Paper - Multiple Regression Model 4

*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, 12 Dec 2010 20:11:12 +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/12/t12921854793cybi4ez96hzge8.htm/, Retrieved Sun, 12 Dec 2010 21:24:49 +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/12/t12921854793cybi4ez96hzge8.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:

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No (this computation is public)

User-defined keywords:

Dataseries X:

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25.94 23688100 39.18 3940.35 144.7 28.66 13741000 35.78 4696.69 140.8 33.95 14143500 42.54 4572.83 137.1 31.01 16763800 27.92 3860.66 137.7 21.00 16634600 25.05 3400.91 144.7 26.19 13693300 32.03 3966.11 139.2 25.41 10545800 27.95 3766.99 143.0 30.47 9409900 27.95 4206.35 140.8 12.88 39182200 24.15 3672.82 142.5 9.78 37005800 27.57 3369.63 135.8 8.25 15818500 22.97 2597.93 132.6 7.44 16952000 17.37 2470.52 128.6 10.81 24563400 24.45 2772.73 115.7 9.12 14163200 23.62 2151.83 109.2 11.03 18184800 21.90 1840.26 116.9 12.74 20810300 27.12 2116.24 109.9 9.98 12843000 27.70 2110.49 116.1 11.62 13866700 29.23 2160.54 118.9 9.40 15119200 26.50 2027.13 116.3 9.27 8301600 22.84 1805.43 114.0 7.76 14039600 20.49 1498.80 97.0 8.78 12139700 23.28 1690.20 85.3 10.65 9649000 25.71 1930.58 84.9 10.95 8513600 26.52 1950.40 94.6 12.36 15278600 25.51 1934.03 97.8 10.85 15590900 23.36 1731.49 95.0 11.84 9691100 24.15 1845.35 110.7 12.14 10882700 20.92 1688.23 108.5 11.65 10 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 8 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Apple[t] = -135.264627706655 -6.77815767354195e-07Volume[t] + 4.10342145389171Microsoft[t] + 0.027348992500557NASDAQ[t] -0.488752826704873Consumentenvertrouwen[t] + 1.68515979988809t + 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) -135.264627706655 19.178931 -7.0528 0 0 Volume -6.77815767354195e-07 0 -2.7791 0.0063 0.00315 Microsoft 4.10342145389171 0.905561 4.5314 1.4e-05 7e-06 NASDAQ 0.027348992500557 0.006566 4.1654 5.8e-05 2.9e-05 Consumentenvertrouwen -0.488752826704873 0.162837 -3.0015 0.003249 0.001625 t 1.68515979988809 0.124389 13.5475 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.940892489712407 R-squared 0.885278677197211 Adjusted R-squared 0.880652817406776 F-TEST (value) 191.376028955248 F-TEST (DF numerator) 5 F-TEST (DF denominator) 124 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 26.4769156006578 Sum Squared Residuals 86927.35540582 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 25.94 48.178485553421 -22.2384855534210 2 28.66 65.2455866415472 -36.5855866415473 3 33.95 92.8179938710718 -58.8679938710718 4 31.01 12.9646676747204 18.0453323252796 5 21 -13.0343873899839 34.0343873899839 6 26.19 37.4321047827792 -11.2421047827792 7 25.41 17.2057380503468 8.20426194965317 8 30.47 32.752138344168 -2.28213834416801 9 12.88 -16.7582255253522 29.6382255253522 10 9.78 -4.58146321440604 14.3614632144060 11 8.25 -26.9521645619805 35.2021645619805 12 7.44 -50.5439929038584 57.9839929038584 13 10.81 -10.3956856539705 21.2056856539705 14 9.12 -18.8710421871896 27.9910421871896 15 11.03 -39.254193537013 50.284193537013 16 12.74 -6.95973430776079 19.6997343077608 17 9.98 -0.681752733822847 10.6617527338228 18 11.62 6.58807104935829 5.03192895064171 19 9.4 -6.15594570855574 15.5559457085557 20 9.27 -19.8073717903496 29.0773717903496 21 7.76 -31.7317827966484 39.4917827966484 22 8.78 -6.35728972695249 15.1372897269525 23 10.65 13.7570718856074 -3.10707188560737 24 10.95 15.3367496977254 -4.38674969772545 25 12.36 6.28031811034205 6.07968188965795 26 10.85 -5.23931710607091 16.0893171060709 27 11.84 -0.87293998652521 12.7129399865252 28 12.14 -16.4713342340234 