Paper - Regressie analyse - Dummy & seizonale dummy

*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 13:39:32 -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/t1228942043f3rfy33xyrbsrk8.htm/, Retrieved Wed, 10 Dec 2008 20:47:44 +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/t1228942043f3rfy33xyrbsrk8.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:

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User-defined keywords:

Dataseries X:

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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 7 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Consumentenvertrouwen[t] = + 107.288461538462 -21.7307692307692Dummy[t] + 4.00000000000007M1[t] + 2.33333333333331M2[t] + 4.16666666666666M3[t] + 5.00000000000001M4[t] + 6.95512820512821M5[t] + 7.12179487179487M6[t] + 4.9551282051282M7[t] + 5.28846153846154M8[t] + 3.78846153846154M9[t] + 3.62179487179488M10[t] + 3.5254315917032e-15M11[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) 107.288461538462 3.347044 32.0547 0 0 Dummy -21.7307692307692 2.259431 -9.6178 0 0 M1 4.00000000000007 4.703381 0.8505 0.398512 0.199256 M2 2.33333333333331 4.703381 0.4961 0.621669 0.310835 M3 4.16666666666666 4.703381 0.8859 0.379275 0.189637 M4 5.00000000000001 4.703381 1.0631 0.292084 0.146042 M5 6.95512820512821 4.718432 1.474 0.145788 0.072894 M6 7.12179487179487 4.718432 1.5094 0.136545 0.068272 M7 4.9551282051282 4.718432 1.0502 0.297925 0.148963 M8 5.28846153846154 4.718432 1.1208 0.266911 0.133455 M9 3.78846153846154 4.718432 0.8029 0.425251 0.212626 M10 3.62179487179488 4.718432 0.7676 0.445795 0.222898 M11 3.5254315917032e-15 4.703381 0 1 0.5 Multiple Linear Regression - Regression Statistics Multiple R 0.786831965790102 R-squared 0.619104542389115 Adjusted R-squared 0.54163427982419 F-TEST (value) 7.99151212209022 F-TEST (DF numerator) 12 F-TEST (DF denominator) 59 p-value 1.30550332766433e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 8.14649523509249 Sum Squared Residuals 3915.55769230769 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 108 111.288461538461 -3.28846153846118 2 99 109.621794871795 -10.6217948717950 3 108 111.455128205128 -3.45512820512820 4 104 112.288461538462 -8.28846153846153 5 111 114.243589743590 -3.24358974358974 6 110 114.410256410256 -4.41025641025643 7 106 112.243589743590 -6.24358974358975 8 101 112.576923076923 -11.5769230769231 9 102 111.076923076923 -9.07692307692307 10 99 110.910256410256 -11.9102564102564 11 100 107.288461538462 -7.28846153846154 12 98 107.288461538462 -9.28846153846154 13 92 89.5576923076924 2.44230769230762 14 87 87.8910256410256 -0.89102564102562 15 79 89.724358974359 -10.7243589743590 16 87 90.5576923076923 -3.55769230769231 17 87 92.5128205128205 -5.51282051282052 18 88 92.6794871794872 -4.67948717948717 19 83 90.5128205128205 -7.51282051282051 20 85 90.8461538461539 -5.84615384615385 21 92 89.3461538461538 2.65384615384615 22 84 89.1794871794872 -5.17948717948718 23 92 85.5576923076923 6.44230769230769 24 98 85.5576923076923 12.4423076923077 25 103 111.288461538462 -8.28846153846161 26 104 109.621794871795 -5.62179487179485 27 109 111.455128205128 -2.45512820512820 28 107 112.288461538462 -5.28846153846154 29 106 114.243589743590 -8.24358974358974 30 113 114.410256410256 -1.41025641025641 31 107 112.243589743590 -5.24358974358974 32 114 112.576923076923 1.42307692307692 33 108 111.076923076923 -3.07692307692308 34 104 110.910256410256 -6.91025641025641 35 105 107.288461538462 -2.28846153846154 36 109 107.288461538462 1.71153846153846 37 109 111.288461538462 -2.28846153846161 38 112 109.621794871795 2.37820512820515 39 118 111.455128205128 6.5448717948718 40 111 112.288461538462 -1.28846153846154 41 99 92.5128205128205 6.48717948717948 42 92 92.6794871794872 -0.679487179487176 43 92 90.5128205128205 1.48717948717949 44 98 90.8461538461539 