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 15:10:54 +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/t1258035104fui5g595g77aupf.htm/, Retrieved Thu, 12 Nov 2009 15:11:47 +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/t1258035104fui5g595g77aupf.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 «

1632 0 1385 1507 1508 1687 1511 0 1632 1385 1507 1508 1559 0 1511 1632 1385 1507 1630 0 1559 1511 1632 1385 1579 0 1630 1559 1511 1632 1653 0 1579 1630 1559 1511 2152 0 1653 1579 1630 1559 2148 0 2152 1653 1579 1630 1752 0 2148 2152 1653 1579 1765 0 1752 2148 2152 1653 1717 0 1765 1752 2148 2152 1558 0 1717 1765 1752 2148 1575 0 1558 1717 1765 1752 1520 0 1575 1558 1717 1765 1805 0 1520 1575 1558 1717 1800 0 1805 1520 1575 1558 1719 0 1800 1805 1520 1575 2008 0 1719 1800 1805 1520 2242 0 2008 1719 1800 1805 2478 0 2242 2008 1719 1800 2030 0 2478 2242 2008 1719 1655 0 2030 2478 2242 2008 1693 0 1655 2030 2478 2242 1623 0 1693 1655 2030 2478 1805 0 1623 1693 1655 2030 1746 0 1805 1623 1693 1655 1795 0 1746 1805 1623 1693 1926 0 1795 1746 1805 1623 1619 0 1926 1795 1746 1805 1992 0 1619 1926 1795 1746 2233 0 1992 1619 1926 1795 2192 0 2233 1992 1619 1926 2080 0 2192 2233 1992 1619 1768 0 2080 2192 2233 1992 1835 0 1768 2080 2192 2233 1569 0 1835 1768 2080 2192 1976 0 1569 1835 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 7 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation Y[t] = + 522.918085028905 -80.7982303933677X[t] + 0.389747913943074Y1[t] + 0.172724627545124Y2[t] + 0.0359567363109739Y3[t] + 0.0354648834548642Y4[t] + 188.662307824867M1[t] + 104.987349633496M2[t] + 181.667324587968M3[t] + 176.541027973435M4[t] + 208.395663285797M5[t] + 324.64288106546M6[t] + 458.312477153942M7[t] + 471.425528086186M8[t] -54.2481744163299M9[t] -111.187507110586M10[t] + 86.6003491334288M11[t] -0.767119250424237t + 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) 522.918085028905 164.86157 3.1719 0.001797 0.000899 X -80.7982303933677 38.149531 -2.1179 0.035634 0.017817 Y1 0.389747913943074 0.076719 5.0802 1e-06 0 Y2 0.172724627545124 0.082127 2.1031 0.036925 0.018463 Y3 0.0359567363109739 0.081903 0.439 0.661206 0.330603 Y4 0.0354648834548642 0.075174 0.4718 0.637697 0.318849 M1 188.662307824867 56.521258 3.3379 0.001037 0.000519 M2 104.987349633496 63.651567 1.6494 0.100911 0.050455 M3 181.667324587968 63.233767 2.8729 0.004585 0.002293 M4 176.541027973435 68.289505 2.5852 0.010571 0.005286 M5 208.395663285797 62.640601 3.3268 0.001076 0.000538 M6 324.64288106546 66.375276 4.891 2e-06 1e-06 M7 458.312477153942 65.936628 6.9508 0 0 M8 471.425528086186 73.305438 6.431 0 0 M9 -54.2481744163299 80.31085 -0.6755 0.50029 0.250145 M10 -111.187507110586 77.361225 -1.4373 0.152485 0.076242 M11 86.6003491334288 62.44811 1.3868 0.167332 0.083666 t -0.767119250424237 0.256233 -2.9938 0.003166 0.001583 Multiple Linear Regression - Regression Statistics Multiple R 0.909113674036662 R-squared 0.82648767232044 Adjusted R-squared 0.809136439552483 F-TEST (value) 47.6327926305489 F-TEST (DF numerator) 17 F-TEST (DF denominator) 170 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 127.324879886795 Sum Squared Residuals 2755976.25649176 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1632 1624.96216487031 7.03783512969226 2 1511 1609.33124673722 -98.3312467372175 3 1559 1676.32540114441 -117.325401144406 4 1630 1672.79480330307 -42.7948033030729 5 1579 1744.25426449686 -165.254264496858 6 1653 1849.55534041559 -196.555340415592 7 2152 2006.74544956455 145.254550435451 8 2148 2227.04142591574 -79.0414259157364 9 1752 1786.08329108286 -34.0832910828553 10 1765 1593.91257950137 171.087420498627 11 1717 1745.15423676709 -28.1542367670882 12 1558 1626.94356155909 -68.9435615590894 13 1575 