7

*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, 21 Dec 2008 06:40:29 -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/Dec/21/t1229866877kdrh0gc0v2lfdsb.htm/, Retrieved Sun, 21 Dec 2008 14:41:25 +0100

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/Dec/21/t1229866877kdrh0gc0v2lfdsb.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}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

7

Dataseries X:

» Textbox « » Textfile « » CSV «

99984 0 99981 0 99972 0 99989 0 99996 0 99991 0 99988 0 99990 0 99998 0 99987 0 100000 0 100000 0 100004 0 100007 0 100005 0 100002 0 99998 0 100006 0 99997 0 100001 0 100000 0 99993 0 99994 0 99996 0 99996 0 99998 0 100002 0 99995 0 99985 0 99984 0 99982 0 99987 0 99977 0 99990 0 99990 0 99994 0 99997 0 99996 0 99993 0 99993 0 99993 0 99997 0 100000 0 99995 0 99997 0 100003 0 100002 0 99993 0 99999 1 100000 1 99997 1 100004 1 100002 1 100003 1 100000 1 99990 1 99990 1 99991 1 99978 1 99984 1 99982 1 99986 1 99988 1 99983 1 99977 1 99972 1 99969 1 99979 1 99981 1 99978 1 99978 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 Economie[t] = + 99994.125 -6.69021739130032Kredietcrisis[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) 99994.125 1.242721 80463.8822 0 0 Kredietcrisis -6.69021739130032 2.183427 -3.0641 0.003114 0.001557 Multiple Linear Regression - Regression Statistics Multiple R 0.346078716489396 R-squared 0.119770478006947 Adjusted R-squared 0.107013528412845 F-TEST (value) 9.38864554754686 F-TEST (DF numerator) 1 F-TEST (DF denominator) 69 p-value 0.00311367226414694 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 8.60982096290564 Sum Squared Residuals 5114.90217391696 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 99984 99994.1250000002 -10.1250000001896 2 99981 99994.125 -13.1249999999960 3 99972 99994.125 -22.1249999999960 4 99989 99994.125 -5.12499999999597 5 99996 99994.125 1.87500000000403 6 99991 99994.125 -3.12499999999597 7 99988 99994.125 -6.12499999999597 8 99990 99994.125 -4.12499999999597 9 99998 99994.125 3.87500000000403 10 99987 99994.125 -7.12499999999597 11 1e+05 99994.125 5.87500000000403 12 1e+05 99994.125 5.87500000000403 13 100004 99994.125 9.87500000000403 14 100007 99994.125 12.8750000000040 15 100005 99994.125 10.8750000000040 16 100002 99994.125 7.87500000000403 17 99998 99994.125 3.87500000000403 18 100006 99994.125 11.8750000000040 19 99997 99994.125 2.87500000000403 20 100001 99994.125 6.87500000000403 21 1e+05 99994.125 5.87500000000403 22 99993 99994.125 -1.12499999999597 23 99994 99994.125 -0.124999999995967 24 99996 99994.125 1.87500000000403 25 99996 99994.125 1.87500000000403 26 99998 99994.125 3.87500000000403 27 100002 99994.125 7.87500000000403 28 99995 99994.125 0.875000000004033 29 99985 99994.125 -9.12499999999597 30 99984 99994.125 -10.1249999999960 31 99982 99994.125 -12.1249999999960 32 99987 99994.125 -7.12499999999597 33 99977 99994.125 -17.1249999999960 34 99990 99994.125 -4.12499999999597 35 99990 99994.125 -4.12499999999597 36 99994 99994.125 -0.124999999995967 37 99997 99994.125 2.87500000000403 38 99996 99994.125 1.87500000000403 39 99993 99994.125 -1.12499999999597 40 99993 99994.125 -1.12499999999597 41 99993 99994.125 -1.12499999999597 42 99997 99994.125 2.87500000000403 43 1e+05 99994.125 5.87500000000403 44 99995 99994.125 0.875000000004033 45 99997 99994.125 2.87500000000403 46 100003 99994.125 8.87500000000403 47 100002 99994.125 7.87500000000403 48 99993 99994.125 -1.12499999999597 49 99999 99987.4347826087 11.5652173913043 50 1e+05 99987.4347826087 12.5652173913043 51 99997 99987.4347826087 9.56521739130435 52 100004 99987.4347826087 16.5652173913044 53 100002 99987.4347826087 14.5652173913043 54 100003 99987.4347826087 15.5652173913043 55 1e+05 99987.4347826087 12.5652173913043 56 99990 99987.4347826087 2.56521739130435 57 99990 99987.4347826087 2.56521739130435 58 99991 99987.4347826087 3.56521739130435 59 99978 99987.4347826087 -9.43478260869565 60 99984 99987.4347826087 -3.43478260869565 61 99982 99987.4347826087 -5.43478260869565 62 99986 99987.4347826087 -1.43478260869565 63 99988 99987.4347826087 0.565217391304348 64 99983 99987.4347826087 -4.43478260869565 65 99977 99987.4347826087 -10.4347826086957 66 99972 99987.4347826087 -15.4347826086957 67 99969 99987.4347826087 -18.4347826086956 68 99979 99987.4347826087 -8.43478260869565 69 99981 99987.4347826087 -6.43478260869565 70 99978 99987.4347826087 -9.43478260869565 71 99978 99987.4347826087 -9.43478260869565

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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