W6Q1

*Unverified author*

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

Title produced by software: Multiple Regression

Date of computation: Mon, 17 Nov 2008 11:07:12 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/17/t1226945271ufqfpiavqy9ua5k.htm/, Retrieved Mon, 17 Nov 2008 18:07:52 +0000

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Nov/17/t1226945271ufqfpiavqy9ua5k.htm/}, year = {2008}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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1687 0 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 10 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation y[t] = + 1717.75147928994 -396.055827116028x[t] + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 1717.75147928994 20.000334 85.8861 0 0 x -396.055827116028 57.786173 -6.8538 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.445226892939612 R-squared 0.198226986196661 Adjusted R-squared 0.194007128229275 F-TEST (value) 46.9748005095662 F-TEST (DF numerator) 1 F-TEST (DF denominator) 190 p-value 9.762957109416e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 260.004336317031 Sum Squared Residuals 12844428.4316954 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1687 1717.75147928994 -30.7514792899354 2 1508 1717.75147928994 -209.751479289941 3 1507 1717.75147928994 -210.751479289941 4 1385 1717.75147928994 -332.751479289941 5 1632 1717.75147928994 -85.7514792899409 6 1511 1717.75147928994 -206.751479289941 7 1559 1717.75147928994 -158.751479289941 8 1630 1717.75147928994 -87.7514792899409 9 1579 1717.75147928994 -138.751479289941 10 1653 1717.75147928994 -64.7514792899408 11 2152 1717.75147928994 434.248520710059 12 2148 1717.75147928994 430.248520710059 13 1752 1717.75147928994 34.2485207100591 14 1765 1717.75147928994 47.2485207100591 15 1717 1717.75147928994 -0.751479289940856 16 1558 1717.75147928994 -159.751479289941 17 1575 1717.75147928994 -142.751479289941 18 1520 1717.75147928994 -197.751479289941 19 1805 1717.75147928994 87.2485207100591 20 1800 1717.75147928994 82.2485207100591 21 1719 1717.75147928994 1.24852071005914 22 2008 1717.75147928994 290.248520710059 23 2242 1717.75147928994 524.248520710059 24 2478 1717.75147928994 760.248520710059 25 2030 1717.75147928994 312.248520710059 26 1655 1717.75147928994 -62.7514792899409 27 1693 1717.75147928994 -24.7514792899409 28 1623 1717.75147928994 -94.7514792899409 29 1805 1717.75147928994 87.2485207100591 30 1746 1717.75147928994 28.2485207100591 31 1795 1717.75147928994 77.2485207100591 32 1926 1717.75147928994 208.248520710059 33 1619 1717.75147928994 -98.7514792899409 34 1992 1717.75147928994 274.248520710059 35 2233 1717.75147928994 515.248520710059 36 2192 1717.75147928994 474.248520710059 37 2080 1717.75147928994 362.248520710059 38 1768 1717.75147928994 50.2485207100591 39 1835 1717.75147928994 117.248520710059 40 1569 1717.75147928994 -148.751479289941 41 1976 1717.75147928994 258.248520710059 42 1853 1717.75147928994 135.248520710059 43 1965 1717.75147928994 247.248520710059 44 1689 1717.75147928994 -28.7514792899409 45 1778 1717.75147928994 60.2485207100591 46 1976 1717.75147928994 258.248520710059 47 2397 1717.75147928994 679.248520710059 48 2654 1717.75147928994 936.24852071006 49 2097 1717.75147928994 379.248520710059 50 1963 1717.75147928994 245.248520710059 51 1677 1717.75147928994 -40.7514792899409 52 1941 1717.75147928994 223.248520710059 53 2003 1717.75147928994 285.248520710059 54 