Multiple Lineair Regression q1 part2

*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: Mon, 24 Nov 2008 03:19:31 -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/24/t1227522090oxdzzao2tifj02p.htm/, Retrieved Mon, 24 Nov 2008 10:21:30 +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/24/t1227522090oxdzzao2tifj02p.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:

Multiple Lineair Regression

Dataseries X:

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1687 0 1508 0 1507 0 1385 0 1632 0 1511 0 1559 0 1630 0 1579 0 1653 0 2152 0 2148 0 1752 0 1765 0 1717 0 1558 0 1575 0 1520 0 1805 0 1800 0 1719 0 2008 0 2242 0 2478 0 2030 0 1655 0 1693 0 1623 0 1805 0 1746 0 1795 0 1926 0 1619 0 1992 0 2233 0 2192 0 2080 0 1768 0 1835 0 1569 0 1976 0 1853 0 1965 0 1689 0 1778 0 1976 0 2397 0 2654 0 2097 0 1963 0 1677 0 1941 0 2003 0 1813 0 2012 0 1912 0 2084 0 2080 0 2118 0 2150 0 1608 0 1503 0 1548 0 1382 0 1731 0 1798 0 1779 0 1887 0 2004 0 2077 0 2092 0 2051 0 1577 0 1356 0 1652 0 1382 0 1519 0 1421 0 1442 0 1543 0 1656 0 1561 0 1905 0 2199 0 1473 0 1655 0 1407 0 1395 0 1530 0 1309 0 1526 0 1327 0 1627 0 1748 0 1958 0 2274 0 1648 0 1401 0 1411 0 1403 0 1394 0 1520 0 1528 0 1643 0 1515 0 1685 0 2000 0 2215 0 1956 0 1462 0 1563 0 1459 0 1446 0 1622 0 1657 0 1638 0 1643 0 1683 0 2050 0 2262 0 1813 0 1445 0 1762 0 1461 0 1556 0 1431 0 1427 0 1554 0 1645 0 1653 0 2016 0 2207 0 1665 0 1361 0 1506 0 1360 0 1453 0 1522 0 1460 0 1552 0 1548 0 1827 0 1737 0 1941 0 1474 0 1458 0 1542 0 1404 0 1522 0 1385 0 1641 0 1510 0 1681 0 1938 0 1868 0 1726 0 1456 0 1445 0 1456 0 1365 0 1487 0 1558 0 1488 0 1684 0 1594 0 1850 0 1998 0 2079 0 1494 0 1057 1 1218 1 1168 1 1236 1 1076 1 1174 1 1139 1 1427 1 1487 1 1483 1 1513 1 1357 1 1165 1 1282 1 1110 1 1297 1 1185 1 1222 1 1284 1 1444 1 1575 1 1737 1 1763 1

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation deaths[t] = + 1846.02995173260 -251.176611180784law[t] -1.50915849932545t + 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) 1846.02995173260 38.78143 47.6009 0 0 law -251.176611180784 67.520939 -3.72 0.000263 0.000131 t -1.50915849932545 0.395585 -3.815 0.000184 9.2e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.505523756005193 R-squared 0.255554267885597 Adjusted R-squared 0.247676535270630 F-TEST (value) 32.4400789384574 F-TEST (DF numerator) 2 F-TEST (DF denominator) 189 p-value 7.73048292046496e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 251.198646170456 Sum Squared Residuals 11926043.6093574 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1687 1844.52079323327 -157.520793233273 2 1508 1843.01163473395 -335.011634733953 3 1507 1841.50247623463 -334.502476234628 4 1385 1839.99331773530 -454.993317735302 5 1632 1838.48415923598 -206.484159235977 6 1511 1836.97500073665 -325.975000736652 7 1559 1835.46584223733 -276.465842237326 8 1630 1833.956683738 -203.956683738001 9 1579 1832.44752523868 -253.447525238675 10 1653 1830.93836673935 -177.938366739350 11 2152 1829.42920824002 322.570791759976 12 2148 1827.9200497407 320.079950259301 13 1752 1826.41089124137 -74.4108912413734 14 1765 1824.90173274205 -59.901732742048 15 1717 1823.39257424272 -106.392574242722 16 1558 1821.88341574340 -263.883415743397 17 1575 1820.37425724407 -245.374257244072 18 1520 1818.86509874475 -298.865098744746 19 1805 1817.35594024542 -12.3559402454207 20 1800 1815.84678174610 -15.8467817460953 21 1719 1814.33762324677 -95.3376232467698 22 2008 1812.82846474744 195.171535252556 23 2242 1811.31930624812 430.680693751881 24 2478 1809.81014774879 668.189852251207 25 2030 1808.30098924947 221.699010750532 26 1655 1806.79183075014 -151.791830750143 27 1693 1805.28267225082 -112.282672250817 28 1623 1803.77351375149 -180.773513751492 29 1805 1802.26435525217 2.73564474783382 30 1746 1800.75519675284 -54.7551967528407 31 1795 1799.24603825352 -4.24603825351528 32 1926 1797.73687975419 128.263120245810 33 1619 1796.22772125486 -177.227721254864 34 1992 1794.71856275554 197.281437244461 35 2233 1793.20940425621 439.790595743787 36 2192 1791.70024575689 400.299754243112 37 2080 1790.19108725756 289.808912742437 38 1768 1788.68192875824 -20.6819287582371 39 1835 1787.17277025891 47.8272297410883 40 1569 1785.66361175959 -216.663611759586 41 1976 1784.15445326026 191.845546739739 42 1853 1782.64529476094 70.3547052390647 43 1965 1781.13613626161 183.86386373839 44 1689 1779.62697776228 -90.6269777622844 45 1778 1778.11781926296 -0.117819262958949 46 1976 1776.60866076363 199.391339236366 47 2397 1775.09950226431 621.900497735692 48 2654 1773.59034376498 880.409656235017 49 2097 1772.08118526566 324.918814734343 50 1963 1770.57202676633 192.427973233668 51 1677 1769.06286826701 -92.0628682670062 52 1941 1767.55370976768 173.446290232319 53 2003 1766.04455126836 236.955448731645 54 1813 1764.53539276903 48.4646072309701 55 2012 1763.02623426970 248.973765730296 56 1912 1761.51707577038 150.482924229621 57 2084 1760.00791727105 323.992082728947 58 2080 1758.49875877173 321.501241228272 59 2118 1756.98960027240 361.010399727597 60 2150 1755.48044177308 394.519558226923 61 1608 1753.97128327375 -145.971283273752 62 1503 1752.46212477443 -249.462124774426 63 1548 1750.9529662751 -202.952966275101 64 1382 1749.44380777578 -367.443807775775 65 1731 1747.93464927645 -16.9346492764499 66 1798 1746.42549077712 51.5745092228755 67 1779 1744.9163322778 34.083667722201 68 1887 1743.40717377847 143.592826221526 69 2004 1741.89801527915 262.101984720852 70 2077 1740.38885677982 336.611143220177 71 2092 1738.87969828050 353.120301719503 72 2051 1737.37053978117 313.629460218828 73 1577 1735.86138128185 -158.861381281846 74 1356 1734.35222278252 -378.352222782521 75 1652 1732.84306428320 -80.8430642831954 76 1382 1731.33390578387 -349.33390578387 77 1519 1729.82474728454 -210.824747284544 78 1421 1728.31558878522 -307.315588785219 79 1442 1726.80643028589 -284.806430285894 80 1543 1725.29727178657 -182.297271786568 81 1656 1723.78811328724 -67.7881132872427 82 1561 1722.27895478792 -161.278954787917 83 1905 1720.76979628859 184.230203711408 84 2199 1719.26063778927 479.739362210734 85 1473 1717.75147928994 -244.751479289941 86 1655 1716.24232079062 -61.2423207906154 87 1407 1714.73316229129 -307.73316229129 88 1395 1713.22400379196 -318.224003791964 89 1530 1711.71484529264 -181.714845292639 90 1309 1710.20568679331 -401.205686793314 91 1526 1708.69652829399 -182.696528293988 92 1327 1707.18736979466 -380.187369794663 93 1627 1705.67821129534 -78.6782112953373 94 1748 1704.16905279601 43.8309472039882 95 1958 1702.65989429669 255.340105703314 96 2274 1701.15073579736 572.849264202639 97 1648 1699.64157729804 -51.6415772980354 98 1401 1698.13241879871 -297.13241879871 99 1411 1696.62326029938 -285.623260299385 100 1403 1695.11410180006 -292.114101800059 101 1394 1693.60494330073 -299.604943300734 102 1520 1692.09578480141 -172.095784801408 103 1528 1690.58662630208 -162.586626302083 104 1643 1689.07746780276 -46.0774678027573 105 1515 1687.56830930343 -172.568309303432 106 1685 1686.05915080411 -1.05915080410638 107 2000 1684.54999230478 315.450007695219 108 2215 1683.04083380546 531.959166194545 109 1956 1681.53167530613 274.46832469387 110 1462 1680.02251680680 -218.022516806805 111 1563 1678.51335830748 -115.513358307479 112 1459 1677.00419980815 -218.004199808154 113 1446 1675.49504130883 -229.495041308828 114 1622 1673.98588280950 -51.9858828095028 115 1657 1672.47672431018 -15.4767243101773 116 1638 1670.96756581085 -32.9675658108519 117 1643 1669.45840731153 -26.4584073115264 118 1683 1667.9492488122 15.0507511877990 119 2050 1666.44009031288 383.559909687125 120 2262 1664.93093181355 597.06906818645 121 1813 1663.42177331422 149.578226685775 122 1445 1661.9126148149 -216.912614814899 123 1762 1660.40345631557 101.596543684426 124 1461 1658.89429781625 -197.894297816248 125 1556 1657.38513931692 -101.385139316923 126 1431 1655.87598081760 -224.875980817597 127 1427 1654.36682231827 -227.366822318272 128 1554 1652.85766381895 -98.8576638189464 129 1645 1651.34850531962 -6.34850531962099 130 1653 1649.83934682030 3.16065317970447 131 2016 1648.33018832097 367.66981167903 132 2207 1646.82102982164 560.178970178355 133 1665 1645.31187132232 19.6881286776808 134 1361 1643.80271282299 -282.802712822994 135 1506 1642.29355432367 -136.293554323668 136 1360 1640.78439582434 -280.784395824343 137 1453 1639.27523732502 -186.275237325017 138 1522 1637.76607882569 -115.766078825692 139 1460 1636.25692032637 -176.256920326366 140 1552 1634.74776182704 -82.747761827041 141 1548 1633.23860332772 -85.2386033277156 142 1827 1631.72944482839 195.27055517161 143 1737 1630.22028632906 106.779713670935 144 1941 1628.71112782974 312.288872170261 145 1474 1627.20196933041 -153.201969330414 146 1458 1625.69281083109 -167.692810831088 147 1542 1624.18365233176 -82.1836523317628 148 1404 1622.67449383244 -218.674493832437 149 1522 1621.16533533311 -99.165335333112 150 1385 1619.65617683379 -234.656176833787 151 1641 1618.14701833446 22.8529816655390 152 1510 1616.63785983514 -106.637859835136 153 1681 1615.12870133581 65.8712986641899 154 1938 1613.61954283648 324.380457163515 155 1868 1612.11038433716 255.889615662841 156 1726 1610.60122583783 115.398774162166 157 1456 1609.09206733851 -153.092067338508 158 1445 1607.58290883918 -162.582908839183 159 1456 1606.07375033986 -150.073750339857 160 1365 1604.56459184053 -239.564591840532 161 1487 1603.05543334121 -116.055433341207 162 1558 1601.54627484188 -43.5462748418811 163 1488 1600.03711634256 -112.037116342556 164 1684 1598.52795784323 85.4720421567698 165 1594 1597.01879934390 -3.01879934390471 166 1850 1595.50964084458 254.490359155421 167 1998 1594.00048234525 403.999517654746 168 2079 1592.49132384593 486.508676154072 169 1494 1590.98216534660 -96.9821653466029 170 1057 1338.29639566649 -281.296395666493 171 1218 1336.78723716717 -118.787237167168 172 1168 1335.27807866784 -167.278078667842 173 1236 1333.76892016852 -97.7689201685167 174 1076 1332.25976166919 -256.259761669191 175 1174 1330.75060316987 -156.750603169866 176 1139 1329.24144467054 -190.241444670540 177 1427 1327.73228617121 99.2677138287851 178 1487 1326.22312767189 