Seatbeltlaw Q1 multiple lineair regression

*Unverified author*

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

Title produced by software: Multiple Regression

Date of computation: Mon, 17 Nov 2008 01:30:47 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/17/t1226910712w2mhicried1jv7f.htm/, Retrieved Mon, 17 Nov 2008 08:32:05 +0000

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/2008/Nov/17/t1226910712w2mhicried1jv7f.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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1687 0 -183.9235445 1508 0 -177.0726091 1507 0 -228.6351091 1385 0 -237.4476091 1632 0 -127.7601091 1511 0 -193.0101091 1559 0 -220.6351091 1630 0 -164.5101091 1579 0 -268.3226091 1653 0 -333.6976091 2152 0 -34.26010911 2148 0 -154.8851091 1752 0 -97.74528053 1765 0 101.1056549 1717 0 2.543154874 1558 0 -43.26934513 1575 0 -163.5818451 1520 0 -162.8318451 1805 0 46.54315487 1800 0 26.66815487 1719 0 -107.1443451 2008 0 42.48065487 2242 0 76.91815487 2478 0 196.2931549 2030 0 201.4329835 1655 0 12.28391886 1693 0 -0.278581137 1623 0 42.90891886 1805 0 87.59641886 1746 0 84.34641886 1795 0 57.72141886 1926 0 173.8464189 1619 0 -185.9660811 1992 0 47.65891886 2233 0 89.09641886 2192 0 -68.52858114 2080 0 272.6112475 1768 0 146.4621829 1835 0 162.8996829 1569 0 10.08718285 1976 0 279.7746829 1853 0 212.5246829 1965 0 248.8996829 1689 0 -41.97531715 1778 0 -5.787817149 1976 0 52.83718285 2397 0 274.2746829 2654 0 414.6496829 2097 0 310.7895114 1963 0 362.6404468 1677 0 26.07794684 1941 0 403.2654468 2003 0 327.9529468 1813 0 193.7029468 2012 0 317.0779468 1912 0 202.2029468 2084 0 321.3904468 2080 0 178.0154468 2118 0 16.45294684 2150 0 -68.17205316 1608 0 -157.0322246 1503 0 -76.18128917 1548 0 -81.74378917 1382 0 -134.5562892 1731 0 77.13121083 1798 0 199.8812108 1779 0 105.2562108 1887 0 198.3812108 2004 0 262.5687108 2077 0 196.1937108 2092 0 11.63121083 2051 0 -145.9937892 1577 0 -166.8539606 1356 0 -202.0030252 1652 0 43.43447482 1382 0 -113.3780252 1519 0 -113.6905252 1421 0 -155.9405252 1442 0 -210.5655252 1543 0 -124.4405252 1656 0 -64.25302518 1561 0 -298.6280252 1905 0 -154.1905252 2199 0 23.18447482 1473 0 -249.6756966 1655 0 118.1752388 1407 0 -180.3872612 1395 0 -79.19976119 1530 0 -81.51226119 1309 0 -246.7622612 1526 0 -105.3872612 1327 0 -319.2622612 1627 0 -72.07476119 1748 0 -90.44976119 1958 0 -80.01226119 2274 0 119.3627388 1648 0 -53.49743261 1401 0 -114.6464972 1411 0 -155.2089972 1403 0 -50.02149721 1394 0 -196.3339972 1520 0 -14.58399721 1528 0 -82.20899721 1643 0 17.91600279 1515 0 -162.8964972 1685 0 -132.2714972 2000 0 -16.83399721 2215 0 81.54100279 1956 0 275.6808314 1462 0 -32.46823322 1563 0 17.96926678 1459 0 27.15676678 1446 0 -123.1557332 1622 0 108.5942668 1657 0 67.96926678 1638 0 34.09426678 1643 0 -13.71823322 1683 0 -113.0932332 2050 0 54.34426678 2262 0 149.7192668 1813 0 153.8590954 1445 0 -28.28996923 1762 0 238.1475308 1461 0 50.33503077 1556 0 8.022530771 1431 0 -61.22746923 1427 0 -140.8524692 1554 0 -28.72746923 1645 0 9.460030771 1653 0 -121.9149692 2016 0 41.52253077 2207 0 115.8975308 1665 0 27.03735936 1361 0 -91.11170524 1506 0 3.325794759 1360 0 -29.48670524 1453 0 -73.79920524 1522 0 50.95079476 1460 0 -86.67420524 1552 0 -9.54920524 1548 0 -66.36170524 1827 0 73.26329476 1737 0 -216.2992052 1941 0 -128.9242052 1474 0 -142.7843767 1458 0 27.06655875 1542 0 60.50405875 1404 0 35.69155875 1522 0 16.37905875 