28.6113342340234 29 11.65 -19.4660911739685 31.1160911739685 30 8.86 -17.6486846324182 26.5086846324182 31 7.63 -24.7508601572977 32.3808601572977 32 7.38 -16.8161448520036 24.1961448520036 33 7.25 -28.2377450331806 35.4877450331806 34 8.03 0.0777435765113541 7.95225642348865 35 7.75 11.7533176503373 -4.00331765033733 36 7.16 1.97060781692436 5.18939218307564 37 7.18 -4.69951075701846 11.8795107570185 38 7.51 6.31871938976005 1.19128061023995 39 7.07 11.9987940748728 -4.92879407487285 40 7.11 7.39334991482251 -0.283349914822512 41 8.98 4.83417174391928 4.14582825608072 42 9.53 16.3104560719259 -6.78045607192589 43 10.54 27.9742580726626 -17.4342580726626 44 11.31 30.5992926827847 -19.2892926827847 45 10.36 36.9407336498574 -26.5807336498574 46 11.44 34.1904168829836 -22.7504168829836 47 10.45 31.1330765380166 -20.6830765380166 48 10.69 40.1281408273606 -29.4381408273606 49 11.28 38.550062417357 -27.270062417357 50 11.96 42.320148104994 -30.360148104994 51 13.52 31.9588739559964 -18.4388739559964 52 12.89 35.2150934122132 -22.3250934122132 53 14.03 43.2362206602436 -29.2062206602436 54 16.27 46.2472004379849 -29.9772004379849 55 16.17 40.3373119130283 -24.1673119130283 56 17.25 42.6726688073329 -25.4226688073329 57 19.38 47.9848972643424 -28.6048972643424 58 26.2 44.5803588710128 -18.3803588710128 59 33.53 54.3017221318908 -20.7717221318908 60 32.2 56.3061317155998 -24.1061317155998 61 38.45 36.7895944503496 1.66040554965040 62 44.86 39.660840872117 5.19915912788298 63 41.67 48.2111183459934 -6.5411183459934 64 36.06 48.4285626169065 -12.3685626169065 65 39.76 61.340004805694 -21.5800048056940 66 36.81 59.9961225741562 -23.1861225741562 67 42.65 69.3475785377138 -26.6975785377138 68 46.89 78.6821490239058 -31.7921490239058 69 53.61 78.4706396928341 -24.8606396928341 70 57.59 72.569278062371 -14.9792780623710 71 67.82 85.0207464490563 -17.2007464490563 72 71.89 77.9401074249624 -6.0501074249624 73 75.51 76.6091575212 -1.09915752120007 74 68.49 77.2272524293938 -8.73725242939383 75 62.72 79.6857544919912 -16.9657544919912 76 70.39 66.9510915701674 3.43890842983263 77 59.77 69.8821421863585 -10.1121421863585 78 57.27 71.3890333027405 -14.1190333027405 79 67.96 71.41897909899 -3.45897909899003 80 67.85 88.322986969919 -20.4729869699190 81 76.98 92.9925372751243 -16.0125372751243 82 81.08 108.757906315931 -27.6779063159307 83 91.66 114.387992192707 -22.7279921927065 84 84.84 110.458228276817 -25.6182282768172 85 85.73 104.92785294832 -19.1978529483201 86 84.61 110.284764178585 -25.6747641785849 87 92.91 112.915501662618 -20.0055016626176 88 99.8 127.417353473631 -27.6173534736308 89 121.19 129.944100025998 -8.75410002599787 90 122.04 120.867878238308 1.17212176169202 91 131.76 114.351076350367 17.4089236496335 92 138.48 123.025822550719 15.4541774492809 93 153.47 132.512964352385 20.9570356476149 94 189.95 170.914809724386 19.0351902756140 95 182.22 152.718847807530 29.5011521924698 96 198.08 170.532218788816 27.5477812111839 97 135.36 134.225746519343 1.13425348065748 98 125.02 128.339813119608 -3.31981311960778 99 143.5 142.897610200019 0.602389799981412 100 173.95 152.885254917168 21.064745082832 101 188.75 163.894935060509 24.8550649394914 102 167.44 158.357081011564 9.08291898843592 103 158.95 154.068229902799 4.88177009720097 104 169.53 166.816641752092 2.71335824790794 105 113.66 143.363418163676 -29.7034181636756 106 107.59 113.233153703027 -5.64315370302663 107 92.67 114.027267493110 -21.3572674931099 108 85.35 124.450843499766 -39.1008434997655 109 90.13 131.315761246626 -41.1857612466257 110 89.31 120.700582249832 -31.3905822498319 111 105.12 135.478213328747 -30.3582133287469 112 125.83 146.395363505359 -20.5653635053587 113 135.81 148.036926548736 -12.2269265487360 114 142.43 