workshop 7 berekening 3

*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, 19 Nov 2009 10:08:08 -0700

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/19/t1258650552dl3gc2irkcep2qh.htm/, Retrieved Thu, 19 Nov 2009 18:09:24 +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/19/t1258650552dl3gc2irkcep2qh.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 «

4716.99 0 4926.65 0 4920.10 0 5170.09 0 5246.24 0 5283.61 0 4979.05 0 4825.20 0 4695.12 0 4711.54 0 4727.22 0 4384.96 0 4378.75 0 4472.93 0 4564.07 0 4310.54 0 4171.38 0 4049.38 0 3591.37 0 3720.46 0 4107.23 0 4101.71 0 4162.34 0 4136.22 0 4125.88 0 4031.48 0 3761.36 0 3408.56 0 3228.47 0 3090.45 0 2741.14 0 2980.44 0 3104.33 0 3181.57 0 2863.86 0 2898.01 0 3112.33 0 3254.33 0 3513.47 0 3587.61 0 3727.45 0 3793.34 0 3817.58 0 3845.13 0 3931.86 0 4197.52 0 4307.13 0 4229.43 0 4362.28 0 4217.34 0 4361.28 0 4327.74 0 4417.65 0 4557.68 0 4650.35 0 4967.18 0 5123.42 0 5290.85 0 5535.66 0 5514.06 0 5493.88 0 5694.83 0 5850.41 0 6116.64 0 6175.00 0 6513.58 0 6383.78 0 6673.66 0 6936.61 0 7300.68 0 7392.93 0 7497.31 0 7584.71 0 7160.79 0 7196.19 0 7245.63 0 7347.51 0 7425.75 0 7778.51 0 7822.33 0 8181.22 0 8371.47 0 8347.71 0 8672.11 0 8802.79 0 9138.46 0 9123.29 0 9023.21 1 8850.41 1 8864.58 1 9163.74 1 8516.66 1 8553.44 1 7 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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 2850.80433638344 -529.242454901961X[t] + 606.554587799569M1[t] + 626.875762091508M2[t] + 542.308047494557M3[t] + 509.450605664492M4[t] + 460.512891067541M5[t] + 350.105176470591M6[t] + 131.211906318086M7[t] + 79.4308583878024M8[t] + 138.930921568630M9[t] + 95.2054291939026M10[t] + 85.7332701525081M11[t] + 45.3132701525054t + 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) 2850.80433638344 559.729488 5.0932 2e-06 1e-06 X -529.242454901961 476.40413 -1.1109 0.26944 0.13472 M1 606.554587799569 670.050174 0.9052 0.367654 0.183827 M2 626.875762091508 669.805105 0.9359 0.351719 0.175859 M3 542.308047494557 669.614433 0.8099 0.420054 0.210027 M4 509.450605664492 670.001167 0.7604 0.448935 0.224467 M5 460.512891067541 669.592638 0.6878 0.493303 0.246652 M6 350.105176470591 669.238378 0.5231 0.602108 0.301054 M7 131.211906318086 668.938473 0.1961 0.844917 0.422458 M8 79.4308583878024 668.692996 0.1188 0.905699 0.452849 M9 138.930921568630 668.502007 0.2078 0.835816 0.417908 M10 95.2054291939026 668.365553 0.1424 0.887033 0.443517 M11 85.7332701525081 668.283667 0.1283 0.898195 0.449097 t 45.3132701525054 6.040215 7.5019 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.694078414024687 R-squared 0.481744844815025 Adjusted R-squared 0.410071259523486 F-TEST (value) 6.72137221621442 F-TEST (DF numerator) 13 F-TEST (DF denominator) 94 p-value 6.17242346123703e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1417.58583194669 Sum Squared Residuals 188897661.547984 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4716.99 3502.67219433550 1214.31780566450 2 4926.65 3568.30663877996 1358.34336122004 3 4920.1 3529.05219433551 1391.04780566449 4 5170.09 3541.50802265795 1628.58197734205 5 5246.24 3537.88357821351 1708.35642178649 6 5283.61 3472.78913376906 1810.82086623094 7 4979.05 3299.20913376906 1679.84086623094 8 4825.2 3292.74135599128 1532.45864400871 9 4695.12 3397.55468932462 1297.56531067538 10 4711.54 3399.14246710240 1312.39753289760 11 4727.22 3434.98357821351 1292.23642178649 12 4384.96 3394.56357821351 990.396421786495 13 4378.75 4046.43143616558 332.318563834421 14 4472.93 4112.06588061002 360.864119389976 15 4564.07 4072.81143616558 491.258563834422 16 4310.54 4085.26726448802 225.272735511982 