1385 0 -64.87094125 1641 0 115.5040587 1510 0 -30.37094125 1681 0 87.81655875 1938 0 205.4415587 1868 0 -64.12094125 1726 0 -322.7459413 1456 0 -139.6061127 1445 0 35.24482274 1456 0 -4.317677263 1365 0 17.86982274 1487 0 2.557322737 1558 0 129.3073227 1488 0 -16.31767726 1684 0 164.8073227 1594 0 21.99482274 1850 0 138.6198227 1998 0 87.05732274 2079 0 51.43232274 1494 0 -80.42784867 1057 1 -105.1918797 1218 1 5.245620328 1168 1 68.43312033 1236 1 -0.879379672 1076 1 -105.1293797 1174 1 -82.75437967 1139 1 -132.6293797 1427 1 102.5581203 1487 1 23.18312033 1483 1 -180.3793797 1513 1 -267.0043797 1357 1 30.13544892 1165 1 23.98638432 1282 1 90.42388432 1110 1 31.61138432 1297 1 81.29888432 1185 1 25.04888432 1222 1 -13.57611568 1284 1 33.54888432 1444 1 140.7363843 1575 1 132.3613843 1737 1 94.79888432 1763 1 4.173884316

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 7 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 R Framework error message Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Multiple Linear Regression - Estimated Regression Equation #dead/m[t] = + 1717.75147928992 -396.055827109141S[t] + 1.00000000002839parameter[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) 1717.75147928992 16.512653 104.0264 0 0 S -396.055827109141 47.709356 -8.3014 0 0 parameter 1.00000000002839 0.105564 9.473 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.675537295805097 R-squared 0.456350638023663 Adjusted R-squared 0.450597734722326 F-TEST (value) 79.3252752775477 F-TEST (DF numerator) 2 F-TEST (DF denominator) 189 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 214.664492264491 Sum Squared Residuals 8709279.56120347 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1687 1533.82793478468 153.172065215319 2 1508 1540.67887018490 -32.6788701848964 3 1507 1489.11637018343 17.8836298165677 4 1385 1480.30387018318 -95.3038701831818 5 1632 1589.99137018630 42.0086298137040 6 1511 1524.74137018444 -13.7413701844435 7 1559 1497.11637018366 61.8836298163408 8 1630 1553.24137018525 76.7586298147474 9 1579 1449.42887018231 129.571129817695 10 1653 1384.05387018045 268.946129819551 11 2152 1683.49137017895 468.508629821049 12 2148 1562.86637018553 585.133629814474 13 1752 1620.00619875715 131.993801242852 14 1765 1818.85713419279 -53.8571341927937 15 1717 1720.29463416400 -3.29463416399540 16 1558 1674.48213415869 -116.482134158695 17 1575 1554.16963418528 20.8303658147210 18 1520 1554.9196341853 -34.9196341853003 19 1805 1764.29463416124 40.7053658387554 20 1800 1744.41963416068 55.5803658393197 21 1719 1610.60713418688 108.392865813119 22 2008 1760.23213416113 247.767865838871 23 2242 1794.66963416211 447.330365837893 24 2478 1914.04463419550 563.955365804504 25 2030 1919.18446279564 110.815537204358 26 1655 1730.03539815027 -75.0353981502719 27 1693 1717.47289815292 -24.4728981529153 28 1623 1760.66039815114 -137.660398151141 29 1805 1805.34789815241 -0.347898152410115 30 1746 1802.09789815232 -56.0978981523178 31 1795 1775.47289815156 19.5271018484381 32 1926 1891.59789819486 34.4021018051411 33 1619 1531.78539818464 87.2146018153565 34 1992 1765.41039815128 226.589601848724 35 2233 1806.84789815245 426.152101847547 36 2192 1649.22289814798 542.777101852022 37 2080 1990.36272679766 89.6372732023371 38 1768 1864.21366219408 -96.2136621940814 39 1835 1880.65116219455 -45.6511621945481 40 1569 1727.83866214021 -158.838662140210 41 1976 1997.52616219787 -21.5261621978663 