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-25 tov economische situatie met seisoen en met trend

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 06:08:32 -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/t1195131813cw1zrw591m3ywa3.htm/, Retrieved Thu, 15 Nov 2007 14:03:44 +0100

User-defined keywords:

Dataseries X:

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140 -1 132 -2 117 -2 114 -1 113 1 110 1 107 1 103 1 98 1 98 1 137 0 148 -1 147 -1 139 -1 130 -1 128 -1 127 -2 123 -2 118 -2 114 -1 108 -1 111 -1 151 -1 159 -1 158 -1 148 -1 138 0 137 0 136 1 133 1 126 1 120 1 114 -1 116 1 153 -1 162 1 161 0 149 -1 139 -1 135 -1 130 -1 127 -1 122 1 117 -1 112 -2 113 -2 149 -2 157 -1 157 -2 147 -1 137 -1 132 -1 125 -1 123 -1 117 -1 114 -1 111 -1 112 -1 144 0 150 -1 149 -1 134 1 123 1 116 -1 117 -1 111 0 105 -1 102 1 95 1 93 1 124 0 130 -1 124 -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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation <25[t] = + 151.992990089437 -1.43908629441624eco[t] -3.71212173532696M1[t] -10.2047003234457M2[t] -20.7517006802721M3[t] -24.6117298019038M4[t] -26.4188824429941M5[t] -29.6325494664871M6[t] -34.6795498233134M7[t] -38.5598835134731M8[t] -44.5662747332435M9[t] -43.2067607076672M10[t] -8.04648526077097M11[t] -0.0464852607709747t + 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) 151.992990089437 4.562212 33.3156 0 0 eco -1.43908629441624 1.176507 -1.2232 0.226123 0.113061 M1 -3.71212173532696 5.325328 -0.6971 0.488497 0.244249 M2 -10.2047003234457 5.53377 -1.8441 0.070195 0.035097 M3 -20.7517006802721 5.525375 -3.7557 0.000398 0.000199 M4 -24.6117298019038 5.52445 -4.4551 3.8e-05 1.9e-05 M5 -26.4188824429941 5.520563 -4.7855 1.2e-05 6e-06 M6 -29.6325494664871 5.527635 -5.3608 1e-06 1e-06 M7 -34.6795498233134 5.542157 -6.2574 0 0 M8 -38.5598835134731 5.564071 -6.9302 0 0 M9 -44.5662747332435 5.510182 -8.088 0 0 M10 -43.2067607076672 5.536731 -7.8037 0 0 M11 -8.04648526077097 5.504612 -1.4618 0.14911 0.074555 t -0.0464852607709747 0.053503 -0.8688 0.388462 0.194231 Multiple Linear Regression - Regression Statistics Multiple R 0.871375398871458 R-squared 0.759295085758392 Adjusted R-squared 0.706258409739054 F-TEST (value) 14.316415408114 F-TEST (DF numerator) 13 F-TEST (DF denominator) 59 p-value 9.83657599817889e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 9.53381798208228 Sum Squared Residuals 5362.72743361305 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 140 149.673469387755 -9.67346938775538 2 132 144.573491833282 -12.5734918332815 3 117 133.980006215684 -16.9800062156843 4 114 128.634405538865 -14.6344055388653 5 113 123.902595048172 -10.9025950481715 6 110 120.642442763908 -10.6424427639076 7 107 115.548957146310 -8.54895714631028 8 103 111.622138195380 -8.62213819537963 9 98 105.569261714838 -7.5692617148382 10 98 106.882290479644 -8.88229047964363 11 137 143.435166960185 -6.43516696018508 12 148 152.874253254601 -4.87425325460132 13 147 149.115646258503 -2.11564625850336 14 139 142.576582409614 -3.57658240961359 15 130 131.983096792016 -1.98309679201628 16 128 128.076582409614 -0.076582409613576 17 127 127.662030802169 -0.662030802168579 18 123 124.401878517905 -1.40187851790461 19 118 119.308392900307 -1.30839290030731 20 114 113.942487654960 0.057512345039542 21 108 107.889611174419 0.110388825580997 22 111 109.202639939224 1.79736006077559 23 151 144.316430125350 6.68356987465038 24 159 152.316430125350 6.68356987465039 25 158 148.557823129252 9.44217687074835 26 148 142.018759280362 5.98124071963811 27 138 129.986187368348 8.01381263165165 28 137 126.079672985946 10.9203270140544 29 136 122.786948789668 13.2130512103318 30 133 119.526796505404 13.4732034945958 31 126 114.433310887807 11.5666891121931 32 120 110.506491936876 9.49350806312371 33 114 107.331788045167 6.66821195483269 34 116 105.766644221140 10.2333557788598 35 153 143.758606996098 9.24139300390207 36 162 148.880434407265 13.1195655927346 37 161 146.560913705584 14.4390862944163 38 149 141.460936151110 7.5390638488898 39 139 130.867450533513 8.1325494664871 40 135 126.960936151110 8.03906384888981 41 130 125.107298249249 4.89270175075106 42 127 121.847145964985 5.15285403501503 43 122 113.875487758555 8.12451224144479 44 117 112.826841396457 4.17315860354293 45 112 108.213051210332 3.78694878966816 46 113 109.526079975137 3.47392002486274 47 149 144.639870161262 4.36012983873753 48 157 151.200783866846 5.79921613315379 49 157 148.881263165165 8.1187368348355 50 147 140.903113021859 6.0968869781415 51 137 130.309627404261 6.69037259573881 52 132 126.403113021858 5.59688697814151 53 125 124.549475119997 0.450524880002751 54 123 121.289322835733 1.71067716426672 55 117 116.195837218136 0.804162781864004 56 114 112.269018267205 1.73098173279463 57 111 106.216141786664 4.78385821333609 58 112 107.529170551469 4.47082944853068 59 144 141.203874443178 2.7961255568217 60 150 150.642960737595 -0.64296073759453 61 149 146.884353741497 2.11564625850344 62 134 137.467117303774 -3.46711730377433 63 123 126.873631686177 -3.87363168617702 64 116 125.845289892607 -9.8452898926068 65 117 123.991651990746 -6.99165199074555 66 111 119.292413412065 -8.29241341206535 67 105 115.638014088884 -10.6380140888843 68 102 108.833022549121 -6.83302254912119 69 95 102.780146068580 -7.78014606857973 70 93 104.093174833385 -11.0931748333851 71 124 140.646051313927 -16.6460513139266 72 130 150.085137608343 -20.0851376083428 73 124 146.326530612245 -22.3265306122449

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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