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WS6 Q3 G6 eigen reeks lin. Trend

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

Title produced by software: Multiple Regression

Date of computation: Thu, 15 Nov 2007 04:05:24 -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/Nov/15/t119512443903gwqxiei6s7asy.htm/, Retrieved Thu, 15 Nov 2007 12:00:40 +0100

User-defined keywords:

Dataseries X:

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120.3 0 133.4 0 109.4 0 93.2 0 91.2 0 99.2 0 108.2 0 101.5 0 106.9 0 104.4 0 77.9 0 60 0 99.5 0 95 0 105.6 0 102.5 0 93.3 0 97.3 0 127 0 111.7 0 96.4 0 133 0 72.2 0 95.8 0 124.1 0 127.6 0 110.7 0 104.6 0 112.7 0 115.3 0 139.4 0 119 0 97.4 0 154 0 81.5 0 88.8 0 127.7 1 105.1 1 114.9 1 106.4 1 104.5 1 121.6 1 141.4 1 99 1 126.7 1 134.1 1 81.3 1 88.6 1 132.7 1 132.9 1 134.4 1 103.7 1 119.7 1 115 1 132.9 1 108.5 1 113.9 1 142.9 1 95.2 1 93 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 5 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 67.555 -7.35000000000001X[t] + 41.9220833333333M1[t] + 39.2891666666667M2[t] + 34.91625M3[t] + 21.4233333333333M4[t] + 23.0504166666667M5[t] + 27.8775M6[t] + 47.4045833333333M7[t] + 24.9916666666667M8[t] + 24.73875M9[t] + 49.5858333333333M10[t] -3.04708333333333M11[t] + 0.572916666666667t + 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) 67.555 6.026079 11.2104 0 0 X -7.35000000000001 5.411579 -1.3582 0.181025 0.090513 M1 41.9220833333333 6.71741 6.2408 0 0 M2 39.2891666666667 6.679154 5.8824 0 0 M3 34.91625 6.644352 5.255 4e-06 2e-06 M4 21.4233333333333 6.613059 3.2395 0.002226 0.001113 M5 23.0504166666667 6.585323 3.5003 0.001044 0.000522 M6 27.8775 6.561191 4.2488 0.000104 5.2e-05 M7 47.4045833333333 6.540702 7.2476 0 0 M8 24.9916666666667 6.52389 3.8308 0.000385 0.000193 M9 24.73875 6.510784 3.7997 0.000424 0.000212 M10 49.5858333333333 6.501407 7.6269 0 0 M11 -3.04708333333333 6.495774 -0.4691 0.641223 0.320612 t 0.572916666666667 0.156219 3.6674 0.000634 0.000317 Multiple Linear Regression - Regression Statistics Multiple R 0.877750586007237 R-squared 0.770446091236047 Adjusted R-squared 0.705572160498408 F-TEST (value) 11.8760507105984 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 1.12051257161738e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 10.2677492135834 Sum Squared Residuals 4849.627 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 120.3 110.050000000000 10.2499999999999 2 133.4 107.99 25.41 3 109.4 104.19 5.21 4 93.2 91.27 1.93000000000001 5 91.2 93.47 -2.27000000000001 6 99.2 98.87 0.33000000000002 7 108.2 118.97 -10.77 8 101.5 97.13 4.37000000000001 9 106.9 97.45 9.45000000000001 10 104.4 122.87 -18.47 11 77.9 70.81 7.09 12 60 74.43 -14.43 13 99.5 116.925 -17.4250000000000 14 95 114.865 -19.865 15 105.6 111.065 -5.46500000000001 16 102.5 98.145 4.355 17 93.3 100.345 -7.045 18 97.3 105.745 -8.445 19 127 125.845 1.15500000000000 20 111.7 104.005 7.695 21 96.4 104.325 -7.925 22 133 129.745 3.25500000000000 23 72.2 77.685 -5.48499999999999 24 95.8 81.305 14.495 25 124.1 123.8 0.300000000000029 26 127.6 121.74 5.85999999999999 27 110.7 117.94 -7.24000000000001 28 104.6 105.02 -0.420000000000013 29 112.7 107.22 5.48 30 115.3 112.62 2.67999999999999 31 139.4 132.72 6.68 32 119 110.88 8.12 33 97.4 111.2 -13.8 34 154 136.62 17.38 35 81.5 84.56 -3.06 36 88.8 88.18 0.62 37 127.7 123.325 4.37500000000004 38 105.1 121.265 -16.165 39 114.9 117.465 -2.56499999999999 40 106.4 104.545 1.85500000000000 41 104.5 106.745 -2.245 42 121.6 112.145 9.455 43 141.4 132.245 9.155 44 99 110.405 -11.405 45 126.7 110.725 15.975 46 134.1 136.145 -2.04500000000002 47 81.3 84.085 -2.78500000000001 48 88.6 87.705 0.894999999999997 49 132.7 130.2 2.50000000000002 50 132.9 128.14 4.76 51 134.4 124.34 10.06 52 103.7 111.42 -7.72 53 119.7 113.62 6.08 54 115 119.02 -4.02000000000000 55 132.9 139.12 -6.22000000000001 56 108.5 117.28 -8.78 57 113.9 117.6 -3.70000000000001 58 142.9 143.02 -0.120000000000002 59 95.2 90.96 4.24 60 93 94.58 -1.58

Charts produced by software:

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Parameters:

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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