*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, 05 Dec 2010 21:39:06 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/05/t12915850991ebz0in7ewg9hgv.htm/, Retrieved Sun, 05 Dec 2010 22:38:21 +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/2010/Dec/05/t12915850991ebz0in7ewg9hgv.htm/}, year = {2010}, } @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 = {2010}, 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 «

2293,41 10430,35 9374,63 -18,2 -11 3,3 -0,8 2443,27 2513,17 2466,92 2502,66 2070,83 9691,12 8679,75 -22,8 -17 3,47 -1,7 2293,41 2443,27 2513,17 2466,92 2029,6 9810,31 8593 -23,6 -18 3,72 -1,1 2070,83 2293,41 2443,27 2513,17 2052,02 9304,43 8398,37 -27,6 -19 3,67 -0,4 2029,6 2070,83 2293,41 2443,27 1864,44 8767,96 7992,12 -29,4 -22 3,82 0,6 2052,02 2029,6 2070,83 2293,41 1670,07 7764,58 7235,47 -31,8 -24 3,85 0,6 1864,44 2052,02 2029,6 2070,83 1810,99 7694,78 7690,5 -31,4 -24 3,9 1,9 1670,07 1864,44 2052,02 2029,6 1905,41 8331,49 8396,2 -27,6 -20 3,99 2,3 1810,99 1670,07 1864,44 2052,02 1862,83 8460,94 8595,56 -28,8 -25 4,35 2,6 1905,41 1810,99 1670,07 1864,44 2014,45 8531,45 8614,55 -21,9 -22 4,98 3,1 1862,83 1905,41 1810,99 1670,07 2197,82 9117,03 9181,73 -13,9 -17 5,46 4,7 2014,45 1862,83 1905,41 1810,99 2962,34 12123,53 11114,08 -8 -9 5,19 5,5 2197,82 2014,45 1862,83 1905,41 3047,03 12989,35 11530,75 -2,8 -11 5,03 5,4 2962,34 2197,82 2014,45 1862,83 3032,6 13168,91 11322,38 -3,3 -13 5,38 5,9 3 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 10 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation BEL_20[t] = -546.230265905034 + 0.00497848663458504Nikkei[t] + 0.064130924727598DJ_Indust[t] -2.4442084265653Conjunct_Seizoenzuiver[t] -0.956816977273839Cons_vertrouw[t] + 37.9019963078767Rend_oblig_EUR[t] + 11.9162996323731Alg_consumptie_index_BE[t] + 1.0619313863985Y1[t] -0.292689132011974Y2[t] + 0.13605984089728Y3[t] -0.0183487610508147Y4[t] -51.4908803453574M1[t] -56.7853158988978M2[t] -58.0309927479335M3[t] -37.7722465200661M4[t] -68.7764884632851M5[t] -120.354286713861M6[t] -2.68155983648654M7[t] -59.9732492342926M8[t] -85.7452911011672M9[t] -67.6665101098873M10[t] -76.3701833397756M11[t] + 0.22183130685296t + 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) -546.230265905034 194.981219 -2.8015 0.005745 0.002872 Nikkei 0.00497848663458504 0.00472 1.0549 0.293151 0.146575 DJ_Indust 0.064130924727598 0.014233 4.5056 1.3e-05 7e-06 Conjunct_Seizoenzuiver -2.4442084265653 2.172125 -1.1253 0.26224 0.13112 Cons_vertrouw -0.956816977273839 2.022311 -0.4731 0.636794 0.318397 Rend_oblig_EUR 37.9019963078767 15.505785 2.4444 0.015646 0.007823 Alg_consumptie_index_BE 11.9162996323731 10.622703 1.1218 0.263715 0.131857 Y1 1.0619313863985 0.081115 13.0916 0 0 Y2 -0.292689132011974 0.117551 -2.4899 0.013848 0.006924 Y3 0.13605984089728 0.117008 1.1628 0.24671 0.123355 Y4 -0.0183487610508147 0.077425 -0.237 0.812984 0.406492 M1 -51.4908803453574 44.407475 -1.1595 0.248055 0.124027 M2 -56.7853158988978 44.374047 -1.2797 0.202589 0.101294 M3 -58.0309927479335 44.473916 -1.3048 0.193909 0.096955 M4 -37.7722465200661 44.263057 -0.8534 0.394795 0.197397 M5 -68.7764884632851 44.332146 -1.5514 0.122874 0.061437 M6 -120.354286713861 44.281582 -2.7179 0.007327 0.003664 M7 -2.68155983648654 44.350327 -0.0605 0.951866 0.475933 M8 -59.9732492342926 44.730392 -1.3408 0.181982 0.090991 M9 -85.7452911011672 45.283421 -1.8935 0.060176 0.030088 M10 -67.6665101098873 45.069847 -1.5014 0.135321 0.06766 M11 -76.3701833397756 44.836184 -1.7033 0.090539 0.04527 t 0.22183130685296 0.460599 0.4816 0.630768 0.315384 Multiple Linear Regression - Regression Statistics Multiple R 0.991017486025751 R-squared 0.9821156576088 Adjusted R-squared 0.979544052820524 F-TEST (value) 381.907695181581 F-TEST (DF numerator) 22 F-TEST (DF denominator) 153 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 118.049470789014 Sum Squared Residuals 2132158.66569565 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2293.41 2374.9204471504 -81.5104471504024 2 2070.83 2202.57371470657 -131.743714706575 3 2029.6 2013.25585210259 16.3441478974135 4 2052.02 2038.17203813227 13.8479618677283 5 1864.44 2011.87887631872 -147.438876318724 6 1670.07 1708.63486552215 -38.5648655221507 7 1810.99 1724.07403084451 86.9159691554925 8 1905.41 1891.09753153172 14.3124684682847 9 1862.83 1939.93138912236 -77.1013891223556 10 2014.45 1919.78905437597 94.6609456240305 11 2197.82 2147.25138070115 50.5686192988492 12 2962.34 2482.78165706429 479.558342935708 13 3047.03 3224.10037520864 -177.070375208638 14 3032.6 3117.25386171145 -84.6538617114457 15 3504.37 3220.051107333 284.318892667005 16 3801.06 3758.84984999166 42.2101500083401 17 3857.62 3873.95620071193 -16.3362007119252 18 3674.4 3804.49764065487 -130.097640654871 19 3720.98 3752.22292525193 -31.2429252519323 20 3844.49 3816.64542731655 27.8445726834464 21 4116.68 3954.91391412283 161.766085877175 22 4105.18 4209.35864198702 -104.178641987023 23 4435.23 4163.75328139702 271.476718602975 24 4296.49 4589.22157073622 -292.73157073622 25 4202.52 4263.82694919623 -61.3069491962283 26 4562.84 4283.33681543981 279.503184560186 27 4621.4 4648.60804914092 -27.2080491409183 28 4696.96 4602.32788113832 94.6321188616842 29 4591.27 4646.24544698546 -54.9754469854603 30 4356.98 4428.72085025161 -71.7408502516143 31 4502.64 4363.09234730264 139.547652697363 32 4443.91 4500.42739811638 -56.517398116376 33 4290.89 4324.30978991275 -33.4197899127477 34 4199.75 4195.81978062859 3.93021937141131 35 4138.52 4106.5725112486 31.9474887513999 36 3970.1 4099.96964712113 -129.869647121127 37 3862.27 3864.70524671014 -2.43524671013965 38 3701.61 3771.67611451071 -70.0661145107054 39 3570.12 3611.25520684942 -41.135206849423 40 3801.06 3562.79875125954 238.261248740461 41 3895.51 3787.19839548962 108.311604510381 42 3917.96 3736.48258497383 181.477415026173 43 3813.06 3872.42338578189 -59.3633857818872 44 3667.03 3698.1397454553 -31.1097454553004 45 3494.17 3551.6690102607 -57.4990102607003 46 3363.99 3403.16267708351 -39.1726770835065 47 3295.32 3250.12797553285 45.1920244671476 48 3277.01 3293.02375837092 -16.0137583709221 49 3257.16 3234.81216030253 22.347839697471 50 3161.69 3205.35087759409 -43.66087759409 51 3097.31 3096.96091714295 0.349082857051021 52 3061.26 3069.31577633949 -8.05577633949236 53 3119.31 3003.58924867598 115.720751324023 54 3106.22 3046.7472420563 59.4727579436985 55 3080.58 3120.75263737136 -40.1726373713582 56 2981.85 3031.17338196733 -49.3233819673311 57 2921.44 2917.71234493518 3.72765506482012 58 2849.27 2886.9687823469 -37.6987823469014 59 2756.76 2783.8214812394 -27.0614812393987 60 