Q3 - omzet ind prod with seasonal dummies

*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: Mon, 24 Nov 2008 14:04:57 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/24/t1227560776h2v6rqutd6z4djg.htm/, Retrieved Mon, 24 Nov 2008 21:06:25 +0000

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/2008/Nov/24/t1227560776h2v6rqutd6z4djg.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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104.2 0 103.2 0 112.7 0 106.4 0 102.6 0 110.6 0 95.2 0 89.0 0 112.5 0 116.8 0 107.2 0 113.6 0 101.8 0 102.6 0 122.7 0 110.3 0 110.5 0 121.6 0 100.3 0 100.7 0 123.4 0 127.1 0 124.1 0 131.2 0 111.6 0 114.2 0 130.1 0 125.9 0 119.0 0 133.8 0 107.5 0 113.5 0 134.4 0 126.8 0 135.6 0 139.9 0 129.8 0 131.0 0 153.1 0 134.1 1 144.1 1 155.9 1 123.3 1 128.1 1 144.3 1 153.0 1 149.9 1 150.9 1 141.0 1 138.9 1 157.4 1 142.9 1 151.7 1 161.0 1 138.5 1 135.9 1 151.5 1 164.0 1 159.1 1 157.0 1 142.1 1 144.8 1 152.1 1 154.6 1 148.7 1 157.7 1 146.7 1

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 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation y[t] = + 109.194965986394 + 5.76411564625848x[t] -12.6330328798186M1[t] -12.6835714285714M2[t] + 2.1325566893424M3[t] -8.56200113378684M4[t] -8.9125396825397M5[t] + 1.00358843537414M6[t] -21.2636167800454M7[t] -22.0778458049887M8[t] -3.04838435374149M9[t] + 0.521077097505679M10[t] -2.58946145124716M11[t] + 0.750538548752835t + 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) 109.194965986394 2.62668 41.5715 0 0 x 5.76411564625848 2.377237 2.4247 0.018762 0.009381 M1 -12.6330328798186 2.977126 -4.2434 8.9e-05 4.4e-05 M2 -12.6835714285714 2.974374 -4.2643 8.3e-05 4.1e-05 M3 2.1325566893424 2.972844 0.7173 0.476311 0.238155 M4 -8.56200113378684 2.991534 -2.8621 0.006013 0.003007 M5 -8.9125396825397 2.985597 -2.9852 0.004281 0.002141 M6 1.00358843537414 2.980868 0.3367 0.73769 0.368845 M7 -21.2636167800454 2.977356 -7.1418 0 0 M8 -22.0778458049887 3.112868 -7.0924 0 0 M9 -3.04838435374149 3.108773 -0.9806 0.331257 0.165629 M10 0.521077097505679 3.105844 0.1678 0.8674 0.4337 M11 -2.58946145124716 3.104085 -0.8342 0.407907 0.203953 t 0.750538548752835 0.060333 12.4399 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.974355616693778 R-squared 0.949368867782713 Adjusted R-squared 0.936949910823755 F-TEST (value) 76.4451371335154 F-TEST (DF numerator) 13 F-TEST (DF denominator) 53 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.90706280371496 Sum Squared Residuals 1276.20106405895 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 104.2 97.312471655329 6.88752834467097 2 103.2 98.0124716553288 5.18752834467121 3 112.7 113.579138321995 -0.879138321995444 4 106.4 103.635119047619 2.76488095238095 5 102.6 104.035119047619 -1.43511904761904 6 110.6 114.701785714286 -4.10178571428572 7 95.2 93.185119047619 2.01488095238098 8 89 93.1214285714286 -4.12142857142856 9 112.5 112.901428571429 -0.401428571428566 10 116.8 117.221428571429 -0.42142857142853 11 107.2 114.861428571429 -7.66142857142855 12 113.6 118.201428571429 -4.60142857142857 13 101.8 106.318934240363 -4.51893424036275 14 102.6 107.018934240363 -4.41893424036281 15 122.7 122.585600907029 0.114399092970537 16 110.3 112.641581632653 -2.34158163265306 17 110.5 113.041581632653 -2.54158163265305 18 121.6 123.708248299320 -2.10824829931972 19 100.3 102.191581632653 -1.89158163265306 20 100.7 102.127891156463 -1.42789115646258 21 123.4 121.907891156463 1.49210884353742 22 127.1 126.227891156463 0.872108843537406 23 124.1 123.867891156463 0.232108843537413 24 131.2 127.207891156463 3.9921088435374 25 111.6 115.325396825397 -3.72539682539679 26 114.2 116.025396825397 -1.82539682539682 27 130.1 131.592063492063 -1.49206349206350 28 125.9 121.648044217687 4.25195578231293 29 119 122.048044217687 -3.04804421768708 30 133.8 132.714710884354 1.08528911564627 31 107.5 111.198044217687 -3.69804421768708 32 113.5 111.134353741497 2.36564625850339 33 134.4 130.914353741497 3.48564625850340 34 126.8 135.234353741497 -8.43435374149661 35 135.6 132.874353741497 2.72564625850339 36 139.9 136.214353741497 3.68564625850340 37 129.8 124.331859410431 5.46814058956921 38 131 125.031859410431 5.96814058956915 39 153.1 140.598526077098 12.5014739229025 40 134.1 136.418622448980 -2.31862244897959 41 144.1 136.818622448980 7.28137755102042 42 155.9 147.485289115646 8.41471088435376 43 123.3 125.968622448980 -2.66862244897959 44 128.1 125.904931972789 2.19506802721088 45 144.3 145.684931972789 -1.38493197278910 46 153 150.004931972789 2.99506802721088 47 149.9 147.644931972789 2.25506802721089 48 150.9 150.984931972789 -0.0849319727891088 49 141 139.102437641723 1.89756235827669 50 138.9 139.802437641723 -0.90243764172335 51 157.4 155.36910430839 2.03089569160999 52 142.9 145.425085034014 -2.5250850340136 53 151.7 145.825085034014 5.87491496598639 54 161 156.491751700680 4.50824829931973 55 138.5 134.975085034014 3.52491496598639 56 135.9 134.911394557823 0.988605442176873 57 151.5 154.691394557823 -3.19139455782314 58 164 159.011394557823 4.98860544217685 59 159.1 156.651394557823 2.44860544217686 60 157 159.991394557823 -2.99139455782314 61 142.1 148.108900226757 -6.00890022675734 62 144.8 148.808900226757 -4.00890022675737 63 152.1 164.375566893424 -12.2755668934240 64 154.6 154.431547619048 0.168452380952364 65 148.7 154.831547619048 -6.13154761904764 66 157.7 165.498214285714 -7.79821428571431 67 146.7 143.981547619048 2.71845238095236

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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Software written by Ed van Stee & Patrick Wessa

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