160.776872328111 179 1483 1324.71396917256 158.286030827436 180 1513 1323.20481067324 189.795189326761 181 1357 1321.69565217391 35.3043478260869 182 1165 1320.18649367459 -155.186493674588 183 1282 1318.67733517526 -36.6773351752622 184 1110 1317.16817667594 -207.168176675937 185 1297 1315.65901817661 -18.6590181766113 186 1185 1314.14985967729 -129.149859677286 187 1222 1312.64070117796 -90.6407011779603 188 1284 1311.13154267864 -27.1315426786349 189 1444 1309.62238417931 134.377615820691 190 1575 1308.11322567998 266.886774320016 191 1737 1306.60406718066 430.395932819342 192 1763 1305.09490868133 457.905091318667 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.159385312092601 0.318770624185202 0.840614687907399 7 0.0760063765695588 0.152012753139118 0.923993623430441 8 0.0420912804540693 0.0841825609081385 0.95790871954593 9 0.0170614232025410 0.0341228464050820 0.982938576797459 10 0.00789397320379491 0.0157879464075898 0.992106026796205 11 0.190586983859796 0.381173967719592 0.809413016140204 12 0.241802413845465 0.48360482769093 0.758197586154535 13 0.210227648437516 0.420455296875032 0.789772351562484 14 0.173049454377891 0.346098908755782 0.826950545622109 15 0.154756867378735 0.309513734757471 0.845243132621265 16 0.206990094094381 0.413980188188762 0.793009905905619 17 0.217496954781679 0.434993909563359 0.78250304521832 18 0.237213677688148 0.474427355376295 0.762786322311852 19 0.182402893030626 0.364805786061251 0.817597106969374 20 0.136046549348651 0.272093098697302 0.863953450651349 21 0.102804531061953 0.205609062123907 0.897195468938047 22 0.0958882549144537 0.191776509828907 0.904111745085546 23 0.159893558023163 0.319787116046326 0.840106441976837 24 0.379375260086556 0.758750520173113 0.620624739913444 25 0.320081732625254 0.640163465250508 0.679918267374746 26 0.396918970406943 0.793837940813886 0.603081029593057 27 0.424341677045522 0.848683354091044 0.575658322954478 28 0.476965509994824 0.953931019989648 0.523034490005176 29 0.433927886066391 0.867855772132782 0.566072113933609 30 0.408001233813836 0.816002467627673 0.591998766186164 31 0.366091320466267 0.732182640932533 0.633908679533733 32 0.312293295925299 0.624586591850599 0.687706704074701 33 0.339574226629027 0.679148453258054 0.660425773370973 34 0.294404404980164 0.588808809960328 0.705595595019836 35 0.322187533800511 0.644375067601021 0.67781246619949 36 0.318409617541308 0.636819235082617 0.681590382458692 37 0.280619325012189 0.561238650024379 0.71938067498781 38 0.277471910963523 0.554943821927047 0.722528089036477 39 0.252179320013595 0.504358640027191 0.747820679986405 40 0.331982283929003 0.663964567858005 0.668017716070997 41 0.287852805964299 0.575705611928598 0.712147194035701 42 0.254098575481449 0.508197150962898 0.745901424518551 43 0.216316856366674 0.432633712733347 0.783683143633326 44 0.225476101153399 0.450952202306797 0.774523898846602 45 0.206266798610893 0.412533597221785 0.793733201389107 46 0.174299122988181 0.348598245976361 0.82570087701182 47 0.268512521441974 0.537025042883948 0.731487478558026 48 0.594522133244731 0.810955733510539 0.405477866755269 49 0.569258644831644 0.861482710336713 0.430741355168356 50 0.538917408528752 0.922165182942496 0.461082591471248 51 0.586195735796923 0.827608528406154 0.413804264203077 52 0.555310241638484 0.889379516723032 0.444689758361516 53 0.52498846718763 0.95002306562474 