17 4171.38 4081.64282004357 89.7371799564272 18 4049.38 4016.54837559913 32.8316244008712 19 3591.37 3842.96837559913 -251.598375599129 20 3720.46 3836.50059782135 -116.040597821351 21 4107.23 3941.31393115468 165.916068845316 22 4101.71 3942.90170893246 158.808291067539 23 4162.34 3978.74282004357 183.597179956428 24 4136.22 3938.32282004357 197.897179956430 25 4125.88 4590.19067799564 -464.310677995644 26 4031.48 4655.82512244009 -624.345122440088 27 3761.36 4616.57067799564 -855.210677995644 28 3408.56 4629.02650631808 -1220.46650631808 29 3228.47 4625.40206187364 -1396.93206187364 30 3090.45 4560.30761742919 -1469.85761742919 31 2741.14 4386.72761742919 -1645.58761742919 32 2980.44 4380.25983965142 -1399.81983965142 33 3104.33 4485.07317298475 -1380.74317298475 34 3181.57 4486.66095076253 -1305.09095076253 35 2863.86 4522.50206187364 -1658.64206187364 36 2898.01 4482.08206187364 -1584.07206187364 37 3112.33 5133.94991982571 -2021.61991982571 38 3254.33 5199.58436427015 -1945.25436427015 39 3513.47 5160.32991982571 -1646.85991982571 40 3587.61 5172.78574814815 -1585.17574814815 41 3727.45 5169.1613037037 -1441.71130370370 42 3793.34 5104.06685925926 -1310.72685925926 43 3817.58 4930.48685925926 -1112.90685925926 44 3845.13 4924.01908148148 -1078.88908148148 45 3931.86 5028.83241481481 -1096.97241481481 46 4197.52 5030.42019259259 -832.900192592592 47 4307.13 5066.2613037037 -759.131303703703 48 4229.43 5025.8413037037 -796.4113037037 49 4362.28 5677.70916165577 -1315.42916165577 50 4217.34 5743.34360610022 -1526.00360610022 51 4361.28 5704.08916165577 -1342.80916165577 52 4327.74 5716.54498997821 -1388.80498997821 53 4417.65 5712.92054553377 -1295.27054553377 54 4557.68 5647.82610108932 -1090.14610108932 55 4650.35 5474.24610108932 -823.896101089325 56 4967.18 5467.77832331155 -500.598323311547 57 5123.42 5572.59165664488 -449.17165664488 58 5290.85 5574.17943442266 -283.329434422657 59 5535.66 5610.02054553377 -74.3605455337688 60 5514.06 5569.60054553377 -55.5405455337657 61 5493.88 6221.46840348584 -727.58840348584 62 5694.83 6287.10284793028 -592.272847930284 63 5850.41 6247.84840348584 -397.438403485840 64 6116.64 6260.30423180828 -143.664231808279 65 6175 6256.67978736383 -81.6797873638341 66 6513.58 6191.58534291939 321.99465708061 67 6383.78 6018.00534291939 365.77465708061 68 6673.66 6011.53756514161 662.122434858388 69 6936.61 6116.35089847495 820.259101525054 70 7300.68 6117.93867625272 1182.74132374728 71 7392.93 6153.77978736383 1239.15021263617 72 7497.31 6113.35978736383 1383.95021263617 73 7584.71 6765.2276453159 819.482354684095 74 7160.79 6830.86208976035 329.927910239651 75 7196.19 6791.6076453159 404.582354684094 76 7245.63 6804.06347363835 441.566526361654 77 7347.51 6800.4390291939 547.0709708061 78 7425.75 6735.34458474946 690.405415250543 79 7778.51 6561.76458474946 1216.74541525054 80 7822.33 6555.29680697168 1267.03319302832 81 8181.22 6660.11014030501 1521.10985969499 82 8371.47 6661.69791808279 1709.77208191721 83 8347.71 6697.5390291939 1650.1709708061 84 8672.11 6657.1190291939 2014.99097080610 85 8802.79 7308.98688714597 1493.80311285403 86 9138.46 7374.62133159042 1763.83866840958 87 9123.29 7335.36688714597 1787.92311285403 88 9023.21 6818.58026056645 2204.62973943355 89 8850.41 6814.955816122 2035.45418387800 90 8864.58 6749.86137167756 2114.71862832244 91 9163.74 6576.28137167756 2587.45862832244 92 8516.66 6569.81359389978 1946.84640610022 93 8553.44 6674.62692723311 1878.81307276689 94 7555.2 6676.21470501089 878.985294989107 95 7851.22 6712.055816122 1139.16418387800 96 7442 6671.635816122 770.364183877999 97 7992.53 7323.50367407408 669.026325925924 