Q2bis

*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: Sun, 23 Nov 2008 15:06:22 -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/23/t1227478078gf5kttmylkawyk7.htm/, Retrieved Sun, 23 Nov 2008 22:08:07 +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/23/t1227478078gf5kttmylkawyk7.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}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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1687 0 -183.923544 1508 0 -177.0726091 1507 0 -228.6351091 1385 0 -237.4476091 1632 0 -127.7601091 1511 0 -193.0101091 1559 0 -220.6351091 1630 0 -164.5101091 1579 0 -268.3226091 1653 0 -333.6976091 2152 0 -34.26010911 2148 0 -154.8851091 1752 0 -97.74528053 1765 0 101.1056549 1717 0 2.543154874 1558 0 -43.26934513 1575 0 -163.5818451 1520 0 -162.8318451 1805 0 46.54315487 1800 0 26.66815487 1719 0 -107.1443451 2008 0 42.48065487 2242 0 76.91815487 2478 0 196.2931549 2030 0 201.4329835 1655 0 12.28391886 1693 0 -0.278581137 1623 0 42.90891886 1805 0 87.59641886 1746 0 84.34641886 1795 0 57.72141886 1926 0 173.8464189 1619 0 -185.9660811 1992 0 47.65891886 2233 0 89.09641886 2192 0 -68.52858114 2080 0 272.6112475 1768 0 146.4621829 1835 0 162.8996829 1569 0 10.08718285 1976 0 279.7746829 1853 0 212.5246829 1965 0 248.8996829 1689 0 -41.97531715 1778 0 -5.787817149 1976 0 52.83718285 2397 0 274.2746829 2654 0 414.6496829 2097 0 310.7895114 1963 0 362.6404468 1677 0 26.07794684 1941 0 403.2654468 2003 0 327.9529468 1813 0 193.7029468 2012 0 317.0779468 1912 0 202.2029468 2084 0 321.3904468 2080 0 178.0154468 2118 0 16.45294684 2150 0 -68.17205316 1608 0 -157.0322246 1503 0 -76.18128917 1548 0 -81.74378917 1382 0 -134.5562892 1731 0 77.13121083 1798 0 199.8812108 1779 0 105.2562108 1887 0 198.3812108 2004 0 262.5687108 2077 0 196.1937108 2092 0 11.63121083 2051 0 -145.9937892 1577 0 -166.8539606 1356 0 -202.0030252 1652 0 43.43447482 1382 0 -113.3780252 1519 0 -113.6905252 1421 0 -155.9405252 1442 0 -210.5655252 1543 0 -124.4405252 1656 0 -64.25302518 1561 0 -298.6280252 1905 0 -154.1905252 2199 0 23.18447482 1473 0 -249.6756966 1655 0 118.1752388 1407 0 -180.3872612 1395 0 -79.19976119 1530 0 -81.51226119 1309 0 -246.7622612 1526 0 -105.3872612 1327 0 -319.2622612 1627 0 -72.07476119 1748 0 -90.44976119 1958 0 -80.01226119 2274 0 119.3627388 1648 0 -53.49743261 1401 0 -114.6464972 1411 0 -155.2089972 1403 0 -50.02149721 1394 0 -196.3339972 1520 0 -14.58399721 1528 0 -82.20899721 1643 0 17.91600279 1515 0 -162.8964972 1685 0 -132.2714972 2000 0 -16.83399721 2215 0 81.54100279 1956 0 275.6808314 1462 0 -32.46823322 1563 0 17.96926678 1459 0 27.15676678 1446 0 -123.1557332 1622 0 108.5942668 1657 0 67.96926678 1638 0 34.09426678 1643 0 -13.71823322 1683 0 -113.0932332 2050 0 54.34426678 2262 0 149.7192668 1813 0 153.8590954 1445 0 -28.28996923 1762 0 238.1475308 1461 0 50.33503077 1556 0 8.022530771 1431 0 -61.22746923 1427 0 -140.8524692 1554 0 -28.72746923 1645 0 9.460030771 1653 0 -121.9149692 2016 0 41.52253077 2207 0 115.8975308 1665 0 27.03735936 1361 0 -91.11170524 1506 0 3.325794759 1360 0 -29.48670524 1453 0 -73.79920524 1522 0 50.95079476 1460 0 -86.67420524 1552 0 -9.54920524 1548 0 -66.36170524 1827 0 73.26329476 1737 0 -216.2992052 1941 0 -128.9242052 1474 0 -142.7843767 1458 0 27.06655875 1542 0 60.50405875 1404 0 35.69155875 1522 0 16.37905875 1385 0 -64.87094125 1641 0 115.5040587 1510 0 -30.37094125 1681 0 87.81655875 1938 0 205.4415587 1868 0 -64.12094125 1726 0 -322.7459413 1456 0 -139.6061127 1445 0 35.24482274 1456 0 -4.317677263 1365 0 17.86982274 1487 0 2.557322737 1558 0 129.3073227 1488 0 -16.31767726 1684 0 164.8073227 1594 0 21.99482274 1850 0 138.6198227 1998 0 87.05732274 2079 0 51.43232274 1494 0 -80.42784867 1057 1 -105.1918797 1218 1 5.245620328 1168 1 68.43312033 1236 1 -0.879379672 1076 1 -105.1293797 1174 1 -82.75437967 1139 1 -132.6293797 1427 1 102.5581203 1487 1 23.18312033 1483 1 -180.3793797 1513 1 -267.0043797 1357 1 30.13544892 1165 1 23.98638432 1282 1 90.42388432 1110 1 31.61138432 1297 1 81.29888432 1185 1 25.04888432 1222 1 -13.57611568 1284 1 33.54888432 1444 1 140.7363843 1575 1 132.3613843 1737 1 94.79888432 1763 1 4.173884316

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 3 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 2324.063373081 -226.385033611841X[t] + 1.00000000002621T[t] -451.374973280107M1[t] -635.461053318426M2[t] -583.13369799192M3[t] -694.55634264904M4[t] -555.478987325348M5[t] -609.464131985905M6[t] -532.074276653713M7[t] -515.43442131777M8[t] -460.857065991328M9[t] -319.71721065276M10[t] -118.389855331193M11[t] -1.76485533219257t + 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) 2324.063373081 0 192077335803.009 0 0 X -226.385033611841 0 -20074556266.918 0 0 T 1.00000000002621 0 48549665700.6437 0 0 M1 -451.374973280107 0 -30449437595.7309 0 0 M2 -635.461053318426 0 -42868898969.0739 0 0 M3 -583.13369799192 0 -39346272512.0117 0 0 M4 -694.55634264904 0 -46872313675.4439 0 0 M5 -555.478987325348 0 -37492239027.2897 0 0 M6 -609.464131985905 0 -41141308230.8278 0 0 M7 -532.074276653713 0 -35921112399.3736 0 0 M8 -515.43442131777 0 -34800850614.1218 0 0 M9 -460.857065991328 0 -31118092940.749 0 0 M10 -319.71721065276 0 -21589091681.1598 0 0 M11 -118.389855331193 0 -7994583180.9462 0 0 t -1.76485533219257 0 -26697919015.9864 0 0 Multiple Linear Regression - Regression Statistics Multiple R 1 R-squared 1 Adjusted R-squared 1 F-TEST (value) 6.52253850065383e+20 F-TEST (DF numerator) 14 F-TEST (DF denominator) 177 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.18850782199914e-08 Sum Squared Residuals 3.1052168061658e-13 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1687 1687.00000046385 -4.63853101212266e-07 2 1508 1507.99999999355 6.45163094042839e-09 3 1507 1506.99999998651 1.34905022320705e-08 4 1385 1384.99999999696 3.0385422212696e-09 5 1632 1631.99999999134 8.6612357754156e-09 6 1511 1510.99999999688 3.12070072137048e-09 7 1559 1558.99999999615 3.84630070006613e-09 8 1630 1630.00000000137 -1.37298399990506e-09 9 1579 1578.99999999290 7.0952570688324e-09 10 1653 1652.99999999757 2.43500370872625e-09 11 2152 2151.99999998479 1.52105195552314e-08 12 2148 2147.99999999063 9.3725421112474e-09 13 1752 1751.99999994982 5.01752722999672e-08 14 1765 1765.00000001453 -1.45252162780456e-08 15 1717 1716.99999998026 1.97444874187426e-08 16 1558 1557.99999998574 1.42582747577653e-08 17 1575 1575.00000000409 -4.08816291113719e-09 18 1520 1520.00000001136 -1.13578031416535e-08 19 1805 1804.99999998685 1.31545460548017e-08 20 1800 1799.99999999007 9.92531268164211e-09 21 1719 1719.00000001082 -1.08175355619094e-08 22 2008 2007.99999999111 8.88581750829107e-09 23 2242 2241.99999998139 1.86084392287976e-08 