workshop 3 eigen tijdreeksen q2, deel 2

*Unverified author*

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Thu, 27 Nov 2008 06:40:54 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/27/t1227793517pl3veu4aop2x0n6.htm/, Retrieved Thu, 27 Nov 2008 13:45:26 +0000

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/2008/Nov/27/t1227793517pl3veu4aop2x0n6.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

92.7 0 105.2 0 91.5 0 75.3 0 60.5 0 80.4 0 84.5 0 93.9 0 78 0 92.3 0 90 0 72.1 0 76.9 0 76 0 88.7 0 55.4 0 46.6 0 90.9 0 84.9 0 89 0 90.2 0 72.3 0 83 0 71.6 0 75.4 0 85.1 0 81.2 0 68.7 0 68.4 0 93.7 0 96.6 0 101.8 0 93.6 0 88.9 0 114.1 0 82.3 0 96.4 0 104 0 88.2 0 85.2 0 87.1 0 85.5 0 89.1 0 105.2 0 82.9 0 86.8 0 112 0 97.4 0 88.9 0 109.4 0 87.8 0 90.5 0 79.3 0 114.9 0 118.8 0 125 0 96.1 0 116.7 0 119.5 0 104.1 0 121 0 127.3 0 117.7 0 108 0 89.4 0 137.4 1 142 1 137.3 1 122.8 1 126.1 1 147.6 1 115.7 1 139.2 1 151.2 1 123.8 1 109 1 112.1 1 136.4 1 135.5 1 138.7 1 137.5 1 141.5 1 143.6 1 146.5 1 200.7 1

