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verklaring verloop werkloosheid

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

Title produced by software: Multiple Regression

Date of computation: Mon, 24 Dec 2007 15:06:57 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Dec/24/t11985329311fddyda0iju2hmd.htm/, Retrieved Mon, 24 Dec 2007 22:48:51 +0100

User-defined keywords:

s0650062

Dataseries X:

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8,0 0 8,1 0 8,3 0 8,2 0 8,1 0 7,7 0 7,6 0 7,7 0 8,2 0 8,4 0 8,4 0 8,6 0 8,4 0 8,5 0 8,7 0 8,7 0 8,6 0 7,4 0 7,3 0 7,4 0 9,0 0 9,2 0 9,2 0 8,5 0 8,3 0 8,3 0 8,6 0 8,6 0 8,5 0 8,1 0 8,1 0 8,0 0 8,6 0 8,7 0 8,7 0 8,6 0 8,4 0 8,4 0 8,7 0 8,7 0 8,5 0 8,3 1 8,3 1 8,3 1 8,1 1 8,2 1 8,1 1 8,1 1 7,9 1 7,7 1 8,1 1 8,0 1 7,7 1 7,8 1 7,6 1 7,4 1 7,7 1 7,8 1 7,5 1 7,2 1

Text written by user:

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 compuational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 6 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation werkloosheidsgraad[t] = + 8.2445540796964 -0.587855787476281generatiepact[t] -0.05933586337761M1[t] -0.0646299810246674M2[t] + 0.210075901328273M3[t] + 0.164781783681214M4[t] -0.000512333965844187M5[t] -0.308235294117647M6[t] -0.393529411764706M7[t] -0.418823529411764M8[t] + 0.135882352941177M9[t] + 0.270588235294118M10[t] + 0.185294117647059M11[t] + 0.00529411764705884t + 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) 8.2445540796964 0.205935 40.0348 0 0 generatiepact -0.587855787476281 0.17735 -3.3147 0.001795 0.000898 M1 -0.05933586337761 0.237197 -0.2502 0.803581 0.401791 M2 -0.0646299810246674 0.236768 -0.273 0.7861 0.39305 M3 0.210075901328273 0.236434 0.8885 0.378885 0.189442 M4 0.164781783681214 0.236195 0.6977 0.488907 0.244454 M5 -0.000512333965844187 0.236052 -0.0022 0.998278 0.499139 M6 -0.308235294117647 0.23678 -1.3018 0.199474 0.099737 M7 -0.393529411764706 0.236255 -1.6657 0.102571 0.051286 M8 -0.418823529411764 0.235825 -1.776 0.082349 0.041175 M9 0.135882352941177 0.23549 0.577 0.566739 0.28337 M10 0.270588235294118 0.23525 1.1502 0.256 0.128 M11 0.185294117647059 0.235106 0.7881 0.434664 0.217332 t 0.00529411764705884 0.004751 1.1144 0.270915 0.135458 Multiple Linear Regression - Regression Statistics Multiple R 0.701757416636056 R-squared 0.492463471803711 Adjusted R-squared 0.349029235574325 F-TEST (value) 3.43337465830782 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0.000966121413879861 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.371659585225281 Sum Squared Residuals 6.35401897533207 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8 8.19051233396585 -0.190512333965852 2 8.1 8.19051233396584 -0.0905123339658446 3 8.3 8.47051233396584 -0.170512333965843 4 8.2 8.43051233396584 -0.230512333965844 5 8.1 8.27051233396584 -0.170512333965844 6 7.7 7.9680834914611 -0.2680834914611 7 7.6 7.8880834914611 -0.288083491461101 8 7.7 7.8680834914611 -0.1680834914611 9 8.2 8.4280834914611 -0.228083491461101 10 8.4 8.5680834914611 -0.168083491461099 11 8.4 8.4880834914611 -0.0880834914610995 12 8.6 8.3080834914611 0.2919165085389 13 8.4 8.25404174573055 0.145958254269452 14 8.5 8.25404174573055 0.245958254269450 15 8.7 8.53404174573055 0.165958254269449 16 8.7 8.49404174573055 0.205958254269450 17 8.6 8.33404174573055 0.26595825426945 18 7.4 8.0316129032258 -0.631612903225806 19 7.3 7.9516129032258 -0.651612903225806 20 7.4 7.9316129032258 -0.531612903225806 21 9 8.4916129032258 0.508387096774194 22 9.2 8.6316129032258 0.568387096774194 23 9.2 8.5516129032258 0.648387096774194 24 8.5 8.3716129032258 0.128387096774194 25 8.3 8.31757115749526 -0.0175711574952541 26 8.3 8.31757115749526 -0.0175711574952556 27 8.6 8.59757115749526 0.00242884250474375 28 8.6 8.55757115749526 0.0424288425047439 29 8.5 8.39757115749526 0.102428842504744 30 8.1 8.09514231499051 0.00485768500948694 31 8.1 8.01514231499051 0.0848576850094873 32 8 7.99514231499051 0.00485768500948718 33 8.6 8.55514231499051 0.0448576850094874 34 8.7 8.69514231499051 0.00485768500948707 35 8.7 8.61514231499051 0.084857685009487 36 8.6 8.43514231499051 0.164857685009487 37 8.4 8.38110056925996 0.0188994307400394 38 8.4 8.38110056925996 0.0188994307400379 39 8.7 8.66110056925996 0.0388994307400372 40 8.7 8.62110056925996 0.0788994307400374 41 8.5 8.46110056925996 0.0388994307400377 42 8.3 7.57081593927894 0.729184060721063 43 8.3 7.49081593927894 0.809184060721063 44 8.3 7.47081593927894 0.829184060721063 45 8.1 8.03081593927894 0.0691840607210624 46 8.2 8.17081593927894 0.0291840607210622 47 8.1 8.09081593927894 0.00918406072106244 48 8.1 7.91081593927894 0.189184060721062 49 7.9 7.85677419354839 0.0432258064516144 50 7.7 7.85677419354839 -0.156774193548387 51 8.1 8.13677419354839 -0.0367741935483875 52 8 8.09677419354839 -0.0967741935483869 53 7.7 7.93677419354839 -0.236774193548387 54 7.8 7.63434535104364 0.165654648956356 55 7.6 7.55434535104364 0.0456546489563561 56 7.4 7.53434535104364 -0.134345351043644 57 7.7 8.09434535104364 -0.394345351043643 58 7.8 8.23434535104364 -0.434345351043643 59 7.5 8.15434535104364 -0.654345351043643 60 7.2 7.97434535104364 -0.774345351043643

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) 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)) 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$resid, main='Residual Normal Q-Q Plot') grid() dev.off() (myerror <- as.ts(mysum$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() 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')

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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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