24 2478 2478.00000001352 -1.35203527434689e-08 25 2030 2030.00000000136 -1.35578639162345e-09 26 1655 1654.99999998589 1.41133596941643e-08 27 1693 1692.99999998287 1.71302699459866e-08 28 1623 1622.99999999169 8.3105283741126e-09 29 1805 1804.99999998436 1.56393125330223e-08 30 1746 1745.99999999153 8.47450039778052e-09 31 1795 1794.99999999083 9.17220921799506e-09 32 1926 1926.00000003762 -3.76213532351291e-08 33 1619 1619.00000002244 -2.24407010701534e-08 34 1992 1991.99999999494 5.06102479505894e-09 35 2233 2232.9999999854 1.46000694511427e-08 36 2192 2191.99999998027 1.97313964982862e-08 37 2080 2080.00000001691 -1.69103820603123e-08 38 1768 1768.00000004309 -4.3092363497887e-08 39 1835 1835.00000003784 -3.78357053784845e-08 40 1569 1568.99999999452 5.48151374814656e-09 41 1976 1976.00000004309 -4.30866809413219e-08 42 1853 1853.00000004857 -4.85739877567863e-08 43 1965 1965.00000004953 -4.95275026255433e-08 44 1689 1688.99999999565 4.3460430569994e-09 45 1778 1777.99999999185 8.147807765049e-09 46 1976 1975.99999999876 1.23617679272019e-09 47 2397 2397.00000004394 -4.39425139363216e-08 48 2654 2654.00000004662 -4.66215621081571e-08 49 2097 2096.9999999316 6.83998090422434e-08 50 1963 1962.99999996245 3.75524586687549e-08 51 1677 1676.99999998794 1.20610988277490e-08 52 1941 1940.99999996851 3.14874221073971e-08 53 2003 2002.99999995804 4.19614043959106e-08 54 1813 1812.99999996177 3.82301564701196e-08 55 2012 2011.99999996500 3.49963996027525e-08 56 1912 1911.99999996574 3.42570359970427e-08 57 2084 2083.99999996312 3.68834401752212e-08 58 2080 2079.99999996573 3.42661130989587e-08 59 2118 2117.99999999087 9.1256971996912e-09 60 2150 2149.99999998766 1.23436681471875e-08 61 1608 1607.99999993303 6.69719964763075e-08 62 1503 1502.99999999464 5.36459374402041e-09 63 1548 1547.99999998880 1.11978916525611e-08 64 1382 1381.99999996811 3.18943001607315e-08 65 1731 1730.99999999515 4.84622108934104e-09 66 1798 1797.99999997562 2.43789569535093e-08 67 1779 1778.99999997314 2.68590631376220e-08 68 1887 1886.99999997933 2.06681589612900e-08 69 2004 2003.99999997526 2.47360915580404e-08 70 2077 2076.9999999799 2.01005678523583e-08 71 2092 2091.99999999444 5.56299071185696e-09 72 2051 2050.99999995931 4.06941266188854e-08 73 1577 1576.99999994646 5.35402230276331e-08 74 1356 1355.99999997503 2.49731412981074e-08 75 1652 1651.99999999577 4.22791857329353e-09 76 1382 1381.99999998235 1.76500547947959e-08 77 1519 1518.99999997384 2.61583841755763e-08 78 1421 1420.99999997998 2.00157907423436e-08 79 1442 1441.99999997855 2.14472607023431e-08 80 1543 1542.99999998456 1.54399193795792e-08 81 1656 1656.00000000039 -3.87328689010117e-10 82 1561 1560.99999998062 1.93805012489273e-08 83 1905 1904.99999997378 2.62198813911787e-08 84 2199 2198.99999999743 2.57084438911917e-09 85 1473 1472.99999995798 4.20218287712448e-08 86 1655 1654.99999999711 2.89227905041581e-09 87 1407 1406.99999998359 1.64050254166095e-08 88 1395 1395.00000000693 -6.93483829945449e-09 89 1530 1529.99999999837 1.62581098205074e-09 90 1309 1308.99999999129 8.70691412067095e-09 91 1526 1525.999999995 5.00154451140613e-09 92 1327 1326.99999999314 6.8571061420962e-09 93 1627 1627.00000000387 -3.87145496159576e-09 94 1748 1748.00000000977 -9.76503660283739e-09 95 1958 1957.99999999941 5.86496845897515e-10 96 2274 2273.99999999364 6.36092778662298e-09 97 1648 1647.99999996681 