seatbelt_3.2.

*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 07:44:53 -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/t1227451558unsbsh8j82uvpwl.htm/, Retrieved Sun, 23 Nov 2008 14:46:10 +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/t1227451558unsbsh8j82uvpwl.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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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] = + 79.1305704534373 + 11.9203071672355`Wel(1)_geen(0)_financiële_crisis`[t] -6.51526592718996M1[t] + 23.2423472289940M2[t] + 25.0826883227694M3[t] + 19.3087437022591M4[t] + 17.4347990817488M5[t] + 11.1037116040956M6[t] + 17.9297669835853M7[t] + 36.0415366487892M8[t] + 23.0818777425647M9[t] + 23.5079331220543M10[t] + 39.7197027872583M11[t] + 0.27394462051032t + 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) 79.1305704534373 3.412073 23.1914 0 0 `Wel(1)_geen(0)_financiële_crisis` 11.9203071672355 2.996823 3.9776 0.000166 8.3e-05 M1 -6.51526592718996 4.017722 -1.6216 0.109315 0.054658 M2 23.2423472289940 4.162029 5.5844 0 0 M3 25.0826883227694 4.16036 6.029 0 0 M4 19.3087437022591 4.159184 4.6424 1.5e-05 8e-06 M5 17.4347990817488 4.1585 4.1926 7.8e-05 3.9e-05 M6 11.1037116040956 4.158309 2.6702 0.00939 0.004695 M7 17.9297669835853 4.15861 4.3115 5.1e-05 2.6e-05 M8 36.0415366487892 4.159404 8.6651 0 0 M9 23.0818777425647 4.160691 5.5476 0 0 M10 23.5079331220543 4.162469 5.6476 0 0 M11 39.7197027872583 4.164739 9.5371 0 0 t 0.27394462051032 0.045268 6.0516 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.913826884329267 R-squared 0.835079574522935 Adjusted R-squared 0.804882876900374 F-TEST (value) 27.6546655849881 F-TEST (DF numerator) 13 F-TEST (DF denominator) 71 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 7.7554292617078 Sum Squared Residuals 4270.41449536811 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 78.4 72.8892491467577 5.51075085324226 2 114.6 102.920806923452 11.679193076548 3 113.3 105.035092637738 8.26490736226228 4 117 99.5350926377377 17.4649073622623 5 99.6 97.9350926377377 1.66490736226234 6 99.4 91.8779497805948 7.52205021940522 7 101.9 98.9779497805948 2.92205021940517 8 115.2 117.363664066309 -2.1636640663091 9 108.5 104.677949780595 3.82205021940515 10 113.8 105.377949780595 8.4220502194052 11 121 121.863664066309 -0.863664066309158 12 92.2 82.4179058995612 9.78209410043881 13 90.2 76.1765845928815 14.0234154071185 14 101.5 106.208142369576 -4.70814236957579 15 126.6 108.322428083862 18.2775719161385 16 93.9 102.822428083862 -8.92242808386152 17 89.8 101.222428083862 -11.4224280838615 18 93.4 95.1652852267187 -1.76528522671867 19 101.5 102.265285226719 -0.76528522671867 20 110.4 120.650999512433 -10.2509995124330 21 105.9 107.965285226719 -2.06528522671866 22 108.4 108.665285226719 -0.265285226718667 23 113.9 125.150999512433 -11.2509995124329 24 86.1 85.705241345685 0.394758654314984 25 69.4 79.4639200390054 -10.0639200390054 26 101.2 109.495477815700 -8.29547781569966 27 100.5 111.609763529985 -11.1097635299854 28 98 106.109763529985 -8.10976352998537 29 106.6 104.509763529985 2.09023647001462 30 90.1 98.4526206728425 -8.35262067284252 31 96.9 105.552620672843 -8.65262067284251 32 125.9 123.938334958557 1.9616650414432 33 112 111.252620672843 0.747379327157493 34 100 111.952620672843 -11.9526206728425 35 123.9 128.438334958557 -4.53833495855679 36 79.8 88.9925767918089 -9.19257679180886 37 83.4 82.7512554851292 0.648744514870806 38 113.6 112.782813261824 0.817186738176487 39 112.9 114.897098976109 -1.99709897610920 40 104 109.397098976109 -5.39709897610921 41 109.9 107.797098976109 2.10290102389079 42 99 101.739956118966 -2.73995611896636 43 106.3 108.839956118966 -2.53995611896636 44 128.9 127.225670404681 1.67432959531936 45 111.1 114.539956118966 -3.43995611896636 46 102.9 115.239956118966 -12.3399561189664 47 130 131.725670404681 -1.72567040468064 48 87 92.2799122379327 -5.2799122379327 49 87.5 86.038590931253 1.46140906874696 50 117.6 116.070148707947 1.52985129205264 51 103.4 118.184434422233 -14.7844344222330 52 110.8 112.684434422233 -1.88443442223306 53 112.6 111.084434422233 1.51556557776693 54 102.5 105.027291565090 -2.52729156509021 55 112.4 112.127291565090 0.272708434909803 56 135.6 130.513005850804 5.0869941491955 57 105.1 117.827291565090 -12.7272915650902 58 127.7 118.527291565090 9.1727084349098 59 137 135.013005850804 1.98699414919552 60 91 95.5672476840565 -4.56724768405654 61 90.5 89.3259263773769 1.17407362262311 62 122.4 119.357484154071 3.04251584592881 63 123.3 121.471769868357 1.82823013164310 64 124.3 115.971769868357 8.3282301316431 65 120 114.371769868357 5.6282301316431 66 118.1 108.314627011214 9.78537298878594 67 119 115.414627011214 3.58537298878596 68 142.7 133.800341296928 8.89965870307165 69 123.6 121.114627011214 2.48537298878596 70 129.6 121.814627011214 7.78537298878595 71 151.6 138.300341296928 13.2996587030717 72 110.4 110.774890297416 -0.374890297415874 73 99.2 104.533568990736 -5.33356899073622 74 130.5 134.565126767431 -4.06512676743053 75 136.2 136.679412481716 -0.47941248171624 76 129.7 131.179412481716 -1.47941248171624 77 128 129.579412481716 -1.57941248171624 78 121.6 123.522269624573 -1.92226962457339 79 135.8 130.622269624573 5.17773037542662 80 143.8 149.007983910288 -5.20798391028766 81 147.5 136.322269624573 11.1777303754266 82 136.2 137.022269624573 -0.822269624573396 83 156.6 153.507983910288 3.09201608971234 84 123.3 114.062225743540 9.23777425646027 85 100.4 107.82090443686 -7.42090443686006

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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