2645.64 2778.30985333788 -132.66985333788 61 2497.84 2616.86660354774 -119.026603547745 62 2448.05 2491.23828209012 -43.1882820901185 63 2454.62 2489.38285036294 -34.7628503629438 64 2407.6 2498.38874798934 -90.7887479893355 65 2472.81 2423.96515884054 48.8448411594604 66 2408.64 2435.52616212029 -26.8861621202918 67 2440.25 2480.68220209258 -40.4322020925778 68 2350.44 2488.08293811056 -137.642938110562 69 2196.72 2330.03621112739 -133.316211127386 70 2174.56 2200.91163908127 -26.3516390812745 71 2120.88 2205.61008319479 -84.7300831947874 72 2093.48 2193.56220403328 -100.08220403328 73 2061.41 2126.71982718502 -65.3098271850213 74 1969.6 2073.85992270252 -104.259922702524 75 1959.67 1965.72653343761 -6.05653343760915 76 1910.43 1959.15861293408 -48.7286129340816 77 1833.42 1873.67116790276 -40.2511679027626 78 1635.25 1732.83946066238 -97.589460662383 79 1765.9 1631.87417005499 134.025829945005 80 1946.81 1801.11047532871 145.699524671287 81 1995.37 1916.38672592259 78.983274077409 82 2042 1959.67007713636 82.32992286364 83 1940.49 1977.68739397482 -37.1973939748218 84 2065.81 1942.20142822077 123.608571779232 85 2214.95 2105.41933306558 109.530666934419 86 2304.98 2208.84258523757 96.1374147624267 87 2555.28 2333.83332997212 221.446670027884 88 2799.43 2663.73254935437 135.697450645627 89 2811.7 2843.8723466043 -32.1723466042971 90 2735.7 2798.96105380288 -63.2610538028835 91 2745.88 2814.46362948746 -68.5836294874634 92 2720.25 2792.0368219694 -71.7868219694018 93 2638.53 2730.50374825098 -91.9737482509784 94 2659.81 2659.57241339245 0.237586607545997 95 2641.65 2663.91840467373 -22.2684046737264 96 2604.42 2679.41992016769 -74.9999201676892 97 2892.63 2683.72544724087 208.90455275913 98 2915.02 3006.14246334576 -91.1224633457558 99 2845.26 2965.75871842271 -120.49871842271 100 2794.83 2940.76805300687 -145.938053006872 101 2848.96 2844.09349007077 4.86650992922868 102 2833.18 2814.6130085051 18.5669914948993 103 2995.55 2945.79641455374 49.7535854462584 104 2987.1 3061.27195663224 -74.1719566322435 105 3013.24 2983.76210616412 29.4778938358788 106 3110.52 3076.36029947537 34.159700524627 107 3045.78 3141.6725783741 -95.8925783741013 108 3032.93 3170.03247039503 -137.102470395026 109 3142.95 3130.08103371404 12.868966285963 110 3012.61 3215.55169409775 -202.941694097748 111 2897.06 3024.84982791778 -127.789827917784 112 2863.36 2979.2181566094 -115.858156609396 113 2882.6 2948.08469363016 -65.4846936301613 114 2767.63 2886.90873411199 -119.278734111993 115 2803.47 2884.03721998166 -80.567219981657 116 3030.29 2943.98233797001 86.3076620299932 117 3210.52 3111.36552741052 99.1544725894839 118 3249.57 3232.50865300419 17.0613469958054 119 2999.93 3222.0270719571 -222.097071957098 120 3181.96 3060.31747045725 121.642529542751 121 3053.05 3294.27060727036 -241.220607270362 122 3092.71 3057.07497923688 35.6350207631186 123 3165.26 3132.76177537831 32.49822462169 124 3173.95 3181.80721821289 -7.85721821289137 125 3280.37 3128.45373017278 151.916269827222 126 3288.18 3163.97081792921 124.209182070795 127 3411.13 3216.68322204783 194.446777952173 128 3484.74 3298.03463367133 186.70536632867 129 3361.13 3306.23262478699 54.8973752130068 130 3230.66 3194.33333659355 36.3266634064473 131 3006.84 3040.56073411741 -33.720734117409 132 3149.9 2874.44644042819 275.453559571811 