Seatbelt

*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: Thu, 12 Nov 2009 15:14:11 +0100

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/12/t1258035301gehccu34anmb0m8.htm/, Retrieved Thu, 12 Nov 2009 15:15:14 +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/Nov/12/t1258035301gehccu34anmb0m8.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

1507 0 1508 1687 1385 0 1507 1508 1632 0 1385 1507 1511 0 1632 1385 1559 0 1511 1632 1630 0 1559 1511 1579 0 1630 1559 1653 0 1579 1630 2152 0 1653 1579 2148 0 2152 1653 1752 0 2148 2152 1765 0 1752 2148 1717 0 1765 1752 1558 0 1717 1765 1575 0 1558 1717 1520 0 1575 1558 1805 0 1520 1575 1800 0 1805 1520 1719 0 1800 1805 2008 0 1719 1800 2242 0 2008 1719 2478 0 2242 2008 2030 0 2478 2242 1655 0 2030 2478 1693 0 1655 2030 1623 0 1693 1655 1805 0 1623 1693 1746 0 1805 1623 1795 0 1746 1805 1926 0 1795 1746 1619 0 1926 1795 1992 0 1619 1926 2233 0 1992 1619 2192 0 2233 1992 2080 0 2192 2233 1768 0 2080 2192 1835 0 1768 2080 1569 0 1835 1768 1976 0 1569 1835 1853 0 1976 1569 1965 0 1853 1976 1689 0 1965 1853 1778 0 1689 1965 1976 0 1778 1689 2397 0 1976 1778 2654 0 2397 1976 2097 0 2654 2397 1963 0 2097 2654 1677 0 1963 2097 1941 0 1677 1963 2003 0 1941 1677 1813 0 2003 1941 2012 0 1813 2003 1912 0 2012 1813 2084 0 1912 2012 2080 0 2084 1912 2118 0 2080 2084 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] = + 432.674018921448 -85.6151937996543X[t] + 0.412253807726456Y1[t] + 0.208748882344717Y2[t] + 221.708450693677M1[t] + 130.164095261294M2[t] + 304.321659011619M3[t] + 216.329773410414M4[t] + 287.012043536047M5[t] + 283.086050769294M6[t] + 314.717592403885M7[t] + 429.953249810296M8[t] + 561.771276261432M9[t] + 567.769451532068M10[t] + 38.9218710448567M11[t] -0.737951251841748t + 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) 432.674018921448 157.025546 2.7554 0.006485 0.003243 X -85.6151937996543 37.53598 -2.2809 0.023768 0.011884 Y1 0.412253807726456 0.074231 5.5537 0 0 Y2 0.208748882344717 0.073339 2.8464 0.004954 0.002477 M1 221.708450693677 53.510674 4.1433 5.3e-05 2.7e-05 M2 130.164095261294 62.330183 2.0883 0.038227 0.019113 M3 304.321659011619 58.790068 5.1764 1e-06 0 M4 216.329773410414 65.820422 3.2867 0.001226 0.000613 M5 287.012043536047 58.277937 4.9249 2e-06 1e-06 M6 283.086050769294 61.985341 4.567 9e-06 5e-06 M7 314.717592403885 58.641459 5.3668 0 0 M8 429.953249810296 59.011856 7.2859 0 0 M9 561.771276261432 60.371807 9.3052 0 0 M10 567.769451532068 61.589033 9.2187 0 0 M11 38.9218710448567 59.89609 0.6498 0.516663 0.258332 t -0.737951251841748 0.239714 -3.0785 0.002418 0.001209 Multiple Linear Regression - Regression Statistics Multiple R 0.908326322560294 R-squared 0.825056708255908 Adjusted R-squared 0.809975390002107 F-TEST (value) 54.7072009469706 F-TEST (DF numerator) 15 F-TEST (DF denominator) 174 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 126.806940269663 Sum Squared Residuals 2797920.01749639 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1507 1627.48262493032 -120.482624930317 2 1385 1497.42201449866 -112.422014498661 3 1632 1620.33791357217 11.6620864278279 4 1511 1607.96740358150 -96.967403581504 5 1559 1679.58998565954 -120.589985659538 6 1630 1669.45560964810 -39.4556096481024 7 1579 1739.63916673198 -160.639166731977 8 1653 1847.93309933897 -194.933099338972 9 2152 1998.87376331044 153.126236689556 10 2148 2225.29605467825 -77.2960546782486 11 1752 1798.22719999830 -46.2271999983028 12 1765 1594.47987431255 170.520125687451 13 1717 1738.14511584632 -21.1451158463211 14 1558 1628.78836186171 -70.7883618617085 15 1575 1726.63967257914 -151.639672579138 16 1520 1611.72707816463 -91.727078164631 17 1805 1662.54616861333 142.453831386673 18 1800 1763.89337126781 36.1066287321876 19 1719 1852.21912408017 -133.219124080174 20 2008 1932.28052739718 75.7194726028235 21 2242 2165.59329355950 76.406706440505 22 2478 2327.64933558390 150.350664416097 23 2030 1944.20294093696 85.7970590630432 24 1655 1769.11814901216 -114.118149012159 25 1693 1741.97397126614 -48.9739712661412 26 1623 1587.07647839625 35.9235216037480 27 1805 1739.57078188298 65.4292181170171 28 1746 1711.25871627202 34.7412837279785 29 1795 1794.87235707669 0.127642923309917 30 1926 1798.09266557835 127.907334421647 31 1619 1893.22020000816 -274.220200008159 32 1992 1908.50209077786 83.497909222136 33 2233 2129.2669293793 103.733070620701 34 2192 2311.74365417475 -119.743654174749 35 2080 1815.56419696399 264.435803036013 36 1768 1721.17324402579 46.8267559742079 37 1835 1790.14068063437 44.8593193656343 38 1569 1660.34972777626 -91.3497277762608 39 1976 1738.09600253660 237.903997463397 40 1853 1761.62626272453 91.3737372754704 41 1965 1865.82415836227 99.1758416377336 42 1689 1881.65652828063 -192.656528280634 43 1778 1822.14794255349 -44.1479425534903 44 1976 1915.72154606857 60.2784539314281 45 2397 2147.00652572639 249.993474273615 46 2654 2367.15788150227 286.842118497729 47 2097 2031.40485781604 65.5951421839577 48 1963 1815.7681273783 147.2318726217 49 1677 1865.22348911878 -188.223489118784 50 1941 1627.0642431906 313.935756809400 51 2003 1849.61668057828 153.383319421722 52 1813 1841.55628474328 -28.5562847432778 53 2012 1846.11481085441 165.885189145585 54 1912 1883.82708692789 28.1729130721122 55 2084 1915.03632412459 168.963675875409 56 2080 2079.56679697364 0.433203026361845 57 2118 2244.90266470532 -126.902664705319 58 2150 2264.99353788834 -114.993537888339 59 1608 1756.53258552563 -148.532585525632 60 1503 1500.11116367622 2.88883632377516 61 1548 1564.65311907595 -16.6531190759465 62 1382 1469.00360109322 -87.003601093216 63 1731 1583.38278121462 147.617218785380 64 1798 1603.87720878888 194.122791211116 65 1779 1774.29589271865 4.70410728134624 66 1887 1775.78530147035 111.214698529648 67 2004 1847.23607432301 156.763925676991 68 2077 2032.51235527480 44.4876447251971 69 2092 2218.11057767246 -126.110577672461 70 2051 2244.79327721832 -193.793277218316 71 1577 1701.43657259765 -124.436572597649 72 1356 1457.80974126248 -101.809741262477 73 1652 1488.72517896537 163.274821034630 74 1382 1472.33649636999 -90.3364963699931 75 1519 1596.23724995637 -77.2372499563697 76 1421 1507.62398652877 -86.6239865287743 77 1442 1565.7660291266 -123.766029126599 78 1543 1549.30202460048 -6.30202460047699 79 1656 1626.21697609284 29.7830239071621 80 1561 1808.38299963731 -247.382999637313 81 1905 1923.88758680755 -18.8875868075472 82 2199 2051.13197686149 147.868023138506 83 1473 1714.55868012060 -241.558680120601 84 1655 1436.97476482384 218.025235176158 85 1407 1581.42376868963 -174.423768689629 86 1395 1424.89481427598 -29.8948142759807 87 1530 1541.59765826026 -11.5976582602570 88 1309 1506.01709886215 -197.017098862146 89 1526 1513.03442534493 12.9655746550732 90 1327 1551.69605460479 -224.69605460479 91 1627 1545.84964471878 81.1503552812214 92 1748 1742.48246560469 5.51753439531457 