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paper_multipleregression_2dummies_11

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

Title produced by software: Multiple Regression

Date of computation: Wed, 19 Dec 2007 03:33:11 -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/19/t11980595437wx49lzth7kqf8d.htm/, Retrieved Wed, 19 Dec 2007 11:19:15 +0100

User-defined keywords:

s0650921, s0650125

Dataseries X:

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102.7 0 0 103.2 0 0 105.6 0 0 103.9 0 0 107.2 0 0 100.7 0 0 92.1 0 0 90.3 0 0 93.4 0 0 98.5 0 0 100.8 0 0 102.3 0 0 104.7 0 0 101.1 0 0 101.4 0 0 99.5 0 0 98.4 0 0 96.3 0 0 100.7 0 0 101.2 0 0 100.3 0 0 97.8 0 0 97.4 0 0 98.6 0 0 99.7 0 0 99.0 0 0 98.1 0 0 97.0 0 0 98.5 0 0 103.8 0 0 114.4 0 0 124.5 0 0 134.2 0 0 131.8 0 0 125.6 0 0 119.9 0 0 114.9 0 0 115.5 0 0 112.5 0 0 111.4 0 0 115.3 0 0 110.8 0 0 103.7 0 0 111.1 0 1 113.0 0 1 111.2 0 1 117.6 0 1 121.7 0 1 127.3 0 1 129.8 0 1 137.1 0 1 141.4 0 1 137.4 0 1 130.7 0 1 117.2 0 1 110.8 0 -1 111.4 0 -1 108.2 0 -1 108.8 0 -1 110.2 0 -1 109.5 0 -1 109.5 0 -1 116.0 0 -1 111.2 0 -1 112.1 0 -1 114.0 0 -1 119.1 0 -1 114.1 1 -1 115.1 1 -1 115.4 1 -1 110.8 1 0 116.0 1 0 119.2 1 0 126.5 1 0 127.8 1 0 131.3 1 0 140.3 1 0 137.3 1 0 143.0 1 0 134.5 1 0 139.9 1 0 159.3 1 0 170.4 1 0 175.0 1 0 175.8 1 0 180.9 1 0 180.3 1 0 169.6 1 0 172.3 1 0 184.8 1 0 177.7 1 0 184.6 1 0 211.4 1 0 215.3 1 0 215.9 1 0