133 3403.13 3067.21656677318 335.913433226817 134 3564.95 3315.31490667 249.635093330002 135 3327.7 3423.80820567826 -96.1082056782637 136 3141.12 3198.17848633517 -57.0584863351692 137 3064.42 3050.45291859861 13.9670814013898 138 2880.4 2913.52888842161 -33.1288884216134 139 2661.39 2813.08074213255 -151.690742132549 140 2504.67 2532.58673780743 -27.9167378074278 141 2450.41 2412.20583945692 38.2041605430753 142 2354.32 2384.26533795801 -29.945337958006 143 2401.33 2285.24628083222 116.083719167783 144 2394.36 2450.68101267712 -56.3210126771239 145 2409.36 2383.1393825455 26.2206174545002 146 2525.56 2412.53394000328 113.026059996723 147 2346.9 2514.33703692578 -167.437036925776 148 2250.27 2292.69287878474 -42.4228787847382 149 2152.18 2185.0165022864 -32.8365022864033 150 2154.87 2038.94769763982 115.922302360184 151 2097.76 2171.73630691704 -73.9763069170388 152 1989.31 2033.50591120422 -44.1959112042209 153 1877.1 1907.52772959679 -30.4277295967861 154 1852.13 1834.3775120989 17.752487901105 155 1795.65 1805.45132722119 -9.80132722119151 156 1751.01 1812.21086532155 -61.2008653215477 157 1745.74 1731.40507175475 14.3349282452514 158 1703.45 1729.40753203478 -25.9575320347792 159 1748.09 1699.66645097634 48.4235490236638 160 1734.1 1778.90514115895 -44.8051411589505 161 1711.74 1725.4022030362 -13.6622030361979 162 1690.6 1661.44777810645 29.1522218935463 163 1665.5 1756.2660243397 -90.7660243396975 164 1631.59 1641.95805136251 -10.3680513625139 165 1538.09 1580.56303892989 -42.4730389298938 166 1452.46 1501.5717948379 -49.111794837901 167 1429.12 1411.61949553562 17.500504464379 168 1471.16 1470.43170166869 0.728298331314978 169 1475.57 1457.81094833502 17.7590516649845 170 1464.65 1440.99231061871 23.6576893812863 171 1433.75 1416.13413835928 17.6158616407206 172 1451.04 1414.17585875291 36.8641412470865 173 1365.41 1405.87962067577 -40.469620675774 174 1299.88 1248.13321524149 51.7467847585055 175 1349.03 1316.92474184013 32.105258159869 176 1368.43 1326.2666515563 42.1633484436966 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 26 0.233365674554259 0.466731349108518 0.766634325445741 27 0.369642860291797 0.739285720583595 0.630357139708203 28 0.531750554984165 0.93649889003167 0.468249445015835 29 0.406565109216489 0.813130218432977 0.593434890783511 30 0.29960648985227 0.599212979704539 0.70039351014773 31 0.22199487616825 0.443989752336501 0.77800512383175 32 0.169627456283352 0.339254912566704 0.830372543716648 33 0.13492894075912 0.26985788151824 0.86507105924088 34 0.113837336697472 0.227674673394944 0.886162663302528 35 0.08575633829477 0.17151267658954 0.91424366170523 36 0.0595029648985613 0.119005929797123 0.940497035101439 37 0.0377467516247298 0.0754935032494596 0.96225324837527 38 0.0341716355942876 0.0683432711885753 0.965828364405712 39 0.079597736077448 0.159195472154896 0.920402263922552 40 0.145535827692397 0.291071655384794 0.854464172307603 41 0.11568235350844 0.23136470701688 0.88431764649156 42 0.147799648584667 0.295599297169333 0.852200351415333 43 0.111511686332834 0.223023372665668 0.888488313667166 44 0.112682341415242 0.225364682830483 0.887317658584758 45 0.105303586556776 0.210607173113552 0.894696413443224 46 0.0794412362057952 0.15888247241159 0.920558763794205 47 0.103498426853254 0.206996853706508 0.896501573146746 48 