1731.00139341833 -156.001393418334 14 1520 1624.45693487588 -104.456934875882 15 1805 1674.45053850205 130.549461497950 16 1800 1765.10777164385 34.8922283561497 17 1719 1842.09834950806 -123.098349508062 18 2008 1933.44234512880 74.5576548712037 19 2242 2174.91898236833 67.0810176316715 20 2478 2325.29352321490 152.706476785095 21 2030 1938.76961323212 91.2303867678834 22 1655 1765.88233555681 -110.882335556812 23 1693 1756.15154417936 -63.1515441793628 24 1623 1611.08385582396 11.9161441760431 25 1805 1748.88818236471 56.111817635295 26 1746 1711.35652601663 34.6434739833669 27 1795 1794.54083104077 0.459168959230808 28 1926 1801.61589410062 124.384105899383 29 1619 1896.55705498525 -277.557054985246 30 1992 1914.68092209777 77.3190779022267 31 2233 2146.38102192627 86.6189780737299 32 2192 2310.68966862782 -118.689668627819 33 2080 1812.41996106494 267.580038935061 34 1768 1725.87400800889 42.1259919911072 35 1835 1789.02104829106 45.9789517089369 36 1569 1668.39539165884 -99.395391658839 37 1976 1748.99961649398 227.000383506021 38 1853 1768.58424679493 84.4157532050709 39 1965 1859.6686878276 105.331312172398 40 1689 1881.38264181579 -192.382641815791 41 1778 1834.25642091437 -56.2564209143736 42 1976 1936.41706038397 39.5829396160272 43 2397 2155.91012375939 241.089876240609 44 2654 2359.95124516331 294.048754836687 45 2097 2016.66851390730 80.3314860927041 46 1963 1808.42253608640 154.577463913597 47 1677 1881.18103223541 -204.181032235406 48 1941 1648.28713329548 292.712866704525 49 2003 1865.10438492295 137.895615077045 50 1813 1835.39005884965 -22.3900588496519 51 2012 1847.30935953032 164.690640469680 52 1912 1897.75014618983 14.2498538101749 53 2084 1919.60211461405 164.397885385949 54 2080 2085.26345425645 -5.26345425644624 55 2118 2249.77741355291 -131.777413552913 56 2150 2278.88093775439 -128.88093775439 57 1608 1777.43171810334 -169.431718103336 58 1503 1515.23358132895 -12.2335813289512 59 1548 1580.21232036230 -32.2123203622983 60 1382 1473.89374740365 -91.8937474036534 61 1731 1581.86596635789 149.134033642112 62 1798 1602.66786308097 195.332136919032 63 1779 1760.60182556030 18.3981744397026 64 1887 1765.53747969497 121.462520305033 65 2004 1850.22234819798 153.777651802018 66 2077 2031.650181635 45.3498183649984 67 2092 2216.42253234963 -124.422532349626 68 2051 2255.26072611289 -204.260726112894 69 1577 1722.20534241639 -145.205342416386 70 1356 1475.80495707021 -119.804957070208 71 1652 1503.87767868906 148.122321310936 72 1382 1475.20589691184 -93.2058969118374 73 1519 1584.23884499268 -65.2388449926761 74 1421 1509.36203702842 -88.3620370284215 75 1442 1571.53215783841 -129.532157838408 76 1543 1552.24698900862 -9.2469890086225 77 1656 1627.6611904321 28.3388095679010 78 1561 1801.90752350292 -240.907523502917 79 1905 1921.67822434894 -16.6782243489416 80 2199 2059.33366324247 139.666336757527 81 1473 1707.48764194518 -234.487641945176 82 1655 1426.60519833885 228.394801661146 83 1407 1591.93317645622 -184.933176456224 84 1395 1423.66619280166 -28.666192801664 85 1530 1544.84531939797 -14.8453193979652 86 1309 1508.48385299161 -199.483852991607 87 1526 1512.35347250029 13.6465274997104 88 1327 1557.29179207403 -230.29179207403 89 1627 1545.14203798027 81.8579620197308 90 1748 1743.13918234691 4.86081765309311 91 1958 1975.55903421944 -17.5590342194350 92 2274 2094.38121684803 179.618783151966 93 1648 1742.36313781567 -94.3631378156688 94 1401 1507.09763957023 -106.097639570226 95 1411 1518.53497917642 -107.534979176420 96 1403 1381.09999316942 21.9000068305806 97 1394 1536.52211379621 -142.522113796213 98 1520 1438.79024925833 81.2097507416726 99 1528 1562.32381541536 -34.3238154153577 100 1643 1580.70435623819 62.2956437618072 101 1515 1662.20604424803 -147.206044248034 102 1685 