42 1853 1930.27616219596 -77.276162195957 43 1965 1966.65116219699 -1.65116219698961 44 1689 1675.77616213873 13.2238378612685 45 1778 1711.96366214076 66.0363378592411 46 1976 1770.58866214142 205.411337858577 47 2397 1992.02616219771 404.97383780229 48 2654 2132.40116220170 521.598837798305 49 2097 2028.54099069875 68.4590093012532 50 1963 2080.39192610022 -117.391926100219 51 1677 1743.82942613066 -66.8294261306636 52 1941 2121.01692610137 -180.016926101372 53 2003 2045.70442609923 -42.7044260992341 54 1813 1911.45442609542 -98.4544260954226 55 2012 2034.82942609893 -22.8294260989253 56 1912 1919.95442609566 -7.95442609566395 57 2084 2039.14192609905 44.8580739009522 58 2080 1895.76692609498 184.233073905023 59 2118 1734.20442613039 383.79557386961 60 2150 1649.57942612799 500.420573872012 61 1608 1560.71925468546 47.2807453145351 62 1503 1641.57019011776 -138.570190117760 63 1548 1636.00769011760 -88.0076901176024 64 1382 1583.19519008610 -201.195190086103 65 1731 1794.88269012211 -63.882690122113 66 1798 1917.63269009560 -119.632690095598 67 1779 1823.00769009291 -44.0076900929115 68 1887 1916.13269009556 -29.1326900955554 69 2004 1980.32019009738 23.6798099026222 70 2077 1913.94519009549 163.054809904507 71 2092 1729.38269012025 362.617309879747 72 2051 1571.75769008578 479.242309914222 73 1577 1550.89751868519 26.1024813148139 74 1356 1515.74845408419 -159.748454084188 75 1652 1761.18595411116 -109.185954111156 76 1382 1604.37345408670 -222.373454086704 77 1519 1604.06095408670 -85.0609540866954 78 1421 1561.81095408550 -140.810954085496 79 1442 1507.18595408395 -65.1859540839451 80 1543 1593.31095408639 -50.3109540863902 81 1656 1653.4984541081 2.50154589190100 82 1561 1419.12345408144 141.876545918555 83 1905 1563.56095408555 341.439045914454 84 2199 1740.93595411058 458.064045889419 85 1473 1468.07578268283 4.92421731716533 86 1655 1835.92671809328 -180.926718093278 87 1407 1537.36421808480 -130.364218084802 88 1395 1638.55171809767 -243.551718097675 89 1530 1636.23921809761 -106.239218097609 90 1309 1470.98921808292 -161.989218082917 91 1526 1612.36421808693 -86.3642180869312 92 1327 1398.48921808086 -71.489218080859 93 1627 1645.67671809788 -18.6767180978769 94 1748 1627.30171809736 120.698281902645 95 1958 1637.73921809765 320.260781902348 96 2274 1837.11421809331 436.885781906688 97 1648 1664.25404667840 -16.2540466784044 98 1401 1603.10498208667 -202.104982086668 99 1411 1562.54248208552 -151.542482085517 100 1403 1667.72998207850 -264.729982078503 101 1394 1521.41748208435 -127.417482084349 102 1520 1703.16748207951 -183.167482079509 103 1528 1635.54248207759 -107.542482077589 104 1643 1735.66748208043 -92.6674820804318 105 1515 1554.85498208530 -39.8549820852984 106 1685 1585.47998208617 99.5200179138321 107 2000 1700.91748207945 299.082517920555 108 2215 1799.29248208224 415.707517917762 109 1956 1993.43231069775 -37.4323106977500 110 1462 1685.28324606900 -223.283246069001 111 1563 1735.72074607043 -172.720746070433 112 1459 1744.90824607069 -285.908246070694 113 1446 1594.59574608643 -148.595746086427 114 1622 1826.34574609301 -204.345746093006 115 1657 1785.72074607185 -128.720746071853 116 1638 1751.84574607089 -113.845746070891 117 1643 1704.03324606953 -61.0332460695337 118 1683 1604.65824608671 78.3417539132876 119 2050 1772.09574607147 277.904253928534 120 2262 1867.47074609417 394.529253905826 121 1813 1871.61057469429 -58.6105746942914 122 1445 1689.46151005912 -244.46151005912 123 1762 1955.89901009668 -193.899010096684 124 1461 1768.08651006135 -307.086510061352 125 1556 1725.77401006115 -169.774010061151 126 1431 1656.52401005819 -225.524010058185 127 1427 1576.89901008592 -149.899010085924 128 1554 1689.02401005911 -135.024010059108 129 1645 1727.21151006119 -82.2115100611918 130 1653 1595.83651008646 57.1634899135381 131 2016 1759.27401006110 256.725989938898 132 2207 1833.64901009321 373.350989906786 133 1665 1744.78883865069 -79.7888386506908 134 1361 1626.63977404734 -265.639774047336 135 1506 1721.07727404902 -215.077274049018 136 1360 1688.26477404909 -328.264774049086 137 1453 1643.95227404783 -190.952274047828 138 1522 1768.70227405137 -246.70227405137 139 1460 1631.07727404746 -171.077274047462 140 1552 1708.20227404965 -156.202274049652 141 1548 1651.38977404804 -103.389774048039 142 1827 1791.01477405200 35.9852259479968 143 1737 1501.45227408378 235.547725916218 144 1941 1588.82727408626 352.172725913737 145 1474 1574.96710258587 -100.967102585869 146 1458 1744.81803804069 -286.818038040692 147 1542 1778.25553804164 -236.255538041641 148 1404 1753.44303804094 -349.443038040937 149 1522 1734.13053804039 -212.130538040388 150 1385 1652.88053803808 -267.880538038081 151 1641 1833.25553799320 -192.255537993202 152 1510 1687.38053803906 -177.380538039061 153 1681 1805.56803804242 -124.568038042416 154 1938 1923.19303799576 14.8069620042441 155 1868 1653.63053803810 214.369461961897 156 1726 1395.00553798076 330.99446201924 157 1456 1578.14536658596 -122.145366585960 158 1445 1752.99630203092 -307.996302030924 159 1456 1713.4338020268 -257.433802026801 160 1365 1735.62130203043 -370.621302030431 161 1487 1720.30880202700 -233.308802026996 162 1558 1847.05880199359 -289.058801993594 163 1488 1701.43380202946 -213.43380202946 164 1684 1882.55880199460 -198.558801994602 165 1594 1739.74630203055 -145.746302030548 166 1850 1856.37130199386 -6.37130199385873 167 1998 1804.80880203239 193.191197967605 168 2079 1769.18380203138 309.816197968617 169 1494 1637.32363061764 -143.323630617640 170 1057 1216.50377247780 -159.503772477796 171 1218 1326.94127250893 -108.941272508932 172 1168 1390.12877251273 -222.128772512725 173 1236 1320.81627250876 -84.8162725087576 174 1076 1216.56627247780 -140.566272477798 175 1174 1238.94127250843 -64.9412725084331 176 1139 1189.06627247702 -50.0662724770171 177 1427 1424.25377248369 2.74622751630567 178 1487 1344.87877251144 142.121227488559 179 1483 1141.31627247566 341.683727524339 180 1513 1054.69127247320 458.308727526798 181 1357 1351.83110110164 5.16889889836181 182 1165 1345.68203650146 -180.682036501464 183 1282 1412.11953650335 -130.119536503350 184 1110 1353.30703650168 -243.30703650168 185 1297 1402.99453650309 -105.994536503091 186 1185 1346.74453650149 -161.744536501494 187 1222 1308.11953650040 -86.1195365003972 188 1284 1355.24453650174 -71.2445365017351 189 1444 1462.43203648478 -18.4320364847782 190 1575 1454.05703648454 120.942963515460 191 1737 1416.49453650347 320.505463496526 192 1763 1325.86953649690 437.130463503099 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.104563251590028 0.209126503180055 0.895436748409972 7 0.0486195872829747 0.0972391745659494 0.951380412717025 8 0.0181795048743342 0.0363590097486683 0.981820495125666 9 0.0159783485936607 0.0319566971873214 0.98402165140634 10 0.0192423904790045 0.038484780958009 0.980757609520996 11 0.219723824627286 0.439447649254572 