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werkloosheid en industriële prod lineaire trend en dummy month

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

Title produced by software: Multiple Regression

Date of computation: Tue, 18 Dec 2007 10:41:09 -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/18/t1197998658z72dduuh7vbwu9w.htm/, Retrieved Tue, 18 Dec 2007 18:24:29 +0100

User-defined keywords:

Dataseries X:

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8.1 359 8.3 304.6 8.2 297.7 8.1 303.3 7.7 304.7 7.6 331.3 7.7 318.8 8.2 306.8 8.4 331.1 8.4 284.1 8.6 259.7 8.4 335.8 8.5 338.5 8.7 310.3 8.7 322.1 8.6 289.3 7.4 300.8 7.3 360.6 7.4 327.3 9 304.1 9.2 362 9.2 287.8 8.5 286.1 8.3 358.2 8.3 346 8.6 329.9 8.6 334.3 8.5 303.7 8.1 307.6 8.1 351.7 8 324.6 8.6 311.9 8.7 361.5 8.7 271.1 8.6 286.5 8.4 352.8 8.4 322.4 8.7 335 8.7 322.2 8.5 313.6 8.3 323.3 8.3 379.1 8.3 315.6 8.1 353.6 8.2 371.7 8.1 282.9 8.1 298.8 7.9 361.8 7.7 365.9 8.1 357.6 8 335.4 7.7 340.1 7.8 337.8 7.6 389.6 7.4 342.5 7.7 354.6 7.8 391.6 7.5 317.7 7.2 312.8 7 356.2

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 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation werkl[t] = + 11.2733558593295 -0.00898720362548001Iprod[t] + 0.109752313169581M1[t] + 0.222885921711642M2[t] + 0.139503708067787M3[t] -0.128586371679523M4[t] -0.502276293141087M5[t] -0.151493643504616M6[t] -0.49851200356862M7[t] + 0.0682543790177037M8[t] + 0.547008063529259M9[t] -0.202961986883062M10[t] -0.37961074167442M11[t] -0.00281201299111269t + 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) 11.2733558593295 1.620446 6.9569 0 0 Iprod -0.00898720362548001 0.00492 -1.8267 0.074237 0.037119 M1 0.109752313169581 0.264388 0.4151 0.679986 0.339993 M2 0.222885921711642 0.278508 0.8003 0.42766 0.21383 M3 0.139503708067787 0.28873 0.4832 0.631272 0.315636 M4 -0.128586371679523 0.320183 -0.4016 0.689836 0.344918 M5 -0.502276293141087 0.308896 -1.626 0.110774 0.055387 M6 -0.151493643504616 0.271472 -0.558 0.579519 0.289759 M7 -0.49851200356862 0.286829 -1.738 0.0889 0.04445 M8 0.0682543790177037 0.287268 0.2376 0.813248 0.406624 M9 0.547008063529259 0.269667 2.0285 0.048326 0.024163 M10 -0.202961986883062 0.405014 -0.5011 0.618674 0.309337 M11 -0.37961074167442 0.407526 -0.9315 0.356459 0.178229 t -0.00281201299111269 0.004808 -0.5849 0.561474 0.280737 Multiple Linear Regression - Regression Statistics Multiple R 0.657206628108399 R-squared 0.431920552029611 Adjusted R-squared 0.271376360211893 F-TEST (value) 2.69035302454300 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0.00676045586162599 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.414257639036294 Sum Squared Residuals 7.89403200899652 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.1 8.15389005796068 -0.0538900579606841 2 8.3 8.75311553073769 -0.453115530737686 3 8.2 8.72893300911853 -0.528933009118533 4 8.1 8.40770257607742 -0.307702576077421 5 7.7 8.01861855654907 -0.318618556549072 6 7.6 8.12752957675666 -0.527529576756662 7 7.7 7.89003924902005 -0.190039249020046 8 8.2 8.56184006212102 -0.361840062121017 9 8.4 8.8193926855423 -0.419392685542295 10 8.4 8.48900919253642 -0.0890091925364214 11 8.6 8.52883619321566 0.0711638067843368 12 8.4 8.22170872599994 0.178291274000059 13 8.5 8.30438357638961 0.195616423610387 14 8.7 8.6681443141791 0.0318556858209007 15 8.7 8.47590108476347 0.224098915236533 16 8.6 8.49977927094079 0.100220729059211 17 7.4 8.0199244947951 -0.619924494795091 18 7.3 7.83046035463675 -0.530460354636745 19 7.4 7.77990386231011 -0.379903862310113 20 9 8.55236135601646 0.44763864398354 21 9.2 8.50794393762161 0.692056062378389 22 9.2 8.42201238322879 0.777987616771206 23 8.5 8.25782986160964 0.242170138390362 24 8.3 7.98665120889584 0.313348791104163 25 8.3 8.20323539330516 0.0967646066948395 26 8.6 8.45825096722634 0.141749032773661 27 8.6 8.33251304463926 0.267486955360741 28 8.5 8.33661938284052 0.163380617159476 29 8.1 7.92506735424848 0.174932645751524 30 8.1 7.87670231101017 0.223297688989835 31 8 7.77042515620556 0.229574843794443 32 8.6 8.44851701184436 0.151482988155635 33 8.7 8.478693383541 0.221306616459001 34 8.7 8.53835452788096 0.161645472119042 35 8.6 8.2204908242661 0.379509175733905 36 8.4 8.00143795258008 0.398562047419923 37 8.4 8.38158924297314 0.0184107570268628 38 8.7 8.37867207284304 0.321327927156961 39 8.7 8.40751405261421 0.292485947385785 40 8.5 8.21390191105492 0.286098088945080 41 8.3 7.75022410143509 0.549775898564914 42 8.3 7.59670877577866 0.703291224221341 43 8.3 7.81756583294152 0.482434167058476 44 8.1 8.0400064647685 0.0599935352315046 45 8.2 8.35327975066775 -0.153279750667751 46 8.1 8.39856136920694 -0.298561369206942 47 8.1 8.07620406377934 0.0237959362206616 48 7.9 7.8868089640574 0.0131910359425956 49 7.7 7.9569017293714 -0.256901729371404 50 8.1 8.14181711501384 -0.0418171150138374 51 8 8.25513880886453 -0.255138808864526 52 7.7 7.94199685908635 -0.241996859086347 53 7.8 7.58616549297227 0.213834507027725 54 7.6 7.46859898181777 0.131401018182232 55 7.4 7.54206589952276 -0.14206589952276 56 7.7 7.99727510524966 -0.297275105249663 57 7.8 8.14069024262735 -0.340690242627345 58 7.5 8.05206252714688 -0.552062527146885 59 7.2 7.91663905712927 -0.716639057129265 60 7 7.90339314846674 -0.90339314846674

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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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