Q3

*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 15:07:23 -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/24/t1227564539225wxarlnjqj9nr.htm/, Retrieved Mon, 24 Nov 2008 22:09:08 +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/24/t1227564539225wxarlnjqj9nr.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:

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8,4 0 8,4 0 8,4 0 8,6 0 8,9 0 8,8 0 8,3 0 7,5 0 7,2 0 7,5 0 8,8 0 9,3 0 9,3 0 8,7 0 8,2 0 8,3 0 8,5 0 8,6 0 8,6 0 8,2 0 8,1 0 8 0 8,6 1 8,7 1 8,8 1 8,5 1 8,4 1 8,5 1 8,7 1 8,7 1 8,6 1 8,5 1 8,3 1 8,1 1 8,2 1 8,1 1 8,1 1 7,9 1 7,9 1 7,9 1 8 1 8 1 7,9 1 8 1 7,7 1 7,2 1 7,5 1 7,3 1 7 1 7 1 7 1 7,2 1 7,3 1 7,1 1 6,8 1 6,6 1 6,2 1 6,2 1 6,8 1 6,9 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 y[t] = + 9.21361344537814 + 0.872268907563026x[t] -0.131260504201686M1[t] -0.299831932773109M2[t] -0.368403361344537M3[t] -0.196974789915966M4[t] + 0.0344537815126055M5[t] + 0.0458823529411772M6[t] -0.102689075630251M7[t] -0.331260504201680M8[t] -0.539831932773108M9[t] -0.588403361344538M10[t] -0.131428571428571M11[t] -0.0514285714285714t + 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) 9.21361344537814 0.218311 42.204 0 0 x 0.872268907563026 0.208785 4.1778 0.00013 6.5e-05 M1 -0.131260504201686 0.265577 -0.4942 0.623484 0.311742 M2 -0.299831932773109 0.264995 -1.1315 0.263724 0.131862 M3 -0.368403361344537 0.264541 -1.3926 0.170432 0.085216 M4 -0.196974789915966 0.264217 -0.7455 0.45976 0.22988 M5 0.0344537815126055 0.264022 0.1305 0.896743 0.448372 M6 0.0458823529411772 0.263957 0.1738 0.862766 0.431383 M7 -0.102689075630251 0.264022 -0.3889 0.699114 0.349557 M8 -0.331260504201680 0.264217 -1.2537 0.216269 0.108135 M9 -0.539831932773108 0.264541 -2.0406 0.047051 0.023525 M10 -0.588403361344538 0.264995 -2.2204 0.031356 0.015678 M11 -0.131428571428571 0.263057 -0.4996 0.619724 0.309862 t -0.0514285714285714 0.005857 -8.7803 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.867016950491026 R-squared 0.751718392438757 Adjusted R-squared 0.68155185117145 F-TEST (value) 10.7133454045426 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 5.98915250726861e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.415826823795257 Sum Squared Residuals 7.95394957983198 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.4 9.03092436974793 -0.630924369747925 2 8.4 8.8109243697479 -0.410924369747902 3 8.4 8.6909243697479 -0.290924369747898 4 8.6 8.8109243697479 -0.210924369747898 5 8.9 8.9909243697479 -0.0909243697478978 6 8.8 8.9509243697479 -0.150924369747896 7 8.3 8.7509243697479 -0.450924369747897 8 7.5 8.4709243697479 -0.970924369747898 9 7.2 8.2109243697479 -1.01092436974790 10 7.5 8.1109243697479 -0.610924369747899 11 8.8 8.5164705882353 0.283529411764707 12 9.3 8.5964705882353 0.703529411764709 13 9.3 8.41378151260504 0.886218487394966 14 8.7 8.19378151260504 0.506218487394959 15 8.2 8.07378151260504 0.126218487394958 16 8.3 8.19378151260504 0.106218487394959 17 8.5 8.37378151260504 0.126218487394959 18 8.6 8.33378151260504 0.266218487394958 19 8.6 8.13378151260504 0.466218487394958 20 8.2 7.85378151260504 0.346218487394958 21 8.1 7.59378151260504 0.506218487394958 22 8 7.49378151260504 0.506218487394959 23 8.6 8.77159663865546 -0.171596638655462 24 8.7 8.85159663865546 -0.151596638655462 25 8.8 8.6689075630252 0.131092436974797 26 8.5 8.4489075630252 0.0510924369747912 27 8.4 8.32890756302521 0.0710924369747904 28 8.5 8.44890756302521 0.0510924369747898 29 8.7 8.62890756302521 0.0710924369747896 30 8.7 8.5889075630252 0.111092436974790 31 8.6 8.38890756302521 0.21109243697479 32 8.5 8.1089075630252 0.391092436974791 33 8.3 7.84890756302521 0.451092436974791 34 8.1 7.74890756302521 0.35109243697479 35 8.2 8.1544537815126 0.0455462184873946 36 8.1 8.2344537815126 -0.134453781512605 37 8.1 8.05176470588235 0.0482352941176525 38 7.9 7.83176470588235 0.0682352941176479 39 7.9 7.71176470588235 0.188235294117647 40 7.9 7.83176470588235 0.0682352941176468 41 8 8.01176470588235 -0.0117647058823532 42 8 7.97176470588235 0.0282352941176468 43 7.9 7.77176470588235 0.128235294117647 44 8 7.49176470588235 0.508235294117647 45 7.7 7.23176470588235 0.468235294117646 46 7.2 7.13176470588235 0.0682352941176468 47 7.5 7.53731092436975 -0.0373109243697483 48 7.3 7.61731092436975 -0.317310924369749 49 7 7.43462184873949 -0.434621848739491 50 7 7.2146218487395 -0.214621848739496 51 7 7.0946218487395 -0.0946218487394972 52 7.2 7.2146218487395 -0.0146218487394974 53 7.3 7.3946218487395 -0.0946218487394973 54 7.1 7.3546218487395 -0.254621848739497 55 6.8 7.1546218487395 -0.354621848739497 56 6.6 6.8746218487395 -0.274621848739497 57 6.2 6.6146218487395 -0.414621848739497 58 6.2 6.5146218487395 -0.314621848739497 59 6.8 6.9201680672269 -0.120168067226893 60 6.9 7.00016806722689 -0.100168067226892

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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