0.780276175372714 12 0.571180833573928 0.857638332852144 0.428819166426072 13 0.491989442091924 0.983978884183848 0.508010557908076 14 0.55321826367848 0.89356347264304 0.44678173632152 15 0.490719344365077 0.981438688730153 0.509280655634923 16 0.483394632143188 0.966789264286375 0.516605367856813 17 0.413099555803301 0.826199111606602 0.586900444196699 18 0.36388383069052 0.72776766138104 0.63611616930948 19 0.29332934681601 0.58665869363202 0.70667065318399 20 0.231152143202673 0.462304286405347 0.768847856797326 21 0.180016599946823 0.360033199893645 0.819983400053177 22 0.174546475480029 0.349092950960058 0.82545352451997 23 0.282171870782838 0.564343741565675 0.717828129217162 24 0.434105384489874 0.868210768979749 0.565894615510126 25 0.395986733039673 0.791973466079347 0.604013266960327 26 0.403184057547567 0.806368115095134 0.596815942452433 27 0.376426966604951 0.752853933209901 0.623573033395049 28 0.412811060802619 0.825622121605237 0.587188939197381 29 0.375291154462548 0.750582308925095 0.624708845537453 30 0.354798262426649 0.709596524853298 0.645201737573351 31 0.309421965395945 0.61884393079189 0.690578034604055 32 0.265819765413198 0.531639530826395 0.734180234586802 33 0.221839698768797 0.443679397537594 0.778160301231203 34 0.201514412274349 0.403028824548698 0.798485587725651 35 0.273414649318165 0.546829298636331 0.726585350681835 36 0.479624373581602 0.959248747163203 0.520375626418398 37 0.433192180911219 0.866384361822438 0.566807819088781 38 0.43371227375768 0.86742454751536 0.56628772624232 39 0.408243535375596 0.816487070751191 0.591756464624404 40 0.427520935878811 0.855041871757623 0.572479064121189 41 0.390047100966762 0.780094201933525 0.609952899033237 42 0.365650408853422 0.731300817706844 0.634349591146578 43 0.323171670017546 0.646343340035092 0.676828329982454 44 0.284098987218201 0.568197974436402 0.715901012781799 45 0.244687185941151 0.489374371882302 0.755312814058849 46 0.226665898820119 0.453331797640238 0.773334101179881 47 0.301796183419256 0.603592366838513 0.698203816580744 48 0.465333726971043 0.930667453942086 0.534666273028957 49 0.427349433133541 0.854698866267081 0.572650566866459 50 0.434520673892757 0.869041347785515 0.565479326107243 51 0.410900457884235 0.82180091576847 0.589099542115765 52 0.433781520567404 0.867563041134807 0.566218479432596 53 0.400898034533241 0.801796069066481 0.59910196546676 54 0.381677188361665 0.76335437672333 0.618322811638335 55 0.344777610042998 0.689555220085997 0.655222389957002 56 0.308154285184658 0.616308570369316 0.691845714815342 57 0.271897035907274 0.543794071814548 0.728102964092726 58 0.256571205426893 0.513142410853786 0.743428794573107 59 0.324430332259204 0.648860664518409 0.675569667740796 60 0.487634670582985 0.97526934116597 0.512365329417015 61 0.448282898728679 0.896565797457357 0.551717101271321 62 0.448963210114266 0.897926420228531 0.551036789885734 63 0.430194595236723 0.860389190473445 0.569805404763277 64 0.456525601630492 0.913051203260985 0.543474398369508 65 0.42737957302731 0.85475914605462 0.57262042697269 66 0.409988836192972 0.819977672385945 0.590011163807028 67 0.377072826259055 0.75414565251811 0.622927173740945 68 0.342712908260045 0.68542581652009 0.657287091739955 69 0.308205797807595 0.616411595615191 0.691794202192405 70 0.294984490534626 0.589968981069252 0.705015509465374 71 0.362574179148157 0.725148358296315 0.637425820851843 72 0.512046155685292 0.975907688629417 