0.47501153281237 54 0.514994775230873 0.970010449538254 0.485005224769127 55 0.487224603054371 0.974449206108742 0.512775396945629 56 0.461458274212469 0.922916548424939 0.538541725787531 57 0.447787503988395 0.89557500797679 0.552212496011605 58 0.43672865540669 0.87345731081338 0.56327134459331 59 0.438213342232266 0.876426684464532 0.561786657767734 60 0.454138177718843 0.908276355437686 0.545861822281157 61 0.540246619260786 0.919506761478428 0.459753380739214 62 0.662375971115574 0.675248057768852 0.337624028884426 63 0.728860203248329 0.542279593503342 0.271139796751671 64 0.842361001183864 0.315277997632272 0.157638998816136 65 0.832722616890901 0.334554766218197 0.167277383109099 66 0.815790606700014 0.368418786599971 0.184209393299985 67 0.798576567393617 0.402846865212766 0.201423432606383 68 0.779326616877758 0.441346766244484 0.220673383122242 69 0.774517927033611 0.450964145932778 0.225482072966389 70 0.789097452759444 0.421805094481112 0.210902547240556 71 0.811422253986229 0.377155492027543 0.188577746013771 72 0.82745447991948 0.34509104016104 0.17254552008052 73 0.845270019135023 0.309459961729954 0.154729980864977 74 0.907943018718746 0.184113962562507 0.0920569812812535 75 0.904058292635556 0.191883414728889 0.0959417073644445 76 0.934606283178922 0.130787433642156 0.0653937168210781 77 0.938410446080716 0.123179107838568 0.0615895539192842 78 0.950511274947297 0.098977450105406 0.049488725052703 79 0.957039057482193 0.0859218850356143 0.0429609425178071 80 0.954577166245556 0.0908456675088887 0.0454228337544444 81 0.946399454901072 0.107201090197856 0.0536005450989279 82 0.941055174510053 0.117889650979894 0.058944825489947 83 0.937330837037128 0.125338325925744 0.062669162962872 84 0.96805086400715 0.0638982719857002 0.0319491359928501 85 0.968542176973437 0.0629156460531258 0.0314578230265629 86 0.96230821028667 0.0753835794266604 0.0376917897133302 87 0.966153237952017 0.0676935240959654 0.0338467620479827 88 0.969816718809579 0.0603665623808429 0.0301832811904214 89 0.965824161872095 0.0683516762558102 0.0341758381279051 90 0.974738687475034 0.0505226250499329 0.0252613125249664 91 0.970928096984761 0.0581438060304772 0.0290719030152386 92 0.977175321602151 0.0456493567956973 0.0228246783978486 93 0.97128024554166 0.0574395089166818 0.0287197544583409 94 0.964450261368233 0.071099477263534 0.035549738631767 95 0.966904951258318 0.0661900974833643 0.0330950487416821 96 0.99111166958707 0.0177766608258603 0.00888833041293016 97 0.988479999208507 0.0230400015829856 0.0115200007914928 98 0.988741163145165 0.0225176737096706 0.0112588368548353 99 0.988718579844266 0.0225628403114677 0.0112814201557338 100 0.988905617296321 0.0221887654073575 0.0110943827036787 101 0.989375068470935 0.0212498630581293 0.0106249315290647 102 0.98723039893182 0.0255392021363580 0.0127696010681790 103 0.984600923859293 0.0307981522814135 0.0153990761407067 104 0.980058524578278 0.0398829508434445 0.0199414754217223 105 0.976637815012981 0.0467243699740373 0.0233621849870186 106 0.97019996460384 0.0596000707923195 0.0298000353961598 107 0.975943366931487 0.048113266137026 0.024056633068513 108 0.992679583309864 0.0146408333802712 0.00732041669013562 109 0.994278132774964 0.0114437344500723 0.00572186722503613 110 0.993305759414881 0.0133884811702376 0.00669424058511882 111 0.991235055457554 0.0175298890848917 0.00876494454244584 112 