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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 09:00:01 -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/t1197560696anb7lps2n7iamkn.htm/, Retrieved Thu, 13 Dec 2007 16:45:07 +0100

User-defined keywords:

multiple regression

Dataseries X:

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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 0 99 98 95.2 98.2 0 99 104.3 103.8 104.5 0 91 100.6 97 100.8 0 96.2 101.1 95.5 101.5 0 96.9 103.9 101 103.9 0 96.2 96.9 67.5 99.6 0 100.1 95.5 64 98.4 0 99 108.4 106.7 112.7 0 115.4 117 100.6 118.4 0 106.9 103.8 101.2 108.1 0 107.1 100.8 93.1 105.4 0 99.3 110.6 84.2 114.6 0 99.2 104 85.8 106.9 0 108.3 112.6 91.8 115.9 0 105.6 107.3 92.4 109.8 0 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:

aanval USA in Irak 1 mei 2003

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 intermediaire-goederen[t] = + 68.0873734438617 + 0.189856395390054`totale-consumptiegoederen`[t] -0.0184033439239251`duurzame-consumptiegoederen`[t] + 0.096680713353948`niet-duurzame-consumptiegoederen`[t] -2.87863091100782`inval-USA-in-Irak`[t] + 4.25369055093826M1[t] + 2.88273763365504M2[t] + 7.90784012799898M3[t] + 4.24573766642082M4[t] + 3.0642567361827M5[t] + 5.90145014519717M6[t] -3.17162982247658M7[t] -3.1057799907332M8[t] + 5.7594812951929M9[t] + 8.92848470101635M10[t] + 6.6561488976943M11[t] + 0.0374113990247136t + 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) 68.0873734438617 18.532509 3.6739 0.000495 0.000247 `totale-consumptiegoederen` 0.189856395390054 0.911374 0.2083 0.835652 0.417826 `duurzame-consumptiegoederen` -0.0184033439239251 0.170058 -0.1082 0.914166 0.457083 `niet-duurzame-consumptiegoederen` 0.096680713353948 0.843388 0.1146 0.9091 0.45455 `inval-USA-in-Irak` -2.87863091100782 3.013434 -0.9553 0.343095 0.171547 M1 4.25369055093826 3.382275 1.2576 0.213163 0.106582 M2 2.88273763365504 3.437678 0.8386 0.404881 0.20244 M3 7.90784012799898 3.388468 2.3338 0.022813 0.011406 M4 4.24573766642082 3.431883 1.2371 0.220625 0.110312 M5 3.0642567361827 3.445471 0.8894 0.377194 0.188597 M6 5.90145014519717 3.430978 1.72 0.090333 0.045166 M7 -3.17162982247658 4.566401 -0.6946 0.489886 0.244943 M8 -3.1057799907332 4.254788 -0.7299 0.468127 0.234063 M9 5.7594812951929 3.818093 1.5085 0.136433 0.068217 M10 8.92848470101635 3.761503 2.3736 0.020675 0.010337 M11 6.6561488976943 3.388917 1.9641 0.053935 0.026967 t 0.0374113990247136 0.089278 0.419 0.676608 0.338304 Multiple Linear Regression - Regression Statistics Multiple R 0.743506799184985 R-squared 0.552802360434302 Adjusted R-squared 0.439228356735077 F-TEST (value) 4.86733180506935 F-TEST (DF numerator) 16 F-TEST (DF denominator) 63 p-value 2.58953877430024e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.64222600287052 Sum Squared Residuals 2005.58699885050 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 103.1 98.8256662770466 4.27433372295339 2 100.6 97.2649924617696 3.33500753823039 3 103.1 104.664999472846 -1.56499947284622 4 95.5 98.4548774942852 -2.95487749428521 5 90.5 98.1903854393855 -7.69038543938552 6 90.9 103.085777451152 -12.1857774511523 7 88.8 90.148513809067 -1.34851380906700 8 90.7 91.9746101766381 -1.27461017663809 9 94.3 103.016090025409 -8.71609002540881 10 104.6 109.010723032559 -4.4107230325595 11 111.1 103.536691733328 7.5633082666724 12 110.8 94.7339800382725 16.0660199617275 13 107.2 99.7809568692868 7.41904313071322 14 99 97.8418451218881 1.15815487811189 15 99 104.551274042598 -5.55127404259823 16 91 99.9915384163747 -8.99153841637466 17 96.2 99.03767859809 -2.83767859808993 18 96.9 102.574696633689 -5.67469663368915 19 96.2 92.4108182513393 3.78918174866075 20 100.1 92.1966753762703 7.90332462372973 21 99 104.145206977163 -5.14520697716264 22 115.4 109.647727246419 5.75227275358128 23 106.9 103.899845069073 3.00015493092736 24 107.1 96.599567543961 10.5004324560390 25 99.3 103.804514492526 -4.5045144925258 26 99.2 100.444033921589 -1.24403392158924 27 108.3 107.899019171954 0.400980828045647 28 105.6 102.667294856020 2.93270514397982 29 99.5 96.4990354471704 3.0009645528296 30 107.4 102.652957816904 4.74704218309552 31 93.1 92.6748160009323 0.425183999067729 32 88.1 92.132809309287 -4.03280930928695 33 110.7 106.197741269787 4.50225873021319 34 113.1 109.702201589107 3.39779841089323 35 99.6 104.257709087700 -4.65770908770031 36 93.6 100.485012162614 -6.88501216261364 37 98.6 98.7781633667652 -0.178163366765164 38 99.6 98.3593974707591 1.24060252924088 39 114.3 107.866806112654 6.4331938873457 40 107.8 100.672277757904 7.12772224209647 41 101.2 98.191242520069 3.00875747993099 42 112.5 107.398697988035 5.10130201196487 43 100.5 94.1136147985568 6.38638520144321 44 93.9 94.5148280962495 -0.614828096249517 45 116.2 108.309809244594 7.89019075540626 46 112 109.510066073306 2.48993392669372 47 106.4 107.049081354036 -0.649081354036092 48 95.7 103.203678588899 -7.50367858889925 49 96 101.784647389267 -5.78464738926660 50 95.8 99.4273972020658 -3.62739720206584 51 103 108.399236506178 -5.39923650617759 52 102.2 102.441105946527 -0.241105946527237 53 98.4 101.259834326945 -2.85983432694520 54 111.4 106.519709948042 4.8802900519581 55 86.6 91.6805669636791 -5.08056696367913 56 91.3 94.6692841426174 -3.36928414261744 57 107.9 108.454130820253 -0.554130820252828 58 101.8 109.061932391418 -7.26193239141758 59 104.4 107.312907930597 -2.91290793059671 60 93.4 99.8816871593461 -6.4816871593461 61 100.1 102.895392660814 -2.79539266081363 62 98.5 101.760049386057 -3.26004938605743 63 112.9 111.975509477903 0.924490522096986 64 101.4 102.313030792966 -0.913030792966373 65 107.1 103.845337753697 3.25466224630285 66 110.8 108.062567616471 2.73743238352924 67 90.3 93.4493017047557 -3.14930170475568 68 95.5 96.6251526721475 -1.12515267214746 69 111.4 109.377021662795 2.02297833720484 70 113 112.967349667191 0.0326503328088348 71 107.5 109.843764825267 -2.34376482526664 72 95.9 101.596074506907 -5.69607450690742 73 106.3 104.730658944295 1.56934105570456 74 105.2 102.802284435871 2.39771556412935 75 117.2 112.443155215866 4.7568447841337 76 106.9 103.859874735923 3.04012526407719 77 108.2 104.076485914643 4.1235140853572 78 110 109.605592545706 0.394407454293737 79 96.1 97.122368471670 -1.02236847166987 80 100.6 98.0866402267903 2.51335977320973

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')

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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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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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