3.31908887709715e-08 98 1401 1401.00000000469 -4.69475787615798e-09 99 1411 1410.99999999794 2.05597415985985e-09 100 1403 1403.00000000139 -1.38884744669785e-09 101 1394 1393.99999999905 9.46099158871057e-10 102 1520 1520.00000000107 -1.06740590644269e-09 103 1528 1527.99999999930 7.04851286468344e-10 104 1643 1643.00000000567 -5.66946652945735e-09 105 1515 1515.00000000518 -5.18033075567497e-09 106 1685 1685.00000001236 -1.23580707748843e-08 107 2000 1999.99999999476 5.24147375781639e-09 108 2215 2214.99999999634 3.66304953208995e-09 109 1956 1955.99999999913 8.74203337526007e-10 110 1462 1462.00000000054 -5.37725074934182e-10 111 1563 1562.99999999617 3.82790844548949e-09 112 1459 1459.0000000071 -7.10083364467954e-09 113 1446 1446.00000001466 -1.46609674008739e-08 114 1622 1622.00000002798 -2.79849168552685e-08 115 1657 1657.00000000692 -6.92034357354289e-09 116 1638 1638.00000000978 -9.78250097755767e-09 117 1643 1643.00000000278 -2.77920763015005e-09 118 1683 1683.00000002655 -2.65497590964571e-08 119 2050 2050.00000000031 -3.13327140672359e-10 120 2262 2262.00000002181 -2.18128512857492e-08 121 1813 1813.00000000962 -9.62211698993559e-09 122 1445 1445.00000000434 -4.33646708374954e-09 123 1762 1762.00000003563 -3.56320008328546e-08 124 1461 1461.00000001140 -1.13975410804720e-08 125 1556 1556.00000000279 -2.78828407932238e-09 126 1431 1431.00000000722 -7.22322294966797e-09 127 1427 1427.00000003514 -3.51363347397393e-08 128 1554 1554.00000001183 -1.18253546269562e-08 129 1645 1645.00000000808 -8.07596133397973e-09 130 1653 1653.00000004001 -4.00077928596553e-08 131 2016 2016.00000000367 -3.66628329104506e-09 132 2207 2207.00000003462 -3.461572721705e-08 133 1665 1664.99999997999 2.00126792717708e-08 134 1361 1361.00000000638 -6.37919994088301e-09 135 1506 1506.00000000217 -2.16667893843353e-09 136 1360 1360.00000001299 -1.29945875551458e-08 137 1453 1453.00000000333 -3.3328773437491e-09 138 1522 1522.00000001385 -1.38525864317079e-08 139 1460 1460.00000001025 -1.02456315140992e-08 140 1552 1552.00000001602 -1.60171060697818e-08 141 1548 1548.00000000878 -8.7780738529852e-09 142 1827 1827.00000001881 -1.88124398645581e-08 143 1737 1737.00000004060 -4.05980351944526e-08 144 1941 1941.00000004189 -4.18882354488792e-08 145 1474 1473.99999992923 7.07744680307075e-08 146 1458 1458.00000001317 -1.31656563518603e-08 147 1542 1542.00000000835 -8.35446434666936e-09 148 1404 1404.00000001839 -1.83920539401672e-08 149 1522 1522.00000000939 -9.3856934072065e-09 150 1385 1385.00000001451 -1.45059953077997e-08 151 1641 1640.99999996923 3.07663485764418e-08 152 1510 1510.00000001916 -1.91605055055884e-08 153 1681 1681.00000001651 -1.65078836454502e-08 154 1938 1937.99999997597 2.40340389987146e-08 155 1868 1868.00000000828 -8.27583263826581e-09 156 1726 1725.99999995050 4.95026388789162e-08 157 1456 1455.99999994300 5.70019499816856e-08 158 1445 1445.00000001707 -1.70691482962492e-08 159 1456 1456.00000000734 -7.34471540632764e-09 160 1365 1365.00000002161 -2.16139998404424e-08 161 1487 1487.00000000971 -9.71248491804666e-09 162 1558 1557.99999998328 1.67154767208677e-08 163 1488 1488.00000001947 -1.94678870596390e-08 164 1684 1683.99999998797 1.20347133139826e-08 165 1594 1594.00000001847 -1.84718924024311e-08 166 1850 1849.99999998790 1.20963607829376e-08 167 1998 1998.00000001593 -1.59271243879716e-08 168 2079 