1752.41797116605 -67.4179711660492 103 2000 1933.88758479205 66.1124152079459 104 2215 2097.84329539812 117.156704601882 105 1956 1711.17967291030 244.820327089704 106 1462 1607.01970830184 -145.019708301844 107 1563 1585.67143386851 -22.6714338685113 108 1459 1450.65469402387 8.34530597612882 109 1446 1588.51325437786 -142.513254377861 110 1622 1467.15307073082 154.846929269182 111 1657 1609.25859178336 47.7414082166392 112 1638 1643.25010190300 -5.25010190300413 113 1643 1678.84511166992 -35.8451116699208 114 1683 1800.49248710446 -117.492487104458 115 2050 1950.40659656898 99.5934034310243 116 2262 2112.20494866562 149.795051334379 117 1813 1733.39621684739 79.603783152614 118 1445 1551.92529014615 -106.925290146154 119 1762 1548.60387736679 213.396122633205 120 1461 1512.59781545509 -51.5978154550942 121 1556 1608.77677723080 -52.7767772308038 122 1431 1507.71784702171 -76.7178470217067 123 1427 1551.74044352525 -124.740443525246 124 1554 1515.43841759100 38.5615824089955 125 1645 1594.20759210287 50.7924078971276 126 1653 1762.51384112206 -109.513841122060 127 2016 1918.67688835594 97.3231116440577 128 2207 2081.65921302252 125.340786977475 129 1665 1695.87424091647 -30.8742409164725 130 1361 1473.25083782429 -112.250837824287 131 1506 1477.91295017924 28.0870498207617 132 1360 1381.83588420274 -21.8358842027445 133 1453 1507.72013366447 -54.7201336644692 134 1522 1428.73921879260 93.2607812073961 135 1460 1547.50079551997 -87.500795519974 136 1552 1527.52711178367 24.4728882163302 137 1548 1589.54175798733 -41.541757987332 138 1827 1719.57128990206 107.428710097945 139 1737 1961.63173318646 -224.631733186458 140 1941 1990.20946603109 -49.2094660310937 141 1474 1537.62207214042 -63.6220721404223 142 1458 1339.79776461945 118.202235380549 143 1542 1454.06346862288 87.9365313771192 144 1404 1387.11427133709 16.8857286629086 145 1522 1518.59570814678 3.40429185321661 146 1385 1458.76081366389 -73.7608136638874 147 1641 1499.67673180735 141.323268192647 148 1510 1569.24424890606 -59.2442489060646 149 1681 1592.75107626608 88.2489237339183 150 1938 1756.59737733347 181.402622666532 151 1868 2023.56965707282 -155.569657072819 152 1726 2054.52616623431 -328.526166234309 153 1456 1475.95579307600 -19.9557930759967 154 1445 1295.08801076141 149.911989238589 155 1456 1433.59747286645 22.4025271335545 156 1365 1333.87292837842 31.1270716215838 157 1487 1478.22998505480 8.7700149451982 158 1558 1425.62462238887 132.375377611128 159 1488 1547.40003525709 -59.4000352570887 160 1684 1527.64713140737 156.352868592634 161 1594 1629.91415873356 -35.91415873356 162 1850 1744.17200719029 105.827992809706 163 1998 1965.86971199383 32.1302880061727 164 2079 2083.83085047994 -4.83085047993892 165 1494 1620.53593961774 -126.535939617738 166 1057 1282.42002959262 -225.420029592616 167 1218 1216.23831947170 1.76168052830480 168 1168 1097.97756781338 70.0224321866176 169 1236 1257.73397513645 -21.7339751364453 170 1076 1181.44940494181 -105.449404941814 171 1174 1210.65987850872 -36.659878508723 172 1139 1215.99763169937 -76.9976316993702 173 1427 1247.02951853790 179.970481462103 174 1487 1466.56103312436 20.4389668756409 175 1483 1674.81015033969 -191.810150339689 176 1513 1705.07483715508 -192.074837155084 177 1357 1202.00684492392 154.993155076085 178 1165 1090.66552329252 74.334476707483 179 1282 1186.84646146751 95.1535385324919 180 1110 1107.37106616546 2.62893383453497 181 1297 1236.00217977381 60.9978202261871 182 1185 1192.13200682666 -7.13200682666083 183 1222 1254.65743423875 -32.6574342387546 184 1284 1244.46348264055 39.5365173594474 185 1444 1308.71095932536 135.289040674639 186 1575 1494.61798328985 80.3820167101494 187 1737 1709.75489560078 27.2451043992194 188 1763 1815.81881613375 -52.8188161337465 