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Q3 - metaalverwerking - monthly dummies

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

Title produced by software: Multiple Regression

Date of computation: Sun, 18 Nov 2007 08:36:57 -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/18/t1195399950vk0saoqov44p8mv.htm/, Retrieved Sun, 18 Nov 2007 16:32:41 +0100

User-defined keywords:

Dataseries X:

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106.8 0 113.7 0 102.5 0 96.6 0 92.1 0 95.6 0 102.3 0 98.6 0 98.2 0 104.5 0 84 0 73.8 0 103.9 0 106 0 97.2 0 102.6 0 89 0 93.8 0 116.7 0 106.8 0 98.5 0 118.7 0 90 0 91.9 1 113.3 1 113.1 1 104.1 1 108.7 1 96.7 1 101 1 116.9 1 105.8 1 99 1 129.4 1 83 1 88.9 1 115.9 1 104.2 1 113.4 1 112.2 1 100.8 1 107.3 1 126.6 1 102.9 1 117.9 1 128.8 1 87.5 1 93.8 1 122.7 1 126.2 1 124.6 1 116.7 1 115.2 1 111.1 1 129.9 1 113.3 1 118.5 1 133.5 1 102.1 1 102.4 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation y[t] = + 80.6502857142857 + 11.8871428571428x[t] + 24.7374285714286M1[t] + 24.8574285714286M2[t] + 20.5774285714286M3[t] + 19.5774285714286M4[t] + 10.9774285714285M5[t] + 13.9774285714286M6[t] + 30.6974285714285M7[t] + 17.6974285714285M8[t] + 18.6374285714286M9[t] + 35.1974285714286M10[t] + 1.53742857142857M11[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) 80.6502857142857 3.36062 23.9986 0 0 x 11.8871428571428 1.811925 6.5605 0 0 M1 24.7374285714286 4.303084 5.7488 1e-06 0 M2 24.8574285714286 4.303084 5.7767 1e-06 0 M3 20.5774285714286 4.303084 4.782 1.8e-05 9e-06 M4 19.5774285714286 4.303084 4.5496 3.8e-05 1.9e-05 M5 10.9774285714285 4.303084 2.5511 0.014055 0.007027 M6 13.9774285714286 4.303084 3.2482 0.002147 0.001073 M7 30.6974285714285 4.303084 7.1338 0 0 M8 17.6974285714285 4.303084 4.1127 0.000156 7.8e-05 M9 18.6374285714286 4.303084 4.3312 7.7e-05 3.9e-05 M10 35.1974285714286 4.303084 8.1796 0 0 M11 1.53742857142857 4.303084 0.3573 0.722478 0.361239 Multiple Linear Regression - Regression Statistics Multiple R 0.883269342311904 R-squared 0.780164731068104 Adjusted R-squared 0.724036577298258 F-TEST (value) 13.899704135418 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 1.14690479335877e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.77960283421276 Sum Squared Residuals 2160.26168571429 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 106.8 105.387714285714 1.41228571428576 2 113.7 105.507714285714 8.19228571428573 3 102.5 101.227714285714 1.27228571428569 4 96.6 100.227714285714 -3.62771428571431 5 92.1 91.6277142857143 0.47228571428566 6 95.6 94.6277142857143 0.972285714285704 7 102.3 111.347714285714 -9.04771428571428 8 98.6 98.3477142857143 0.252285714285688 9 98.2 99.2877142857143 -1.08771428571426 10 104.5 115.847714285714 -11.3477142857143 11 84 82.1877142857143 1.81228571428573 12 73.8 80.6502857142857 -6.8502857142857 13 103.9 105.387714285714 -1.48771428571430 14 106 105.507714285714 0.492285714285705 15 97.2 101.227714285714 -4.02771428571428 16 102.6 100.227714285714 2.37228571428571 17 89 91.6277142857143 -2.62771428571428 18 93.8 94.6277142857143 -0.827714285714281 19 116.7 111.347714285714 5.35228571428571 20 106.8 98.3477142857143 8.45228571428572 21 98.5 99.2877142857143 -0.787714285714292 22 118.7 115.847714285714 2.85228571428571 23 90 82.1877142857143 7.81228571428571 24 91.9 92.5374285714286 -0.637428571428575 25 113.3 117.274857142857 -3.97485714285716 26 113.1 117.394857142857 -4.29485714285715 27 104.1 113.114857142857 -9.01485714285714 28 108.7 112.114857142857 -3.41485714285713 29 96.7 103.514857142857 -6.81485714285712 30 101 106.514857142857 -5.51485714285714 31 116.9 123.234857142857 -6.33485714285714 32 105.8 110.234857142857 -4.43485714285714 33 99 111.174857142857 -12.1748571428571 34 129.4 127.734857142857 1.66514285714285 35 83 94.0748571428571 -11.0748571428571 36 88.9 92.5374285714286 -3.63742857142858 37 115.9 117.274857142857 -1.37485714285715 38 104.2 117.394857142857 -13.1948571428571 39 113.4 113.114857142857 0.285142857142872 40 112.2 112.114857142857 0.0851428571428692 41 100.8 103.514857142857 -2.71485714285713 42 107.3 106.514857142857 0.785142857142858 43 126.6 123.234857142857 3.36514285714284 44 102.9 110.234857142857 -7.33485714285713 45 117.9 111.174857142857 6.72514285714286 46 128.8 127.734857142857 1.06514285714286 47 87.5 94.0748571428571 -6.57485714285715 48 93.8 92.5374285714286 1.26257142857142 49 122.7 117.274857142857 5.42514285714285 50 126.2 117.394857142857 8.80514285714285 51 124.6 113.114857142857 11.4851428571429 52 116.7 112.114857142857 4.58514285714287 53 115.2 103.514857142857 11.6851428571429 54 111.1 106.514857142857 4.58514285714286 55 129.9 123.234857142857 6.66514285714286 56 113.3 110.234857142857 3.06514285714286 57 118.5 111.174857142857 7.32514285714285 58 133.5 127.734857142857 5.76514285714285 59 102.1 94.0748571428571 8.02514285714285 60 102.4 92.5374285714286 9.86257142857143

Charts produced by software:

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Parameters:

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')

Copyright

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Software written by Ed van Stee & Patrick Wessa

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