Model 5, kijken naar het verleden tot Y(t-3)

*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, 16 Dec 2009 08:21:57 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/16/t1260977183y1innofha53fic5.htm/, Retrieved Wed, 16 Dec 2009 16:26:36 +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/2009/Dec/16/t1260977183y1innofha53fic5.htm/}, year = {2009}, } @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 = {2009}, 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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102.9 120 112.7 97 95.1 97.4 114 102.9 112.7 97 111.4 116 97.4 102.9 112.7 87.4 153 111.4 97.4 102.9 96.8 162 87.4 111.4 97.4 114.1 161 96.8 87.4 111.4 110.3 149 114.1 96.8 87.4 103.9 139 110.3 114.1 96.8 101.6 135 103.9 110.3 114.1 94.6 130 101.6 103.9 110.3 95.9 127 94.6 101.6 103.9 104.7 122 95.9 94.6 101.6 102.8 117 104.7 95.9 94.6 98.1 112 102.8 104.7 95.9 113.9 113 98.1 102.8 104.7 80.9 149 113.9 98.1 102.8 95.7 157 80.9 113.9 98.1 113.2 157 95.7 80.9 113.9 105.9 147 113.2 95.7 80.9 108.8 137 105.9 113.2 95.7 102.3 132 108.8 105.9 113.2 99 125 102.3 108.8 105.9 100.7 123 99 102.3 108.8 115.5 117 100.7 99 102.3 100.7 114 115.5 100.7 99 109.9 111 100.7 115.5 100.7 114.6 112 109.9 100.7 115.5 85.4 144 114.6 109.9 100.7 100.5 150 85.4 114.6 109.9 114.8 149 100.5 85.4 114.6 116.5 134 114.8 100.5 85.4 112.9 123 116.5 114.8 100.5 102 116 112.9 116.5 114.8 106 117 102 112.9 116.5 105.3 111 106 102 112.9 118.8 105 105.3 106 102 106.1 102 118.8 105.3 106 109.3 95 106.1 118.8 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = -23.3563271745923 + 0.0503661112985457X[t] + 0.137335934853832Y1[t] + 0.44197286432973Y2[t] + 0.71371757685287Y3[t] -7.3392913869526M1[t] -12.6020682925414M2[t] -6.88849991241403M3[t] -30.9409798345795M4[t] -20.1475895309494M5[t] -2.05730628225174M6[t] + 10.2155687017701M7[t] -10.1579795949487M8[t] -27.2356280091489M9[t] -22.8543489826544M10[t] -14.1311859451063M11[t] -0.0656504752053687t + 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) -23.3563271745923 38.666223 -0.604 0.549138 0.274569 X 0.0503661112985457 0.135396 0.372 0.711816 0.355908 Y1 0.137335934853832 0.140158 0.9799 0.332899 0.166449 Y2 0.44197286432973 0.148912 2.968 0.004986 0.002493 Y3 0.71371757685287 0.166002 4.2994 0.000103 5.2e-05 M1 -7.3392913869526 3.040656 -2.4137 0.020342 0.010171 M2 -12.6020682925414 3.243173 -3.8857 0.000365 0.000182 M3 -6.88849991241403 3.439432 -2.0028 0.051841 0.02592 M4 -30.9409798345795 5.357523 -5.7752 1e-06 0 M5 -20.1475895309494 6.038678 -3.3364 0.001812 0.000906 M6 -2.05730628225174 5.568339 -0.3695 0.713683 0.356841 M7 10.2155687017701 4.84061 2.1104 0.04097 0.020485 M8 -10.1579795949487 4.406753 -2.3051 0.026298 0.013149 M9 -27.2356280091489 4.669276 -5.8329 1e-06 0 M10 -22.8543489826544 4.022714 -5.6813 1e-06 1e-06 M11 -14.1311859451063 3.347037 -4.222 0.000131 6.6e-05 t -0.0656504752053687 0.098949 -0.6635 0.51074 0.25537 Multiple Linear Regression - Regression Statistics Multiple R 0.923644579935657 R-squared 0.853119310044516 Adjusted R-squared 0.795800016403352 F-TEST (value) 14.8836326453235 F-TEST (DF numerator) 16 F-TEST (DF denominator) 41 p-value 2.99338331899435e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.12775134037727 Sum Squared Residuals 698.57157624744 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 102.9 101.506333575794 1.39366642420611 2 97.4 102.824854731638 -5.42485473163798 3 111.4 114.692189103620 -3.29218910361967 4 87.4 84.935024905277 2.46497509472299 5 96.8 95.0821707268221 1.71782927317787 6 114.1 