0.109659859341316 0.219319718682632 0.890340140658684 49 0.12515942655806 0.250318853116119 0.87484057344194 50 0.0970558911095236 0.194111782219047 0.902944108890476 51 0.0758158330662261 0.151631666132452 0.924184166933774 52 0.0699034424163061 0.139806884832612 0.930096557583694 53 0.0646981612114731 0.129396322422946 0.935301838788527 54 0.0982399319756259 0.196479863951252 0.901760068024374 55 0.085014312328148 0.170028624656296 0.914985687671852 56 0.0655470001405659 0.131094000281132 0.934452999859434 57 0.0543410922252439 0.108682184450488 0.945658907774756 58 0.0461536843894002 0.0923073687788004 0.9538463156106 59 0.0479414593353357 0.0958829186706713 0.952058540664664 60 0.0649858148337862 0.129971629667572 0.935014185166214 61 0.089555576504575 0.17911115300915 0.910444423495425 62 0.1239412947629 0.247882589525799 0.8760587052371 63 0.1984840213172 0.396968042634401 0.8015159786828 64 0.24069636320611 0.48139272641222 0.75930363679389 65 0.272349110769039 0.544698221538077 0.727650889230961 66 0.248094804053126 0.496189608106253 0.751905195946874 67 0.209779354870407 0.419558709740814 0.790220645129593 68 0.217965669954708 0.435931339909415 0.782034330045292 69 0.195707342256194 0.391414684512388 0.804292657743806 70 0.162033192395441 0.324066384790881 0.83796680760456 71 0.155658167630351 0.311316335260702 0.84434183236965 72 0.153645607732668 0.307291215465336 0.846354392267332 73 0.142535968330449 0.285071936660898 0.857464031669551 74 0.135240827342809 0.270481654685617 0.864759172657191 75 0.114898120900597 0.229796241801194 0.885101879099403 76 0.140477456212342 0.280954912424684 0.859522543787658 77 0.154238974443909 0.308477948887819 0.84576102555609 78 0.168847381788903 0.337694763577807 0.831152618211097 79 0.26576740534609 0.531534810692181 0.73423259465391 80 0.518385790898749 0.963228418202502 0.481614209101251 81 0.697614911982535 0.60477017603493 0.302385088017465 82 0.762829302661534 0.474341394676932 0.237170697338466 83 0.77342412171892 0.453151756562161 0.22657587828108 84 0.787780435972033 0.424439128055935 0.212219564027967 85 0.805781060825589 0.388437878348822 0.194218939174411 86 0.801053254011453 0.397893491977094 0.198946745988547 87 0.804601444227876 0.390797111544249 0.195398555772124 88 0.794231989744888 0.411536020510224 0.205768010255112 89 0.778153605401246 0.443692789197508 0.221846394598754 90 0.815776068165752 0.368447863668496 0.184223931834248 91 0.800597456875147 0.398805086249705 0.199402543124853 92 0.78005936058798 0.439881278824039 0.219940639412019 93 0.760264535073468 0.479470929853063 0.239735464926532 94 0.724106236673245 0.551787526653509 0.275893763326755 95 0.691967385670344 0.616065228659312 0.308032614329656 96 0.680221632098798 0.639556735802404 0.319778367901202 97 0.720792724551602 0.558414550896797 0.279207275448398 98 0.727828095205706 0.544343809588588 0.272171904794294 99 0.789686040176788 0.420627919646423 0.210313959823212 100 0.876980981499409 0.246038037001183 0.123019018500591 101 0.861557911252837 0.276884177494327 0.138442088747163 102 0.837049666525285 0.325900666949429 0.162950333474715 103 0.814811465809775 0.370377068380449 0.185188534190225 104 0.823304921569125 0.353390156861749 0.176695078430875 105 0.789767688071299 0.420464623857402 0.210232311928701 106 0.787396661914596 