e-12 1.45240665880423e-11 0.999999999992738 61 2.99773834583325e-12 5.9954766916665e-12 0.999999999997002 62 1.11504846877296e-12 2.23009693754592e-12 0.999999999998885 63 6.26302348018417e-13 1.25260469603683e-12 0.999999999999374 64 2.46068597871230e-13 4.92137195742461e-13 0.999999999999754 65 9.48347131057598e-14 1.89669426211520e-13 0.999999999999905 66 3.59455669605720e-14 7.18911339211439e-14 0.999999999999964 67 4.80927123469128e-14 9.61854246938256e-14 0.999999999999952 68 2.49645869872536e-14 4.99291739745072e-14 0.999999999999975 69 8.88982862405407e-15 1.77796572481081e-14 0.99999999999999 70 2.32135593830841e-14 4.64271187661682e-14 0.999999999999977 71 9.4347775885208e-15 1.88695551770416e-14 0.99999999999999 72 3.20870221717152e-15 6.41740443434305e-15 0.999999999999997 73 1.39625200389364e-15 2.79250400778729e-15 0.999999999999999 74 6.22368160450782e-16 1.24473632090156e-15 1 75 2.5135518799057e-16 5.0271037598114e-16 1 76 9.03702151149203e-17 1.80740430229841e-16 1 77 2.58167891738803e-16 5.16335783477606e-16 1 78 9.14945655799429e-17 1.82989131159886e-16 1 79 8.87482458878098e-17 1.77496491775620e-16 1 80 6.44346270996427e-17 1.28869254199285e-16 1 81 1.31439497495713e-16 2.62878994991426e-16 1 82 5.57884789996516e-17 1.11576957999303e-16 1 83 4.24751601058713e-17 8.49503202117425e-17 1 84 3.05687217111534e-17 6.11374434223067e-17 1 85 1.17320359285788e-17 2.34640718571577e-17 1 86 6.70664631433826e-18 1.34132926286765e-17 1 87 2.43235739040793e-18 4.86471478081586e-18 1 88 8.2604445982458e-19 1.65208891964916e-18 1 89 2.9258413488026e-19 5.8516826976052e-19 1 90 1.59541182734444e-19 3.19082365468888e-19 1 91 1.27524982189468e-19 2.55049964378935e-19 1 92 4.68490512581827e-20 9.36981025163655e-20 1 93 2.74270424833523e-20 5.48540849667047e-20 1 94 1.27432309322228e-20 2.54864618644456e-20 1 95 4.30334837639926e-21 8.60669675279852e-21 1 96 1.43506818057316e-21 2.87013636114632e-21 1 97 5.84711841273181e-22 1.16942368254636e-21 1 98 5.94798521485604e-22 1.18959704297121e-21 1 99 2.02163173018307e-22 4.04326346036615e-22 1 100 3.23741406802124e-22 6.47482813604247e-22 1 101 1.28303797341589e-22 2.56607594683179e-22 1 102 1.31993860796538e-22 2.63987721593075e-22 1 103 4.21214497247513e-20 8.42428994495026e-20 1 104 1.77997077883085e-20 3.55994155766171e-20 1 105 1.47436612273315e-19 2.94873224546630e-19 1 106 6.94955036668124e-18 1.38991007333625e-17 1 107 4.58921393179378e-18 9.17842786358756e-18 1 108 2.22221057514245e-18 4.4444211502849e-18 1 109 1.24342180935936e-18 2.48684361871872e-18 1 110 4.82770576921595e-19 9.6554115384319e-19 1 111 2.97608174649378e-19 5.95216349298756e-19 1 112 1.55425948393775e-19 3.1085189678755e-19 1 113 7.62313672321588e-20 1.52462734464318e-19 1 114 1.15855883277740e-18 2.31711766555480e-18 1 115 4.54925163677502e-18 9.09850327355004e-18 1 116 1.75159115727003e-16 3.50318231454005e-16 1 117 1.56318856505945e-15 3.12637713011891e-15 0.999999999999998 118 8.91055516190888e-16 1.78211103238178e-15 1 119 1.21267840915774e-15 2.42535681831548e-15 0.999999999999999 120 6.07908193155314e-16 1.21581638631063e-15 1 121 8.14771676626216e-16 1.62954335325243e-15 1 122 1.59211672814437e-15 3.18423345628873e-15 0.999999999999998 123 1.15378198966875e-15 2.3075639793375e-15 0.999999999999999 124 5.81364074988943e-16 1.16272814997789e-15 1 125 4.66453539165664e-16 9.32907078331327e-16 1 126 2.52313652180084e-14 5.04627304360168e-14 0.999999999999975 127 2.03202265689459e-14 4.06404531378919e-14 0.99999999999998 128 1.34327339214077e-13 2.68654678428155e-13 0.999999999999866 129 6.94813703636337e-14 1.38962740727267e-13 0.99999999999993 130 3.4906241227469e-14 6.9812482454938e-14 