Multiple Linear Regression en Trend - Paper

*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: Wed, 15 Dec 2010 17:58:44 +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/15/t1292435844mfbb8g9q3toi140.htm/, Retrieved Wed, 15 Dec 2010 18:57:34 +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/15/t1292435844mfbb8g9q3toi140.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:

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198563 44164 25943 -7.7 -9 195722 40399 21698 -4.9 -13 202196 36763 20077 -2.4 -8 205816 37903 25673 -3.6 -13 212588 35532 19094 -7 -15 214320 35533 19306 -7 -15 220375 32110 15443 -7.9 -15 204442 33374 15179 -8.8 -10 206903 35462 18288 -14.2 -12 214126 33508 18264 -17.8 -11 226899 36080 16406 -18.2 -11 223532 34560 15678 -22.8 -17 195309 38737 19657 -23.6 -18 186005 38144 18821 -27.6 -19 188906 37594 19493 -29.4 -22 191563 36424 21078 -31.8 -24 189226 36843 19296 -31.4 -24 186413 37246 19985 -27.6 -20 178037 38661 16972 -28.8 -25 166827 40454 16951 -21.9 -22 169362 44928 23126 -13.9 -17 174330 48441 24890 -8 -9 187069 48140 21042 -2.8 -11 186530 45998 20842 -3.3 -13 158114 47369 23904 -1.3 -11 151001 49554 22578 0.5 -9 159612 47510 25452 -1.9 -7 161914 44873 21928 2 -3 164182 45344 25227 1.7 -3 169701 42413 26210 1.9 -6 171297 36912 17436 0.1 -4 166444 43452 21258 2.4 -8 173476 42142 25638 2.3 -1 182516 44382 23516 4.7 -2 202388 43636 23891 5 -2 202300 44167 24617 7.2 -1 1 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 7 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation OPENVAC[t] = + 23528.0020280154 -0.0317774202545951NWWZ[t] + 1.10395761931889ONTVANGJOB[t] + 140.222922862401Producentenvertrouwen[t] -150.700900200537consumentenvertrouwen[t] -47.4908001085652t + 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) 23528.0020280154 5710.710909 4.12 8e-05 4e-05 NWWZ -0.0317774202545951 0.015476 -2.0534 0.042754 0.021377 ONTVANGJOB 1.10395761931889 0.136001 8.1173 0 0 Producentenvertrouwen 140.222922862401 67.106434 2.0896 0.039302 0.019651 consumentenvertrouwen -150.700900200537 101.88884 -1.4791 0.142395 0.071198 t -47.4908001085652 24.483546 -1.9397 0.055351 0.027676 Multiple Linear Regression - Regression Statistics Multiple R 0.927803902499586 R-squared 0.86082008149346 Adjusted R-squared 0.853571127404578 F-TEST (value) 118.750935781715 F-TEST (DF numerator) 5 F-TEST (DF denominator) 96 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3249.86402713710 Sum Squared Residuals 1013915154.70846 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 44164 46087.2554436479 -1923.25544364793 2 40399 42439.1719852908 -2040.17198529084 3 36763 39993.4916716914 -3230.4916716914 4 37903 46593.9504415375 -8690.95044153753 5 35532 38892.9696366348 -3360.96963663479 6 35533 39024.4793599409 -3491.47935994087 7 32110 34393.7873661857 -2283.7873661857 8 33374 33681.4562599146 -307.456259914567 9 35462 36532.163483966 -1070.16348396598 10 33508 35573.1459719896 -2065.14597198964 11 36080 33012.5197571297 3067.48024287033 12 34560 32527.5223401904 2032.47765980964 13 38737 37808.0556011077 928.944398892288 14 38144 36723.1225580482 1420.87744195176 15 37594 37525.0064214127 68.9935785873161 16 36424 39107.7226278394 -2683.72262783941 17 36843 37223.3323503845 -380.332350384535 18 37246 37955.9017392378 -709.901739237833 19 38661 35433.5912977418 3227.40870225825 20 40454 36234.5777358305 4219.42226416955 21 44928 43291.7483565671 1636.25164343286 22 48441 44655.4766163961 3785.52338360387 23 48140 40985.7053398108 7154.29466018925 24 45998 40965.8413843255 5032.15861567449 25 47369 45180.7000338497 2188.29996615032 26 49554 43846.3936815465 5707.60631845355 27 47510 46060.1048982772 1449.89510172278 28 44873 41993.181624624 2879.81837537597 29 45344 45473.5089446523 -129.508944652331 30 42413 46815.9761871232 -4402.97618712321 31 36912 36477.841410831 434.158589169004 32 43452 41729.2087756404 1722.79122435956 33 42142 45224.6649352283 -3082.66493522829 34 44382 43034.5441028938 1347.45589710620 35 43636 42811.6233915892 824.376608410775 36 44167 43726.1917661853 