seatbelt3CG2

*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 08:00:12 -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/t12274524635lxohs4wh0lg1dv.htm/, Retrieved Sun, 23 Nov 2008 15:01:03 +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/t12274524635lxohs4wh0lg1dv.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}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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Original text written by user:

IsPrivate?

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User-defined keywords:

Dataseries X:

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97,8 0 107,4 0 117,5 0 105,6 0 97,4 0 99,5 0 98 0 104,3 0 100,6 0 101,1 0 103,9 0 96,9 0 95,5 0 108,4 0 117 0 103,8 0 100,8 0 110,6 0 104 0 112,6 0 107,3 0 98,9 0 109,8 0 104,9 0 102,2 0 123,9 0 124,9 0 112,7 0 121,9 0 100,6 0 104,3 0 120,4 0 107,5 0 102,9 0 125,6 0 107,5 0 108,8 0 128,4 0 121,1 0 119,5 0 128,7 0 108,7 0 105,5 0 119,8 0 111,3 0 110,6 0 120,1 0 97,5 0 107,7 0 127,3 0 117,2 0 119,8 0 116,2 0 111 0 112,4 0 130,6 0 109,1 0 118,8 0 123,9 0 101,6 0 112,8 0 128 0 129,6 0 125,8 0 119,5 0 115,7 0 113,6 0 129,7 0 112 0 116,8 0 127 0 112,1 1 114,2 1 121,1 1 131,6 1 125 1 120,4 1 117,7 1 117,5 1 120,6 1 127,5 1 112,3 1 124,5 1 115,2 1 105,4 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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Consumptiegoederen[t] = + 92.5783032666992 -4.01552901023891`Wel(1)_geen(0)_financiële_crisis`[t] + 1.73044145132453M1[t] + 17.8169165447749M2[t] + 19.5892887615797M3[t] + 12.6330895498131M4[t] + 11.3054617666179M5[t] + 5.14926255485129M6[t] + 3.65020620022753M7[t] + 15.1797212741752M8[t] + 5.93780777669429M9[t] + 3.66732285064196M10[t] + 13.8682664960182M11[t] + 0.284770640338047t + 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) 92.5783032666992 2.20249 42.0335 0 0 `Wel(1)_geen(0)_financiële_crisis` -4.01552901023891 1.934446 -2.0758 0.041535 0.020767 M1 1.73044145132453 2.593436 0.6672 0.506782 0.253391 M2 17.8169165447749 2.686586 6.6318 0 0 M3 19.5892887615797 2.685509 7.2944 0 0 M4 12.6330895498131 2.684749 4.7055 1.2e-05 6e-06 M5 11.3054617666179 2.684308 4.2117 7.3e-05 3.7e-05 M6 5.14926255485129 2.684184 1.9184 0.059085 0.029543 M7 3.65020620022753 2.684379 1.3598 0.178197 0.089099 M8 15.1797212741752 2.684891 5.6538 0 0 M9 5.93780777669429 2.685722 2.2109 0.030267 0.015133 M10 3.66732285064196 2.68687 1.3649 0.176593 0.088296 M11 13.8682664960182 2.688335 5.1587 2e-06 1e-06 t 0.284770640338047 0.029221 9.7455 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.881771504579187 R-squared 0.777520986287843 Adjusted R-squared 0.73678539222787 F-TEST (value) 19.0870172445048 F-TEST (DF numerator) 13 F-TEST (DF denominator) 71 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.00612210608242 Sum Squared Residuals 1779.34935641150 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 97.8 94.593515358362 3.20648464163802 2 107.4 110.964761092150 -3.56476109215017 3 117.5 113.021903949293 4.47809605070698 4 105.6 106.350475377864 -0.750475377864452 5 97.4 105.307618235007 -7.9076182350073 6 99.5 99.4361896635787 0.0638103364212654 7 98 98.221903949293 -0.221903949293019 8 104.3 110.036189663579 -5.73618966357873 9 100.6 101.079046806436 -0.479046806435882 10 101.1 99.0933325207216 2.00666747927841 11 103.9 109.579046806436 -5.67904680643587 