7.15384615384615 45 87 89.3461538461538 -2.34615384615385 46 97 89.1794871794872 7.82051282051282 47 102 107.288461538462 -5.28846153846154 48 105 107.288461538462 -2.28846153846153 49 111 111.288461538462 -0.288461538461613 50 110 109.621794871795 0.378205128205146 51 109 111.455128205128 -2.45512820512820 52 111 112.288461538462 -1.28846153846154 53 113 114.243589743590 -1.24358974358974 54 114 114.410256410256 -0.410256410256406 55 120 112.243589743590 7.75641025641025 56 114 112.576923076923 1.42307692307692 57 120 111.076923076923 8.92307692307692 58 122 110.910256410256 11.0897435897436 59 123 107.288461538462 15.7115384615385 60 115 107.288461538462 7.71153846153846 61 123 111.288461538462 11.7115384615384 62 124 109.621794871795 14.3782051282051 63 124 111.455128205128 12.5448717948718 64 132 112.288461538462 19.7115384615385 65 126 114.243589743590 11.7564102564103 66 126 114.410256410256 11.5897435897436 67 122 112.243589743590 9.75641025641025 68 120 112.576923076923 7.42307692307691 69 114 111.076923076923 2.92307692307692 70 116 110.910256410256 5.08974358974359 71 100 107.288461538462 -7.28846153846154 72 97 107.288461538462 -10.2884615384615 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.258138758448109 0.516277516896218 0.741861241551891 17 0.161863736812941 0.323727473625883 0.838136263187059 18 0.0838391961804154 0.167678392360831 0.916160803819585 19 0.0453757695871345 0.0907515391742689 0.954624230412866 20 0.0276225101452309 0.0552450202904618 0.97237748985477 21 0.033980105404294 0.067960210808588 0.966019894595706 22 0.0211286869849761 0.0422573739699521 0.978871313015024 23 0.0269789597412141 0.0539579194824281 0.973021040258786 24 0.100218749354541 0.200437498709083 0.899781250645459 25 0.0829657087137001 0.165931417427400 0.9170342912863 26 0.0634410584281565 0.126882116856313 0.936558941571843 27 0.0605198044778826 0.121039608955765 0.939480195522117 28 0.0474890265215946 0.0949780530431892 0.952510973478405 29 0.0402061398325646 0.0804122796651293 0.959793860167435 30 0.0317979935090996 0.0635959870181991 0.9682020064909 31 0.028498552867803 0.056997105735606 0.971501447132197 32 0.0476562170368591 0.0953124340737181 0.95234378296314 33 0.0336799558236703 0.0673599116473406 0.96632004417633 34 0.0407853239020007 0.0815706478040015 0.959214676098 35 0.0258362787641553 0.0516725575283105 0.974163721235845 36 0.0163024957454952 0.0326049914909904 0.983697504254505 37 0.0115967234936312 0.0231934469872623 0.988403276506369 38 0.0136249687969969 0.0272499375939937 0.986375031203003 39 0.0236827013321687 0.0473654026643374 0.976317298667831 40 0.0228492823760885 0.0456985647521771 0.977150717623911 41 0.0242167374614801 0.0484334749229602 0.97578326253852 42 0.0146682534703968 0.0293365069407936 0.985331746529603 43 0.0104156611811928 0.0208313223623856 0.989584338818807 44 0.0105637101500871 0.0211274203001743 0.989436289849913 45 0.00664820794775178 0.0132964158955036 0.993351792052248 46 0.00781116954544545 0.0156223390908909 0.992188830454555 47 0.00599074555398629 0.0119814911079726 0.994009254446014 48 0.00314335509017268 0.00628671018034536 0.996856644909827 49 0.00262619259543355 0.00525238519086709 0.997373807404566 50 0.00284132576860391 0.00568265153720783 0.997158674231396 51 0.00312431552259475 0.0062486310451895 0.996875684477405 52 0.0102099465106673 0.0204198930213346 0.989790053489333 53 0.0113647126246689 0.0227294252493378 0.988635287375331 54 0.0118285082558632 0.0236570165117264 0.988171491744137 55 0.0101089003517107 0.0202178007034215 0.98989109964829 56 0.00515694102466482 0.0103138820493296 0.994843058975335 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 4 0.097560975609756 NOK 5% type I error level 22 0.536585365853659 NOK 10% type I error level 34 0.829268292682927 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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