0.487953844314708 73 0.47485638591366 0.94971277182732 0.52514361408634 74 0.48139520538713 0.96279041077426 0.51860479461287 75 0.461597082788812 0.923194165577625 0.538402917211188 76 0.489005726109227 0.978011452218455 0.510994273890772 77 0.463566685743385 0.92713337148677 0.536433314256615 78 0.453674309665355 0.90734861933071 0.546325690334645 79 0.423469902292871 0.846939804585743 0.576530097707129 80 0.390396631696731 0.780793263393461 0.609603368303269 81 0.353771410445997 0.707542820891995 0.646228589554003 82 0.326793140095775 0.65358628019155 0.673206859904225 83 0.38395959641232 0.76791919282464 0.61604040358768 84 0.546218944098903 0.907562111802194 0.453781055901097 85 0.508519854691201 0.982960290617599 0.491480145308799 86 0.505199670202957 0.989600659594086 0.494800329797043 87 0.488656561785936 0.977313123571872 0.511343438214064 88 0.513076767736511 0.973846464526977 0.486923232263489 89 0.48751930292458 0.97503860584916 0.51248069707542 90 0.478418153168128 0.956836306336257 0.521581846831872 91 0.447964283360306 0.895928566720612 0.552035716639694 92 0.415432729419201 0.830865458838402 0.584567270580799 93 0.378490232910393 0.756980465820787 0.621509767089607 94 0.354755067983788 0.709510135967576 0.645244932016212 95 0.413888115503936 0.827776231007871 0.586111884496064 96 0.580873438865925 0.83825312226815 0.419126561134075 97 0.54443540673044 0.911129186539121 0.455564593269560 98 0.544829043696172 0.910341912607655 0.455170956303828 99 0.527823318586403 0.944353362827194 0.472176681413597 100 0.552725938528388 0.894548122943224 0.447274061471612 101 0.52874166983713 0.94251666032574 0.47125833016287 102 0.518222032064782 0.963555935870435 0.481777967935218 103 0.488222274535392 0.976444549070785 0.511777725464608 104 0.455922906608978 0.911845813217956 0.544077093391022 105 0.417112185773235 0.83422437154647 0.582887814226765 106 0.388606075844037 0.777212151688074 0.611393924155963 107 0.448557531120974 0.897115062241947 0.551442468879026 108 0.614533497770131 0.770933004459738 0.385466502229869 109 0.590762889899077 0.818474220201846 0.409237110100923 110 0.591113444686182 0.817773110627636 0.408886555313818 111 0.573288537817149 0.853422924365702 0.426711462182851 112 0.59662387736953 0.80675224526094 0.40337612263047 113 0.574164838184757 0.851670323630485 0.425835161815243 114 0.561911135708872 0.876177728582257 0.438088864291128 115 0.5318766719997 0.9362466560006 0.4681233280003 116 0.498955723763327 0.997911447526654 0.501044276236673 117 0.460322671574974 0.920645343149948 0.539677328425026 118 0.42867283411693 0.85734566823386 0.57132716588307 119 0.497021293448793 0.994042586897586 0.502978706551207 120 0.687646003920753 0.624707992158495 0.312353996079247 121 0.661517730205866 0.676964539588267 0.338482269794134 122 0.662249197410519 0.675501605178963 0.337750802589481 123 0.643230762483687 0.713538475032626 0.356769237516313 124 0.661874500228115 0.67625099954377 0.338125499771885 125 0.636964988137688 0.726070023724623 0.363035011862312 126 0.631412591907204 0.737174816185592 0.368587408092796 127 0.60818042373522 0.78363915252956 0.39181957626478 128 0.575496070674022 0.849007858651957 0.424503929325978 129 0.535602107971021 0.928795784057958 0.464397892028979 130 0.497375240562656 0.994750481125312 0.502624759437344 131 0.569801246566715 0.86039750686657 0.430198753433285 132 0.768533629593068 0.462932740813863 0.231466370406932 133 