0.989898735718822 0.0202025285623564 0.0101012642811782 113 0.988720415002805 0.0225591699943899 0.0112795849971950 114 0.985122510158373 0.0297549796832538 0.0148774898416269 115 0.98057712954163 0.0388457409167384 0.0194228704583692 116 0.974848572009283 0.0503028559814342 0.0251514279907171 117 0.96775691037369 0.0644861792526215 0.0322430896263107 118 0.959456371765561 0.081087256468877 0.0405436282344385 119 0.975729592028825 0.04854081594235 0.024270407971175 120 0.996801084519333 0.00639783096133364 0.00319891548066682 121 0.996958250290787 0.00608349941842604 0.00304174970921302 122 0.996184306916831 0.00763138616633744 0.00381569308316872 123 0.99591866450883 0.00816267098233855 0.00408133549116927 124 0.994752613057822 0.0104947738843555 0.00524738694217774 125 0.992898283897043 0.0142034322059138 0.00710171610295692 126 0.99133333587231 0.0173333282553805 0.00866666412769027 127 0.989600542799027 0.0207989144019457 0.0103994572009729 128 0.986112742943584 0.0277745141128329 0.0138872570564164 129 0.98202065664984 0.0359586867003206 0.0179793433501603 130 0.97713157800035 0.0457368439993004 0.0228684219996502 131 0.990106820688954 0.0197863586220914 0.00989317931104568 132 0.999558738053052 0.000882523893895736 0.000441261946947868 133 0.999526055316334 0.000947889367332992 0.000473944683666496 134 0.999390472782038 0.00121905443592459 0.000609527217962293 135 0.999111811596353 0.00177637680729431 0.000888188403647153 136 0.998885952737298 0.00222809452540488 0.00111404726270244 137 0.998406157061675 0.00318768587664959 0.00159384293832480 138 0.997681789095467 0.00463642180906536 0.00231821090453268 139 0.996735092250918 0.00652981549816372 0.00326490774908186 140 0.99534459140884 0.0093108171823183 0.00465540859115915 141 0.993411823641679 0.0131763527166422 0.00658817635832109 142 0.99526147369562 0.00947705260875988 0.00473852630437994 143 0.995558589969093 0.00888282006181386 0.00444141003090693 144 0.998991956690427 0.00201608661914553 0.00100804330957277 145 0.998494927587033 0.0030101448259331 0.00150507241296655 146 0.997761701106607 0.00447659778678615 0.00223829889339307 147 0.996815640412161 0.00636871917567707 0.00318435958783853 148 0.995577070635125 0.00884585872974995 0.00442292936487497 149 0.993565093262941 0.0128698134741179 0.00643490673705897 150 0.991818430722872 0.0163631385542555 0.00818156927712775 151 0.989294737343524 0.0214105253129516 0.0107052626564758 152 0.984778471666361 0.0304430566672776 0.0152215283336388 153 0.981245408681158 0.0375091826376842 0.0187545913188421 154 0.992579591667191 0.0148408166656172 0.00742040833280862 155 0.99672372604442 0.00655254791116198 0.00327627395558099 156 0.997147534497527 0.00570493100494572 0.00285246550247286 157 0.995628707878538 0.00874258424292492 0.00437129212146246 158 0.99361689848401 0.0127662030319816 0.00638310151599079 159 0.99097586066673 0.0180482786665416 0.00902413933327079 160 0.991132088288447 0.0177358234231065 0.00886791171155325 161 0.988567324492778 0.0228653510144439 0.0114326755072219 162 0.984171356226383 0.0316572875472341 0.0158286437736170 163 0.983849511802051 0.0323009763958977 0.0161504881979488 164 0.976736611169 0.046526777662 0.023263388831 165 0.974530118087485 0.0509397638250308 0.0254698819125154 166 0.964272725481133 0.0714545490377332 0.0357272745188666 167 0.964283896714486 0.0714322065710285 0.0357161032855142 168 