0.425206676170807 0.212603338085404 107 0.788408411572224 0.423183176855552 0.211591588427776 108 0.802063400729695 0.395873198540609 0.197936599270305 109 0.797779841292404 0.404440317415191 0.202220158707596 110 0.83801477417013 0.323970451659741 0.161985225829871 111 0.836407404169914 0.327185191660173 0.163592595830086 112 0.831607813498042 0.336784373003915 0.168392186501958 113 0.81531113373491 0.369377732530181 0.184688866265091 114 0.855207700070054 0.289584599859892 0.144792299929946 115 0.846041717513704 0.307916564972592 0.153958282486296 116 0.827927542126658 0.344144915746684 0.172072457873342 117 0.830335141515073 0.339329716969855 0.169664858484927 118 0.800478029881252 0.399043940237495 0.199521970118748 119 0.878394800687403 0.243210398625195 0.121605199312597 120 0.899384197143004 0.201231605713992 0.100615802856996 121 0.967469804070556 0.0650603918588887 0.0325301959294444 122 0.959242052144934 0.0815158957101314 0.0407579478550657 123 0.944907844640333 0.110184310719333 0.0550921553596666 124 0.942140450532175 0.11571909893565 0.0578595494678251 125 0.936427866220696 0.127144267558608 0.0635721337793038 126 0.937681768336265 0.12463646332747 0.0623182316637352 127 0.945033936815995 0.109932126368009 0.0549660631840046 128 0.944525217902105 0.110949564195791 0.0554747820978953 129 0.924937438439358 0.150125123121284 0.0750625615606418 130 0.902422277277797 0.195155445444406 0.097577722722203 131 0.93069380830492 0.138612383390159 0.0693061916950793 132 0.974430388109605 0.0511392237807908 0.0255696118903954 133 0.99692842939862 0.00614314120276062 0.00307157060138031 134 0.99997546256503 4.90748699407833e-05 2.45374349703917e-05 135 0.999999839619039 3.2076192275549e-07 1.60380961377745e-07 136 0.999999997298429 5.40314262823092e-09 2.70157131411546e-09 137 0.999999992544035 1.4911930388853e-08 7.45596519442648e-09 138 0.9999999760058 4.7988400345572e-08 2.3994200172786e-08 139 0.999999941540636 1.16918728134318e-07 5.84593640671591e-08 140 0.999999905695635 1.8860873044122e-07 9.43043652206102e-08 141 0.99999973229181 5.3541638007725e-07 2.67708190038625e-07 142 0.999998777746246 2.44450750808191e-06 1.22225375404095e-06 143 0.999997387339385 5.22532123064641e-06 2.61266061532321e-06 144 0.999991035166893 1.79296662132601e-05 8.96483310663005e-06 145 0.999978075955544 4.38480889128657e-05 2.19240444564329e-05 146 0.999981299021832 3.74019563356824e-05 1.87009781678412e-05 147 0.99991752758197 0.000164944836060923 8.24724180304616e-05 148 0.999886595531148 0.000226808937703659 0.00011340446885183 149 0.999939092214705 0.000121815570589053 6.09077852945267e-05 150 0.999273281351517 0.00145343729696659 0.000726718648483293 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 18 0.144 NOK 5% type I error level 18 0.144 NOK 10% type I error level 25 0.2 NOK

Charts produced by software:

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Parameters (Session):

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

Parameters (R input):

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

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

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

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Software written by Ed van Stee & Patrick Wessa

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