dummy

*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: Mon, 24 Nov 2008 17:19:35 -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/25/t1227572465kc1xfml8k61k1ld.htm/, Retrieved Tue, 25 Nov 2008 00:21:14 +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/25/t1227572465kc1xfml8k61k1ld.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?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

10.400 1 10.800 1 10.600 1 11.200 1 11.800 1 11.300 1 10.800 1 10.600 1 10.900 1 10.200 1 10.100 1 10.100 1 10.000 1 10.100 0 10.300 0 10.900 0 10.700 0 10.500 0 10.600 0 10.600 0 10.800 0 10.700 0 10.400 0 10.400 0 10.600 0 10.900 0 10.900 0 10.500 0 10.100 0 10.200 0 10.300 0 10.600 0 10.800 0 10.500 0 10.500 0 10.500 0 10.400 0 10.500 0 10.700 0 11.000 0 11.600 0 11.600 0 11.700 0 11.700 0 11.800 0 12.100 0 11.800 0 11.300 0 11.200 0 11.700 0 11.900 0 12.600 0 12.500 0 12.800 0 13.500 0 13.900 0 14.500 0 14.100 0 13.200 0 13.100 0 13.300 0 13.200 0 13.200 0 14.000 0 14.300 0 14.300 0 14.500 0 14.500 1 13.300 1 12.700 1 12.700 1 12.900 1 12.500 1 12.600 0 13.200 0 13.600 0 14.000 0 14.100 0 14.200 0 13.900 0 13.800 0 14.100 0 14.700 0 14.400 0 14.700 0 14.500 0 14.700 0 14.900 0 15.400 0 16.100 0 16.300 0

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 Y[t] = + 12.3555555555556 -0.91345029239766D[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) 12.3555555555556 0.1954 63.2322 0 0 D -0.91345029239766 0.42763 -2.1361 0.035418 0.017709 Multiple Linear Regression - Regression Statistics Multiple R 0.220833767021393 R-squared 0.0487675526568587 Adjusted R-squared 0.0380795476305312 F-TEST (value) 4.56283025098988 F-TEST (DF numerator) 1 F-TEST (DF denominator) 89 p-value 0.0354183230423479 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.65802133857879 Sum Squared Residuals 244.664093567251 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 10.4 11.4421052631579 -1.04210526315786 2 10.8 11.4421052631579 -0.642105263157902 3 10.6 11.4421052631579 -0.842105263157897 4 11.2 11.4421052631579 -0.242105263157898 5 11.8 11.4421052631579 0.357894736842104 6 11.3 11.4421052631579 -0.142105263157896 7 10.8 11.4421052631579 -0.642105263157896 8 10.6 11.4421052631579 -0.842105263157897 9 10.9 11.4421052631579 -0.542105263157896 10 10.2 11.4421052631579 -1.24210526315790 11 10.1 11.4421052631579 -1.34210526315790 12 10.1 11.4421052631579 -1.34210526315790 13 10 11.4421052631579 -1.44210526315790 14 10.1 12.3555555555556 -2.25555555555556 15 10.3 12.3555555555556 -2.05555555555555 16 10.9 12.3555555555556 -1.45555555555556 17 10.7 12.3555555555556 -1.65555555555556 18 10.5 12.3555555555556 -1.85555555555556 19 10.6 12.3555555555556 -1.75555555555556 20 10.6 12.3555555555556 -1.75555555555556 21 10.8 12.3555555555556 -1.55555555555555 22 10.7 12.3555555555556 -1.65555555555556 23 10.4 12.3555555555556 -1.95555555555556 24 10.4 12.3555555555556 -1.95555555555556 25 10.6 12.3555555555556 -1.75555555555556 26 10.9 12.3555555555556 -1.45555555555556 27 10.9 12.3555555555556 -1.45555555555556 28 10.5 12.3555555555556 -1.85555555555556 29 10.1 12.3555555555556 -2.25555555555556 30 10.2 12.3555555555556 -2.15555555555556 31 10.3 12.3555555555556 -2.05555555555555 32 10.6 12.3555555555556 -1.75555555555556 33 10.8 12.3555555555556 -1.55555555555555 34 10.5 12.3555555555556 -1.85555555555556 35 10.5 12.3555555555556 -1.85555555555556 36 10.5 12.3555555555556 -1.85555555555556 37 10.4 12.3555555555556 -1.95555555555556 38 10.5 12.3555555555556 -1.85555555555556 39 10.7 12.3555555555556 -1.65555555555556 40 11 12.3555555555556 -1.35555555555556 41 11.6 12.3555555555556 -0.755555555555556 42 11.6 12.3555555555556 -0.755555555555556 43 11.7 12.3555555555556 -0.655555555555556 44 11.7 12.3555555555556 -0.655555555555556 45 11.8 12.3555555555556 -0.555555555555555 46 12.1 12.3555555555556 -0.255555555555556 47 11.8 12.3555555555556 -0.555555555555555 48 11.3 12.3555555555556 -1.05555555555555 49 11.2 12.3555555555556 -1.15555555555556 50 11.7 12.3555555555556 -0.655555555555556 51 11.9 12.3555555555556 -0.455555555555555 52 12.6 12.3555555555556 0.244444444444444 53 12.5 12.3555555555556 0.144444444444445 54 12.8 12.3555555555556 0.444444444444445 55 13.5 12.3555555555556 1.14444444444444 56 13.9 12.3555555555556 1.54444444444444 57 14.5 12.3555555555556 2.14444444444444 58 14.1 12.3555555555556 1.74444444444444 59 13.2 12.3555555555556 0.844444444444444 60 13.1 12.3555555555556 0.744444444444444 61 13.3 12.3555555555556 0.944444444444445 62 13.2 12.3555555555556 0.844444444444444 63 13.2 12.3555555555556 0.844444444444444 64 14 12.3555555555556 1.64444444444444 65 14.3 12.3555555555556 1.94444444444444 66 14.3 12.3555555555556 1.94444444444444 67 14.5 12.3555555555556 2.14444444444444 68 14.5 11.4421052631579 3.0578947368421 69 13.3 11.4421052631579 1.85789473684210 70 12.7 11.4421052631579 1.25789473684210 71 12.7 11.4421052631579 1.25789473684210 72 12.9 11.4421052631579 1.45789473684210 73 12.5 11.4421052631579 1.05789473684210 74 12.6 12.3555555555556 0.244444444444444 75 13.2 12.3555555555556 0.844444444444444 76 13.6 12.3555555555556 1.24444444444444 77 14 12.3555555555556 1.64444444444444 78 14.1 12.3555555555556 1.74444444444444 79 14.2 12.3555555555556 1.84444444444444 80 13.9 12.3555555555556 1.54444444444444 81 13.8 12.3555555555556 1.44444444444445 82 14.1 12.3555555555556 1.74444444444444 83 14.7 12.3555555555556 2.34444444444444 84 14.4 12.3555555555556 2.04444444444444 85 14.7 12.3555555555556 2.34444444444444 86 14.5 12.3555555555556 2.14444444444444 87 14.7 12.3555555555556 2.34444444444444 88 14.9 12.3555555555556 2.54444444444444 89 15.4 12.3555555555556 3.04444444444444 90 16.1 12.3555555555556 3.74444444444445 91 16.3 12.3555555555556 3.94444444444445

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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