2079.00000001399 -1.39934947831975e-08 169 1494 1493.99999998824 1.17618005889031e-08 170 1057 1056.99999997524 2.47640119375862e-08 171 1218 1218.00000000044 -4.429559240538e-10 172 1168 1168.00000001479 -1.47869272039392e-08 173 1236 1236.00000000247 -2.47011583854521e-09 174 1076 1075.99999997899 2.10122359918279e-08 175 1174 1174.00000000957 -9.57427466848145e-09 176 1139 1138.99999998202 1.79828330533908e-08 177 1427 1426.99999998243 1.75688298937464e-08 178 1487 1487.00000001673 -1.67259623525099e-08 179 1483 1482.99999997077 2.92344948483731e-08 180 1513 1512.99999996750 3.25047981310921e-08 181 1357 1356.99999998298 1.70162670551771e-08 182 1165 1165.00000001231 -1.23109409337109e-08 183 1282 1282.00000000836 -8.36455584553912e-09 184 1110 1110.00000001751 -1.75110071532204e-08 185 1297 1297.00000001031 -1.0313201269985e-08 186 1185 1185.00000001609 -1.60888137691638e-08 187 1222 1222.00000001508 -1.50765496088521e-08 188 1284 1284.00000002006 -2.00618516416477e-08 189 1444 1443.99999999712 2.87894344245049e-09 190 1575 1575.00000000328 -3.27654323579139e-09 191 1737 1737.00000001167 -1.16669464012566e-08 192 1763 1763.00000000429 -4.29176850694790e-09

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227478078gf5kttmylkawyk7/1qwbj1227477977.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227478078gf5kttmylkawyk7/1qwbj1227477977.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227478078gf5kttmylkawyk7/2yw391227477977.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227478078gf5kttmylkawyk7/2yw391227477977.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227478078gf5kttmylkawyk7/3juhu1227477977.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227478078gf5kttmylkawyk7/3juhu1227477977.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227478078gf5kttmylkawyk7/4qydg1227477977.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227478078gf5kttmylkawyk7/4qydg1227477977.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227478078gf5kttmylkawyk7/5uum31227477977.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227478078gf5kttmylkawyk7/5uum31227477977.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227478078gf5kttmylkawyk7/6fimx1227477977.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227478078gf5kttmylkawyk7/6fimx1227477977.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227478078gf5kttmylkawyk7/7v38i1227477977.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227478078gf5kttmylkawyk7/7v38i1227477977.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227478078gf5kttmylkawyk7/8czfe1227477977.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227478078gf5kttmylkawyk7/8czfe1227477977.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227478078gf5kttmylkawyk7/9cgwj1227477977.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227478078gf5kttmylkawyk7/9cgwj1227477977.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) 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)) 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$resid, main='Residual Normal Q-Q Plot') grid() dev.off() (myerror <- as.ts(mysum$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() 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')

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Software written by Ed van Stee & Patrick Wessa

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