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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation L&S[t] = + 65.0887417218543 + 20.0648178807947D[t] + 16.4741776056448M1[t] + 18.4244136313465M2[t] + 6.51861252365184M3[t] -6.45861715547149M4[t] -13.9929896917376M5[t] + 10.5348066461684M6[t] + 11.7004341099022M7[t] + 16.7660615736361M8[t] + 3.36026046594133M9[t] + 6.14017364396088M10[t] + 17.7343725362661M11[t] + 0.577229679123305t + 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) 65.0887417218543 5.212027 12.4882 0 0 D 20.0648178807947 4.39856 4.5617 2.1e-05 1e-05 M1 16.4741776056448 5.987784 2.7513 0.007527 0.003764 M2 18.4244136313465 6.199034 2.9721 0.004035 0.002018 M3 6.51861252365184 6.195877 1.0521 0.296326 0.148163 M4 -6.45861715547149 6.193644 -1.0428 0.300587 0.150294 M5 -13.9929896917376 6.192336 -2.2597 0.026908 0.013454 M6 10.5348066461684 6.193866 1.7008 0.093348 0.046674 M7 11.7004341099022 6.188775 1.8906 0.06276 0.03138 M8 16.7660615736361 6.184606 2.7109 0.008408 0.004204 M9 3.36026046594133 6.181363 0.5436 0.588412 0.294206 M10 6.14017364396088 6.179044 0.9937 0.323739 0.16187 M11 17.7343725362661 6.177653 2.8707 0.005393 0.002697 t 0.577229679123305 0.075701 7.6251 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.913091388812815 R-squared 0.833735884324115 Adjusted R-squared 0.803293158918671 F-TEST (value) 27.3870316543679 F-TEST (DF numerator) 13 F-TEST (DF denominator) 71 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 11.5564627533259 Sum Squared Residuals 9482.18002719962 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 92.7 82.1401490066226 10.5598509933774 2 105.2 84.6676147114475 20.5323852885525 3 91.5 73.339043282876 18.1609567171240 4 75.3 60.9390432828761 14.3609567171239 5 60.5 53.9819004257332 6.5180995742668 6 80.4 79.0869264427625 1.31307355723751 7 84.5 80.8297835856197 3.67021641438035 8 93.9 86.4726407284768 7.42735927152319 9 78 73.6440692999054 4.35593070009461 10 92.3 77.0012121570483 15.2987878429517 11 90 89.1726407284768 0.8273592715232 12 72.1 72.015497871334 0.0845021286660279 13 76.9 89.0669051561022 -12.1669051561022 14 76 91.5943708609271 -15.5943708609271 15 88.7 80.2657994323557 8.43420056764426 16 55.4 67.8657994323557 -12.4657994323557 17 46.6 60.9086565752129 -14.3086565752129 18 90.9 86.0136825922422 4.8863174077578 19 84.9 87.7565397350993 -2.85653973509934 20 89 93.3993968779565 -4.39939687795648 21 90.2 80.570825449385 9.62917455061495 22 72.3 83.9279683065279 -11.6279683065279 23 83 96.0993968779565 -13.0993968779565 24 71.6 78.9422540208136 -7.34225402081364 25 75.4 95.9936613055818 -20.5936613055818 26 85.1 98.5211270104068 -13.4211270104068 27 81.2 87.1925555818354 -5.9925555818354 28 68.7 74.7925555818354 -6.09255558183539 29 68.4 67.8354127246925 0.564587275307474 30 93.7 92.9404387417219 0.759561258278139 31 96.6 94.683295884579 1.91670411542100 32 101.8 100.326153027436 1.47384697256386 33 93.6 87.4975815988647 6.10241840113529 34 88.9 90.8547244560076 -1.95472445600756 35 114.1 103.026153027436 11.0738469725638 36 82.3 85.8690101702933 -3.56901017029329 37 96.4 102.920417455061 -6.52041745506146 38 104 105.447883159886 -1.44788315988646 39 88.2 94.119311731315 -5.91931173131506 40 85.2 81.719311731315 3.48068826868495 41 87.1 74.7621688741722 12.3378311258278 42 85.5 99.8671948912015 -14.3671948912015 43 89.1 101.610052034059 -12.5100520340587 44 105.2 107.252909176916 -2.0529091769158 45 82.9 94.4243377483444 -11.5243377483444 46 86.8 97.7814806054872 -10.9814806054872 47 112 109.952909176916 2.0470908230842 48 97.4 92.795766319773 4.60423368022707 49 88.9 109.847173604541 -20.9471736045411 50 109.4 112.374639309366 -2.97463930936611 51 87.8 101.046067880795 -13.2460678807947 52 90.5 88.6460678807947 1.85393211920530 53 79.3 81.6889250236518 -2.38892502365185 54 114.9 106.793951040681 8.10604895931882 55 118.8 108.536808183538 10.2631918164617 56 125 114.179665326395 10.8203346736045 57 96.1 101.351093897824 -5.25109389782403 58 116.7 104.708236754967 11.9917632450331 59 119.5 116.879665326395 2.62033467360453 60 104.1 99.7225224692526 4.37747753074739 61 121 116.773929754021 4.22607024597922 62 127.3 119.301395458846 7.99860454115422 63 117.7 107.972824030274 9.72717596972563 64 108 95.5728240302744 12.4271759697256 65 89.4 88.6156811731315 0.784318826868499 66 137.4 133.785525070956 3.61447492904446 67 142 135.528382213813 6.47161778618732 68 137.3 141.171239356670 -3.87123935666981 69 122.8 128.342667928098 -5.5426679280984 70 126.1 131.699810785241 -5.59981078524125 71 147.6 143.871239356670 3.72876064333017 72 115.7 126.714096499527 -11.0140964995270 73 139.2 143.765503784295 -4.56550378429516 74 151.2 146.29296948912 4.90703051087985 75 123.8 134.964398060549 -11.1643980605487 76 109 122.564398060549 -13.5643980605487 77 112.1 115.607255203406 -3.50725520340587 78 136.4 140.712281220435 -4.31228122043519 79 135.5 142.455138363292 -6.95513836329234 80 138.7 148.097995506149 -9.3979955061495 81 137.5 135.269424077578 2.23057592242195 82 141.5 138.626566934721 2.87343306527910 83 143.6 150.797995506149 -7.19799550614948 84 146.5 133.640852649007 12.8591473509934 85 200.7 150.692259933775 50.0077400662252

Charts produced by software:

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Parameters (Session):

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

Parameters (R input):

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

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

library(lattice) 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)) 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$resid, main='Residual Normal Q-Q Plot') grid() dev.off() (myerror <- as.ts(mysum$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() 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')

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Software written by Ed van Stee & Patrick Wessa

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