93 1958 1986.06991624230 -28.0699162422966 94 2274 2103.16205464736 170.837945352643 95 1648 1747.68599144225 -99.6859914422545 96 1401 1515.91993232973 -114.919932329725 97 1411 1504.38694091533 -93.3869409153337 98 1403 1364.66619836923 38.3338016307725 99 1394 1536.87526922935 -142.875269229347 100 1520 1442.76515704800 77.2348429519955 101 1528 1562.77471575423 -34.7747157542265 102 1643 1587.71116137288 55.2888386271229 103 1515 1667.68393070293 -152.683930702927 104 1685 1753.41927093815 -68.419270938152 105 2000 1927.86263651082 72.1373634891794 106 2215 2098.47011996205 116.529880037950 107 1956 1723.27505482277 232.724945177229 108 1462 1621.72250602903 -159.722506029034 109 1563 1584.97366392672 -21.9736639267193 110 1459 1431.20704394458 27.7929560554245 111 1446 1582.83589755632 -136.835897556324 112 1622 1467.03687743898 154.963122561017 113 1657 1606.82413100215 50.1758689978507 114 1638 1653.32887354665 -15.3288735466502 115 1643 1683.69585246466 -40.6958524646623 116 1683 1796.28859889331 -113.288598893314 117 2050 1944.90257081339 105.097429186609 118 2262 2109.80989756158 152.190102438417 119 1813 1744.23301288105 68.766987118951 120 1445 1563.72599397225 -118.725993972252 121 1762 1539.25884399797 222.741156002026 122 1461 1500.84140566018 -39.8414056601791 123 1556 1616.34601773627 -60.3460177362747 124 1431 1503.94687903148 -72.946879031482 125 1427 1542.19061576221 -115.190615762214 126 1554 1509.78404621962 44.2159537803766 127 1645 1592.19887465425 52.8011253457458 128 1653 1770.72278536971 -117.722785369709 129 2016 1924.09703932419 91.9029606758149 130 2207 2080.67538660644 126.324613393559 131 1665 1705.60617643427 -40.6061764342725 132 1361 1482.37582687768 -121.375826877676 133 1506 1464.87927453983 41.1207254601673 134 1360 1368.91410974315 -8.91410974314917 135 1453 1512.41325425355 -59.4132542535541 136 1522 1431.54568469674 90.4543153032604 137 1460 1549.34916236171 -89.3491623617147 138 1552 1533.52915514586 18.4708448541353 139 1548 1589.40766513408 -41.4076651340758 140 1827 1721.46125323345 105.538746766547 141 1737 1966.72514525905 -229.72514525905 142 1941 1993.12346475664 -52.1234647566392 143 1474 1528.85031038276 -54.8503103827582 144 1458 1339.25273187613 118.747268123873 145 1542 1456.14144233936 85.858557660643 146 1404 1395.14847338664 8.85152661336181 147 1522 1529.21196653583 -7.211966535827 148 1385 1460.32073323093 -75.3207332309316 149 1641 1498.41864856287 142.581351437125 150 1510 1570.69308244103 -60.6930824410261 151 1681 1601.02113789186 79.9788621081426 152 1938 1758.66814158049 179.331858419508 153 1868 2031.39350424643 -163.393504246433 154 1726 2061.44442448697 -335.444424486968 155 1456 1458.70643028663 -2.70643028662715 156 1445 1278.09573861084 166.904261389164 157 1456 1438.16924793461 17.8307520653928 158 1365 1348.12549542958 16.8745045704194 159 1487 1486.32624913075 0.673750869251373 160 1558 1428.89522852696 129.104771473039 161 1488 1553.57693139539 -65.5769313953855 162 1684 1534.87639148241 149.123608517587 163 1594 1631.95930641542 -37.9593064154182 164 1850 1750.26895081417 99.7310491858294 165 1998 1968.09860138041 29.9013986195864 166 2079 2087.81210282297 -8.81210282297075 167 1494 1622.51396409678 -128.513964096778 168 1057 1272.97912995037 -215.979129950371 169 1218 1191.67661924409 26.323380755914 170 1168 1074.54391401918 93.4560859808216 171 1236 1260.95940618884 -24.9594061888386 172 1076 