113.732092508669 0.367907491331412 7 110.3 114.736158435104 -4.43615843510442 8 103.9 107.626497773072 -3.72649777307151 9 101.6 100.070601650509 1.52939834949111 10 94.6 98.2777738713903 -3.67777387139034 11 95.9 100.238506476044 -4.33850647604386 12 104.7 109.495387627692 -4.79538762769227 13 102.8 98.6257131214139 4.17428687858613 14 98.1 97.601710963915 0.498289036084906 15 113.9 108.095482320401 5.80451767959866 16 80.9 84.5271038420985 -3.6271038420985 17 95.7 94.7543853559364 0.945614644063591 18 113.2 111.503223156660 1.69677684334033 19 105.9 108.598683768368 -2.69868376836808 20 108.8 104.950816822218 3.84918317778176 21 102.3 97.2176172727142 5.08238272728578 22 99 96.359582463894 2.64041753610607 23 100.7 103.660111573352 -2.96011157335197 24 115.5 111.559246762881 3.94075323711865 25 100.7 104.431864268411 -3.73186426841052 26 109.9 104.674284990614 5.22571500938608 27 114.6 115.657881352832 -1.05788135283217 28 85.4 87.3000756252388 -1.90007562523883 29 100.5 102.963276993119 -2.46327699311909 30 114.8 113.460181244386 1.33981875561393 31 116.5 112.709054959409 3.79094504059068 32 112.9 109.046647422846 3.85335257715387 33 102 102.013891607234 -0.013891607233505 34 106 104.505142148977 1.49485785102269 35 105.3 106.022914285080 -0.722914285079682 36 118.8 113.678487802414 5.12151219758574 37 106.1 110.521972029268 -4.42197202926804 38 109.3 108.563846861395 0.736153138605223 39 117.2 118.572639445778 -1.37263944577807 40 92.5 89.4509123238311 3.04908767616888 41 104.2 102.864133103292 1.33586689670847 42 112.5 116.915038754976 -4.41503875497573 43 122.4 117.351114885784 5.04888511421591 44 113.3 109.837117290341 3.46288270965872 45 100 101.693082527210 -1.69308252721041 46 110.7 107.225994090386 3.47400590961351 47 112.8 104.778467665524 8.02153233447551 48 109.8 114.066877807012 -4.26687780701211 49 117.3 114.714117005114 2.58588299488632 50 109.1 110.135302452438 -1.03530245243822 51 115.9 115.981807777369 -0.0818077773687492 52 96 95.9868833035545 0.0131166964454565 53 99.8 101.336033820831 -1.53603382083084 54 116.8 115.78946433531 1.01053566469005 55 115.7 117.404987951334 -1.7049879513341 56 99.4 106.838920691523 -7.43892069152284 57 94.3 99.204806942333 -4.90480694233298 58 91 94.931507425352 -3.93150742535194 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 20 0.40697369271562 0.81394738543124 0.59302630728438 21 0.329293569748824 0.658587139497648 0.670706430251176 22 0.355428382348811 0.710856764697621 0.64457161765119 23 0.413657477709245 0.827314955418489 0.586342522290755 24 0.468361887497372 0.936723774994744 0.531638112502628 25 0.50771244766977 0.98457510466046 0.49228755233023 26 0.577441992966782 0.845116014066436 0.422558007033218 27 0.457230849199069 0.914461698398138 0.542769150800931 28 0.395009843265445 0.79001968653089 0.604990156734555 29 0.330658939987452 0.661317879974904 0.669341060012548 30 0.275750553341353 0.551501106682707 0.724249446658647 31 0.315197777164632 0.630395554329264 0.684802222835368 32 0.438567289170851 0.877134578341702 0.561432710829149 33 0.442181564738156 0.884363129476311 0.557818435261844 34 0.491445300571319 0.982890601142637 0.508554699428681 35 0.59647201526906 0.80705596946188 0.40352798473094 36 0.632417654979471 0.735164690041057 0.367582345020529 37 0.49932244015963 0.99864488031926 0.50067755984037 38 0.373043846448639 0.746087692897278 0.626956153551361 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 0 0 OK

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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