1813 1717.75147928994 95.2485207100591 55 2012 1717.75147928994 294.248520710059 56 1912 1717.75147928994 194.248520710059 57 2084 1717.75147928994 366.248520710059 58 2080 1717.75147928994 362.248520710059 59 2118 1717.75147928994 400.248520710059 60 2150 1717.75147928994 432.248520710059 61 1608 1717.75147928994 -109.751479289941 62 1503 1717.75147928994 -214.751479289941 63 1548 1717.75147928994 -169.751479289941 64 1382 1717.75147928994 -335.751479289941 65 1731 1717.75147928994 13.2485207100591 66 1798 1717.75147928994 80.2485207100591 67 1779 1717.75147928994 61.2485207100591 68 1887 1717.75147928994 169.248520710059 69 2004 1717.75147928994 286.248520710059 70 2077 1717.75147928994 359.248520710059 71 2092 1717.75147928994 374.248520710059 72 2051 1717.75147928994 333.248520710059 73 1577 1717.75147928994 -140.751479289941 74 1356 1717.75147928994 -361.751479289941 75 1652 1717.75147928994 -65.7514792899408 76 1382 1717.75147928994 -335.751479289941 77 1519 1717.75147928994 -198.751479289941 78 1421 1717.75147928994 -296.751479289941 79 1442 1717.75147928994 -275.751479289941 80 1543 1717.75147928994 -174.751479289941 81 1656 1717.75147928994 -61.7514792899409 82 1561 1717.75147928994 -156.751479289941 83 1905 1717.75147928994 187.248520710059 84 2199 1717.75147928994 481.248520710059 85 1473 1717.75147928994 -244.751479289941 86 1655 1717.75147928994 -62.7514792899409 87 1407 1717.75147928994 -310.751479289941 88 1395 1717.75147928994 -322.751479289941 89 1530 1717.75147928994 -187.751479289941 90 1309 1717.75147928994 -408.751479289941 91 1526 1717.75147928994 -191.751479289941 92 1327 1717.75147928994 -390.751479289941 93 1627 1717.75147928994 -90.7514792899409 94 1748 1717.75147928994 30.2485207100591 95 1958 1717.75147928994 240.248520710059 96 2274 1717.75147928994 556.248520710059 97 1648 1717.75147928994 -69.7514792899408 98 1401 1717.75147928994 -316.751479289941 99 1411 1717.75147928994 -306.751479289941 100 1403 1717.75147928994 -314.751479289941 101 1394 1717.75147928994 -323.751479289941 102 1520 1717.75147928994 -197.751479289941 103 1528 1717.75147928994 -189.751479289941 104 1643 1717.75147928994 -74.7514792899409 105 1515 1717.75147928994 -202.751479289941 106 1685 1717.75147928994 -32.7514792899409 107 2000 1717.75147928994 282.248520710059 108 2215 1717.75147928994 497.248520710059 109 1956 1717.75147928994 238.248520710059 110 1462 1717.75147928994 -255.751479289941 111 1563 1717.75147928994 -154.751479289941 112 1459 1717.75147928994 -258.751479289941 113 1446 1717.75147928994 -271.751479289941 114 1622 1717.75147928994 -95.7514792899409 115 1657 1717.75147928994 -60.7514792899409 116 1638 1717.75147928994 -79.7514792899409 117 1643 1717.75147928994 -74.7514792899409 118 1683 1717.75147928994 -34.7514792899409 119 2050 1717.75147928994 332.248520710059 120 2262 1717.75147928994 544.248520710059 121 1813 1717.75147928994 95.2485207100591 122 1445 1717.75147928994 -272.751479289941 123 1762 1717.75147928994 44.2485207100591 124 1461 1717.75147928994 -256.751479289941 125 1556 1717.75147928994 -161.751479289941 126 1431 1717.75147928994 -286.751479289941 127 1427 1717.75147928994 -290.751479289941 128 1554 1717.75147928994 -163.751479289941 129 1645 1717.75147928994 -72.7514792899409 130 1653 1717.75147928994 -64.7514792899408 131 2016 1717.75147928994 298.248520710059 132 2207 1717.75147928994 489.248520710059 133 1665 1717.75147928994 -52.7514792899409 134 1361 1717.75147928994 -356.751479289941 135 1506 1717.75147928994 -211.751479289941 136 1360 1717.75147928994 -357.751479289941 137 1453 1717.75147928994 -264.751479289941 138 1522 1717.75147928994 -195.751479289941 139 1460 1717.75147928994 -257.751479289941 140 1552 1717.75147928994 -165.751479289941 141 1548 1717.75147928994 -169.751479289941 142 1827 1717.75147928994 109.248520710059 143 1737 1717.75147928994 19.2485207100591 144 1941 1717.75147928994 223.248520710059 145 1474 1717.75147928994 -243.751479289941 146 1458 1717.75147928994 -259.751479289941 147 1542 1717.75147928994 -175.751479289941 148 1404 1717.75147928994 -313.751479289941 149 1522 1717.75147928994 -195.751479289941 150 1385 1717.75147928994 -332.751479289941 151 1641 1717.75147928994 -76.7514792899409 152 1510 1717.75147928994 -207.751479289941 153 1681 1717.75147928994 -36.7514792899409 154 1938 1717.75147928994 220.248520710059 155 1868 1717.75147928994 150.248520710059 156 1726 1717.75147928994 8.24852071005914 157 1456 1717.75147928994 -261.751479289941 158 1445 1717.75147928994 -272.751479289941 159 1456 1717.75147928994 -261.751479289941 160 1365 1717.75147928994 -352.751479289941 161 1487 1717.75147928994 -230.751479289941 162 1558 1717.75147928994 -159.751479289941 163 1488 1717.75147928994 -229.751479289941 164 1684 1717.75147928994 -33.7514792899409 165 1594 1717.75147928994 -123.751479289941 166 1850 1717.75147928994 132.248520710059 167 1998 1717.75147928994 280.248520710059 168 2079 1717.75147928994 361.248520710059 169 1494 1717.75147928994 -223.751479289941 170 1057 1321.69565217391 -264.695652173913 171 1218 1321.69565217391 -103.695652173913 172 1168 1321.69565217391 -153.695652173913 173 1236 1321.69565217391 -85.695652173913 174 1076 1321.69565217391 -245.695652173913 175 1174 1321.69565217391 -147.695652173913 176 1139 1321.69565217391 -182.695652173913 177 1427 1321.69565217391 105.304347826087 178 1487 1321.69565217391 165.304347826087 179 1483 1321.69565217391 161.304347826087 180 1513 1321.69565217391 191.304347826087 181 1357 1321.69565217391 35.3043478260869 182 1165 1321.69565217391 -156.695652173913 183 1282 1321.69565217391 -39.6956521739131 184 1110 1321.69565217391 -211.695652173913 185 1297 1321.69565217391 -24.6956521739131 186 1185 1321.69565217391 -136.695652173913 187 1222 1321.69565217391 -99.695652173913 188 1284 1321.69565217391 -37.6956521739131 189 1444 1321.69565217391 122.304347826087 190 1575 1321.69565217391 253.304347826087 191 1737 1321.69565217391 415.304347826087 192 1763 1321.69565217391 441.304347826087 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.155930802918944 0.311861605837888 0.844069197081056 6 0.0664935273773447 0.132987054754689 0.933506472622655 7 0.0256738331429404 0.0513476662858808 0.97432616685706 8 0.0122173968073303 0.0244347936146606 0.98778260319267 9 0.00437997810460292 0.00875995620920583 0.995620021895397 10 0.00224015981786413 0.00448031963572825 0.997759840182136 11 0.223580158345551 0.447160316691101 0.77641984165445 12 0.503981354000825 0.99203729199835 0.496018645999175 13 0.420841205312304 0.841682410624607 0.579158794687696 14 0.345365652564086 0.690731305128172 0.654634347435914 15 0.270018209378630 0.540036418757261 0.72998179062137 16 0.219064424415852 0.438128848831704 0.780935575584148 17 0.171075044874818 0.342150089749637 0.828924955125182 18 0.140711526546593 0.281423053093185 0.859288473453407 19 0.114092242558859 0.228184485117717 0.885907757441141 20 0.0900792873398669 