1189.82538414396 -113.825384143956 173 1174 1208.00401778095 -34.0040177809543 174 1139 1210.34112574440 -71.341125744397 175 1427 1247.26322332650 179.736776673497 176 1487 1473.18381522423 13.8161847757738 177 1483 1689.11879700239 -206.118797002387 178 1513 1705.25493873096 -192.254938730958 179 1357 1187.20202569432 169.797974305680 180 1165 1089.49307586264 75.5069241373646 181 1282 1198.74601857522 83.253981424784 182 1110 1114.6176219848 -4.61762198480007 183 1297 1241.55319878866 55.4468012113349 184 1185 1194.01001621717 -9.01001621717475 185 1222 1256.81794962406 -34.8179496240648 186 1284 1244.02752166874 39.9724783312599 187 1444 1308.20455677728 135.795443222715 188 1575 1501.60530287346 73.3946971265411 189 1737 1720.09044806007 16.9095519399259 190 1763 1819.48189251771 -56.481892517712 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.283747395254332 0.567494790508664 0.716252604745668 20 0.443842298352026 0.887684596704052 0.556157701647974 21 0.341317517828288 0.682635035656576 0.658682482171712 22 0.411983092598218 0.823966185196435 0.588016907401782 23 0.336614923734274 0.673229847468547 0.663385076265727 24 0.430804834464092 0.861609668928185 0.569195165535908 25 0.383743918976957 0.767487837953913 0.616256081023044 26 0.324739160237591 0.649478320475182 0.675260839762409 27 0.243577897369198 0.487155794738396 0.756422102630802 28 0.177583412067839 0.355166824135679 0.82241658793216 29 0.14063275151709 0.28126550303418 0.85936724848291 30 0.101858703988149 0.203717407976298 0.89814129601185 31 0.193648037484651 0.387296074969303 0.806351962515349 32 0.143481418034351 0.286962836068702 0.856518581965649 33 0.142071739635096 0.284143479270192 0.857928260364904 34 0.241608239796838 0.483216479593675 0.758391760203162 35 0.228458806279405 0.456917612558811 0.771541193720595 36 0.192284870313211 0.384569740626422 0.807715129686789 37 0.148166341074156 0.296332682148313 0.851833658925844 38 0.144132664770104 0.288265329540208 0.855867335229896 39 0.157349798634827 0.314699597269654 0.842650201365173 40 0.132585341689329 0.265170683378658 0.867414658310671 41 0.105690686927928 0.211381373855856 0.894309313072072 42 0.233988516223621 0.467977032447242 0.766011483776379 43 0.193589411151391 0.387178822302782 0.80641058884861 44 0.161596380614964 0.323192761229927 0.838403619385036 45 0.154314731992429 0.308629463984858 0.845685268007571 46 0.240413555694264 0.480827111388527 0.759586444305736 47 0.207795940817130 0.415591881634261 0.79220405918287 48 0.190084647796614 0.380169295593227 0.809915352203386 49 0.275441933667111 0.550883867334221 0.72455806633289 50 0.379264302113817 0.758528604227634 0.620735697886183 51 0.370634683954405 0.74126936790881 0.629365316045595 52 0.332325982730529 0.664651965461057 0.667674017269472 53 0.329292066844883 0.658584133689766 0.670707933155117 54 0.298566426123952 0.597132852247904 0.701433573876048 55 0.366370037161037 0.732740074322075 0.633629962838963 56 0.328034400532993 0.656068801065985 0.671965599467007 57 0.567333834112142 0.865332331775715 0.432666165887858 58 0.806317045970772 0.387365908058456 0.193682954029228 59 0.930932880329005 0.138134239341989 0.0690671196709945 60 0.923041806526208 0.153916386947584 0.076958193473792 61 0.904344219013876 0.191311561972248 0.0956557809861242 62 0.898714602316382 0.202570795367237 0.101285397683618 63 0.896609793405677 0.206780413188646 0.103390206594323 64 0.9210144567064 