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.801649266801158 0.396701466397684 0.198350733198842 22 0.722821775335612 0.554356449328777 0.277178224664388 23 0.678532357588734 0.642935284822533 0.321467642411266 24 0.567978922766147 0.864042154467705 0.432021077233853 25 0.449078427837444 0.898156855674888 0.550921572162556 26 0.368611590108847 0.737223180217695 0.631388409891153 27 0.334475367691953 0.668950735383906 0.665524632308047 28 0.253401930519896 0.506803861039791 0.746598069480105 29 0.384691639104942 0.769383278209883 0.615308360895058 30 0.303494665924677 0.606989331849355 0.696505334075323 31 0.315619179187161 0.631238358374322 0.684380820812839 32 0.410851590398728 0.821703180797457 0.589148409601272 33 0.367571582429552 0.735143164859105 0.632428417570448 34 0.308459352708626 0.616918705417252 0.691540647291374 35 0.245148906736743 0.490297813473486 0.754851093263257 36 0.289830159133521 0.579660318267042 0.710169840866479 37 0.317572939872916 0.635145879745832 0.682427060127084 38 0.274864521907315 0.54972904381463 0.725135478092685 39 0.231215072664115 0.462430145328231 0.768784927335885 40 0.394800231163054 0.789600462326107 0.605199768836946 41 0.338779956867354 0.677559913734709 0.661220043132646 42 0.291008616255253 0.582017232510505 0.708991383744747 43 0.274118704694751 0.548237409389502 0.725881295305249 44 0.37219142053736 0.74438284107472 0.62780857946264 45 0.330069594835056 0.660139189670112 0.669930405164944 46 0.304231198494352 0.608462396988703 0.695768801505648 47 0.382038002046189 0.764076004092379 0.61796199795381 48 0.484163996772797 0.968327993545594 0.515836003227203 49 0.475541604267404 0.951083208534809 0.524458395732596 50 0.442666084594239 0.885332169188478 0.557333915405761 51 0.437859784064675 0.87571956812935 0.562140215935325 52 0.396544355627043 0.793088711254086 0.603455644372957 53 0.463982513380265 0.92796502676053 0.536017486619735 54 0.422862994485952 0.845725988971903 0.577137005514048 55 0.661437202427555 0.677125595144891 0.338562797572445 56 0.840085202420299 0.319829595159402 0.159914797579701 57 0.950802021881135 0.0983959562377296 0.0491979781188648 58 0.950035904423808 0.0999281911523836 0.0499640955761918 59 0.93644510093546 0.127109798129079 0.0635548990645394 60 0.935721739624135 0.128556520751730 0.0642782603758652 61 0.934103066098846 0.131793867802307 0.0658969339011536 62 0.94943170655232 0.101136586895360 0.0505682934476802 63 0.945172772902304 0.109654454195392 0.0548272270976961 64 0.947700095291348 0.104599809417304 0.0522999047086518 65 0.96589222652835 0.0682155469432985 0.0341077734716493 66 0.968829560215807 0.0623408795683867 0.0311704397841934 67 0.981458732219156 0.0370825355616874 0.0185412677808437 68 0.986425861623735 0.0271482767525293 0.0135741383762647 69 0.986149241996965 0.0277015160060703 0.0138507580030352 70 0.984740539383128 0.0305189212337442 0.0152594606168721 71 0.98730494455621 0.0253901108875801 0.0126950554437900 72 0.986194294789993 0.0276114104200143 0.0138057052100071 73 0.985291809598491 0.0294163808030172 0.0147081904015086 74 0.98199549894773 0.0360090021045408 0.0180045010522704 75 0.980892358656304 0.0382152826873919 0.0191076413436960 76 0.974808772393933 0.0503824552121339 0.0251912276060670 77 0.969251225871654 0.061497548256691 0.0307487741283455 78 0.982944103903469 0.0341117921930629 0.0170558960965314 79 0.977514710445006 0.0449705791099889 0.0224852895549944 80 0.9800117609157 0.0399764781685981 0.0199882390842990 81 0.988164437110836 0.0236711257783273 0.0118355628891637 82 0.993994751351432 0.0120104972971363 0.00600524864856816 83 0.995150860040335 0.00969827991932937 0.00484913995966469 84 0.993325922041775 0.0133481559164499 0.00667407795822497 85 0.991425584343231 0.0171488313135371 0.00857441565676853 