Paper - Regressie analyse - Seizonale dummy & trend

*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, 10 Dec 2008 13:49:42 -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/Dec/10/t1228942291n9lt9er2cjk0kxu.htm/, Retrieved Wed, 10 Dec 2008 20:51:49 +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/Dec/10/t1228942291n9lt9er2cjk0kxu.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)

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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 «

108.00 0 99.00 0 108.00 0 104.00 0 111.00 0 110.00 0 106.00 0 101.00 0 102.00 0 99.00 0 100.00 0 98.00 0 92.00 1 87.00 1 79.00 1 87.00 1 87.00 1 88.00 1 83.00 1 85.00 1 92.00 1 84.00 1 92.00 1 98.00 1 103.00 0 104.00 0 109.00 0 107.00 0 106.00 0 113.00 0 107.00 0 114.00 0 108.00 0 104.00 0 105.00 0 109.00 0 109.00 0 112.00 0 118.00 0 111.00 0 99.00 1 92.00 1 92.00 1 98.00 1 87.00 1 97.00 1 102.00 0 105.00 0 111.00 0 110.00 0 109.00 0 111.00 0 113.00 0 114.00 0 120.00 0 114.00 0 120.00 0 122.00 0 123.00 0 115.00 0 123.00 0 124.00 0 124.00 0 132.00 0 126.00 0 126.00 0 122.00 0 120.00 0 114.00 0 116.00 0 100.00 0 97.00 0