0.737645406081729 0.524709187836543 0.262354593918271 134 0.747982969237455 0.504034061525091 0.252017030762545 135 0.731132639017264 0.537734721965472 0.268867360982736 136 0.760171619072066 0.479656761855869 0.239828380927934 137 0.744884895010607 0.510230209978785 0.255115104989393 138 0.73242234581156 0.535155308376878 0.267577654188439 139 0.712773065046823 0.574453869906354 0.287226934953177 140 0.682003281837395 0.635993436325211 0.317996718162605 141 0.644034192198494 0.711931615603013 0.355965807801506 142 0.62461007240324 0.750779855193522 0.375389927596761 143 0.623252579459914 0.753494841080173 0.376747420540086 144 0.728527861661579 0.542944276676842 0.271472138338421 145 0.691459272512189 0.617081454975622 0.308540727487811 146 0.688981627350718 0.622036745298564 0.311018372649282 147 0.666217064176354 0.667565871647293 0.333782935823646 148 0.693924137833091 0.612151724333818 0.306075862166909 149 0.669238638699927 0.661522722600145 0.330761361300073 150 0.679427432248642 0.641145135502715 0.320572567751358 151 0.643235322210083 0.713529355579835 0.356764677789917 152 0.614190113352712 0.771619773294576 0.385809886647288 153 0.566914917134927 0.866170165730145 0.433085082865073 154 0.558428304223523 0.883143391552954 0.441571695776477 155 0.583139422898429 0.833721154203142 0.416860577101571 156 0.632339433498223 0.735321133003553 0.367660566501777 157 0.584624783196164 0.830750433607672 0.415375216803836 158 0.583447120541049 0.833105758917902 0.416552879458951 159 0.568700327323502 0.862599345352996 0.431299672676498 160 0.628099981939032 0.743800036121935 0.371900018060968 161 0.620050032196565 0.75989993560687 0.379949967803435 162 0.625793217389783 0.748413565220433 0.374206782610217 163 0.636863795733913 0.726272408532174 0.363136204266087 164 0.616609067712466 0.766781864575068 0.383390932287534 165 0.616767226279384 0.766465547441231 0.383232773720616 166 0.559466921679712 0.881066156640576 0.440533078320288 167 0.521111557988272 0.957776884023455 0.478888442011728 168 0.646769012876295 0.70646197424741 0.353230987123705 169 0.584467588819448 0.831064822361104 0.415532411180552 170 0.592608813530149 0.814782372939701 0.407391186469851 171 0.542574386265775 0.91485122746845 0.457425613734225 172 0.525797397595757 0.948405204808485 0.474202602404243 173 0.471243103740697 0.942486207481394 0.528756896259303 174 0.495487551028168 0.990975102056337 0.504512448971832 175 0.473089331187816 0.946178662375633 0.526910668812184 176 0.495160197857299 0.990320395714598 0.504839802142701 177 0.41569761264995 0.8313952252999 0.58430238735005 178 0.353855188830256 0.707710377660513 0.646144811169744 179 0.300183291360565 0.600366582721131 0.699816708639435 180 0.368821890065158 0.737643780130316 0.631178109934842 181 0.280379352689110 0.560758705378219 0.71962064731089 182 0.236689824020031 0.473379648040061 0.763310175979969 183 0.189489947652913 0.378979895305826 0.810510052347087 184 0.208290535567839 0.416581071135678 0.791709464432161 185 0.163283713651598 0.326567427303196 0.836716286348402 186 0.159750514421299 0.319501028842599 0.8402494855787 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 3 0.0165745856353591 OK 10% type I error level 4 0.0220994475138122 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

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

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

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