86 0.994870375518882 0.0102592489622357 0.00512962448111783 87 0.99301893802279 0.0139621239544207 0.00698106197721033 88 0.996786876100382 0.00642624779923631 0.00321312389961816 89 0.996375477361472 0.0072490452770554 0.0036245226385277 90 0.99537638102042 0.00924723795915795 0.00462361897957897 91 0.993742433951655 0.0125151320966908 0.00625756604834539 92 0.996120010239723 0.00775997952055317 0.00387998976027658 93 0.99529358043805 0.00941283912390263 0.00470641956195132 94 0.994486287797078 0.0110274244058441 0.00551371220292203 95 0.99410296576567 0.0117940684686596 0.00589703423432981 96 0.992367428348186 0.0152651433036275 0.00763257165181375 97 0.993400622763408 0.0131987544731835 0.00659937723659175 98 0.99177492035959 0.0164501592808214 0.00822507964041072 99 0.98902756911461 0.0219448617707814 0.0109724308853907 100 0.9863443605074 0.0273112789851988 0.0136556394925994 101 0.989079644557493 0.021840710885015 0.0109203554425075 102 0.98805085005813 0.023898299883739 0.0119491499418695 103 0.984563123245792 0.030873753508416 0.015436876754208 104 0.982905166012748 0.0341896679745038 0.0170948339872519 105 0.994445509489733 0.0111089810205348 0.00555449051026739 106 0.993723178209841 0.0125536435803183 0.00627682179015915 107 0.991265422744744 0.0174691545105118 0.00873457725525589 108 0.98824637223939 0.0235072555212191 0.0117536277606096 109 0.989413943341885 0.0211721133162294 0.0105860566581147 110 0.99086512137814 0.0182697572437221 0.00913487862186103 111 0.989005069545828 0.0219898609083439 0.0109949304541720 112 0.98505171740992 0.0298965651801585 0.0149482825900792 113 0.979869620528663 0.0402607589426743 0.0201303794713371 114 0.981305746108231 0.0373885077835374 0.0186942538917687 115 0.981214563744104 0.0375708725117915 0.0187854362558958 116 0.98910471054348 0.0217905789130387 0.0108952894565194 117 0.992498155843349 0.0150036883133023 0.00750184415665114 118 0.990807744849714 0.0183845103005723 0.00919225515028616 119 0.997644486359844 0.00471102728031184 0.00235551364015592 120 0.996649441767196 0.00670111646560707 0.00335055823280353 121 0.995507154940087 0.00898569011982501 0.00449284505991251 122 0.99394567184568 0.0121086563086404 0.00605432815432019 123 0.992771032548235 0.0144579349035300 0.00722896745176501 124 0.99012673886097 0.0197465222780583 0.00987326113902914 125 0.986943102620215 0.0261137947595702 0.0130568973797851 126 0.9898950808168 0.0202098383663988 0.0101049191831994 127 0.993790062050542 0.0124198758989164 0.00620993794945819 128 0.999268464022758 0.00146307195448323 0.000731535977241616 129 0.999638252749388 0.000723494501224658 0.000361747250612329 130 0.999532819255345 0.000934361489309245 0.000467180744654623 131 0.99932317637633 0.00135364724733780 0.000676823623668898 132 0.99891065174634 0.00217869650732171 0.00108934825366086 133 0.998324282996934 0.00335143400613137 0.00167571700306568 134 0.998810850538147 0.00237829892370531 0.00118914946185266 135 0.998133076532748 0.0037338469345034 0.0018669234672517 136 0.997703222162197 0.00459355567560556 0.00229677783780278 137 0.996399651142326 0.00720069771534708 0.00360034885767354 138 0.995080748088738 0.00983850382252464 0.00491925191126232 139 0.995427353975671 0.00914529204865734 0.00457264602432867 140 0.99463972617389 0.0107205476522177 0.00536027382610884 141 0.9919943341474 0.0160113317051992 0.00800566585259961 142 0.99115043120684 0.0176991375863182 0.0088495687931591 143 0.99126834055011 0.0174633188997809 0.00873165944989044 144 0.987538276318324 0.0249234473633517 0.0124617236816759 145 0.985134639652206 0.0297307206955882 0.0148653603477941 146 0.978162764415736 0.0436744711685273 0.0218372355842636 147 0.99083474958175 0.0183305008365001 0.00916525041825007 148 0.985816217965303 