workshop 3 eigen tijdreeksen q2

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

Title produced by software: Multiple Regression

Date of computation: Thu, 27 Nov 2008 06:33:58 -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/27/t1227793280rwh1ubhoop4sq2b.htm/, Retrieved Thu, 27 Nov 2008 13:41:30 +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/27/t1227793280rwh1ubhoop4sq2b.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}, }

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Original text written by user:

IsPrivate?

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User-defined keywords:

Dataseries X:

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92,7 0 105,2 0 91,5 0 75,3 0 60,5 0 80,4 0 84,5 0 93,9 0 78 0 92,3 0 90 0 72,1 0 76,9 0 76 0 88,7 0 55,4 0 46,6 0 90,9 0 84,9 0 89 0 90,2 0 72,3 0 83 0 71,6 0 75,4 0 85,1 0 81,2 0 68,7 0 68,4 0 93,7 0 96,6 0 101,8 0 93,6 0 88,9 0 114,1 0 82,3 0 96,4 0 104 0 88,2 0 85,2 0 87,1 0 85,5 0 89,1 0 105,2 0 82,9 0 86,8 0 112 0 97,4 0 88,9 0 109,4 0 87,8 0 90,5 0 79,3 0 114,9 0 118,8 0 125 0 96,1 0 116,7 0 119,5 0 104,1 0 121 0 127,3 0 117,7 0 108 0 89,4 0 137,4 1 142 1 137,3 1 122,8 1 126,1 1 147,6 1 115,7 1 139,2 1 151,2 1 123,8 1 109 1 112,1 1 136,4 1 135,5 1 138,7 1 137,5 1 141,5 1 143,6 1 146,5 1 200,7 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation L&S[t] = + 91.1676923076923 + 46.0623076923077D[t] + 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) 91.1676923076923 2.134528 42.7109 0 0 D 46.0623076923077 4.400442 10.4677 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.754315567030793 R-squared 0.568991974664987 Adjusted R-squared 0.563799106889866 F-TEST (value) 109.571820293801 F-TEST (DF numerator) 1 F-TEST (DF denominator) 83 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 17.2091122380628 Sum Squared Residuals 24580.7441538462 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 92.7 91.1676923076925 1.53230769230753 2 105.2 91.1676923076923 14.0323076923077 3 91.5 91.1676923076923 0.332307692307695 4 75.3 91.1676923076923 -15.8676923076923 5 60.5 91.1676923076923 -30.6676923076923 6 80.4 91.1676923076923 -10.7676923076923 7 84.5 91.1676923076923 -6.6676923076923 8 93.9 91.1676923076923 2.7323076923077 9 78 91.1676923076923 -13.1676923076923 10 92.3 91.1676923076923 1.13230769230769 11 90 91.1676923076923 -1.16769230769230 12 72.1 91.1676923076923 -19.0676923076923 13 76.9 91.1676923076923 -14.2676923076923 14 76 91.1676923076923 -15.1676923076923 15 88.7 91.1676923076923 -2.4676923076923 16 55.4 91.1676923076923 -35.7676923076923 17 46.6 91.1676923076923 -44.5676923076923 18 90.9 91.1676923076923 -0.267692307692299 19 84.9 91.1676923076923 -6.2676923076923 20 89 91.1676923076923 -2.16769230769230 21 90.2 91.1676923076923 -0.967692307692302 22 72.3 91.1676923076923 -18.8676923076923 23 83 91.1676923076923 -8.1676923076923 24 71.6 91.1676923076923 -19.5676923076923 25 75.4 91.1676923076923 -15.7676923076923 26 85.1 91.1676923076923 -6.06769230769231 27 81.2 91.1676923076923 -9.9676923076923 28 68.7 91.1676923076923 -22.4676923076923 29 68.4 91.1676923076923 -22.7676923076923 30 93.7 91.1676923076923 2.5323076923077 31 96.6 91.1676923076923 5.43230769230769 32 101.8 91.1676923076923 10.6323076923077 33 93.6 91.1676923076923 2.43230769230769 34 88.9 91.1676923076923 -2.2676923076923 35 114.1 91.1676923076923 22.9323076923077 36 82.3 91.1676923076923 -8.8676923076923 37 96.4 91.1676923076923 5.2323076923077 38 104 91.1676923076923 12.8323076923077 39 88.2 91.1676923076923 -2.9676923076923 40 85.2 91.1676923076923 -5.9676923076923 41 87.1 91.1676923076923 -4.06769230769231 42 85.5 91.1676923076923 -5.6676923076923 43 89.1 91.1676923076923 -2.06769230769231 44 105.2 91.1676923076923 14.0323076923077 45 82.9 91.1676923076923 -8.2676923076923 46 86.8 91.1676923076923 -4.36769230769231 47 112 91.1676923076923 20.8323076923077 48 97.4 91.1676923076923 6.2323076923077 49 88.9 91.1676923076923 -2.2676923076923 50 109.4 91.1676923076923 18.2323076923077 51 87.8 91.1676923076923 -3.36769230769231 52 90.5 91.1676923076923 -0.667692307692304 53 79.3 91.1676923076923 -11.8676923076923 54 114.9 91.1676923076923 23.7323076923077 55 118.8 91.1676923076923 27.6323076923077 56 125 91.1676923076923 33.8323076923077 57 96.1 91.1676923076923 4.93230769230769 58 116.7 91.1676923076923 25.5323076923077 59 119.5 91.1676923076923 28.3323076923077 60 104.1 91.1676923076923 12.9323076923077 61 121 91.1676923076923 29.8323076923077 62 127.3 91.1676923076923 36.1323076923077 63 117.7 91.1676923076923 26.5323076923077 64 108 91.1676923076923 16.8323076923077 65 89.4 91.1676923076923 -1.7676923076923 66 137.4 137.23 0.170000000000009 67 142 137.23 4.77 68 137.3 137.23 0.0700000000000147 69 122.8 137.23 -14.43 70 126.1 137.23 -11.13 71 147.6 137.23 10.37 72 115.7 137.23 -21.53 73 139.2 137.23 1.96999999999999 74 151.2 137.23 13.97 75 123.8 137.23 -13.43 76 109 137.23 -28.23 77 112.1 137.23 -25.13 78 136.4 137.23 -0.829999999999991 79 135.5 137.23 -1.73000000000000 80 138.7 137.23 1.46999999999999 81 137.5 137.23 0.270000000000003 82 141.5 137.23 4.27 83 143.6 137.23 6.37 84 146.5 137.23 9.27 85 200.7 137.23 63.47

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 = Do not include Seasonal Dummies ; par3 = No 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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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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