0.157971086587199 0.0789855432935993 65 0.916224268742962 0.167551462514076 0.083775731257038 66 0.920582710132405 0.158834579735190 0.0794172898675948 67 0.946944530128345 0.106110939743311 0.0530554698716554 68 0.95121096103887 0.0975780779222575 0.0487890389611287 69 0.96911756876721 0.0617648624655819 0.0308824312327910 70 0.977543196610262 0.0449136067794759 0.0224568033897379 71 0.978284544629553 0.0434309107408932 0.0217154553704466 72 0.977167012948382 0.0456659741032363 0.0228329870516182 73 0.98194764331172 0.0361047133765591 0.0180523566882795 74 0.97951383774818 0.0409723245036406 0.0204861622518203 75 0.978336445811737 0.0433271083765258 0.0216635541882629 76 0.974163244877269 0.0516735102454629 0.0258367551227314 77 0.973073051733022 0.0538538965339557 0.0269269482669779 78 0.96518625970024 0.0696274805995215 0.0348137402997607 79 0.958076713031208 0.0838465739375837 0.0419232869687919 80 0.976714483434936 0.0465710331301283 0.0232855165650641 81 0.96997203847612 0.0600559230477605 0.0300279615238802 82 0.97341588759583 0.0531682248083389 0.0265841124041695 83 0.984088399473798 0.0318232010524045 0.0159116005262023 84 0.991556220538614 0.0168875589227717 0.00844377946138584 85 0.993228321408006 0.0135433571839871 0.00677167859199355 86 0.990774023019498 0.0184519539610042 0.00922597698050211 87 0.987772777796019 0.0244544444079624 0.0122272222039812 88 0.991432181351242 0.0171356372975162 0.0085678186487581 89 0.988542406146988 0.0229151877060248 0.0114575938530124 90 0.995006194381089 0.00998761123782247 0.00499380561891123 91 0.994331138665338 0.0113377226693242 0.0056688613346621 92 0.993267503165544 0.0134649936689123 0.00673249683445614 93 0.99098650019455 0.0180269996108986 0.0090134998054493 94 0.993631959437174 0.0127360811256522 0.00636804056282608 95 0.992293368267568 0.0154132634648647 0.00770663173243235 96 0.991324851153602 0.0173502976927964 0.00867514884639819 97 0.99185185593135 0.0162962881372987 0.00814814406864935 98 0.98946155187126 0.0210768962574795 0.0105384481287398 99 0.991441334126251 0.0171173317474975 0.00855866587374875 100 0.989517061528967 0.0209658769420665 0.0104829384710332 101 0.986572867816526 0.0268542643669474 0.0134271321834737 102 0.983147326159622 0.0337053476807551 0.0168526738403776 103 0.987465956096945 0.0250680878061107 0.0125340439030553 104 0.986125851256263 0.0277482974874739 0.0138741487437369 105 0.98212969398025 0.035740612039501 0.0178703060197505 106 0.980891251335778 0.0382174973284434 0.0191087486642217 107 0.993719364248851 0.0125612715022976 0.00628063575114878 108 0.993242101783816 0.0135157964323673 0.00675789821618364 109 0.990691957689554 0.0186160846208929 0.00930804231044647 110 0.987568884372447 0.0248622312551057 0.0124311156275529 111 0.98806225744982 0.0238754851003581 0.0119377425501791 112 0.98997346881075 0.0200530623784986 0.0100265311892493 113 0.98765211292587 0.0246957741482619 0.0123478870741309 114 0.98357727904016 0.0328454419196823 0.0164227209598411 115 0.978550335631101 0.0428993287377977 0.0214496643688989 116 0.97997280607165 0.0400543878567005 0.0200271939283502 117 0.980546267780243 0.0389074644395142 0.0194537322197571 118 0.989092948310018 0.021814103379963 0.0109070516899815 119 0.99281485864144 0.0143702827171211 0.00718514135856056 120 0.990885826657574 0.0182283466848531 0.00911417334242654 121 0.997486771767299 0.00502645646540243 0.00251322823270121 122 0.996544328130512 0.00691134373897605 