Workshop 8 Regression Analysis of Time Series

*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: Sat, 27 Nov 2010 11:03:14 +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/Nov/27/t1290855710vi0ia4uwv7xdx02.htm/, Retrieved Sat, 27 Nov 2010 12:02:00 +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/Nov/27/t1290855710vi0ia4uwv7xdx02.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 «

0 24 0 25 0 17 0 18 0 18 0 16 1 20 1 16 1 18 1 17 1 23 1 30 1 23 1 18 1 15 1 12 1 21 1 15 1 20 1 31 1 27 1 34 1 21 1 31 1 19 1 16 1 20 1 21 1 22 1 17 1 24 1 25 1 26 1 25 1 17 1 32 1 33 1 13 1 32 1 25 1 29 1 22 1 18 1 17 1 20 1 15 1 20 1 33 1 29 1 23 1 26 1 18 1 20 1 11 1 28 1 26 1 22 1 17 1 12 1 14 1 17 1 21 1 19 1 18 1 10 1 29 1 31 1 19 1 9 1 20 1 28 1 19 1 30 1 29 1 26 1 23 1 13 1 21 1 19 1 28 1 23 1 18 1 21 1 20 1 23 1 21 1 21 1 15 1 28 1 19 1 26 1 10 1 16 1 22 1 19 1 31 1 31 1 29 1 19 1 22 1 23 1 15 1 20 1 18 1 23 1 25 1 21 1 24 1 25 1 17 1 13 1 28 1 21 1 25 1 9 1 16 1 19 1 17 1 25 1 20 1 29 1 14 1 22 1 15 1 19 1 20 1 15 1 20 1 18 1 33 1 22 1 16 1 17 1 16 1 21 1 26 1 18 1 18 1 17 1 22 1 30 1 30 1 24 1 21 1 21 1 29 1 31 1 20 1 16 1 22 1 20 1 28 1 38 1 22 1 20 1 17 1 28 1 22 1 31

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 11 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Concernovermistakes[t] = + 19.6666666666666 + 1.99346405228764Month[t] + 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) 19.6666666666666 2.338558 8.4097 0 0 Month 1.99346405228764 2.383971 0.8362 0.404316 0.202158 Multiple Linear Regression - Regression Statistics Multiple R 0.0665874887665842 R-squared 0.00443389366023998 Adjusted R-squared -0.00190729173045923 F-TEST (value) 0.699221578782946 F-TEST (DF numerator) 1 F-TEST (DF denominator) 157 p-value 0.404316242205358 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.72827389810518 Sum Squared Residuals 5151.66013071895 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 19.6666666666668 4.3333333333332 2 25 19.6666666666666 5.33333333333339 3 17 19.6666666666666 -2.66666666666661 4 18 19.6666666666666 -1.66666666666661 5 18 19.6666666666666 -1.66666666666661 6 16 19.6666666666666 -3.66666666666661 7 20 21.6601307189542 -1.66013071895425 8 16 21.6601307189542 -5.66013071895425 9 18 21.6601307189542 -3.66013071895425 10 17 21.6601307189542 -4.66013071895425 11 23 21.6601307189542 1.33986928104575 12 30 21.6601307189542 8.33986928104575 13 23 21.6601307189542 1.33986928104575 14 18 21.6601307189542 -3.66013071895425 15 15 21.6601307189542 -6.66013071895425 16 12 21.6601307189542 -9.66013071895425 17 21 21.6601307189542 -0.660130718954249 18 15 21.6601307189542 -6.66013071895425 19 20 21.6601307189542 -1.66013071895425 20 31 21.6601307189542 9.33986928104575 21 27 21.6601307189542 5.33986928104575 22 34 21.6601307189542 12.3398692810458 23 21 21.6601307189542 -0.660130718954249 24 31 21.6601307189542 9.33986928104575 25 19 21.6601307189542 -2.66013071895425 26 16 21.6601307189542 -5.66013071895425 27 20 21.6601307189542 -1.66013071895425 28 21 21.6601307189542 -0.660130718954249 29 22 21.6601307189542 0.339869281045751 30 17 21.6601307189542 -4.66013071895425 31 24 21.6601307189542 2.33986928104575 32 25 21.6601307189542 3.33986928104575 33 26 21.6601307189542 4.33986928104575 34 25 21.6601307189542 3.33986928104575 35 17 21.6601307189542 -4.66013071895425 36 32 21.6601307189542 10.3398692810458 37 33 21.6601307189542 11.3398692810458 38 13 21.6601307189542 -8.66013071895425 39 32 21.6601307189542 10.3398692810458 40 25 21.6601307189542 3.33986928104575 41 29 21.6601307189542 7.33986928104575 42 22 21.6601307189542 0.339869281045751 43 18 21.6601307189542 -3.66013071895425 44 17 21.6601307189542 -4.66013071895425 45 20 21.6601307189542 -1.66013071895425 46 15 21.6601307189542 -6.66013071895425 47 20 21.6601307189542 -1.66013071895425 48 33 21.6601307189542 11.3398692810458 49 29 21.6601307189542 7.33986928104575 50 23 21.6601307189542 1.33986928104575 51 26 21.6601307189542 4.33986928104575 52 18 21.6601307189542 -3.66013071895425 53 20 21.6601307189542 -1.66013071895425 54 11 21.6601307189542 -10.6601307189542 55 28 21.6601307189542 6.33986928104575 56 26 21.6601307189542 4.33986928104575 57 22 21.6601307189542 0.339869281045751 58 17 21.6601307189542 -4.66013071895425 59 12 21.6601307189542 -9.66013071895425 60 14 21.6601307189542 -7.66013071895425 61 17 21.6601307189542 -4.66013071895425 62 21 21.6601307189542 -0.660130718954249 63 19 21.6601307189542 -2.66013071895425 64 18 21.6601307189542 -3.66013071895425 65 10 21.6601307189542 -11.6601307189542 66 29 21.6601307189542 7.33986928104575 67 31 21.6601307189542 9.33986928104575 68 19 21.6601307189542 -2.66013071895425 69 9 21.6601307189542 -12.6601307189542 70 20 21.6601307189542 -1.66013071895425 71 28 21.6601307189542 6.33986928104575 72 19 21.6601307189542 -2.66013071895425 73 30 21.6601307189542 8.33986928104575 74 29 21.6601307189542 7.33986928104575 75 26 21.6601307189542 4.33986928104575 76 23 21.6601307189542 1.33986928104575 77 13 21.6601307189542 -8.66013071895425 78 21 21.6601307189542 -0.660130718954249 79 19 21.6601307189542 -2.66013071895425 80 28 21.6601307189542 6.33986928104575 81 23 21.6601307189542 1.33986928104575 82 18 21.6601307189542 -3.66013071895425 83 21 21.6601307189542 -0.660130718954249 84 20 21.6601307189542 -1.66013071895425 85 23 21.6601307189542 1.33986928104575 86 21 21.6601307189542 -0.660130718954249 87 21 21.6601307189542 -0.660130718954249 88 15 21.6601307189542 -6.66013071895425 89 28 21.6601307189542 6.33986928104575 90 19 21.6601307189542 -2.66013071895425 91 26 21.6601307189542 4.33986928104575 92 10 21.6601307189542 -11.6601307189542 93 16 21.6601307189542 -5.66013071895425 94 22 21.6601307189542 0.339869281045751 95 19 21.6601307189542 -2.66013071895425 96 31 21.6601307189542 9.33986928104575 97 31 21.6601307189542 9.33986928104575 98 29 21.6601307189542 7.33986928104575 99 19 21.6601307189542 -2.66013071895425 100 22 21.6601307189542 0.339869281045751 101 23 21.6601307189542 1.33986928104575 102 15 21.6601307189542 -6.66013071895425 103 20 21.6601307189542 -1.66013071895425 104 18 21.6601307189542 -3.66013071895425 105 23 21.6601307189542 1.33986928104575 106 25 21.6601307189542 3.33986928104575 107 21 21.6601307189542 -0.660130718954249 108 24 21.6601307189542 2.33986928104575 109 25 21.6601307189542 3.33986928104575 110 17 21.6601307189542 -4.66013071895425 111 13 21.6601307189542 -8.66013071895425 112 28 21.6601307189542 6.33986928104575 113 21 21.6601307189542 -0.660130718954249 114 25 21.6601307189542 3.33986928104575 115 9 21.6601307189542 -12.6601307189542 116 16 21.6601307189542 -5.66013071895425 117 19 