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Q3_WS8_Werkloosheid<25_outsourcing&>25

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

Title produced by software: Multiple Regression

Date of computation: Thu, 15 Nov 2007 04:28:14 -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/Nov/15/t11951259101xrn65u80yhjogu.htm/, Retrieved Thu, 15 Nov 2007 12:25:20 +0100

User-defined keywords:

Q3, workshop 8, Rik, werkloosheid

Dataseries X:

» Textbox « » Textfile « » CSV «

140 0 0 132 1 0 117 1 0 114 0 0 113 0 0 110 0 0 107 1 0 103 1 0 98 1 0 98 0 0 137 0 0 148 1 0 147 1 1 139 0 1 130 1 1 128 0 1 127 0 1 123 0 1 118 1 1 114 0 1 108 1 1 111 0 1 151 0 1 159 0 1 158 1 1 148 1 1 138 1 1 137 0 1 136 0 1 133 0 1 126 0 1 120 1 1 114 1 1 116 0 1 153 0 1 162 0 1 161 0 1 149 0 1 139 1 1 135 0 1 130 0 1 127 0 1 122 1 1 117 1 1 112 1 1 113 0 1 149 0 1 157 0 1 157 1 1 147 1 1 137 1 1 132 0 1 125 0 1 123 1 1 117 1 1 114 1 1 111 0 1 112 1 1 144 0 1 150 0 1 149 1 1 134 1 1 123 1 1 116 1 1 117 0 1 111 1 1 105 1 1 102 1 1 95 1 1 93 1 1 124 0 1 130 0 1 124 1 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation <25[t] = + 145.357865871655 -1.33837687591762`ST/DL`[t] + 21.6262589242684Outc[t] -4.22921472041965M1[t] -11.7252604896346M2[t] -21.8230233049027M3[t] -26.3155591420747M4[t] -28.5825103953017M5[t] -31.3469398772365M6[t] -35.7216398798517M7[t] -39.5988616537590M8[t] -44.6427500943329M9[t] -44.1891603061991M10[t] -8.51250770541228M11[t] -0.289444892759341t + 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) 145.357865871655 3.345663 43.4467 0 0 `ST/DL` -1.33837687591762 2.351273 -0.5692 0.571409 0.285704 Outc 21.6262589242684 2.90918 7.4338 0 0 M1 -4.22921472041965 4.032372 -1.0488 0.298614 0.149307 M2 -11.7252604896346 4.174553 -2.8087 0.006767 0.003383 M3 -21.8230233049027 4.478975 -4.8723 9e-06 4e-06 M4 -26.3155591420747 3.934067 -6.6891 0 0 M5 -28.5825103953017 3.934324 -7.2649 0 0 M6 -31.3469398772365 3.95506 -7.9258 0 0 M7 -35.7216398798517 4.258035 -8.3892 0 0 M8 -39.5988616537590 4.247708 -9.3224 0 0 M9 -44.6427500943329 4.238038 -10.5338 0 0 M10 -44.1891603061991 3.935521 -11.2283 0 0 M11 -8.51250770541228 3.928519 -2.1668 0.034367 0.017183 t -0.289444892759341 0.053707 -5.3894 1e-06 1e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.93838584467497 R-squared 0.880567993486356 Adjusted R-squared 0.851739578120994 F-TEST (value) 30.5451403528884 F-TEST (DF numerator) 14 F-TEST (DF denominator) 58 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.77324447055734 Sum Squared Residuals 2660.85675816027 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 140 140.839206258476 -0.839206258476054 2 132 131.715338720584 0.284661279416025 3 117 121.328131012557 -4.32813101255654 4 114 117.884527158543 -3.88452715854283 5 113 115.328131012557 -2.32813101255654 6 110 112.274256637862 -2.27425663786241 7 107 106.271734866570 0.728265133429657 8 103 102.105068199904 0.894931800096396 9 98 96.7717348665703 1.22826513342974 10 98 98.2742566378624 -0.274256637862373 11 137 133.661464345890 3.33853565411012 12 148 140.546150282625 7.45384971737482 13 147 157.653749593715 -10.6537495937146 14 139 151.206635807658 -12.2066358076580 15 130 139.481051223713 -9.48105122371286 16 128 136.037447369699 -8.03744736969914 17 127 133.481051223713 -6.48105122371287 18 123 130.427176849019 -7.42717684901875 19 118 124.424655077727 -6.42465507772658 20 114 121.596365286978 -7.59636528697757 21 108 114.924655077727 -6.9246550777266 22 111 116.427176849019 -5.42717684901876 23 151 151.814384557046 -0.814384557046205 24 159 160.037447369699 -1.03744736969914 25 158 154.180410880603 3.81958911939748 26 148 146.394920218628 1.60507978137176 27 138 136.007712510601 1.99228748939922 28 137 132.564108656587 4.43589134341295 29 136 130.007712510601 5.99228748939922 30 133 126.953838135907 6.04616186409334 31 126 122.289693240532 3.71030675946787 32 120 116.784649697948 3.21535030205216 33 114 111.451316364615 2.54868363538549 34 116 112.953838135907 3.04616186409333 35 153 148.341045843934 4.65895415606589 36 162 156.564108656587 5.43589134341294 37 161 152.045449043408 8.95455095659194 38 149 144.259958381434 4.74004161856621 39 139 132.534373797489 6.46562620251131 40 135 129.090769943475 5.90923005652504 41 130 126.534373797489 3.46562620251131 42 127 123.480499422795 3.51950057720543 43 122 117.477977651502 4.52202234849759 44 117 113.311310984836 3.68868901516425 45 112 107.977977651502 4.02202234849757 46 113 109.480499422795 3.51950057720542 47 149 144.867707130822 4.13229286917798 48 157 153.090769943475 3.90923005652504 49 157 147.233733454378 9.76626654562166 50 147 139.448242792404 7.55175720759594 51 137 129.061035084377 7.9389649156234 52 132 125.617431230363 6.38256876963713 53 125 123.061035084377 1.9389649156234 54 123 118.668783833765 4.33121616623516 55 117 114.004638938390 2.99536106160969 56 114 109.837972271724 4.16202772827634 57 111 105.843015814308 5.15698418569204 58 112 104.668783833765 7.33121616623515 59 144 141.39436841771 2.60563158229006 60 150 149.617431230363 0.382568769637127 61 149 143.760394741266 5.23960525873376 62 134 135.974904079292 -1.97490407929197 63 123 125.587696371265 -2.58769637126451 64 116 120.805715641333 -4.80571564133316 65 117 119.587696371265 -2.58769637126451 66 111 115.195445120653 -4.19544512065275 67 105 110.531300225278 -5.53130022527822 68 102 106.364633558612 -4.36463355861158 69 95 101.031300225278 -6.03130022527824 70 93 101.195445120653 -8.19544512065276 71 124 137.921029704598 -13.9210297045978 72 130 146.144092517251 -16.1440925172508 73 124 140.287056028154 -16.2870560281542

Charts produced by software:

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Parameters:

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')

Copyright

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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