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 5 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Consumentenvertrouwen[t] = + 96.2218562874252 -18.2724550898203Dummy[t] + 6.74743845642056M1[t] + 4.83100465735194M2[t] + 6.41457085828343M3[t] + 6.99813705921492M4[t] + 8.1271124417831M5[t] + 8.0440119760479M6[t] + 5.62757817697938M7[t] + 5.71114437791085M8[t] + 3.96137724550899M9[t] + 3.54494344644046M10[t] + 0.249767132401871M11[t] + 0.249767132401862t + 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) 96.2218562874252 3.00379 32.0335 0 0 Dummy -18.2724550898203 1.776943 -10.2831 0 0 M1 6.74743845642056 3.566394 1.8919 0.063493 0.031747 M2 4.83100465735194 3.562395 1.3561 0.18032 0.09016 M3 6.41457085828343 3.558774 1.8025 0.076669 0.038334 M4 6.99813705921492 3.55553 1.9682 0.053827 0.026913 M5 8.1271124417831 3.558832 2.2836 0.026073 0.013036 M6 8.0440119760479 3.557233 2.2613 0.027506 0.013753 M7 5.62757817697938 3.556015 1.5826 0.118962 0.059481 M8 5.71114437791085 3.555178 1.6064 0.113611 0.056805 M9 3.96137724550899 3.554722 1.1144 0.269705 0.134852 M10 3.54494344644046 3.554649 0.9973 0.322776 0.161388 M11 0.249767132401871 3.543484 0.0705 0.944049 0.472025 t 0.249767132401862 0.036843 6.7792 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.887407431949434 R-squared 0.787491950279089 Adjusted R-squared 0.73986083568647 F-TEST (value) 16.5331413512867 F-TEST (DF numerator) 13 F-TEST (DF denominator) 58 p-value 5.99520433297585e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.13716236184112 Sum Squared Residuals 2184.55618762475 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 108 103.219061876247 4.78093812375282 2 99 101.552395209581 -2.55239520958095 3 108 103.385728542914 4.61427145708581 4 104 104.219061876248 -0.219061876247503 5 111 105.597804391218 5.40219560878243 6 110 105.764471057884 4.23552894211574 7 106 103.597804391218 2.40219560878242 8 101 103.931137724551 -2.93113772455091 9 102 102.431137724551 -0.431137724550908 10 99 102.264471057884 -3.26447105788424 11 100 99.2190618762475 0.780938123752485 12 98 99.2190618762475 -1.21906187624751 13 92 87.9438123752496 4.05618762475043 14 87 86.2771457085828 0.7228542914172 15 79 88.1104790419162 -9.11047904191617 16 87 88.9438123752495 -1.94381237524951 17 87 90.3225548902196 -3.32255489021957 18 88 90.4892215568862 -2.48922155688623 19 83 88.3225548902196 -5.32255489021957 20 85 88.6558882235529 -3.6558882235529 21 92 87.155888223553 4.8441117764471 22 84 86.9892215568862 -2.98922155688623 23 92 83.9438123752495 8.0561876247505 24 98 83.9438123752495 14.0561876247505 25 103 109.213473053892 -6.21347305389229 26 104 107.546806387226 -3.54680638722554 27 109 109.380139720559 -0.380139720558889 28 107 110.213473053892 -3.21347305389222 29 106 111.592215568862 -5.59221556886228 30 113 111.758882235529 1.24111776447106 31 107 109.592215568862 -2.59221556886228 32 114 109.925548902196 4.07445109780438 33 108 108.425548902196 -0.425548902195615 34 104 108.258882235529 -4.25888223552895 35 105 105.213473053892 -0.213473053892218 36 109 105.213473053892 3.78652694610779 37 109 112.210678642715 -3.21067864271464 38 112 110.544011976048 1.45598802395211 39 118 112.377345309381 5.62265469061876 40 111 113.210678642715 -2.21067864271458 41 99 96.3169660678643 2.68303393213573 42 92 96.483632734531 -4.48363273453093 43 92 94.3169660678643 -2.31696606786427 44 98 94.6502994011976 3.3497005988024 45 87 93.1502994011976 -6.1502994011976 46 97 92.983632734531 4.01636726546907 47 102 108.210678642715 -6.21067864271457 48 105 108.210678642715 -3.21067864271456 49 111 115.207884231537 -4.20788423153699 50 110 113.541217564870 -3.54121756487024 51 109 115.374550898204 -6.37455089820359 52 111 116.207884231537 -5.20788423153693 53 113 117.586626746507 -4.58662674650698 54 114 117.753293413174 -3.75329341317364 55 120 115.586626746507 4.41337325349302 56 114 115.919960079840 -1.91996007984031 57 120 114.419960079840 5.58003992015968 58 122 114.253293413174 7.74670658682635 59 123 111.207884231537 11.7921157684631 60 115 111.207884231537 3.79211576846309 61 123 118.205089820359 4.79491017964066 62 124 116.538423153693 7.46157684630742 63 124 118.371756487026 5.62824351297406 64 132 119.205089820359 12.7949101796407 65 126 120.583832335329 5.41616766467067 66 126 120.750499001996 5.249500998004 67 122 118.583832335329 3.41616766467067 68 120 118.917165668663 1.08283433133733 69 114 117.417165668663 -3.41716566866267 70 116 117.250499001996 -1.25049900199600 71 100 114.205089820359 -14.2050898203593 72 97 114.205089820359 -17.2050898203593 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.426758943959995 0.85351788791999 0.573241056040005 18 0.269099102854266 0.538198205708532 0.730900897145734 19 0.167867458047163 0.335734916094325 0.832132541952837 20 0.111290378334479 0.222580756668958 0.888709621665521 21 0.133786593906610 0.267573187813220 0.86621340609339 22 0.0884195869064764 0.176839173812953 0.911580413093524 23 0.116593921280825 0.233187842561651 0.883406078719175 24 0.382509646157500 0.765019292315 0.6174903538425 25 0.291968610976464 0.583937221952928 0.708031389023536 26 0.250641779985819 0.501283559971638 0.749358220014181 27 0.224624179718496 0.449248359436991 0.775375820281504 28 0.164448821472047 0.328897642944094 0.835551178527953 29 0.126956885238561 0.253913770477122 0.873043114761439 30 0.0937444902940726 0.187488980588145 0.906255509705927 31 0.0651141101356435 0.130228220271287 0.934885889864357 32 0.0750700569406855 0.150140113881371 0.924929943059315 33 0.0482315850168402 0.0964631700336803 0.95176841498316 34 0.0362697661191899 0.0725395322383799 0.96373023388081 35 0.0232274808995048 0.0464549617990097 0.976772519100495 36 0.0182163839609677 0.0364327679219353 0.981783616039032 37 0.0108275912126650 0.0216551824253299 0.989172408787335 38 0.00799007733476714 0.0159801546695343 0.992009922665233 39 0.0101298247389331 0.0202596494778663 0.989870175261067 40 0.00606304208273037 0.0121260841654607 0.99393695791727 41 0.00415602895054868 0.00831205790109736 0.995843971049451 42 0.00268555857550435 0.00537111715100871 0.997314441424496 43 0.00146082616276027 0.00292165232552055 0.99853917383724 44 0.00100674754090091 0.00201349508180181 0.998993252459099 45 0.000824852706308284 0.00164970541261657 0.999175147293692 46 0.000677222499382734 0.00135444499876547 0.999322777500617 47 0.00056565398164104 0.00113130796328208 0.99943434601836 48 0.000392943161305125 0.00078588632261025 0.999607056838695 49 0.000229454545901529 0.000458909091803057 0.999770545454098 50 0.000165655819339326 0.000331311638678652 0.99983434418066 51 0.000185015459664842 0.000370030919329685 0.999814984540335 52 0.000990648113213865 0.00198129622642773 0.999009351886786 53 0.00221646936801957 0.00443293873603914 0.99778353063198 54 0.00956542734296334 0.0191308546859267 0.990434572657037 55 0.0132802710938146 0.0265605421876293 0.986719728906185 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 13 0.333333333333333 NOK 5% type I error level 21 0.538461538461538 NOK 10% type I error level 23 0.58974358974359 NOK

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) 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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