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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation prijsindex[t] = + 84.8103428034598 + 15.3999034439288ontkoppelde_bedrijfstoeslag[t] + 13.0169061346170oogstomvang[t] + 2.50874347847249M1[t] + 3.31877980737751M2[t] + 4.32881613628249M3[t] + 1.98885246518748M4[t] + 3.36138879409247M5[t] + 2.32142512299745M6[t] + 0.356461451902447M7[t] -0.193876882856545M8[t] + 5.10365944604845M9[t] + 6.80119577495345M10[t] + 5.7466188370313M11[t] + 0.652463671095011t + 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) 84.8103428034598 7.525565 11.2696 0 0 ontkoppelde_bedrijfstoeslag 15.3999034439288 6.342249 2.4281 0.01742 0.00871 oogstomvang 13.0169061346170 3.362696 3.871 0.00022 0.00011 M1 2.50874347847249 8.882023 0.2825 0.778327 0.389163 M2 3.31877980737751 8.878461 0.3738 0.709541 0.354771 M3 4.32881613628249 8.876163 0.4877 0.627103 0.313552 M4 1.98885246518748 8.875131 0.2241 0.823256 0.411628 M5 3.36138879409247 8.875364 0.3787 0.70589 0.352945 M6 2.32142512299745 8.876863 0.2615 0.794368 0.397184 M7 0.356461451902447 8.879627 0.0401 0.968079 0.484039 M8 -0.193876882856545 8.893933 -0.0218 0.982663 0.491331 M9 5.10365944604845 8.891122 0.574 0.567566 0.283783 M10 6.80119577495345 8.889573 0.7651 0.446478 0.223239 M11 5.7466188370313 8.881207 0.6471 0.519449 0.259725 t 0.652463671095011 0.105994 6.1556 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.83675069680224 R-squared 0.700151728599034 Adjusted R-squared 0.647678281103865 F-TEST (value) 13.3429717699317 F-TEST (DF numerator) 14 F-TEST (DF denominator) 80 p-value 1.33226762955019e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 17.1461440004383 Sum Squared Residuals 23519.2203267012 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 102.7 87.9715499530275 14.7284500469725 2 103.2 89.4340499530273 13.7659500469727 3 105.6 91.0965499530273 14.5034500469727 4 103.9 89.4090499530273 14.4909500469727 5 107.2 91.4340499530274 15.7659500469726 6 100.7 91.0465499530274 9.65345004697264 7 92.1 89.7340499530274 2.36595004697263 8 90.3 89.8361752893634 0.463824710636614 9 93.4 95.7861752893634 -2.38617528936337 10 98.5 98.1361752893634 0.363824710636604 11 100.8 97.7340620225362 3.06593797746375 12 102.3 92.6399068566 9.66009314340004 13 104.7 95.8011140061675 8.89888599383255 14 101.1 97.2636140061675 3.83638599383250 15 101.4 98.9261140061675 2.47388599383249 16 99.5 97.2386140061675 2.26138599383252 17 98.4 99.2636140061675 -0.863614006167478 18 96.3 98.8761140061675 -2.57611400616749 19 100.7 97.5636140061675 3.13638599383252 20 101.2 97.6657393425035 3.5342606574965 21 100.3 103.615739342504 -3.31573934250351 22 97.8 105.965739342504 -8.16573934250351 23 97.4 105.563626075676 -8.16362607567637 24 98.6 100.46947090974 -1.86947090974009 25 99.7 103.630678059308 -3.93067805930758 26 99 105.093178059308 -6.09317805930761 27 98.1 106.755678059308 -8.6556780593076 28 97 105.068178059308 -8.0681780593076 29 98.5 107.093178059308 -8.59317805930761 30 103.8 106.705678059308 -2.90567805930761 31 114.4 105.393178059308 9.0068219406924 32 124.5 105.495303395644 19.0046966043564 33 134.2 111.445303395644 22.7546966043564 34 131.8 113.795303395644 18.0046966043564 35 125.6 113.393190128816 12.2068098711835 36 119.9 108.299034962880 11.6009650371198 37 114.9 111.460242112448 3.4397578875523 38 115.5 112.922742112448 2.57725788755226 39 112.5 114.585242112448 -2.08524211244772 40 111.4 112.897742112448 -1.49774211244772 41 115.3 114.922742112448 0.377257887552265 42 110.8 114.535242112448 -3.73524211244773 43 103.7 113.222742112448 -9.52274211244773 44 111.1 126.341773583401 -15.2417735834008 45 113 132.291773583401 -19.2917735834008 46 111.2 134.641773583401 -23.4417735834008 47 117.6 134.239660316574 -16.6396603165737 48 121.7 129.145505150637 -7.44550515063736 49 127.3 132.306712300205 -5.00671230020487 50 129.8 133.769212300205 -3.96921230020489 51 137.1 135.431712300205 1.66828769979511 52 141.4 133.744212300205 7.65578769979512 53 137.4 135.769212300205 1.63078769979512 54 130.7 135.381712300205 -4.68171230020490 55 117.2 134.069212300205 -16.8692123002049 56 110.8 108.137525367307 2.66247463269316 57 111.4 114.087525367307 -2.68752536730684 58 108.2 116.437525367307 -8.23752536730684 59 108.8 116.035412100480 -7.23541210047971 60 110.2 110.941256934543 -0.741256934543417 61 109.5 114.102464084111 -4.60246408411092 62 109.5 115.564964084111 -6.06496408411095 63 116 117.227464084111 -1.22746408411094 64 111.2 115.539964084111 -4.33996408411094 65 112.1 117.564964084111 -5.46496408411096 66 114 117.177464084111 -3.17746408411094 67 119.1 115.864964084111 3.23503591588905 68 114.1 131.366992864376 -17.2669928643758 69 115.1 137.316992864376 -22.2169928643758 70 115.4 139.666992864376 -24.2669928643758 71 110.8 152.281785732166 -41.4817857321657 72 116 147.187630566229 -31.1876305662294 73 119.2 150.348837715797 -31.1488377157969 74 126.5 151.811337715797 -25.3113377157970 75 127.8 153.473837715797 -25.6738377157969 76 131.3 151.786337715797 -20.4863377157969 77 140.3 153.811337715797 -13.5113377157969 78 137.3 153.423837715797 -16.1238377157969 79 143 152.111337715797 -9.11133771579694 80 134.5 152.213463052133 -17.7134630521330 81 139.9 158.163463052133 -18.2634630521330 82 159.3 160.513463052133 -1.21346305213296 83 170.4 160.111349785306 10.2886502146942 84 175 155.017194619370 19.9828053806305 85 175.8 158.178401768937 17.6215982310630 86 180.9 159.640901768937 21.2590982310629 87 180.3 161.303401768937 18.9965982310629 88 169.6 159.615901768937 9.98409823106292 89 172.3 161.640901768937 10.6590982310629 90 184.8 161.253401768937 23.5465982310629 91 177.7 159.940901768937 17.7590982310629 92 184.6 160.043027105273 24.5569728947269 93 211.4 165.993027105273 45.4069728947269 94 215.3 168.343027105273 46.9569728947269 95 215.9 167.940913838446 47.959086161554

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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