163.093091892054 -20.6630918920535 115 163.39 170.565799446791 -7.17579944679118 116 168.21 177.397709892225 -9.18770989222488 117 185.35 184.622354185872 0.727645814127707 118 188.5 191.624364689813 -3.12436468981265 119 199.91 206.662931137023 -6.75293113702316 120 210.73 212.419462191432 -1.68946219143215 121 192.06 192.134425475708 -0.0744254757083966 122 204.62 210.283651493891 -5.66365149389066 123 235 217.086080815919 17.9139191840807 124 261.09 221.272619962765 39.8173800372346 125 256.88 188.281649578984 68.5983504210164 126 251.53 182.455131241217 69.0748687587832 127 257.25 201.650799348650 55.5992006513505 128 243.1 196.983927379366 46.1160726206341 129 283.75 208.601073973491 75.1489260265087 130 300.98 222.230056208288 78.7499437917124 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.00227065435729663 0.00454130871459326 0.997729345642703 10 0.000783668561400259 0.00156733712280052 0.9992163314386 11 0.000262233170977136 0.000524466341954271 0.999737766829023 12 4.54089428549818e-05 9.08178857099635e-05 0.999954591057145 13 7.84540046768715e-06 1.56908009353743e-05 0.999992154599532 14 1.12921531753865e-06 2.25843063507730e-06 0.999998870784683 15 1.18892874298638e-06 2.37785748597277e-06 0.999998811071257 16 3.37602263715364e-07 6.75204527430727e-07 0.999999662397736 17 5.35765536330916e-08 1.07153107266183e-07 0.999999946423446 18 7.90976768039436e-09 1.58195353607887e-08 0.999999992090232 19 1.1202588850449e-09 2.2405177700898e-09 0.999999998879741 20 1.70308949751608e-10 3.40617899503216e-10 0.999999999829691 21 3.54943522992144e-11 7.09887045984289e-11 0.999999999964506 22 4.88324897661246e-12 9.76649795322493e-12 0.999999999995117 23 6.47237807003038e-13 1.29447561400608e-12 0.999999999999353 24 7.88800772346634e-14 1.57760154469327e-13 0.99999999999992 25 2.41924680798591e-14 4.83849361597182e-14 0.999999999999976 26 6.45610225334389e-15 1.29122045066878e-14 0.999999999999994 27 9.79422379477627e-16 1.95884475895525e-15 0.999999999999999 28 3.11140778748183e-16 6.22281557496367e-16 1 29 8.21383320983268e-17 1.64276664196654e-16 1 30 1.70527951000045e-17 3.41055902000091e-17 1 31 4.40047318458629e-18 8.80094636917258e-18 1 32 1.01098881447753e-18 2.02197762895506e-18 1 33 5.18862923003446e-19 1.03772584600689e-18 1 34 9.67472902857229e-20 1.93494580571446e-19 1 35 2.60499498487988e-20 5.20998996975975e-20 1 36 6.96000222125746e-21 1.39200044425149e-20 1 37 2.57922389884548e-21 5.15844779769096e-21 1 38 6.66907861830183e-22 1.33381572366037e-21 1 39 1.80271097390945e-22 3.6054219478189e-22 1 40 8.29864029079795e-23 1.65972805815959e-22 1 41 5.75110656464839e-23 1.15022131292968e-22 1 42 2.63740100989436e-23 5.27480201978871e-23 1 43 6.46709755248152e-24 1.29341951049630e-23 1 44 1.49012390153578e-24 2.98024780307156e-24 1 45 3.36250086907328e-25 6.72500173814657e-25 1 46 5.16653603550891e-26 1.03330720710178e-25 1 47 1.29005361019737e-26 2.58010722039473e-26 1 48 2.88024098481495e-27 5.76048196962991e-27 1 49 3.86270370455062e-28 7.72540740910124e-28 1 50 5.1658044062612e-29 1.03316088125224e-28 1 51 2.78882917668439e-29 5.57765835336878e-29 1 52 6.45605459224193e-30 1.29121091844839e-29 1 53 8.66558766648855e-31 1.73311753329771e-30 1 54 2.16591986304775e-31 4.33183972609549e-31 1 55 1.34029399104026e-31 2.68058798208052e-31 1 56 1.02572369387912e-31 2.05144738775824e-31 1 57 1.27699197340272e-31 2.55398394680545e-31 1 58 1.70020616053307e-27 3.40041232106614e-27 1 59 7.37590853004726e-24 1.47518170600945e-23 1 60 3.88795743629668e-23 7.77591487259337e-23 1 61 2.91270842056247e-21 5.82541684112493e-21 1 62 1.61786901565852e-18 3.23573803131703e-18 1 63 1.28848215709782e-16 2.57696431419565e-16 1 64 1.00382595309837e-15 2.00765190619675e-15 0.999999999999999 65 