21.6601307189542 -2.66013071895425 118 17 21.6601307189542 -4.66013071895425 119 25 21.6601307189542 3.33986928104575 120 20 21.6601307189542 -1.66013071895425 121 29 21.6601307189542 7.33986928104575 122 14 21.6601307189542 -7.66013071895425 123 22 21.6601307189542 0.339869281045751 124 15 21.6601307189542 -6.66013071895425 125 19 21.6601307189542 -2.66013071895425 126 20 21.6601307189542 -1.66013071895425 127 15 21.6601307189542 -6.66013071895425 128 20 21.6601307189542 -1.66013071895425 129 18 21.6601307189542 -3.66013071895425 130 33 21.6601307189542 11.3398692810458 131 22 21.6601307189542 0.339869281045751 132 16 21.6601307189542 -5.66013071895425 133 17 21.6601307189542 -4.66013071895425 134 16 21.6601307189542 -5.66013071895425 135 21 21.6601307189542 -0.660130718954249 136 26 21.6601307189542 4.33986928104575 137 18 21.6601307189542 -3.66013071895425 138 18 21.6601307189542 -3.66013071895425 139 17 21.6601307189542 -4.66013071895425 140 22 21.6601307189542 0.339869281045751 141 30 21.6601307189542 8.33986928104575 142 30 21.6601307189542 8.33986928104575 143 24 21.6601307189542 2.33986928104575 144 21 21.6601307189542 -0.660130718954249 145 21 21.6601307189542 -0.660130718954249 146 29 21.6601307189542 7.33986928104575 147 31 21.6601307189542 9.33986928104575 148 20 21.6601307189542 -1.66013071895425 149 16 21.6601307189542 -5.66013071895425 150 22 21.6601307189542 0.339869281045751 151 20 21.6601307189542 -1.66013071895425 152 28 21.6601307189542 6.33986928104575 153 38 21.6601307189542 16.3398692810458 154 22 21.6601307189542 0.339869281045751 155 20 21.6601307189542 -1.66013071895425 156 17 21.6601307189542 -4.66013071895425 157 28 21.6601307189542 6.33986928104575 158 22 21.6601307189542 0.339869281045751 159 31 21.6601307189542 9.33986928104575 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.36485876605714 0.72971753211428 0.63514123394286 6 0.297158606585139 0.594317213170278 0.702841393414861 7 0.175295763097748 0.350591526195496 0.824704236902252 8 0.122211427826149 0.244422855652298 0.87778857217385 9 0.0665768831580264 0.133153766316053 0.933423116841974 10 0.0354802412423936 0.0709604824847872 0.964519758757606 11 0.0388715980469387 0.0777431960938774 0.961128401953061 12 0.198930405336644 0.397860810673287 0.801069594663356 13 0.146123671697686 0.292247343395372 0.853876328302314 14 0.111457735967519 0.222915471935037 0.888542264032481 15 0.116913429912384 0.233826859824769 0.883086570087616 16 0.178231811987709 0.356463623975417 0.821768188012291 17 0.133030318289025 0.266060636578050 0.866969681710975 18 0.121027268595915 0.242054537191829 0.878972731404085 19 0.0865124303922071 0.173024860784414 0.913487569607793 20 0.250583248156251 0.501166496312502 0.749416751843749 21 0.279382204650854 0.558764409301707 0.720617795349146 22 0.5654047840612 0.8691904318776 0.4345952159388 23 0.498107612612411 0.996215225224823 0.501892387387589 24 0.605120204492821 0.789759591014357 0.394879795507179 25 0.555097536513179 0.889804926973642 0.444902463486821 26 0.548519877469529 0.902960245060942 0.451480122530471 27 0.489336612615717 0.978673225231433 0.510663387384283 28 0.427826244808341 0.855652489616681 0.572173755191659 29 0.369175488186797 0.738350976373593 0.630824511813203 30 0.344963107876315 0.689926215752629 0.655036892123686 31 0.303498851178415 0.606997702356831 