0.999999999999965 131 8.87321085081556e-14 1.77464217016311e-13 0.999999999999911 132 5.82096617596449e-14 1.16419323519290e-13 0.999999999999942 133 6.35837069352818e-14 1.27167413870564e-13 0.999999999999936 134 2.88162774234658e-13 5.76325548469316e-13 0.999999999999712 135 4.47545258928639e-12 8.95090517857277e-12 0.999999999995524 136 1.06248457091986e-11 2.12496914183971e-11 0.999999999989375 137 1.46200551952317e-11 2.92401103904635e-11 0.99999999998538 138 8.06099276667398e-12 1.61219855333480e-11 0.999999999991939 139 8.23986583425835e-12 1.64797316685167e-11 0.99999999999176 140 1.02154600892063e-09 2.04309201784125e-09 0.999999998978454 141 4.71048866497935e-08 9.4209773299587e-08 0.999999952895113 142 3.25013103991964e-07 6.50026207983927e-07 0.999999674986896 143 2.01571406589029e-07 4.03142813178057e-07 0.999999798428593 144 1.83802903346237e-06 3.67605806692475e-06 0.999998161970967 145 1.50435325145885e-06 3.00870650291769e-06 0.999998495646748 146 1.18283031988839e-06 2.36566063977679e-06 0.99999881716968 147 9.95875401689736e-07 1.99175080337947e-06 0.999999004124598 148 7.80689499212362e-07 1.56137899842472e-06 0.9999992193105 149 8.62449491141593e-07 1.72489898228319e-06 0.99999913755051 150 6.44915039090882e-07 1.28983007818176e-06 0.999999355084961 151 2.06534475054701e-06 4.13068950109403e-06 0.99999793465525 152 5.99661998861596e-06 1.19932399772319e-05 0.999994003380011 153 0.00564604040726816 0.0112920808145363 0.994353959592732 154 0.00488250702371844 0.00976501404743687 0.995117492976282 155 0.00364488558528406 0.00728977117056812 0.996355114414716 156 0.00297810126824393 0.00595620253648785 0.997021898731756 157 0.00233859830341031 0.00467719660682061 0.99766140169659 158 0.00194030342229184 0.00388060684458367 0.998059696577708 159 0.00192302012358175 0.0038460402471635 0.998076979876418 160 0.00146279639455376 0.00292559278910751 0.998537203605446 161 0.00102727233456525 0.00205454466913049 0.998972727665435 162 0.000743496273148405 0.00148699254629681 0.999256503726852 163 0.00142093002336360 0.00284186004672719 0.998579069976636 164 0.00203741601612466 0.00407483203224932 0.997962583983875 165 0.00495302038255895 0.0099060407651179 0.99504697961744 166 0.0038039340039716 0.0076078680079432 0.996196065996028 167 0.00404141368882285 0.0080828273776457 0.995958586311177 168 0.00299051635231146 0.00598103270462292 0.997009483647689 169 0.00227565291771662 0.00455130583543324 0.997724347082283 170 0.00269766834589427 0.00539533669178855 0.997302331654106 171 0.00746047978889965 0.0149209595777993 0.9925395202111 172 0.00603250592001323 0.0120650118400265 0.993967494079987 173 0.00565599079860104 0.0113119815972021 0.994344009201399 174 0.0103764156483108 0.0207528312966216 0.989623584351689 175 0.0117766145844550 0.0235532291689101 0.988223385415545 176 0.0122347370878194 0.0244694741756388 0.98776526291218 177 0.0127369100299604 0.0254738200599208 0.98726308997004 178 0.0181392073379252 0.0362784146758504 0.981860792662075 179 0.0141232889613203 0.0282465779226406 0.98587671103868 180 0.0110931576990658 0.0221863153981317 0.988906842300934 181 0.00808570628298806 0.0161714125659761 0.991914293717012 182 0.00727263623883342 0.0145452724776668 0.992727363761167 183 0.00860694257995995 0.0172138851599199 0.99139305742004 184 0.0243776360537770 0.0487552721075539 0.975622363946223 185 0.0455378812976953 0.0910757625953906 0.954462118702305 186 0.0692627576399716 0.138525515279943 0.930737242360028 187 0.0672188681531207 0.134437736306241 0.93278113184688 188 0.0764785960096786 0.152957192019357 0.923521403990321 189 0.093494408892003 0.186988817784006 0.906505591107997 190 0.0796858127392446 0.159371625478489 