3.74199454501944e-15 7.48398909003887e-15 0.999999999999996 66 5.48047793527659e-15 1.09609558705532e-14 0.999999999999994 67 9.19165264595268e-15 1.83833052919054e-14 0.99999999999999 68 3.64622072127117e-14 7.29244144254234e-14 0.999999999999964 69 2.08540147123569e-12 4.17080294247139e-12 0.999999999997915 70 1.23889246662059e-10 2.47778493324118e-10 0.99999999987611 71 2.09618494802648e-08 4.19236989605296e-08 0.99999997903815 72 4.51088677832015e-06 9.02177355664029e-06 0.999995489113222 73 7.07393671053924e-05 0.000141478734210785 0.999929260632895 74 0.000205825396529211 0.000411650793058423 0.999794174603471 75 0.000157868499977219 0.000315736999954437 0.999842131500023 76 0.000200471330016404 0.000400942660032808 0.999799528669984 77 0.000220615370467109 0.000441230740934219 0.999779384629533 78 0.000185758073985888 0.000371516147971777 0.999814241926014 79 0.00151703595391136 0.00303407190782272 0.998482964046089 80 0.00335693186973702 0.00671386373947405 0.996643068130263 81 0.00900195386329636 0.0180039077265927 0.990998046136704 82 0.0136716678443468 0.0273433356886936 0.986328332155653 83 0.0284441286097502 0.0568882572195003 0.97155587139025 84 0.0255214851179051 0.0510429702358103 0.974478514882095 85 0.0200296514052098 0.0400593028104196 0.97997034859479 86 0.0163657460466244 0.0327314920932488 0.983634253953376 87 0.0176874943440083 0.0353749886880167 0.982312505655992 88 0.0256935350408176 0.0513870700816351 0.974306464959182 89 0.0681820476756125 0.136364095351225 0.931817952324387 90 0.164204649901271 0.328409299802543 0.835795350098729 91 0.269982519646002 0.539965039292004 0.730017480353998 92 0.475724247224613 0.951448494449225 0.524275752775387 93 0.824946083740823 0.350107832518353 0.175053916259177 94 0.946022672306675 0.107954655386650 0.0539773276933249 95 0.975073980706578 0.0498520385868444 0.0249260192934222 96 0.999669446876487 0.000661106247025361 0.000330553123512681 97 0.999398939141464 0.00120212171707268 0.000601060858536341 98 0.999305945423068 0.00138810915386385 0.000694054576931923 99 0.999012623305296 0.00197475338940889 0.000987376694704446 100 0.999472547136667 0.00105490572666614 0.000527452863333069 101 0.99969143232711 0.000617135345779361 0.000308567672889680 102 0.999943587909488 0.000112824181024662 5.64120905123308e-05 103 0.999892931118658 0.000214137762683155 0.000107068881341577 104 0.999985930271678 2.81394566438669e-05 1.40697283219335e-05 105 0.999983142940273 3.37141194534049e-05 1.68570597267025e-05 106 0.999965346637842 6.93067243169453e-05 3.46533621584727e-05 107 0.999944483851323 0.000111032297353433 5.55161486767166e-05 108 0.999916378375824 0.000167243248352207 8.36216241761036e-05 109 0.999802263684607 0.000395472630785408 0.000197736315392704 110 0.99953411200284 0.000931775994319226 0.000465887997159613 111 0.999002884984767 0.00199423003046700 0.000997115015233502 112 0.997812236318194 0.0043755273636129 0.00218776368180645 113 0.9954363166532 0.00912736669359867 0.00456368334679933 114 0.99015969042232 0.0196806191553603 0.00984030957768015 115 0.980665602566502 0.0386687948669965 0.0193343974334983 116 0.966198162260553 0.0676036754788937 0.0338018377394469 117 0.970955724920936 0.0580885501581285 0.0290442750790643 118 0.955982179227945 0.0880356415441107 0.0440178207720554 119 0.9684313656718 0.0631372686564009 0.0315686343282005 120 0.965841492380531 0.068317015238938 0.034158507619469 121 0.957549373727507 0.0849012525449852 0.0424506262724926 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 90 0.79646017699115 NOK 5% type I error level 98 0.867256637168142 NOK 10% type I error level 107 0.946902654867257 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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