98 8264.04 7389.13811851852 874.901881481482 99 7517.39 7349.88367407407 167.506325925926 100 7200.4 7362.33950239651 -161.939502396515 101 7193.69 7358.71505795207 -165.025057952070 102 6193.58 7293.62061350763 -1100.04061350763 103 5104.21 7120.04061350763 -2015.83061350763 104 4800.46 7113.57283572985 -2313.11283572985 105 4461.61 7218.38616906318 -2756.77616906318 106 4398.59 7219.97394684096 -2821.38394684096 107 4243.63 7255.81505795207 -3012.18505795207 108 4293.82 7215.39505795207 -2921.57505795207 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0117929439939733 0.0235858879879466 0.988207056006027 18 0.00575506919909182 0.0115101383981836 0.994244930800908 19 0.00307612073067958 0.00615224146135917 0.99692387926932 20 0.000841991975623328 0.00168398395124666 0.999158008024377 21 0.000225584979383739 0.000451169958767477 0.999774415020616 22 5.68447002265703e-05 0.000113689400453141 0.999943155299774 23 1.4828381508291e-05 2.9656763016582e-05 0.999985171618492 24 7.53464851654945e-06 1.50692970330989e-05 0.999992465351483 25 6.56308228762762e-06 1.31261645752552e-05 0.999993436917712 26 2.01521235059438e-06 4.03042470118877e-06 0.99999798478765 27 4.69858614814139e-07 9.39717229628277e-07 0.999999530141385 28 1.72691809052340e-07 3.45383618104681e-07 0.99999982730819 29 8.38240644685006e-08 1.67648128937001e-07 0.999999916175936 30 4.54720949931140e-08 9.09441899862279e-08 0.999999954527905 31 1.88850569637243e-08 3.77701139274487e-08 0.999999981114943 32 4.53626220556216e-09 9.07252441112433e-09 0.999999995463738 33 1.05382139537120e-09 2.10764279074239e-09 0.999999998946179 34 2.24575490603552e-10 4.49150981207104e-10 0.999999999775425 35 8.52059727667224e-11 1.70411945533445e-10 0.999999999914794 36 1.92487905036415e-11 3.84975810072831e-11 0.999999999980751 37 5.69971510789948e-12 1.13994302157990e-11 0.9999999999943 38 1.84885597585640e-12 3.69771195171281e-12 0.99999999999815 39 1.65616826533817e-12 3.31233653067634e-12 0.999999999998344 40 2.64290593981564e-12 5.28581187963128e-12 0.999999999997357 41 7.34564866092312e-12 1.46912973218462e-11 0.999999999992654 42 2.05248590858802e-11 4.10497181717604e-11 0.999999999979475 43 1.74264877568783e-10 3.48529755137566e-10 0.999999999825735 44 4.95472578730786e-10 9.90945157461573e-10 0.999999999504527 45 7.81647368940772e-10 1.56329473788154e-09 0.999999999218353 46 1.75257972048614e-09 3.50515944097228e-09 0.99999999824742 47 4.55773154935894e-09 9.11546309871788e-09 0.999999995442268 48 8.79844052317458e-09 1.75968810463492e-08 0.99999999120156 49 1.77563831468435e-08 3.55127662936871e-08 0.999999982243617 50 1.91119193110616e-08 3.82238386221233e-08 0.99999998088808 51 2.12519667052173e-08 4.25039334104347e-08 0.999999978748033 52 2.68149470385126e-08 5.36298940770252e-08 0.999999973185053 53 3.72871888366175e-08 7.4574377673235e-08 0.999999962712811 54 5.79049361282724e-08 1.15809872256545e-07 0.999999942095064 55 1.39165232473692e-07 2.78330464947383e-07 0.999999860834768 56 3.63906196869596e-07 7.27812393739193e-07 0.999999636093803 57 7.84811036818889e-07 1.56962207363778e-06 0.999999215188963 58 1.45595393884394e-06 2.91190787768787e-06 0.999998544046061 59 3.24567433991579e-06 6.49134867983158e-06 0.99999675432566 60 6.83930442177037e-06 1.36786088435407e-05 0.999993160695578 61 1.85462854846923e-05 3.70925709693847e-05 0.999981453714515 62 5.99438370845473e-05 0.000119887674169095 0.999940056162915 63 0.000188375854048618 0.000376751708097237 0.999811624145951 64 0.000556670533415962 0.00111334106683192 0.999443329466584 65 0.00159731668456078 0.00319463336912155 0.99840268331544 66 0.00388326681530248 0.00776653363060497 