440.808233814679 37 44423 46366.7322901354 -1943.73229013543 38 42868 42824.3066128024 43.693387197598 39 43908 42822.3522937619 1085.64770623808 40 42013 45893.0234385498 -3880.02343854980 41 38846 41007.4500441845 -2161.45004418453 42 35087 41927.1372788408 -6840.13727884085 43 33026 35326.2788252252 -2300.27882522516 44 34646 35963.5198438218 -1317.51984382180 45 37135 38120.5585392369 -985.558539236895 46 37985 37578.6401576255 406.359842374506 47 43121 35855.955968122 7265.04403187797 48 43722 35139.8506435859 8582.1493564141 49 43630 38779.7617580335 4850.23824196649 50 42234 40478.1703024091 1755.82969759092 51 39351 34097.4029177761 5253.59708222391 52 39327 39742.6652892035 -415.665289203483 53 35704 35907.2804870296 -203.280487029623 54 30466 32331.8691788758 -1865.86917887578 55 28155 29393.7899634899 -1238.78996348994 56 29257 30711.2453491812 -1454.24534918123 57 29998 30480.3019198889 -482.301919888932 58 32529 32194.5574004374 334.442599562567 59 34787 29040.4007662888 5746.59923371125 60 33855 27194.3961517712 6660.6038482288 61 34556 34446.0359688073 109.964031192695 62 31348 30707.9973538147 640.002646185345 63 30805 30610.9315681556 194.068431844388 64 28353 31080.0161134401 -2727.01611344010 65 24514 27513.6297827162 -2999.62978271625 66 21106 26189.3372343835 -5083.33723438346 67 21346 23567.8065869733 -2221.80658697325 68 23335 25805.1543469301 -2470.1543469301 69 24379 26415.0709065207 -2036.07090652067 70 26290 27377.5601100558 -1087.56011005576 71 30084 25261.8374178873 4822.16258211265 72 29429 25654.0722768052 3774.92772319483 73 30632 32076.2805090721 -1444.28050907215 74 27349 27230.5143066849 118.485693315118 75 27264 27875.4736928243 -611.473692824317 76 27474 30145.0160761985 -2671.01607619847 77 24482 26346.3226611733 -1864.32266117326 78 21453 25960.4469081404 -4507.44690814039 79 18788 22528.5683204203 -3740.56832042035 80 19282 23100.5929810468 -3818.5929810468 81 19713 24852.9849109702 -5139.98491097016 82 21917 24508.0280029622 -2591.02800296218 83 23812 22287.3068367887 1524.69316321128 84 23785 22090.9932223678 1694.00677763219 85 24696 24652.7922990038 43.2077009962149 86 24562 23980.7029571676 581.297042832432 87 23580 23725.4104716506 -145.410471650557 88 24939 26262.1921329074 -1323.19213290739 89 23899 26732.5469681062 -2833.54696810618 90 21454 24595.0873108153 -3141.08731081530 91 19761 21782.8950455014 -2021.89504550135 92 19815 21888.4682938557 -2073.46829385568 93 20780 24756.4945343301 -3976.49453433011 94 23462 23450.8792778150 11.1207221849578 95 25005 20485.1665583784 4519.83344162164 96 24725 20001.1489496963 4723.85105030368 97 26198 23383.0540050987 2814.94599490130 98 27543 24225.1963612449 3317.80363875514 99 26471 24524.2805347240 1946.71946527598 100 26558 24629.004472779 1928.99552722100 101 25317 24021.0783573512 1295.92164264883 102 22896 23040.0404548957 -144.040454895722 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.00773819271176882 0.0154763854235376 0.992261807288231 10 0.00902481751537063 0.0180496350307413 0.99097518248463 11 0.0541612673554261 0.108322534710852 0.945838732644574 12 0.0224577837048129 0.0449155674096258 0.977542216295187 13 0.0169201525065499 0.0338403050130998 0.98307984749345 14 0.00782506788563771 0.0156501357712754 0.992174932114362 15 0.00349014553179259 0.00698029106358517 0.996509854468207 16 0.00312272898508741 0.00624545797017482 0.996877271014913 17 0.00139662552034829 0.00279325104069658 0.998603374479652 18 0.00151701184226828 0.00303402368453656 0.998482988157732 19 0.00492648571251475 0.0098529714250295 0.995073514287485 20 0.00892934839182726 0.0178586967836545 0.991070651608173 21 0.00818784240096812 0.0163756848019362 0.991812157599032 22 0.00563336747098899 0.0112667349419780 0.99436663252901 23 0.0104403185564405 0.0208806371128810 0.98955968144356 24 0.00690769136052384 0.0138153827210477 0.993092308639476 25 0.00961051913831607 0.0192210382766321 0.990389480861684 26 0.00874719416405723 0.0174943883281145 0.991252805835943 27 0.0160608173820026 0.0321216347640052 0.983939182617997 28 