0.180158574679734 0.909920712660133 21 0.063884764368076 0.127769528736152 0.936115235631924 22 0.0882860430336207 0.176572086067241 0.91171395696638 23 0.254036608717035 0.50807321743407 0.745963391282965 24 0.704134515940508 0.591730968118983 0.295865484059492 25 0.709949406325989 0.580101187348023 0.290050593674011 26 0.661732750333152 0.676534499333696 0.338267249666848 27 0.606522270477901 0.786955459044198 0.393477729522099 28 0.559718943813697 0.880562112372606 0.440281056186303 29 0.503737541569718 0.992524916860564 0.496262458430282 30 0.444960834898958 0.889921669797916 0.555039165101042 31 0.390182856040329 0.780365712080657 0.609817143959671 32 0.362128112746561 0.724256225493123 0.637871887253439 33 0.322724826525609 0.645449653051218 0.677275173474391 34 0.318469939735743 0.636939879471486 0.681530060264257 35 0.447502775999533 0.895005551999066 0.552497224000467 36 0.540190518349439 0.919618963301122 0.459809481650561 37 0.562294509844802 0.875410980310396 0.437705490155198 38 0.510686000293268 0.978627999413463 0.489313999706732 39 0.462277789155232 0.924555578310465 0.537722210844768 40 0.443241446768204 0.886482893536409 0.556758553231796 41 0.425738673525253 0.851477347050505 0.574261326474747 42 0.382073906721554 0.764147813443107 0.617926093278446 43 0.362011567326384 0.724023134652767 0.637988432673616 44 0.321992731747725 0.643985463495451 0.678007268252275 45 0.279428290514558 0.558856581029116 0.720571709485442 46 0.265648617004253 0.531297234008506 0.734351382995747 47 0.493782232847649 0.987564465695298 0.506217767152351 48 0.889937540791619 0.220124918416762 0.110062459208381 49 0.901113662368407 0.197772675263187 0.0988863376315933 50 0.891931280284285 0.216137439431430 0.108068719715715 51 0.874958770476828 0.250082459046344 0.125041229523172 52 0.861924268804623 0.276151462390755 0.138075731195377 53 0.857741867660571 0.284516264678857 0.142258132339429 54 0.83378722062345 0.332425558753099 0.166212779376550 55 0.831683517129929 0.336632965740142 0.168316482870071 56 0.813452152132249 0.373095695735503 0.186547847867751 57 0.829990046479602 0.340019907040796 0.170009953520398 58 0.845293937668114 0.309412124663772 0.154706062331886 59 0.86988655679995 0.260226886400100 0.130113443200050 60 0.899973180621902 0.200053638756195 0.100026819378098 61 0.892911538118977 0.214176923762045 0.107088461881023 62 0.89981365764821 0.200372684703580 0.100186342351790 63 0.898719123289092 0.202561753421815 0.101280876710908 64 0.924221577235453 0.151556845529094 0.0757784227645468 65 0.910274154620367 0.179451690759265 0.0897258453796325 66 0.894792536598393 0.210414926803214 0.105207463401607 67 0.877169794617804 0.245660410764392 0.122830205382196 68 0.864097265370824 0.271805469258351 0.135902734629176 69 0.867873641028726 0.264252717942549 0.132126358971274 70 0.887176441345612 0.225647117308775 0.112823558654388 71 0.908449632411517 0.183100735176966 0.0915503675884829 72 0.920869504333542 0.158260991332917 0.0791304956664583 73 0.916010299414107 0.167979401171786 0.0839897005858932 74 0.940402539413845 0.119194921172311 0.0595974605861555 75 0.931292247693514 0.137415504612973 0.0687077523064863 76 0.946956055853137 0.106087888293726 0.0530439441468632 77 0.945881642017068 0.108236715965863 0.0541183579829316 78 0.953436314940004 0.0931273701199919 0.0465636850599959 79 0.957766908324575 0.0844661833508502 0.0422330916754251 80 0.95441175157656 0.091176496846881 0.0455882484234405 