0.920314187260755 191 0.0839738946956654 0.167947789391331 0.916026105304335 192 0.0705394850424362 0.141078970084872 0.929460514957564 193 0.0866266596371928 0.173253319274386 0.913373340362807 194 0.113104377291989 0.226208754583978 0.886895622708011 195 0.134099350259047 0.268198700518094 0.865900649740953 196 0.159225470915956 0.318450941831913 0.840774529084044 197 0.153510301632350 0.307020603264701 0.84648969836765 198 0.416868341773326 0.833736683546651 0.583131658226674 199 0.386578348056113 0.773156696112227 0.613421651943887 200 0.342817074494350 0.685634148988699 0.65718292550565 201 0.292765456994903 0.585530913989807 0.707234543005097 202 0.258714542975838 0.517429085951675 0.741285457024162 203 0.220172300680183 0.440344601360365 0.779827699319817 204 0.190855684752655 0.381711369505309 0.809144315247345 205 0.149004901741337 0.298009803482674 0.850995098258663 206 0.107847162996717 0.215694325993435 0.892152837003283 207 0.121506580479220 0.243013160958441 0.87849341952078 208 0.0863788844577169 0.172757768915434 0.913621115542283 209 0.581255649851666 0.837488700296667 0.418744350148334 210 0.877999780618701 0.244000438762598 0.122000219381299 211 0.960059872504827 0.079880254990345 0.0399401274951725 212 0.93632368828701 0.127352623425981 0.0636763117129903 213 0.926134876249539 0.147730247500922 0.0738651237504612 214 0.859837034793686 0.280325930412629 0.140162965206314 215 0.742396034717944 0.515207930564112 0.257603965282056 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 148 0.758974358974359 NOK 5% type I error level 164 0.841025641025641 NOK 10% type I error level 166 0.851282051282051 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/29/t126208500330p1w5t28nm4rkh/104ook1262084880.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t126208500330p1w5t28nm4rkh/104ook1262084880.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t126208500330p1w5t28nm4rkh/1wl241262084880.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t126208500330p1w5t28nm4rkh/1wl241262084880.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t126208500330p1w5t28nm4rkh/2mc5h1262084880.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t126208500330p1w5t28nm4rkh/2mc5h1262084880.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t126208500330p1w5t28nm4rkh/3cert1262084880.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t126208500330p1w5t28nm4rkh/3cert1262084880.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t126208500330p1w5t28nm4rkh/4fo7r1262084880.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t126208500330p1w5t28nm4rkh/4fo7r1262084880.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t126208500330p1w5t28nm4rkh/5y4ef1262084880.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t126208500330p1w5t28nm4rkh/5y4ef1262084880.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t126208500330p1w5t28nm4rkh/67ih71262084880.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t126208500330p1w5t28nm4rkh/67ih71262084880.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t126208500330p1w5t28nm4rkh/70olg1262084880.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t126208500330p1w5t28nm4rkh/70olg1262084880.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t126208500330p1w5t28nm4rkh/85fce1262084880.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t126208500330p1w5t28nm4rkh/85fce1262084880.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t126208500330p1w5t28nm4rkh/92r4j1262084880.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/29/t126208500330p1w5t28nm4rkh/92r4j1262084880.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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