seatbelt3CG

*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 07:55:53 -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/t1227452239b1lbitu1xfrh3nn.htm/, Retrieved Sun, 23 Nov 2008 14:57:27 +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/t1227452239b1lbitu1xfrh3nn.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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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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Consumptiegoederen[t] = + 112.170422535211 + 6.76529175050303`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) 112.170422535211 1.125322 99.6785 0 0 `Wel(1)_geen(0)_financiële_crisis` 6.76529175050303 2.772824 2.4399 0.016823 0.008411 Multiple Linear Regression - Regression Statistics Multiple R 0.258692699003801 R-squared 0.066921912517871 Adjusted R-squared 0.0556800078494116 F-TEST (value) 5.95289806233894 F-TEST (DF numerator) 1 F-TEST (DF denominator) 83 p-value 0.016822656077361 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 9.48213286856506 Sum Squared Residuals 7462.60003018111 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 97.8 112.170422535212 -14.3704225352120 2 107.4 112.170422535211 -4.77042253521125 3 117.5 112.170422535211 5.32957746478874 4 105.6 112.170422535211 -6.57042253521126 5 97.4 112.170422535211 -14.7704225352113 6 99.5 112.170422535211 -12.6704225352113 7 98 112.170422535211 -14.1704225352113 8 104.3 112.170422535211 -7.87042253521126 9 100.6 112.170422535211 -11.5704225352113 10 101.1 112.170422535211 -11.0704225352113 11 103.9 112.170422535211 -8.27042253521125 12 96.9 112.170422535211 -15.2704225352113 13 95.5 112.170422535211 -16.6704225352113 14 108.4 112.170422535211 -3.77042253521125 15 117 112.170422535211 4.82957746478874 16 103.8 112.170422535211 -8.37042253521126 17 100.8 112.170422535211 -11.3704225352113 18 110.6 112.170422535211 -1.57042253521126 19 104 112.170422535211 -8.17042253521126 20 112.6 112.170422535211 0.429577464788739 21 107.3 112.170422535211 -4.87042253521126 22 98.9 112.170422535211 -13.2704225352113 23 109.8 112.170422535211 -2.37042253521126 24 104.9 112.170422535211 -7.27042253521125 25 102.2 112.170422535211 -9.97042253521125 26 123.9 112.170422535211 11.7295774647887 27 124.9 112.170422535211 12.7295774647887 28 112.7 112.170422535211 0.529577464788748 29 121.9 112.170422535211 9.72957746478875 30 100.6 112.170422535211 -11.5704225352113 31 104.3 112.170422535211 -7.87042253521126 32 120.4 112.170422535211 8.22957746478875 33 107.5 112.170422535211 -4.67042253521126 34 102.9 112.170422535211 -9.27042253521125 35 125.6 112.170422535211 13.4295774647887 36 107.5 112.170422535211 -4.67042253521126 37 108.8 112.170422535211 -3.37042253521126 38 128.4 112.170422535211 16.2295774647888 39 121.1 112.170422535211 8.92957746478874 40 119.5 112.170422535211 7.32957746478874 41 128.7 112.170422535211 16.5295774647887 42 108.7 112.170422535211 -3.47042253521125 43 105.5 112.170422535211 -6.67042253521126 44 119.8 112.170422535211 7.62957746478874 45 111.3 112.170422535211 -0.870422535211258 46 110.6 112.170422535211 -1.57042253521126 47 120.1 112.170422535211 7.92957746478874 48 97.5 112.170422535211 -14.6704225352113 49 107.7 112.170422535211 -4.47042253521125 50 127.3 112.170422535211 15.1295774647887 51 117.2 112.170422535211 5.02957746478875 52 119.8 112.170422535211 7.62957746478874 53 116.2 112.170422535211 4.02957746478875 54 111 112.170422535211 -1.17042253521126 55 112.4 112.170422535211 0.229577464788750 56 130.6 112.170422535211 18.4295774647887 57 109.1 112.170422535211 -3.07042253521126 58 118.8 112.170422535211 6.62957746478874 59 123.9 112.170422535211 11.7295774647887 60 101.6 112.170422535211 -10.5704225352113 61 112.8 112.170422535211 0.629577464788742 62 128 112.170422535211 15.8295774647887 63 129.6 112.170422535211 17.4295774647887 64 125.8 112.170422535211 13.6295774647887 65 119.5 112.170422535211 7.32957746478874 66 115.7 112.170422535211 3.52957746478875 67 113.6 112.170422535211 1.42957746478874 68 129.7 112.170422535211 17.5295774647887 69 112 112.170422535211 -0.170422535211255 70 116.8 112.170422535211 4.62957746478874 71 127 112.170422535211 14.8295774647887 72 112.1 118.935714285714 -6.83571428571429 73 114.2 118.935714285714 -4.73571428571428 74 121.1 118.935714285714 2.16428571428571 75 131.6 118.935714285714 12.6642857142857 76 125 118.935714285714 6.06428571428571 77 120.4 118.935714285714 1.46428571428572 78 117.7 118.935714285714 -1.23571428571428 79 117.5 118.935714285714 -1.43571428571429 80 120.6 118.935714285714 1.66428571428571 81 127.5 118.935714285714 8.56428571428571 82 112.3 118.935714285714 -6.63571428571429 83 124.5 118.935714285714 5.56428571428571 84 115.2 118.935714285714 -3.73571428571428 85 105.4 118.935714285714 -13.5357142857143

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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