0.991323660435776 0.0173526791284479 0.00867633956422393 169 0.985850250956048 0.0282994980879048 0.0141497490439524 170 0.978667851172272 0.042664297655456 0.021332148827728 171 0.968060003766136 0.0638799924677283 0.0319399962338641 172 0.950985411398801 0.0980291772023975 0.0490145886011987 173 0.929052599513061 0.141894800973878 0.0709474004869388 174 0.90732721914301 0.185345561713979 0.0926727808569896 175 0.870190361433297 0.259619277133407 0.129809638566703 176 0.837385708460636 0.325228583078729 0.162614291539364 177 0.803316776825823 0.393366446348353 0.196683223174177 178 0.808578063876239 0.382843872247522 0.191421936123761 179 0.844814254288313 0.310371491423375 0.155185745711687 180 0.948487595744152 0.103024808511696 0.0515124042558481 181 0.980339296953975 0.0393214060920496 0.0196607030460248 182 0.969429676937547 0.0611406461249061 0.0305703230624530 183 0.988027828308696 0.0239443433826087 0.0119721716913044 184 0.970329817785515 0.0593403644289691 0.0296701822144845 185 0.99566589269589 0.00866821460821924 0.00433410730410962 186 0.991156993354209 0.0176860132915825 0.00884300664579124 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 24 0.132596685082873 NOK 5% type I error level 75 0.414364640883978 NOK 10% type I error level 101 0.558011049723757 NOK

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227522090oxdzzao2tifj02p/10sqeg1227521953.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227522090oxdzzao2tifj02p/10sqeg1227521953.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227522090oxdzzao2tifj02p/1lkja1227521953.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227522090oxdzzao2tifj02p/1lkja1227521953.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227522090oxdzzao2tifj02p/2pmfd1227521953.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227522090oxdzzao2tifj02p/2pmfd1227521953.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227522090oxdzzao2tifj02p/3nsgm1227521953.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227522090oxdzzao2tifj02p/3nsgm1227521953.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227522090oxdzzao2tifj02p/43hl31227521953.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227522090oxdzzao2tifj02p/43hl31227521953.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227522090oxdzzao2tifj02p/5yyn71227521953.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227522090oxdzzao2tifj02p/5yyn71227521953.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227522090oxdzzao2tifj02p/6vfpo1227521953.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227522090oxdzzao2tifj02p/6vfpo1227521953.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227522090oxdzzao2tifj02p/7cb7s1227521953.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227522090oxdzzao2tifj02p/7cb7s1227521953.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227522090oxdzzao2tifj02p/8mwsj1227521953.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227522090oxdzzao2tifj02p/8mwsj1227521953.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227522090oxdzzao2tifj02p/9uduh1227521953.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227522090oxdzzao2tifj02p/9uduh1227521953.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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') }

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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