0.696501148821585 32 0.273697905923255 0.54739581184651 0.726302094076745 33 0.256321362655435 0.512642725310871 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0.568599615976665 0.862800768046671 0.431400384023335 105 0.523127796535761 0.953744406928477 0.476872203464239 106 0.490685348051366 0.981370696102732 0.509314651948634 107 0.442899597050643 0.885799194101286 0.557100402949357 108 0.40282416141117 0.80564832282234 0.59717583858883 109 0.371579860072269 0.743159720144538 0.62842013992773 110 0.35445502863782 0.70891005727564 0.64554497136218 111 0.412710407409377 0.825420814818754 0.587289592590623 112 0.420735421620445 0.84147084324089 0.579264578379555 113 0.372904498262174 0.745808996524347 0.627095501737826 114 0.341008787467324 0.682017574934648 0.658991212532676 115 0.530319460892589 0.939361078214821 0.469680539107411 116 0.532262478080175 0.93547504383965 0.467737521919825 117 0.493910569804335 0.98782113960867 0.506089430195665 118 0.481045402469171 0.962090804938342 0.518954597530829 119 0.442401659554944 0.884803319109888 0.557598340445056 120 0.396913163634522 0.793826327269044 0.603086836365478 121 0.420073338466587 0.840146676933174 0.579926661533413 122 0.468895455162940 0.937790910325879 0.53110454483706 123 0.41493312854216 0.82986625708432 0.58506687145784 124 0.444066868991515 0.88813373798303 0.555933131008485 125 0.407330665563199 0.814661331126397 0.592669334436801 126 0.362721232271978 0.725442464543955 0.637278767728022 127 0.399195163953651 0.798390327907303 0.600804836046349 128 0.356203007775614 0.712406015551228 0.643796992224386 129 0.338695167334677 0.677390334669355 0.661304832665323 130 0.461287316223953 0.922574632447907 0.538712683776047 131 0.402834814984428 0.805669629968857 0.597165185015572 132 0.423933401817167 0.847866803634333 0.576066598182833 133 0.42807175197178 0.85614350394356 0.57192824802822 134 0.464038976666393 0.928077953332785 0.535961023333607 135 0.412211819763294 0.824423639526587 0.587788180236706 136 0.363213473937529 0.726426947875057 0.636786526062471 137 0.356669313315219 0.713338626630438 0.643330686684781 138 0.355592741268194 0.711185482536387 0.644407258731806 139 0.388081727618079 0.776163455236159 0.611918272381921 140 0.333288971445284 0.666577942890568 0.666711028554716 141 0.334227748159106 0.668455496318211 0.665772251840894 142 0.339629341277054 0.679258682554107 0.660370658722947 143 0.272908703481463 0.545817406962927 0.727091296518537 144 0.225878243636261 0.451756487272523 0.774121756363739 145 0.184348995047942 0.368697990095885 0.815651004952058 146 0.165113870664857 0.330227741329714 0.834886129335143 147 0.186258769966535 0.372517539933070 0.813741230033465 148 0.148308201480986 0.296616402961971 0.851691798519014 149 0.189828132285772 0.379656264571544 0.810171867714228 150 0.138969110645357 0.277938221290714 0.861030889354643 151 0.118823249142761 0.237646498285523 0.881176750857239 152 0.0777473706207557 0.155494741241511 0.922252629379244 153 0.397917372392455 0.795834744784909 0.602082627607545 154 0.260370395935625 0.520740791871249 0.739629604064375 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 2 0.0133333333333333 OK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No 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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