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paper berekening zonder trend

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

Title produced by software: Multiple Regression

Date of computation: Wed, 21 Nov 2007 03:56:43 -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/21/t11956421687xkuayqpksb0iw4.htm/, Retrieved Wed, 21 Nov 2007 11:49:28 +0100

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Dataseries X:

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98,6 0 98 0 106,8 0 96,6 0 100,1 0 107,7 0 91,5 0 97,8 0 107,4 0 117,5 0 105,6 0 97,4 0 99,5 0 98 0 104,3 0 100,6 0 101,1 0 103,9 0 96,9 0 95,5 0 108,4 0 117 0 103,8 0 100,8 0 110,6 0 104 0 112,6 0 107,3 0 98,9 0 109,8 0 104,9 0 102,2 0 123,9 0 124,9 0 112,7 0 121,9 0 100,6 0 104,3 1 120,4 1 107,5 1 102,9 1 125,6 1 107,5 1 108,8 1 128,4 1 121,1 1 119,5 1 128,7 1 108,7 1 105,5 1 119,8 1 111,3 1 110,6 1 120,1 1 97,5 1 107,7 1 127,3 1 117,2 1 119,8 1 116,2 1 111 1 112,4 1 130,6 1 109,1 1 118,8 1 123,9 1 101,6 1 112,8 1 128 1 129,6 1 125,8 1 119,5 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 8 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation x[t] = + 108.755295950156 + 10.6560747663551y[t] -7.47398753894077M1[t] -10.3833333333333M2[t] + 1.66666666666666M3[t] -8.68333333333334M4[t] -8.68333333333334M5[t] + 1.08333333333333M6[t] -14.1M7[t] -9.95M8[t] + 6.48333333333334M9[t] + 7.13333333333333M10[t] + 0.449999999999995M11[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) 108.755295950156 2.358358 46.1148 0 0 y 10.6560747663551 1.313808 8.1108 0 0 M1 -7.47398753894077 3.210702 -2.3278 0.02337 0.011685 M2 -10.3833333333333 3.203227 -3.2415 0.001957 0.000979 M3 1.66666666666666 3.203227 0.5203 0.604796 0.302398 M4 -8.68333333333334 3.203227 -2.7108 0.008776 0.004388 M5 -8.68333333333334 3.203227 -2.7108 0.008776 0.004388 M6 1.08333333333333 3.203227 0.3382 0.736413 0.368206 M7 -14.1 3.203227 -4.4018 4.6e-05 2.3e-05 M8 -9.95 3.203227 -3.1062 0.002912 0.001456 M9 6.48333333333334 3.203227 2.024 0.047506 0.023753 M10 7.13333333333333 3.203227 2.2269 0.029782 0.014891 M11 0.449999999999995 3.203227 0.1405 0.888757 0.444378 Multiple Linear Regression - Regression Statistics Multiple R 0.866671377162989 R-squared 0.751119275993591 Adjusted R-squared 0.700499467721101 F-TEST (value) 14.8384456920553 F-TEST (DF numerator) 12 F-TEST (DF denominator) 59 p-value 1.15463194561016e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.54815171325898 Sum Squared Residuals 1816.13725856698 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 98.6 101.281308411215 -2.68130841121474 2 98 98.3719626168224 -0.371962616822415 3 106.8 110.421962616822 -3.62196261682244 4 96.6 100.071962616822 -3.47196261682244 5 100.1 100.071962616822 0.0280373831775618 6 107.7 109.838629283489 -2.13862928348910 7 91.5 94.6552959501558 -3.15529595015576 8 97.8 98.8052959501558 -1.00529595015577 9 107.4 115.238629283489 -7.8386292834891 10 117.5 115.888629283489 1.61137071651090 11 105.6 109.205295950156 -3.60529595015577 12 97.4 108.755295950156 -11.3552959501558 13 99.5 101.281308411215 -1.78130841121500 14 98 98.3719626168224 -0.371962616822438 15 104.3 110.421962616822 -6.12196261682243 16 100.6 100.071962616822 0.528037383177566 17 101.1 100.071962616822 1.02803738317756 18 103.9 109.838629283489 -5.9386292834891 19 96.9 94.6552959501558 2.24470404984424 20 95.5 98.8052959501558 -3.30529595015577 21 108.4 115.238629283489 -6.8386292834891 22 117 115.888629283489 1.11137071651090 23 103.8 109.205295950156 -5.40529595015577 24 100.8 108.755295950156 -7.95529595015577 25 110.6 101.281308411215 9.318691588785 26 104 98.3719626168224 5.62803738317756 27 112.6 110.421962616822 2.17803738317756 28 107.3 100.071962616822 7.22803738317757 29 98.9 100.071962616822 -1.17196261682243 30 109.8 109.838629283489 -0.0386292834891033 31 104.9 94.6552959501558 10.2447040498442 32 102.2 98.8052959501558 3.39470404984423 33 123.9 115.238629283489 8.6613707165109 34 124.9 115.888629283489 9.0113707165109 35 112.7 109.205295950156 3.49470404984424 36 121.9 108.755295950156 13.1447040498442 37 100.6 101.281308411215 -0.681308411215001 38 104.3 109.028037383178 -4.72803738317757 39 120.4 121.078037383178 -0.678037383177559 40 107.5 110.728037383178 -3.22803738317756 41 102.9 110.728037383178 -7.82803738317756 42 125.6 120.494704049844 5.10529595015576 43 107.5 105.311370716511 2.1886292834891 44 108.8 109.461370716511 -0.661370716510902 45 128.4 125.894704049844 2.50529595015577 46 121.1 126.544704049844 -5.44470404984424 47 119.5 119.861370716511 -0.361370716510897 48 128.7 119.411370716511 9.28862928348909 49 108.7 111.937383177570 -3.23738317757013 50 105.5 109.028037383178 -3.52803738317757 51 119.8 121.078037383178 -1.27803738317757 52 111.3 110.728037383178 0.571962616822434 53 110.6 110.728037383178 -0.128037383177572 54 120.1 120.494704049844 -0.39470404984424 55 97.5 105.311370716511 -7.8113707165109 56 107.7 109.461370716511 -1.76137071651090 57 127.3 125.894704049844 1.40529595015576 58 117.2 126.544704049844 -9.34470404984423 59 119.8 119.861370716511 -0.0613707165109002 60 116.2 119.411370716511 -3.2113707165109 61 111 111.937383177570 -0.937383177570131 62 112.4 109.028037383178 3.37196261682243 63 130.6 121.078037383178 9.52196261682243 64 109.1 110.728037383178 -1.62803738317757 65 118.8 110.728037383178 8.07196261682243 66 123.9 120.494704049844 3.40529595015577 67 101.6 105.311370716511 -3.71137071651091 68 112.8 109.461370716511 3.3386292834891 69 128 125.894704049844 2.10529595015576 70 129.6 126.544704049844 3.05529595015576 71 125.8 119.861370716511 5.9386292834891 72 119.5 119.411370716511 0.0886292834890977

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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