0.996116733184698 67 0.00926797949637707 0.0185359589927541 0.990732020503623 68 0.0173717335593256 0.0347434671186512 0.982628266440674 69 0.0301274635001488 0.0602549270002977 0.96987253649985 70 0.04407093437632 0.08814186875264 0.95592906562368 71 0.0623807077649518 0.124761415529904 0.937619292235048 72 0.0894297017478393 0.178859403495679 0.91057029825216 73 0.167809310667641 0.335618621335282 0.83219068933236 74 0.432250046027118 0.864500092054236 0.567749953972882 75 0.815252583934237 0.369494832131526 0.184747416065763 76 0.9113473727565 0.177305254487001 0.0886526272435004 77 0.974856334331663 0.050287331336674 0.025143665668337 78 0.993987440227585 0.0120251195448306 0.00601255977241531 79 0.99778315580063 0.0044336883987414 0.0022168441993707 80 0.998673892647167 0.00265221470566636 0.00132610735283318 81 0.998632191277663 0.00273561744467302 0.00136780872233651 82 0.99737015665496 0.00525968669007768 0.00262984334503884 83 0.995230190105868 0.00953961978826357 0.00476980989413178 84 0.99099574330205 0.0180085133959001 0.00900425669795007 85 0.983550550680676 0.0328988986386478 0.0164494493193239 86 0.972887865449773 0.0542242691004543 0.0271121345502271 87 0.948844081135604 0.102311837728793 0.0511559188643964 88 0.954202101280622 0.0915957974387559 0.0457978987193779 89 0.989195612341582 0.0216087753168365 0.0108043876584183 90 0.989690863985992 0.0206182720280155 0.0103091360140078 91 0.973319805491864 0.0533603890162718 0.0266801945081359 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 53 0.706666666666667 NOK 5% type I error level 62 0.826666666666667 NOK 10% type I error level 68 0.906666666666667 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/19/t1258650552dl3gc2irkcep2qh/10t5kx1258650477.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258650552dl3gc2irkcep2qh/10t5kx1258650477.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258650552dl3gc2irkcep2qh/11ayr1258650477.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258650552dl3gc2irkcep2qh/11ayr1258650477.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258650552dl3gc2irkcep2qh/2rwab1258650477.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258650552dl3gc2irkcep2qh/2rwab1258650477.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258650552dl3gc2irkcep2qh/3deou1258650477.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258650552dl3gc2irkcep2qh/3deou1258650477.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258650552dl3gc2irkcep2qh/4duew1258650477.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258650552dl3gc2irkcep2qh/4duew1258650477.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258650552dl3gc2irkcep2qh/5xu341258650477.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258650552dl3gc2irkcep2qh/5xu341258650477.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258650552dl3gc2irkcep2qh/6iulg1258650477.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258650552dl3gc2irkcep2qh/6iulg1258650477.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258650552dl3gc2irkcep2qh/7qoa11258650477.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258650552dl3gc2irkcep2qh/7qoa11258650477.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258650552dl3gc2irkcep2qh/8fc3x1258650477.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258650552dl3gc2irkcep2qh/8fc3x1258650477.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258650552dl3gc2irkcep2qh/9k2t41258650477.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258650552dl3gc2irkcep2qh/9k2t41258650477.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') }

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