Multiple Regression werklh inflatie 4 vertagingen

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

Title produced by software: Multiple Regression

Date of computation: Thu, 17 Dec 2009 07:29:24 -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/17/t1261060251o0hapdl7fynoss1.htm/, Retrieved Thu, 17 Dec 2009 15:31:03 +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/17/t1261060251o0hapdl7fynoss1.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}, }

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Dataseries X:

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8,3 3,9 8,2 8,7 9,3 9,3 8,5 4 8,3 8,2 8,7 9,3 8,6 4,3 8,5 8,3 8,2 8,7 8,5 4,8 8,6 8,5 8,3 8,2 8,2 4,4 8,5 8,6 8,5 8,3 8,1 4,3 8,2 8,5 8,6 8,5 7,9 4,7 8,1 8,2 8,5 8,6 8,6 4,7 7,9 8,1 8,2 8,5 8,7 4,9 8,6 7,9 8,1 8,2 8,7 5 8,7 8,6 7,9 8,1 8,5 4,2 8,7 8,7 8,6 7,9 8,4 4,3 8,5 8,7 8,7 8,6 8,5 4,8 8,4 8,5 8,7 8,7 8,7 4,8 8,5 8,4 8,5 8,7 8,7 4,8 8,7 8,5 8,4 8,5 8,6 4,2 8,7 8,7 8,5 8,4 8,5 4,6 8,6 8,7 8,7 8,5 8,3 4,8 8,5 8,6 8,7 8,7 8 4,5 8,3 8,5 8,6 8,7 8,2 4,4 8 8,3 8,5 8,6 8,1 4,3 8,2 8 8,3 8,5 8,1 3,9 8,1 8,2 8 8,3 8 3,7 8,1 8,1 8,2 8 7,9 4 8 8,1 8,1 8,2 7,9 4,1 7,9 8 8,1 8,1 8 3,7 7,9 7,9 8 8,1 8 3,8 8 7,9 7,9 8 7,9 3,8 8 8 7,9 7,9 8 3,8 7,9 8 8 7,9 7,7 3,3 8 7,9 8 8 7,2 3,3 7,7 8 7,9 8 7,5 3,3 7,2 7,7 8 7,9 7,3 3,2 7,5 7,2 7,7 8 7 3,4 7,3 7,5 7,2 7,7 7 4,2 7 7,3 7,5 7,2 7 4,9 7 7 7,3 7,5 7,2 5,1 7 7 7 7,3 7,3 5,5 7,2 7 7 7 7,1 5,6 7,3 7,2 7 7 6,8 6,4 7,1 7,3 7,2 7 6,4 6,1 6,8 7,1 7,3 7,2 6,1 7,1 6,4 6,8 7,1 7,3 6,5 7,8 6,1 6,4 6,8 7,1 7,7 7,9 6,5 6,1 6,4 6,8 7,9 7,4 7, 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = -0.0550574197115133 + 0.00893293499343105X[t] + 1.58397870443630Y1[t] -0.915092663015896Y2[t] + 0.042692859676686Y3[t] + 0.279056782460857Y4[t] + 0.178003476798794M1[t] + 0.104752669320572M2[t] -0.0801731217262057M3[t] + 0.0423556268766096M4[t] + 0.0171277878745154M5[t] -0.116439585377464M6[t] + 0.00509285983473205M7[t] + 0.587598277423118M8[t] -0.414899756293283M9[t] + 0.0271031893206197M10[t] + 0.096307817332781M11[t] + 0.00124435720083027t + 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) -0.0550574197115133 1.179969 -0.0467 0.963029 0.481514 X 0.00893293499343105 0.026548 0.3365 0.738355 0.369177 Y1 1.58397870443630 0.159889 9.9068 0 0 Y2 -0.915092663015896 0.30955 -2.9562 0.005327 0.002664 Y3 0.042692859676686 0.309987 0.1377 0.891185 0.445593 Y4 0.279056782460857 0.189057 1.476 0.148171 0.074085 M1 0.178003476798794 0.117207 1.5187 0.137112 0.068556 M2 0.104752669320572 0.12609 0.8308 0.411288 0.205644 M3 -0.0801731217262057 0.131226 -0.611 0.544866 0.272433 M4 0.0423556268766096 0.127969 0.331 0.742475 0.371238 M5 0.0171277878745154 0.122389 0.1399 0.889442 0.444721 M6 -0.116439585377464 0.116067 -1.0032 0.322105 0.161053 M7 0.00509285983473205 0.117448 0.0434 0.965639 0.48282 M8 0.587598277423118 0.119271 4.9266 1.7e-05 8e-06 M9 -0.414899756293283 0.165026 -2.5142 0.016286 0.008143 M10 0.0271031893206197 0.178597 0.1518 0.880182 0.440091 M11 0.096307817332781 0.154263 0.6243 0.536155 0.268078 t 0.00124435720083027 0.004336 0.287 0.775688 0.387844 Multiple Linear Regression - Regression Statistics Multiple R 0.976501869273433 R-squared 0.95355590069451 Adjusted R-squared 0.932778277321001 F-TEST (value) 45.8934057833718 F-TEST (DF numerator) 17 F-TEST (DF denominator) 38 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.172455242697452 Sum Squared Residuals 1.13015080788581 