seatbelt_3

*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: Sun, 23 Nov 2008 07:35:32 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/23/t1227451012c26mj94h82v5zg6.htm/, Retrieved Sun, 23 Nov 2008 14:37:00 +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/23/t1227451012c26mj94h82v5zg6.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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Dataseries X:

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78,4 0 114,6 0 113,3 0 117 0 99,6 0 99,4 0 101,9 0 115,2 0 108,5 0 113,8 0 121 0 92,2 0 90,2 0 101,5 0 126,6 0 93,9 0 89,8 0 93,4 0 101,5 0 110,4 0 105,9 0 108,4 0 113,9 0 86,1 0 69,4 0 101,2 0 100,5 0 98 0 106,6 0 90,1 0 96,9 0 125,9 0 112 0 100 0 123,9 0 79,8 0 83,4 0 113,6 0 112,9 0 104 0 109,9 0 99 0 106,3 0 128,9 0 111,1 0 102,9 0 130 0 87 0 87,5 0 117,6 0 103,4 0 110,8 0 112,6 0 102,5 0 112,4 0 135,6 0 105,1 0 127,7 0 137 0 91 0 90,5 0 122,4 0 123,3 0 124,3 0 120 0 118,1 0 119 0 142,7 0 123,6 0 129,6 0 151,6 0 110,4 1 99,2 1 130,5 1 136,2 1 129,7 1 128 1 121,6 1 135,8 1 143,8 1 147,5 1 136,2 1 156,6 1 123,3 1 100,4 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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Investeringsgoederen[t] = + 108.423943661972 + 20.0903420523139`Wel(1)_geen(0)_financiële_crisis`[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) 108.423943661972 1.895532 57.1998 0 0 `Wel(1)_geen(0)_financiële_crisis` 20.0903420523139 4.670641 4.3014 4.6e-05 2.3e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.426946313838733 R-squared 0.182283154900482 Adjusted R-squared 0.172431144718560 F-TEST (value) 18.5021281479149 F-TEST (DF numerator) 1 F-TEST (DF denominator) 83 p-value 4.60484024791263e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 15.9720337060253 Sum Squared Residuals 21173.7864386318 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 78.4 108.423943661972 -30.023943661972 2 114.6 108.423943661972 6.17605633802817 3 113.3 108.423943661972 4.87605633802817 4 117 108.423943661972 8.57605633802817 5 99.6 108.423943661972 -8.82394366197183 6 99.4 108.423943661972 -9.02394366197182 7 101.9 108.423943661972 -6.52394366197182 8 115.2 108.423943661972 6.77605633802817 9 108.5 108.423943661972 0.0760563380281716 10 113.8 108.423943661972 5.37605633802817 11 121 108.423943661972 12.5760563380282 12 92.2 108.423943661972 -16.2239436619718 13 90.2 108.423943661972 -18.2239436619718 14 101.5 108.423943661972 -6.92394366197183 15 126.6 108.423943661972 18.1760563380282 16 93.9 108.423943661972 -14.5239436619718 17 89.8 108.423943661972 -18.6239436619718 18 93.4 108.423943661972 -15.0239436619718 19 101.5 108.423943661972 -6.92394366197183 20 110.4 108.423943661972 1.97605633802818 21 105.9 108.423943661972 -2.52394366197182 22 108.4 108.423943661972 -0.0239436619718227 23 113.9 108.423943661972 5.47605633802818 24 86.1 108.423943661972 -22.3239436619718 25 69.4 108.423943661972 -39.0239436619718 26 101.2 108.423943661972 -7.22394366197183 27 100.5 108.423943661972 -7.92394366197183 28 98 108.423943661972 -10.4239436619718 29 106.6 108.423943661972 -1.82394366197183 30 90.1 108.423943661972 -18.3239436619718 31 96.9 108.423943661972 -11.5239436619718 32 125.9 108.423943661972 17.4760563380282 33 112 108.423943661972 3.57605633802817 34 100 108.423943661972 -8.42394366197183 35 123.9 108.423943661972 15.4760563380282 36 79.8 108.423943661972 -28.6239436619718 37 83.4 108.423943661972 -25.0239436619718 38 113.6 108.423943661972 5.17605633802817 39 112.9 108.423943661972 4.47605633802818 40 104 108.423943661972 -4.42394366197183 41 109.9 108.423943661972 1.47605633802818 42 99 108.423943661972 -9.42394366197183 43 106.3 108.423943661972 -2.12394366197183 44 128.9 108.423943661972 20.4760563380282 45 111.1 108.423943661972 2.67605633802817 46 102.9 108.423943661972 -5.52394366197182 47 130 108.423943661972 21.5760563380282 48 87 108.423943661972 -21.4239436619718 49 87.5 108.423943661972 -20.9239436619718 50 117.6 108.423943661972 9.17605633802817 51 103.4 108.423943661972 -5.02394366197182 52 110.8 108.423943661972 2.37605633802817 53 112.6 108.423943661972 4.17605633802817 54 102.5 108.423943661972 -5.92394366197183 55 112.4 108.423943661972 3.97605633802818 56 135.6 108.423943661972 27.1760563380282 57 105.1 108.423943661972 -3.32394366197183 58 127.7 108.423943661972 19.2760563380282 59 137 108.423943661972 28.5760563380282 60 91 108.423943661972 -17.4239436619718 61 90.5 108.423943661972 -17.9239436619718 62 122.4 108.423943661972 13.9760563380282 63 123.3 108.423943661972 14.8760563380282 64 124.3 108.423943661972 15.8760563380282 65 120 108.423943661972 11.5760563380282 66 118.1 108.423943661972 9.67605633802817 67 119 108.423943661972 10.5760563380282 68 142.7 108.423943661972 34.2760563380282 69 123.6 108.423943661972 15.1760563380282 70 129.6 108.423943661972 21.1760563380282 71 151.6 108.423943661972 43.1760563380282 72 110.4 128.514285714286 -18.1142857142857 73 99.2 128.514285714286 -29.3142857142857 74 130.5 128.514285714286 1.98571428571429 75 136.2 128.514285714286 7.68571428571427 76 129.7 128.514285714286 1.18571428571427 77 128 128.514285714286 -0.514285714285714 78 121.6 128.514285714286 -6.91428571428572 79 135.8 128.514285714286 7.2857142857143 80 143.8 128.514285714286 15.2857142857143 81 147.5 128.514285714286 18.9857142857143 82 136.2 128.514285714286 7.68571428571427 83 156.6 128.514285714286 28.0857142857143 84 123.3 128.514285714286 -5.21428571428572 85 100.4 128.514285714286 -28.1142857142857

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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Software written by Ed van Stee & Patrick Wessa

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