0.0287902296517686 0.0575804593035371 0.971209770348231 29 0.0496744150994334 0.0993488301988668 0.950325584900567 30 0.158546660597363 0.317093321194726 0.841453339402637 31 0.256542660581789 0.513085321163577 0.743457339418211 32 0.252039874545487 0.504079749090974 0.747960125454513 33 0.262607160810649 0.525214321621299 0.73739283918935 34 0.227332005133713 0.454664010267427 0.772667994866287 35 0.190798419377613 0.381596838755226 0.809201580622387 36 0.152005045929041 0.304010091858081 0.84799495407096 37 0.141381368992667 0.282762737985335 0.858618631007333 38 0.123682713737905 0.247365427475810 0.876317286262095 39 0.104299150123865 0.208598300247730 0.895700849876135 40 0.115205195867414 0.230410391734828 0.884794804132586 41 0.108640079903357 0.217280159806714 0.891359920096643 42 0.258602436125832 0.517204872251664 0.741397563874168 43 0.265757680463478 0.531515360926956 0.734242319536522 44 0.223343429879065 0.446686859758130 0.776656570120935 45 0.19400926337534 0.38801852675068 0.80599073662466 46 0.204603902144894 0.409207804289788 0.795396097855106 47 0.481841143096486 0.963682286192972 0.518158856903514 48 0.74414823708794 0.511703525824119 0.255851762912059 49 0.771833928053839 0.456332143892322 0.228166071946161 50 0.740060465759056 0.519879068481888 0.259939534240944 51 0.840925738561813 0.318148522876374 0.159074261438187 52 0.820566931832131 0.358866136335738 0.179433068167869 53 0.798297668453841 0.403404663092318 0.201702331546159 54 0.802014715204566 0.395970569590869 0.197985284795434 55 0.802339594625327 0.395320810749347 0.197660405374673 56 0.800873796936943 0.398252406126114 0.199126203063057 57 0.769382466201694 0.461235067596612 0.230617533798306 58 0.731593269679003 0.536813460641994 0.268406730320997 59 0.80152905648042 0.39694188703916 0.19847094351958 60 0.934329258599808 0.131341482800385 0.0656707414001924 61 0.936894943373417 0.126210113253167 0.0631050566265833 62 0.957741271007752 0.0845174579844952 0.0422587289922476 63 0.96544182561029 0.0691163487794203 0.0345581743897101 64 0.95999255002769 0.0800148999446177 0.0400074499723088 65 0.955330211197795 0.0893395776044108 0.0446697888022054 66 0.970229083414402 0.0595418331711964 0.0297709165855982 67 0.962769063709011 0.074461872581977 0.0372309362909885 68 0.953858374233938 0.0922832515321237 0.0461416257660618 69 0.942107002513427 0.115785994973146 0.0578929974865729 70 0.92282891158832 0.154342176823358 0.0771710884116791 71 0.947102914822357 0.105794170355286 0.052897085177643 72 0.975163674909702 0.0496726501805966 0.0248363250902983 73 0.968857128562715 0.0622857428745705 0.0311428714372853 74 0.976084624083585 0.0478307518328309 0.0239153759164155 75 0.982812102230537 0.0343757955389253 0.0171878977694627 76 0.985537026438804 0.0289259471223928 0.0144629735611964 77 0.986080170788205 0.0278396584235911 0.0139198292117955 78 0.980265233255456 0.0394695334890883 0.0197347667445442 79 0.971934077063468 0.0561318458730648 0.0280659229365324 80 0.96362521402695 0.0727495719460995 0.0363747859730497 81 0.961461160680156 0.077077678639688 0.038538839319844 82 0.945434978536696 0.109130042926609 0.0545650214633045 83 0.928073409462641 0.143853181074718 0.071926590537359 84 0.92701438946235 0.145971221075301 0.0729856105376506 85 0.90727385222937 0.185452295541261 0.0927261477706303 86 0.899723022387397 0.200553955225206 0.100276977612603 87 0.984511102289632 0.0309777954207358 0.0154888977103679 88 0.995889132371153 0.00822173525769352 0.00411086762884676 89 0.990586437529562 0.0188271249408766 0.00941356247043832 90 0.99464970277186 0.0107005944562791 0.00535029722813956 91 0.989974113279328 0.0200517734413432 0.0100258867206716 92 0.970048467627754 0.059903064744492 0.029951532372246 93 0.955139043842274 0.0897219123154525 0.0448609561577263 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 6 0.0705882352941176 NOK 5% type I error level 29 0.341176470588235 NOK 10% type I error level 44 0.517647058823529 NOK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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