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.3 8.178619740781 0.121380259219002 2 8.5 8.69783507014851 -0.19783507014851 3 8.6 8.5533394920714 0.0466605079286011 4 8.5 8.52169929794945 -0.0216992979494524 5 8.2 8.28067975558702 -0.0806797555870215 6 8.1 7.82385974346707 0.276140256532932 7 7.9 8.08997604061702 -0.189976040617023 8 8.6 8.40772580467148 0.192274195328521 9 8.7 8.61207602015726 0.0879239798427446 10 8.7 8.5376053726224 0.162394627377589 11 8.5 8.48347238882058 0.0165276111794232 12 8.4 8.27211551499098 0.127884485009021 13 8.5 8.50835615689295 -0.0083561568929538 14 8.7 8.67771827142544 0.0222817285745550 15 8.7 8.65924266970532 0.0407573302946741 16 8.6 8.57100108963132 0.0289989103686828 17 8.5 8.42863716156522 0.0713628384347812 18 8.3 8.28702348486289 0.0129765151371135 19 8 8.17756464622455 -0.177564646224547 20 8.2 8.43607108457295 -0.236071084572955 21 8.1 7.98880340416865 0.111196595831355 22 8.1 8.01844191554402 0.081558084455979 23 8 8.103435117257 -0.103435117256995 24 7.9 7.90419573770395 -0.00419573770394694 25 7.9 7.98954258281479 -0.0895425828147887 26 8 8.00120293887395 -0.00120293887394611 27 8 7.94463770475722 0.0553622952427837 28 7.9 7.94899586601319 -0.0489958660131867 29 8 7.77088379973596 0.229116200264037 30 7.7 7.9119071311794 -0.211907131179402 31 7.2 7.46371176999228 -0.263711769992281 32 7.5 7.5063635991897 -0.00636359918970111 33 7.3 7.4520543923567 -0.152054392356704 34 7 7.20070127780149 -0.200701277801494 35 7 6.8594009989541 0.140599001045902 36 7 7.12029685502524 -0.120296855025238 37 7.2 7.23271206162837 -0.0327120616283708 38 7.3 7.39735749149736 -0.0973574914973551 39 7.1 7.1899486889912 -0.0899486889912003 40 6.8 6.92110170753608 -0.121101707536079 41 6.4 6.66234390896892 -0.262343908968915 42 6.1 6.1992572513522 -0.0992572513521968 43 6.5 6.15051134774091 0.349488652259086 44 7.7 7.54247951809983 0.157520481900168 45 7.9 7.9470661833174 -0.0470661833173954 46 7.5 7.54325143403207 -0.0432514340320731 47 6.9 6.95369149496833 -0.0536914949683296 48 6.6 6.60339189227984 -0.00339189227983658 49 6.9 6.89076945788289 0.00923054211711141 50 7.7 7.42588622805474 0.274113771945256 51 8 8.05283144447486 -0.0528314444748587 52 8 7.83720203886996 0.162797961130035 53 7.7 7.65745537414288 0.0425446258571185 54 7.3 7.27795238913845 0.0220476108615526 55 7.4 7.11823619542523 0.281763804574765 56 8.1 8.20735999346603 -0.107359993466033 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.601651362957623 0.796697274084754 0.398348637042377 22 0.51220522438831 0.97558955122338 0.48779477561169 23 0.363272012786349 0.726544025572697 0.636727987213651 24 0.240773124850260 0.481546249700521 0.75922687514974 25 0.142212824980325 0.284425649960650 0.857787175019675 26 0.0850395979428233 0.170079195885647 0.914960402057177 27 0.0579312144090937 0.115862428818187 0.942068785590906 28 0.0285658452078476 0.0571316904156953 0.971434154792152 29 0.300115993547308 0.600231987094615 0.699884006452692 30 0.316722431893336 0.633444863786671 0.683277568106664 31 0.217413195131290 0.434826390262581 0.78258680486871 32 0.262149838448816 0.524299676897632 0.737850161551184 33 0.218796454425799 0.437592908851599 0.7812035455742 34 0.210211434107567 0.420422868215133 0.789788565892433 35 0.296623721204077 0.593247442408153 0.703376278795923 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 1 0.0666666666666667 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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