0.0283675640693941 0.0141837820346971 149 0.984303205884068 0.0313935882318648 0.0156967941159324 150 0.998278551303554 0.0034428973928921 0.00172144869644605 151 0.997068405811504 0.00586318837699159 0.00293159418849580 152 0.998109276357813 0.00378144728437338 0.00189072364218669 153 0.996803448549428 0.00639310290114448 0.00319655145057224 154 0.995266368672986 0.00946726265402715 0.00473363132701357 155 0.995549261651273 0.00890147669745417 0.00445073834872708 156 0.991821563978725 0.0163568720425509 0.00817843602127547 157 0.985264598517004 0.0294708029659920 0.0147354014829960 158 0.975215623551764 0.0495687528964727 0.0247843764482364 159 0.956648857975046 0.0867022840499079 0.0433511420249539 160 0.980051742221655 0.0398965155566905 0.0199482577783453 161 0.975512516742658 0.0489749665146834 0.0244874832573417 162 0.95289725931087 0.094205481378259 0.0471027406891295 163 0.935041953282526 0.129916093434949 0.0649580467174743 164 0.959567888247808 0.0808642235043836 0.0404321117521918 165 0.913746765877767 0.172506468244467 0.0862532341222334 166 0.826831271069708 0.346337457860584 0.173168728930292 167 0.757285146186184 0.485429707627631 0.242714853813816 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 27 0.183673469387755 NOK 5% type I error level 92 0.625850340136054 NOK 10% type I error level 101 0.687074829931973 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/12/t1258035104fui5g595g77aupf/10w26w1258035046.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/12/t1258035104fui5g595g77aupf/10w26w1258035046.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/12/t1258035104fui5g595g77aupf/1dig31258035046.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/12/t1258035104fui5g595g77aupf/1dig31258035046.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/12/t1258035104fui5g595g77aupf/2qizy1258035046.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/12/t1258035104fui5g595g77aupf/2qizy1258035046.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/12/t1258035104fui5g595g77aupf/3civb1258035046.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/12/t1258035104fui5g595g77aupf/3civb1258035046.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/12/t1258035104fui5g595g77aupf/43pxf1258035046.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/12/t1258035104fui5g595g77aupf/43pxf1258035046.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/12/t1258035104fui5g595g77aupf/5bqil1258035046.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/12/t1258035104fui5g595g77aupf/5bqil1258035046.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/12/t1258035104fui5g595g77aupf/6zb8i1258035046.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/12/t1258035104fui5g595g77aupf/6zb8i1258035046.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/12/t1258035104fui5g595g77aupf/7qc3v1258035046.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/12/t1258035104fui5g595g77aupf/7qc3v1258035046.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/12/t1258035104fui5g595g77aupf/8munu1258035046.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/12/t1258035104fui5g595g77aupf/8munu1258035046.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/12/t1258035104fui5g595g77aupf/95i9z1258035046.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/12/t1258035104fui5g595g77aupf/95i9z1258035046.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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

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

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

Copyright

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

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• 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.

FreeStatistics.org is powered by