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Paper_MR_output2

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Thu, 13 Dec 2007 07:58:25 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Dec/13/t119755698355552y1b94nyoog.htm/, Retrieved Thu, 13 Dec 2007 15:43:03 +0100

User-defined keywords:

Dataseries X:

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36409 0 33163 0 34122 0 35225 0 28249 0 30374 0 26311 0 22069 0 23651 0 28628 0 23187 0 14727 0 43080 0 32519 0 39657 0 33614 0 28671 0 34243 0 27336 0 22916 0 24537 0 26128 0 22602 0 15744 0 41086 0 39690 0 43129 0 37863 0 35953 0 29133 0 24693 0 22205 0 21725 0 27192 0 21790 0 13253 0 37702 0 30364 0 32609 0 30212 0 29965 0 28352 0 25814 0 22414 0 20506 0 28806 0 22228 0 13971 0 36845 0 35338 0 35022 0 34777 0 26887 0 23970 0 22780 0 17351 0 21382 0 24561 0 17409 0 11514 0 31514 0 27071 0 29462 0 26105 0 22397 0 23843 0 21705 0 18089 0 20764 0 25316 0 17704 0 15548 0 28029 0 29383 0 36438 0 32034 0 22679 0 24319 0 18004 0 17537 0 20366 0 22782 0 19169 0 13807 0 29743 0 25591 0 29096 1 26482 1 22405 1 27044 1 17970 1 18730 1 19684 1 19785 1 18479 1 10698 1

Text written by user:

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 compuational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 7 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation Inschr[t] = + 14166.525 -4070.2Oliecrisis[t] + 21384.475M1[t] + 17473.35M2[t] + 21284.125M3[t] + 18381.25M4[t] + 13493M5[t] + 14002M6[t] + 9418.875M7[t] + 6506.125M8[t] + 7919.125M9[t] + 11742M10[t] + 6663.25M11[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) 14166.525 1245.265409 11.3763 0 0 Oliecrisis -4070.2 1182.286517 -3.4427 0.000905 0.000452 M1 21384.475 1754.859319 12.1859 0 0 M2 17473.35 1754.859319 9.9571 0 0 M3 21284.125 1748.62534 12.1719 0 0 M4 18381.25 1748.62534 10.5118 0 0 M5 13493 1748.62534 7.7163 0 0 M6 14002 1748.62534 8.0074 0 0 M7 9418.875 1748.62534 5.3864 1e-06 0 M8 6506.125 1748.62534 3.7207 0.00036 0.00018 M9 7919.125 1748.62534 4.5288 2e-05 1e-05 M10 11742 1748.62534 6.715 0 0 M11 6663.25 1748.62534 3.8106 0.000265 0.000133 Multiple Linear Regression - Regression Statistics Multiple R 0.894616415750474 R-squared 0.800338531330225 Adjusted R-squared 0.77147181296833 F-TEST (value) 27.7253036280942 F-TEST (DF numerator) 12 F-TEST (DF denominator) 83 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3497.25068097819 Sum Squared Residuals 1015153273.025 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 36409 35550.9999999999 858.000000000051 2 33163 31639.875 1523.125 3 34122 35450.65 -1328.64999999999 4 35225 32547.775 2677.22500000001 5 28249 27659.525 589.475000000004 6 30374 28168.525 2205.47500000001 7 26311 23585.4 2725.6 8 22069 20672.65 1396.35 9 23651 22085.65 1565.35000000000 10 28628 25908.525 2719.475 11 23187 20829.775 2357.225 12 14727 14166.525 560.475000000003 13 43080 35551 7529 14 32519 31639.875 879.124999999999 15 39657 35450.65 4206.35 16 33614 32547.775 1066.225 17 28671 27659.525 1011.475 18 34243 28168.525 6074.475 19 27336 23585.4 3750.6 20 22916 20672.65 2243.35 21 24537 22085.65 2451.35 22 26128 25908.525 219.475 23 22602 20829.775 1772.225 24 15744 14166.525 1577.475 25 41086 35551 5534.99999999999 26 39690 31639.875 8050.125 27 43129 35450.65 7678.35 28 37863 32547.775 5315.225 29 35953 27659.525 8293.475 30 29133 28168.525 964.475 31 24693 23585.4 1107.6 32 22205 20672.65 1532.35 33 21725 22085.65 -360.649999999999 34 27192 25908.525 1283.475 35 21790 20829.775 960.225 36 13253 14166.525 -913.525 37 37702 35551 2150.99999999999 38 30364 31639.875 -1275.875 39 32609 35450.65 -2841.65 40 30212 32547.775 -2335.775 41 29965 27659.525 2305.475 42 28352 28168.525 183.475 43 25814 23585.4 2228.6 44 22414 20672.65 1741.35 45 20506 22085.65 -1579.65 46 28806 25908.525 2897.475 47 22228 20829.775 1398.225 48 13971 14166.525 -195.525000000000 49 36845 35551 1293.99999999999 50 35338 31639.875 3698.125 51 35022 35450.65 -428.650000000003 52 34777 32547.775 2229.22500000000 53 26887 27659.525 -772.525000000001 54 23970 28168.525 -4198.525 55 22780 23585.4 -805.400000000001 56 17351 20672.65 -3321.65 57 21382 22085.65 -703.649999999999 58 24561 25908.525 -1347.525 59 17409 20829.775 -3420.775 60 11514 14166.525 -2652.525 61 31514 35551 -4037.00000000001 62 27071 31639.875 -4568.875 63 29462 35450.65 -5988.65 64 26105 32547.775 -6442.775 65 22397 27659.525 -5262.525 66 23843 28168.525 -4325.525 67 21705 23585.4 -1880.4 68 18089 20672.65 -2583.65 69 20764 22085.65 -1321.65 70 25316 25908.525 -592.525 71 17704 20829.775 -3125.775 72 15548 14166.525 1381.475 73 28029 35551 -7522.00000000001 74 29383 31639.875 -2256.875 75 36438 35450.65 987.349999999998 76 32034 32547.775 -513.775000000001 77 22679 27659.525 -4980.525 78 24319 28168.525 -3849.525 79 18004 23585.4 -5581.4 80 17537 20672.65 -3135.65 81 20366 22085.65 -1719.65 82 22782 25908.525 -3126.525 83 19169 20829.775 -1660.775 84 13807 14166.525 -359.525000000001 85 29743 35551 -5808.00000000001 86 25591 31639.875 -6048.875 87 29096 31380.45 -2284.45 88 26482 28477.575 -1995.575 89 22405 23589.325 -1184.32500000000 90 27044 24098.325 2945.675 91 17970 19515.2 -1545.2 92 18730 16602.45 2127.55 93 19684 18015.45 1668.55 94 19785 21838.325 -2053.32500000000 95 18479 16759.575 1719.425 96 10698 10096.325 601.674999999998

Charts produced by software:

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Parameters:

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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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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