81 0.945791198150969 0.108417603698063 0.0542088018490313 82 0.940175035777144 0.119649928445711 0.0598249642228557 83 0.936131061979697 0.127737876040607 0.0638689380203034 84 0.966338566371464 0.067322867257073 0.0336614336285365 85 0.96691607478516 0.066167850429681 0.0330839252148405 86 0.960164119344155 0.0796717613116905 0.0398358806558452 87 0.965277069335224 0.069445861329553 0.0347229306647765 88 0.970379455025867 0.0592410899482654 0.0296205449741327 89 0.967464051159065 0.0650718976818692 0.0325359488409346 90 0.977737303238431 0.044525393523138 0.022262696761569 91 0.9753226480452 0.0493547039096 0.0246773519548 92 0.982127603682625 0.0357447926347509 0.0178723963173755 93 0.977903931631157 0.0441921367376859 0.0220960683688429 94 0.972580035455955 0.0548399290880909 0.0274199645440455 95 0.973652199286683 0.0526956014266346 0.0263478007133173 96 0.992147866748658 0.0157042665026847 0.00785213325134237 97 0.989944177220263 0.0201116455594737 0.0100558227797368 98 0.99108047497721 0.0178390500455795 0.00891952502278976 99 0.99185205302911 0.0162958939417815 0.00814794697089075 100 0.992689155839436 0.0146216883211272 0.00731084416056362 101 0.993587965644624 0.0128240687107510 0.00641203435537552 102 0.992587470675183 0.0148250586496335 0.00741252932481676 103 0.991334311192622 0.0173313776147553 0.00866568880737766 104 0.988786623466502 0.0224267530669964 0.0112133765334982 105 0.987197426903214 0.0256051461935712 0.0128025730967856 106 0.983488734830613 0.0330225303387732 0.0165112651693866 107 0.986210074067875 0.0275798518642497 0.0137899259321249 108 0.995481225694707 0.00903754861058545 0.00451877430529273 109 0.996074339401285 0.00785132119742921 0.00392566059871461 110 0.995808213551387 0.00838357289722578 0.00419178644861289 111 0.994712555294524 0.0105748894109525 0.00528744470547626 112 0.99438371667621 0.0112325666475790 0.00561628332378949 113 0.994202765554047 0.0115944688919066 0.0057972344459533 114 0.992371888869807 0.0152562222603854 0.0076281111301927 115 0.98993717879755 0.0201256424048992 0.0100628212024496 116 0.986889938231705 0.0262201235365897 0.0131100617682949 117 0.983038753707429 0.0339224925851423 0.0169612462925711 118 0.97820102961212 0.0435979407757616 0.0217989703878808 119 0.985499028598025 0.0290019428039499 0.0145009714019749 120 0.997273737946519 0.00545252410696247 0.00272626205348123 121 0.996840500171403 0.00631899965719486 0.00315949982859743 122 0.996604328712003 0.00679134257599476 0.00339567128799738 123 0.995731903492709 0.00853619301458284 0.00426809650729142 124 0.995231935474466 0.00953612905106843 0.00476806452553421 125 0.99383571956488 0.0123285608702407 0.00616428043512034 126 0.993579112677005 0.0128417746459893 0.00642088732299466 127 0.993393503511835 0.0132129929763303 0.00660649648816513 128 0.991524685107479 0.0169506297850422 0.00847531489252108 129 0.988655488303615 0.0226890233927702 0.0113445116963851 130 0.98495935978621 0.0300812804275793 0.0150406402137896 131 0.99022162695995 0.0195567460801009 0.00977837304005047 132 0.998279991070906 0.0034400178581885 0.00172000892909425 133 0.997591624783056 0.00481675043388758 0.00240837521694379 134 0.99789281272571 0.00421437454857823 0.00210718727428912 135 0.99729389880209 0.00541220239582078 0.00270610119791039 136 0.997677692215397 0.00464461556920594 0.00232230778460297 137 0.99735459133933 0.00529081732134144 0.00264540866067072 138 0.996546553843356 0.00690689231328845 0.00345344615664422 