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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 08:50:53 -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/t11975601535fiyqakdczc0xw5.htm/, Retrieved Thu, 13 Dec 2007 16:35:54 +0100

User-defined keywords:

multiple regression

Dataseries X:

» Textbox « » Textfile « » CSV «

103.1 98.6 98.1 98.6 0 100.6 98 101.1 98 0 103.1 106.8 111.1 106.8 0 95.5 96.6 93.3 96.7 0 90.5 100.1 100 100.2 0 90.9 107.7 108 107.7 0 88.8 91.5 70.4 92 0 90.7 97.8 75.4 98.4 0 94.3 107.4 105.5 107.4 0 104.6 117.5 112.3 117.7 0 111.1 105.6 102.5 105.7 0 110.8 97.4 93.5 97.5 0 107.2 99.5 86.7 99.9 1 99 98 95.2 98.2 1 99 104.3 103.8 104.5 1 91 100.6 97 100.8 1 96.2 101.1 95.5 101.5 1 96.9 103.9 101 103.9 1 96.2 96.9 67.5 99.6 1 100.1 95.5 64 98.4 1 99 108.4 106.7 112.7 1 115.4 117 100.6 118.4 1 106.9 103.8 101.2 108.1 1 107.1 100.8 93.1 105.4 1 99.3 110.6 84.2 114.6 1 99.2 104 85.8 106.9 1 108.3 112.6 91.8 115.9 1 105.6 107.3 92.4 109.8 1 99.5 98.9 80.3 101.8 1 107.4 109.8 79.7 114.2 1 93.1 104.9 62.5 110.8 1 88.1 102.2 57.1 108.4 1 110.7 123.9 100.8 127.5 1 113.1 124.9 100.7 128.6 1 99.6 112.7 86.2 116.6 1 93.6 121.9 83.2 127.4 1 98.6 100.6 71.7 105 1 99.6 104.3 77.5 108.3 1 114.3 120.4 89.8 125 1 107.8 107.5 80.3 111.6 1 101.2 102.9 78.7 106.5 1 112.5 125.6 93.8 130.3 1 100.5 107.5 57.6 115 1 93.9 108.8 60.6 116.1 1 116.2 128.4 91 134 1 112 121.1 85.3 126.5 1 106.4 119.5 77.4 125.8 1 95.7 128.7 77.3 136.4 1 96 108.7 68.3 114.9 1 95.8 105.5 69.9 110.9 1 103 119.8 81.7 125.5 1 102.2 111.3 75.1 116.8 1 98.4 110.6 69.9 116.8 1 111.4 120.1 84 125.5 1 86.6 97.5 54.3 104.2 1 91.3 107.7 60 115.1 1 107.9 127.3 89.9 132.8 1 101.8 117.2 77 123.3 1 104.4 119.8 85.3 124.8 1 93.4 116.2 77.6 122 1 100.1 111 69.2 117.4 1 98.5 112.4 75.5 117.9 1 112.9 130.6 85.7 137.4 1 101.4 109.1 72.2 114.6 1 107.1 118.8 79.9 124.7 1 110.8 123.9 85.3 129.6 1 90.3 101.6 52.2 109.4 1 95.5 112.8 61.2 120.9 1 111.4 128 82.4 134.9 1 113 129.6 85.4 136.3 1 107.5 125.8 78.2 133.2 1 95.9 119.5 70.2 127.2 1 106.3 115.7 70.2 122.7 1 105.2 113.6 69.3 120.5 1 117.2 129.7 77.5 137.8 1 106.9 112 66.1 119.1 1 108.2 116.8 69 124.3 1 110 126.3 75.3 134.3 1 96.1 112.9 58.2 121.7 1 100.6 115.9 59.7 125 1

Text written by user:

invoering euro

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 6 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation intermediair-goederen[t] = + 63.2918547561732 + 0.492112301221743`totale-consumptie`[t] + 0.069106408222602`Duurzame-consumptiegoederen`[t] -0.246532951311145`Niet-duurzame-consumptiegoederen`[t] + 1.81049508054877`invoering-Euro`[t] + 4.20172076779845M1[t] + 2.26857772228726M2[t] + 7.14366835956165M3[t] + 3.63110271774098M4[t] + 2.16895492885366M5[t] + 4.79576035750822M6[t] -1.77454089871045M7[t] -1.66808691604056M8[t] + 4.56736297935084M9[t] + 7.82975549476553M10[t] + 5.91401219955562M11[t] + 0.0521337471754658t + 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) 63.2918547561732 18.809609 3.3649 0.001308 0.000654 `totale-consumptie` 0.492112301221743 0.959305 0.513 0.609754 0.304877 `Duurzame-consumptiegoederen` 0.069106408222602 0.150071 0.4605 0.646749 0.323375 `Niet-duurzame-consumptiegoederen` -0.246532951311145 0.882686 -0.2793 0.780931 0.390465 `invoering-Euro` 1.81049508054877 2.473339 0.732 0.46688 0.23344 M1 4.20172076779845 3.396405 1.2371 0.220638 0.110319 M2 2.26857772228726 3.448961 0.6578 0.513091 0.256545 M3 7.14366835956165 3.418018 2.09 0.04066 0.02033 M4 3.63110271774098 3.449421 1.0527 0.296513 0.148256 M5 2.16895492885366 3.407965 0.6364 0.526797 0.263399 M6 4.79576035750822 3.401471 1.4099 0.163485 0.081742 M7 -1.77454089871045 4.488736 -0.3953 0.693933 0.346967 M8 -1.66808691604056 4.149851 -0.402 0.689072 0.344536 M9 4.56736297935084 3.7672 1.2124 0.229885 0.114943 M10 7.82975549476553 3.760792 2.0819 0.041416 0.020708 M11 5.91401219955562 3.364982 1.7575 0.083688 0.041844 t 0.0521337471754658 0.089333 0.5836 0.56158 0.28079 Multiple Linear Regression - Regression Statistics Multiple R 0.741721604215162 R-squared 0.550150938159513 Adjusted R-squared 0.435903557374627 F-TEST (value) 4.81543589340908 F-TEST (DF numerator) 16 F-TEST (DF denominator) 63 p-value 3.02267090046549e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.65892758359492 Sum Squared Residuals 2017.47806797140 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 103.1 98.5391718189693 4.56082818103073 2 100.6 96.718134135355 3.88186586464502 3 103.1 104.497520881244 -1.39752088124411 4 95.5 97.2774322560174 -1.77743225601737 5 90.5 97.189958874084 -6.68995887408404 6 90.9 102.312805670147 -11.4128056701465 7 88.8 89.0945852677263 -0.294585267726265 8 90.7 91.1212016479903 -0.421201647990273 9 94.3 101.994369707986 -7.69436970798589 10 104.6 108.209864390325 -3.60986439032454 11 111.1 102.771271072904 8.3287289270964 12 110.8 94.2736842772531 16.5263157227469 13 107.2 100.309867046281 6.89013295371897 14 99 98.6971997832338 0.302800216766244 15 99 105.765889182835 -6.76588918283475 16 91 100.926890117607 -9.92689011760664 17 96.2 99.486699548254 -3.28669954825395 18 96.9 103.331959329582 -6.43195932958242 19 96.2 92.1140327271678 4.08596727283221 20 100.1 91.637630348097 8.46236965190303 21 99 103.69888510378 -4.69888510378004 22 115.4 109.418790244246 5.98120975575422 23 106.9 103.640051563523 3.25994843647731 24 107.1 96.4077132694143 10.6922867305857 25 99.3 102.601118151118 -3.30111815111762 26 99.2 99.4810416429704 -0.281041642970379 27 108.3 106.836273705463 1.46372629453747 28 105.6 102.312961462274 3.28703853772636 29 99.5 97.9052801612948 1.59471983870518 30 107.4 102.84977097925 4.55022902074993 31 93.1 93.5698350072495 -0.469835007249489 32 88.1 92.6182240025408 -4.51822400254083 33 110.7 107.895815250904 2.80418474909566 34 113.1 111.424356927452 1.67564307254827 35 99.6 105.513329801018 -5.91332980101804 36 93.6 101.309009421050 -7.70900942104974 37 98.6 99.8084863348103 -1.20848633481026 38 99.6 99.3355509793593 0.264449020640698 39 114.3 108.918691947721 5.38130805227891 40 107.8 101.75704203677 6.04295796322997 41 101.2 99.2300592079688 1.96994079203116 42 112.5 108.255970144488 4.24402985551156 43 100.5 94.100872160734 6.39912783926596 44 93.9 94.8353388603932 -0.935338860393201 45 116.2 108.456218588404 7.74378141159617 46 112 109.63341566004 2.36658433995998 47 106.4 106.60905887101 -0.209058871010030 48 95.7 102.654453665150 -6.95445366514951 49 96 101.744562934875 -5.74456293487478 50 95.8 99.3854963310302 -3.58549633103023 51 103 108.566001150835 -5.56600115083498 52 102.2 102.611349077943 -0.411349077942749 53 98.4 100.497503102618 -2.09750310261814 54 111.4 106.681072819586 4.71892718041355 55 86.6 92.239858841648 -5.63985884164799 56 91.3 95.1246894015325 -3.82468940153247 57 107.9 108.760322515694 -0.860322515694005 58 101.8 108.555104907329 -6.75510490732889 59 104.4 108.174771103752 -3.77477110375184 60 93.4 100.699461287331 -7.29946128733058 61 100.1 102.947889582913 -2.84788958291286 62 98.5 102.067941402434 -3.56794140243439 63 112.9 111.849102482423 1.05089751757684 64 101.4 102.496270890399 -1.09627089039948 65 107.1 103.90188270561 3.19811729438999 66 110.8 108.255757760648 2.54424223935164 67 90.3 93.4560294386773 -3.1560294386773 68 95.5 96.9131036761314 -1.41310367613142 69 111.4 108.694388833232 2.7056111667681 70 113 112.658467870609 0.341532129390953 71 107.5 109.191517587794 -1.69151758779381 72 95.9 101.155678079803 -5.25567807980271 73 106.3 104.648904131034 1.65109586896583 74 105.2 102.214635725617 2.98536427438304 75 117.2 111.366520649479 5.83347935052061 76 106.9 103.01805415899 3.8819458410099 77 108.2 102.888616400170 5.3113835998298 78 110 108.212663296298 1.78733670370228 79 96.1 97.0247865567971 -0.92478655679712 80 100.6 97.9498120633148 2.65018793668517

Charts produced by software:

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Parameters:

par1 = FALSE ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 2 ; par9 = 0 ;

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

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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We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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