0.00345567186948803 123 0.99583611803899 0.00832776392202152 0.00416388196101076 124 0.994191694005826 0.0116166119883490 0.00580830599417448 125 0.992739356946516 0.0145212861069686 0.0072606430534843 126 0.990177204725667 0.0196455905486654 0.00982279527433268 127 0.98700601717057 0.0259879656588586 0.0129939828294293 128 0.989732510576907 0.0205349788461869 0.0102674894230935 129 0.992559667602978 0.0148806647940450 0.00744033239702252 130 0.998898952689634 0.00220209462073106 0.00110104731036553 131 0.999627286702775 0.000745426594450021 0.000372713297225010 132 0.999438217547885 0.00112356490422947 0.000561782452114733 133 0.999174060455235 0.00165187908952984 0.000825939544764918 134 0.998695070951448 0.00260985809710434 0.00130492904855217 135 0.997986021851595 0.00402795629681027 0.00201397814840513 136 0.998333907711084 0.00333218457783148 0.00166609228891574 137 0.997487493461523 0.00502501307695372 0.00251250653847686 138 0.996799814887022 0.00640037022595651 0.00320018511297826 139 0.995365128112912 0.00926974377417672 0.00463487188708836 140 0.993882495429558 0.0122350091408849 0.00611750457044246 141 0.994780011053265 0.0104399778934695 0.00521998894673473 142 0.994126159437603 0.0117476811247932 0.00587384056239662 143 0.991061796517752 0.0178764069644969 0.00893820348224847 144 0.989324337448397 0.0213513251032055 0.0106756625516027 145 0.986467467786835 0.0270650644263309 0.0135325322131655 146 0.981020305425998 0.0379593891480045 0.0189796945740022 147 0.973347388067079 0.0533052238658423 0.0266526119329211 148 0.962747585854704 0.0745048282905915 0.0372524141452958 149 0.981522499791842 0.0369550004163167 0.0184775002081583 150 0.972700344098097 0.0545993118038057 0.0272996559019029 151 0.96667443426481 0.0666511314703777 0.0333255657351889 152 0.984250667469788 0.0314986650604231 0.0157493325302115 153 0.979735100938607 0.0405297981227867 0.0202648990613934 154 0.988891782043336 0.0222164359133271 0.0111082179566636 155 0.984389489640507 0.0312210207189853 0.0156105103594927 156 0.97667821621864 0.0466435675627184 0.0233217837813592 157 0.970760172293472 0.0584796554130561 0.0292398277065280 158 0.96554304819972 0.0689139036005617 0.0344569518002809 159 0.965791866679807 0.0684162666403866 0.0342081333201933 160 0.952301348551254 0.095397302897492 0.047698651448746 161 0.92614976569476 0.147700468610479 0.0738502343052394 162 0.939745678204728 0.120508643590543 0.0602543217952716 163 0.946897275531771 0.106205448936458 0.0531027244682289 164 0.914915177537774 0.170169644924452 0.085084822462226 165 0.874659287170301 0.250681425659397 0.125340712829699 166 0.970029611269099 0.0599407774618027 0.0299703887309014 167 0.94120703998549 0.117585920029022 0.0587929600145108 168 0.894107650265935 0.211784699468129 0.105892349734065 169 0.834494794290944 0.331010411418112 0.165505205709056 170 0.847828530229965 0.304342939540071 0.152171469770036 171 0.709515745446868 0.580968509106265 0.290484254553132 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 14 0.0915032679738562 NOK 5% type I error level 77 0.503267973856209 NOK 10% type I error level 94 0.61437908496732 NOK

Charts produced by software:

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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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Software written by Ed van Stee & Patrick Wessa

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