139 0.9960452898774 0.00790942024520082 0.00395471012260041 140 0.994686970830008 0.0106260583399844 0.00531302916999218 141 0.992957425200093 0.0140851495998132 0.00704257479990659 142 0.992033009605433 0.0159339807891335 0.00796699039456673 143 0.989583771235881 0.020832457528237 0.0104162287641185 144 0.992081659149131 0.0158366817017377 0.00791834085086885 145 0.990449484404383 0.019101031191235 0.0095505155956175 146 0.988949707339056 0.0221005853218887 0.0110502926609444 147 0.985456060894265 0.0290878782114692 0.0145439391057346 148 0.985571134514045 0.0288577309719094 0.0144288654859547 149 0.981780174692575 0.0364396506148505 0.0182198253074253 150 0.983522709663428 0.0329545806731444 0.0164772903365722 151 0.977248897775252 0.0455022044494958 0.0227511022247479 152 0.972640095312507 0.0547198093749852 0.0273599046874926 153 0.962925549083712 0.0741489018325764 0.0370744509162882 154 0.967302522490983 0.0653949550180346 0.0326974775090173 155 0.966685544248089 0.0666289115038225 0.0333144557519112 156 0.957191721243764 0.0856165575124728 0.0428082787562364 157 0.951103839795078 0.097792320409845 0.0488961602049225 158 0.946573335209496 0.106853329581007 0.0534266647905037 159 0.94198975976146 0.116020480477081 0.0580102402385407 160 0.953946388633883 0.0921072227322349 0.0460536113661174 161 0.951782015166047 0.0964359696679061 0.0482179848339531 162 0.943781675674247 0.112436648651507 0.0562183243257533 163 0.948852829830086 0.102294340339827 0.0511471701699137 164 0.93386958805322 0.132260823893559 0.0661304119467795 165 0.93201799159513 0.13596401680974 0.06798200840487 166 0.908408408610311 0.183183182779377 0.0915915913896886 167 0.896695571660102 0.206608856679795 0.103304428339898 168 0.946324945345166 0.107350109309668 0.0536750546548339 169 0.92576197839223 0.148476043215541 0.0742380216077705 170 0.932074147271306 0.135851705457388 0.0679258527286941 171 0.912198628384566 0.175602743230867 0.0878013716154336 172 0.897139750110684 0.205720499778631 0.102860249889316 173 0.867972375515691 0.264055248968618 0.132027624484309 174 0.884055444197872 0.231889111604255 0.115944555802128 175 0.871741028095492 0.256517943809015 0.128258971904507 176 0.875980463407352 0.248039073185296 0.124019536592648 177 0.829472349328393 0.341055301343215 0.170527650671607 178 0.781248854895941 0.437502290208118 0.218751145104059 179 0.723085429655236 0.553829140689528 0.276914570344764 180 0.668097907094829 0.663804185810341 0.331902092905171 181 0.573634400111419 0.852731199777162 0.426365599888581 182 0.540064085792425 0.91987182841515 0.459935914207575 183 0.449856183719487 0.899712367438975 0.550143816280513 184 0.49102948923368 0.98205897846736 0.50897051076632 185 0.403462687220028 0.806925374440056 0.596537312779972 186 0.428895543286732 0.857791086573464 0.571104456713268 187 0.488140962852545 0.97628192570509 0.511859037147455 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 18 0.098360655737705 NOK 5% type I error level 63 0.344262295081967 NOK 10% type I error level 83 0.453551912568306 NOK

Charts produced by software:

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Parameters (Session):

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

Parameters (R input):

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

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

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

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