ws7verbetering2

*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: Thu, 26 Nov 2009 10:29:10 -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/Nov/26/t1259256596isq1f3iiloj2hze.htm/, Retrieved Thu, 26 Nov 2009 18:30:08 +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/Nov/26/t1259256596isq1f3iiloj2hze.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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30.996 0 30.524 30.167 29.571 29.837 31.033 0 30.996 30.524 30.167 29.571 31.198 0 31.033 30.996 30.524 30.167 30.937 0 31.198 31.033 30.996 30.524 31.649 0 30.937 31.198 31.033 30.996 33.115 0 31.649 30.937 31.198 31.033 34.106 0 33.115 31.649 30.937 31.198 33.926 0 34.106 33.115 31.649 30.937 33.382 0 33.926 34.106 33.115 31.649 32.851 0 33.382 33.926 34.106 33.115 32.948 0 32.851 33.382 33.926 34.106 36.112 0 32.948 32.851 33.382 33.926 36.113 0 36.112 32.948 32.851 33.382 35.210 0 36.113 36.112 32.948 32.851 35.193 0 35.210 36.113 36.112 32.948 34.383 0 35.193 35.210 36.113 36.112 35.349 0 34.383 35.193 35.210 36.113 37.058 0 35.349 34.383 35.193 35.210 38.076 0 37.058 35.349 34.383 35.193 36.630 0 38.076 37.058 35.349 34.383 36.045 0 36.630 38.076 37.058 35.349 35.638 0 36.045 36.630 38.076 37.058 35.114 0 35.638 36.045 36.630 38.076 35.465 0 35.114 35.638 36.045 36.630 35.254 0 35.465 35.114 35.638 36.045 35.299 0 35.254 35.465 35.114 35.638 35.916 0 35.299 35.254 35.465 35.114 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 saldo_zichtrek[t] = + 4.25594081528187 + 0.720234616005331crisis[t] + 0.856141359397383`Yt-1`[t] + 0.0821221882076306`Yt-2`[t] -0.250361502036348`Yt-3`[t] + 0.228921383100153`Yt-4`[t] -1.70906219387124M1[t] -1.01532730724768M2[t] -0.767054591316031M3[t] -1.18454400203984M4[t] -0.537866020905931M5[t] + 0.613409664166027M6[t] -0.685453433357246M7[t] -2.43197864185542M8[t] -1.44235537582931M9[t] -1.1955274997821M10[t] -2.55721615948579M11[t] -0.00737361908607257t + 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) 4.25594081528187 2.781155 1.5303 0.13402 0.06701 crisis 0.720234616005331 0.45011 1.6001 0.117641 0.05882 `Yt-1` 0.856141359397383 0.15499 5.5239 2e-06 1e-06 `Yt-2` 0.0821221882076306 0.194523 0.4222 0.675218 0.337609 `Yt-3` -0.250361502036348 0.192694 -1.2993 0.201479 0.10074 `Yt-4` 0.228921383100153 0.160764 1.424 0.162412 0.081206 M1 -1.70906219387124 0.635516 -2.6893 0.010482 0.005241 M2 -1.01532730724768 0.596114 -1.7032 0.09648 0.04824 M3 -0.767054591316031 0.660432 -1.1614 0.252521 0.12626 M4 -1.18454400203984 0.57887 -2.0463 0.04751 0.023755 M5 -0.537866020905931 0.604839 -0.8893 0.37931 0.189655 M6 0.613409664166027 0.608885 1.0074 0.319937 0.159969 M7 -0.685453433357246 0.714932 -0.9588 0.343582 0.171791 M8 -2.43197864185542 0.705807 -3.4457 0.001377 0.000689 M9 -1.44235537582931 0.686764 -2.1002 0.042227 0.021113 M10 -1.1955274997821 0.627557 -1.9051 0.064166 0.032083 M11 -2.55721615948579 0.609255 -4.1973 0.000151 7.6e-05 t -0.00737361908607257 0.013092 -0.5632 0.576502 0.288251 Multiple Linear Regression - Regression Statistics Multiple R 0.951284299126547 R-squared 0.904941817764685 Adjusted R-squared 0.86350619986724 F-TEST (value) 21.8397085329934 F-TEST (DF numerator) 17 F-TEST (DF denominator) 39 p-value 8.32667268468867e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.797997887006061 Sum Squared Residuals 24.8352244789794 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 30.996 30.5766312390722 0.419368760927771 2 31.033 31.4863003063172 -0.453300306317151 3 31.198 31.8446963943952 -0.64669639439516 4 30.937 31.5276895146551 -0.590689514655115 5 31.649 32.0558786602024 -0.406878660202423 6 33.115 33.7550799262958 -0.640079926295762 7 34.106 33.8655338208098 0.240466179190174 8 33.926 32.8424563378618 1.08354366213825 9 33.382 33.5479456914060 -0.16594569140605 10 32.851 33.3943675540844 -0.543367554084434 11 32.948 31.7979459040885 1.15005409591149 12 36.112 34.4822180825613 1.62978191743874 13 36.113 35.4909881081682 0.622011891831774 14 35.21 36.2921978004303 -1.08219780043035 15 35.193 34.990144953646 0.202855046353993 16 34.383 35.2006280794017 -0.817628079401719 17 35.349 35.3713672208601 -0.0223672208600803 18 37.058 37.0733230041708 -0.0153230041708290 19 38.076 37.5084630577169 0.56753694228308 20 36.63 36.3391874223678 0.290812577632183 21 36.045 35.9603273003092 0.0846726996907642 22 35.638 35.7165488125198 -0.0785488125198321 23 35.114 34.5460602202944 0.567939779705613 24 35.465 36.4293021164978 -0.964302116497802 25 35.254 34.9383180162834 0.315681983716615 26 35.299 35.5108767691942 -0.211876769194184 27 35.916 35.5651427535416 0.350857246458405 28 36.683 35.8053921233471 0.87760787665294 29 37.288 37.0924576187510 0.195542381248963 30 38.536 38.6731413410107 -0.137141341010666 31 38.977 38.4342701861058 0.542729813894208 32 36.407 37.1845321810047 -0.777532181004741 33 34.955 35.8287607015273 -0.873760701527295 34 34.951 34.7893281446608 0.161671855339216 35 32.68 34.0419832733365 -1.36198327333654 36 34.791 34.4223972441813 0.368602755818647 37 34.178 33.9953839492391 0.182616050760897 38 35.213 34.8979457883645 0.315054211635549 39 34.871 34.9262166989959 -0.0552166989958623 40 35.299 34.9302744295397 0.368725570460320 41 35.443 35.5084685425946 -0.0654685425945736 42 37.108 37.1333605260916 -0.0253605260916374 43 36.419 37.078978932089 -0.659978932089023 44 34.471 34.9338584469193 -0.462858446919319 45 33.868 33.8078753163541 0.0601246836459072 46 34.385 33.9247554887349 0.46024451126505 47 33.643 33.9990106022806 -0.356010602280565 48 34.627 35.6610825567596 -1.03408255675958 49 32.919 34.4586786872371 -1.53967868723706 50 35.5 34.0676793356939 1.43232066430613 51 36.11 35.9617991994214 0.148200800578625 52 37.086 36.9240158530564 0.161984146943574 53 37.711 37.4118279575919 0.299172042408114 54 40.427 39.6090952024311 0.817904797568894 55 39.884 40.5747540032784 -0.690754003278439 56 38.512 38.6459656118464 -0.133965611846371 57 38.767 37.8720909904033 0.894909009596673 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.309358967795888 0.618717935591775 0.690641032204112 22 0.161614061327992 0.323228122655983 0.838385938672008 23 0.13988710029793 0.27977420059586 0.86011289970207 24 0.449071255069568 0.898142510139137 0.550928744930432 25 0.498216936491179 0.996433872982359 0.501783063508821 26 0.571828988376596 0.856342023246807 0.428171011623404 27 0.538646435073217 0.922707129853567 0.461353564926783 28 0.554832542794564 0.890334914410872 0.445167457205436 29 0.474816950012249 0.949633900024497 0.525183049987751 30 0.352333913567286 0.704667827134572 0.647666086432714 31 0.555047418014722 0.889905163970557 0.444952581985278 32 0.565303876646763 0.869392246706474 0.434696123353237 33 0.442962996934555 0.88592599386911 0.557037003065445 34 0.309141875570677 0.618283751141354 0.690858124429323 35 0.615149794255518 0.769700411488964 0.384850205744482 36 0.669753866055279 0.660492267889443 0.330246133944721 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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