12 96.9 95.9955509507557 0.904449049244283 13 95.5 98.0107630424183 -2.51076304241829 14 108.4 114.382008776207 -5.98200877620671 15 117 116.439151633350 0.560848366650421 16 103.8 109.767723061921 -5.96772306192101 17 100.8 108.724865919064 -7.92486591906387 18 110.6 102.853437347635 7.7465626523647 19 104 101.639151633350 2.36084836665042 20 112.6 113.453437347635 -0.8534373476353 21 107.3 104.496294490492 2.80370550950756 22 98.9 102.510580204778 -3.61058020477815 23 109.8 112.996294490492 -3.19629449049244 24 104.9 99.4127986348123 5.48720136518773 25 102.2 101.428010726475 0.771989273525143 26 123.9 117.799256460263 6.10074353973672 27 124.9 119.856399317406 5.04360068259387 28 112.7 113.184970745978 -0.484970745977566 29 121.9 112.142113603120 9.75788639687958 30 100.6 106.270685031692 -5.67068503169186 31 104.3 105.056399317406 -0.756399317406144 32 120.4 116.870685031692 3.52931496830816 33 107.5 107.913542174549 -0.413542174548996 34 102.9 105.927827888835 -3.02782788883471 35 125.6 116.413542174549 9.186457825451 36 107.5 102.830046318869 4.66995368113116 37 108.8 104.845258410531 3.95474158946858 38 128.4 121.216504144320 7.18349585568016 39 121.1 123.273647001463 -2.17364700146271 40 119.5 116.602218430034 2.89778156996587 41 128.7 115.559361287177 13.140638712823 42 108.7 109.687932715748 -0.987932715748414 43 105.5 108.473647001463 -2.9736470014627 44 119.8 120.287932715748 -0.487932715748415 45 111.3 111.330789858606 -0.0307898586055590 46 110.6 109.345075572891 1.25492442710872 47 120.1 119.830789858606 0.269210141394436 48 97.5 106.247294002925 -8.7472940029254 49 107.7 108.262506094588 -0.562506094587979 50 127.3 124.633751828376 2.66624817162359 51 117.2 126.690894685519 -9.49089468551926 52 119.8 120.019466114091 -0.219466114090695 53 116.2 118.976608971234 -2.77660897123355 54 111 113.105180399805 -2.10518039980498 55 112.4 111.890894685519 0.509105314480739 56 130.6 123.705180399805 6.89481960019502 57 109.1 114.748037542662 -5.64803754266212 58 118.8 112.762323256948 6.03767674305216 59 123.9 123.248037542662 0.651962457337885 60 101.6 109.664541686982 -8.06454168698197 61 112.8 111.679753778645 1.12024622135546 62 128 128.050999512433 -0.0509995124329651 63 129.6 130.108142369576 -0.508142369575828 64 125.8 123.436713798147 2.36328620185275 65 119.5 122.39385665529 -2.89385665529010 66 115.7 116.522428083862 -0.822428083861532 67 113.6 115.308142369576 -1.70814236957582 68 129.7 127.122428083862 2.57757191613846 69 112 118.165285226719 -6.16528522671867 70 116.8 116.179570941004 0.620429058995612 71 127 126.665285226719 0.334714773281321 72 112.1 109.066260360800 3.03373963920038 73 114.2 111.081472452462 3.11852754753782 74 121.1 127.452718186251 -6.35271818625062 75 131.6 129.509861043393 2.09013895660653 76 125 122.838432471965 2.1615675280351 77 120.4 121.795575329108 -1.39557532910775 78 117.7 115.924146757679 1.77585324232082 79 117.5 114.709861043393 2.79013895660653 80 120.6 126.524146757679 -5.92414675767919 81 127.5 117.567003900536 9.93299609946367 82 112.3 115.581289614822 -3.28128961482205 83 124.5 126.067003900536 -1.56700390053633 84 115.2 112.483508044856 2.71649195514383 85 105.4 114.498720136519 -9.09872013651875

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 = 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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