MR monthly dummies no linear trend

*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: Thu, 09 Dec 2010 16:57:35 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/09/t12919138632qnmy8qr841rlx2.htm/, Retrieved Thu, 09 Dec 2010 17:57:54 +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/2010/Dec/09/t12919138632qnmy8qr841rlx2.htm/}, year = {2010}, } @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 = {2010}, 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:

Dataseries X:

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31514 27071 29462 26105 22397 23843 21705 18089 20764 25316 17704 15548 28029 29383 36438 32034 22679 24319 18004 17537 20366 22782 19169 13807 29743 25591 29096 26482 22405 27044 17970 18730 19684 19785 18479 10698 31956 29506 34506 27165 26736 23691 18157 17328 18205 20995 17382 9367 31124 26551 30651 25859 25100 25778 20418 18688 20424 24776 19814 12738 31566 30111 30019 31934 25826 26835 20205 17789 20520 22518 15572 11509 25447 24090 27786 26195 20516 22759 19028 16971 20036 22485 18730 14538

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 7 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation y[t] = + 12600.7142857143 + 17310.5714285714M1[t] + 14871.1428571429M2[t] + 18536.1428571428M3[t] + 15367M4[t] + 11064.8571428571M5[t] + 12294.8571428572M6[t] + 6754.57142857143M7[t] + 5275.28571428572M8[t] + 7399.14285714286M9[t] + 10064.5714285714M10[t] + 5520.71428571429M11[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) 12600.7142857143 772.408988 16.3135 0 0 M1 17310.5714285714 1092.351266 15.8471 0 0 M2 14871.1428571429 1092.351266 13.6139 0 0 M3 18536.1428571428 1092.351266 16.969 0 0 M4 15367 1092.351266 14.0678 0 0 M5 11064.8571428571 1092.351266 10.1294 0 0 M6 12294.8571428572 1092.351266 11.2554 0 0 M7 6754.57142857143 1092.351266 6.1835 0 0 M8 5275.28571428572 1092.351266 4.8293 7e-06 4e-06 M9 7399.14285714286 1092.351266 6.7736 0 0 M10 10064.5714285714 1092.351266 9.2137 0 0 M11 5520.71428571429 1092.351266 5.054 3e-06 2e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.942751700457095 R-squared 0.888780768714744 Adjusted R-squared 0.87178894171283 F-TEST (value) 52.3063687391958 F-TEST (DF numerator) 11 F-TEST (DF denominator) 72 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2043.60209236161 Sum Squared Residuals 300694284.857143 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 31514 29911.2857142857 1602.71428571434 2 27071 27471.8571428571 -400.85714285711 3 29462 31136.8571428572 -1674.85714285722 4 26105 27967.7142857143 -1862.71428571426 5 22397 23665.5714285714 -1268.57142857144 6 23843 24895.5714285714 -1052.57142857141 7 21705 19355.2857142857 2349.71428571426 8 18089 17876 213.000000000005 9 20764 19999.8571428571 764.142857142866 10 25316 22665.2857142857 2650.71428571428 11 17704 18121.4285714286 -417.428571428569 12 15548 12600.7142857143 2947.28571428571 13 28029 29911.2857142857 -1882.28571428572 14 29383 27471.8571428571 1911.14285714285 15 36438 31136.8571428571 5301.14285714287 16 32034 27967.7142857143 4066.28571428571 17 22679 23665.5714285714 -986.571428571426 18 24319 24895.5714285714 -576.571428571433 19 18004 19355.2857142857 -1351.28571428571 20 17537 17876 -339.000000000001 21 20366 19999.8571428571 366.142857142856 22 22782 22665.2857142857 116.714285714287 23 19169 18121.4285714286 1047.57142857143 24 13807 12600.7142857143 1206.28571428572 25 29743 29911.2857142857 -168.285714285723 26 25591 27471.8571428571 -1880.85714285715 27 29096 31136.8571428571 -2040.85714285713 28 26482 27967.7142857143 -1485.71428571429 29 22405 23665.5714285714 -1260.57142857143 30 27044 24895.5714285714 2148.42857142857 31 17970 19355.2857142857 -1385.28571428571 32 18730 17876 854 33 19684 19999.8571428571 -315.857142857144 34 19785 22665.2857142857 -2880.28571428571 35 18479 18121.4285714286 357.571428571428 36 10698 12600.7142857143 -1902.71428571428 37 31956 29911.2857142857 2044.71428571428 38 29506 27471.8571428571 2034.14285714285 39 34506 31136.8571428571 3369.14285714287 40 27165 27967.7142857143 -802.71428571429 41 26736 23665.5714285714 3070.42857142857 42 23691 24895.5714285714 -1204.57142857143 43 18157 19355.2857142857 -1198.28571428571 44 17328 17876 -548.000000000001 45 18205 19999.8571428571 -1794.85714285714 46 20995 22665.2857142857 -1670.28571428571 47 17382 18121.4285714286 -739.428571428572 48 9367 12600.7142857143 -3233.71428571428 49 31124 29911.2857142857 1212.71428571428 50 26551 27471.8571428571 -920.857142857148 51 30651 31136.8571428571 -485.857142857129 52 25859 27967.7142857143 -2108.71428571429 53 25100 23665.5714285714 1434.42857142857 54 25778 24895.5714285714 882.428571428567 55 20418 19355.2857142857 1062.71428571429 56 18688 17876 812 57 20424 19999.8571428571 424.142857142856 58 24776 22665.2857142857 2110.71428571429 59 19814 18121.4285714286 1692.57142857143 60 12738 12600.7142857143 137.285714285716 61 31566 29911.2857142857 1654.71428571428 62 30111 27471.8571428571 2639.14285714285 63 30019 31136.8571428571 -1117.85714285713 64 31934 27967.7142857143 3966.28571428571 65 25826 23665.5714285714 2160.42857142857 66 26835 24895.5714285714 1939.42857142857 67 20205 19355.2857142857 849.714285714289 68 17789 17876 -87.0000000000007 69 20520 19999.8571428571 520.142857142856 70 22518 22665.2857142857 -147.285714285713 71 15572 18121.4285714286 -2549.42857142857 72 11509 12600.7142857143 -1091.71428571428 73 25447 29911.2857142857 -4464.28571428572 74 24090 27471.8571428571 -3381.85714285715 75 27786 31136.8571428571 -3350.85714285713 76 26195 27967.7142857143 -1772.71428571429 77 20516 23665.5714285714 -3149.57142857143 78 22759 24895.5714285714 -2136.57142857143 79 19028 19355.2857142857 -327.285714285711 80 16971 17876 -905.000000000001 81 20036 19999.8571428571 36.1428571428556 82 22485 22665.2857142857 -180.285714285713 83 18730 18121.4285714286 608.571428571428 84 14538 12600.7142857143 1937.28571428572

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/09/t12919138632qnmy8qr841rlx2/1bds91291913847.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t12919138632qnmy8qr841rlx2/1bds91291913847.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t12919138632qnmy8qr841rlx2/2m4ru1291913847.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t12919138632qnmy8qr841rlx2/2m4ru1291913847.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t12919138632qnmy8qr841rlx2/3m4ru1291913847.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t12919138632qnmy8qr841rlx2/3m4ru1291913847.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t12919138632qnmy8qr841rlx2/4m4ru1291913847.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t12919138632qnmy8qr841rlx2/4m4ru1291913847.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t12919138632qnmy8qr841rlx2/5xd9x1291913847.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t12919138632qnmy8qr841rlx2/5xd9x1291913847.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t12919138632qnmy8qr841rlx2/6xd9x1291913847.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t12919138632qnmy8qr841rlx2/6xd9x1291913847.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t12919138632qnmy8qr841rlx2/7748i1291913847.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t12919138632qnmy8qr841rlx2/7748i1291913847.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t12919138632qnmy8qr841rlx2/8748i1291913847.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t12919138632qnmy8qr841rlx2/8748i1291913847.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t12919138632qnmy8qr841rlx2/9748i1291913847.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t12919138632qnmy8qr841rlx2/9748i1291913847.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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