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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: Wed, 05 Dec 2007 14:58:49 -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/05/t1196891162fe3xl3l18imziqf.htm/, Retrieved Wed, 05 Dec 2007 22:46:02 +0100

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Dataseries X:

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106.7 97.3 0 104.8 93.5 110.2 101 0 105.6 94.7 125.9 113.2 0 118.3 112.9 100.1 101 0 89.9 99.2 106.4 105.7 0 90.2 105.6 114.8 113.9 0 107 113 81.3 86.4 0 64.5 83.1 87 96.5 0 92.6 81.1 104.2 103.3 0 95.8 96.9 108 114.9 0 94.3 104.3 105 105.8 0 91.2 97.7 94.5 94.2 0 86.3 102.6 92 98.4 0 77.6 89.9 95.9 99.4 0 82.5 96 108.8 108.8 0 97.7 112.7 103.4 112.6 0 83.3 107.1 102.1 104.4 0 84.2 106.2 110.1 112.2 0 92.8 121 83.2 81.1 0 77.4 101.2 82.7 97.1 0 72.5 83.2 106.8 112.6 0 88.8 105.1 113.7 113.8 0 93.4 113.3 102.5 107.8 0 92.6 99.1 96.6 103.2 0 90.7 100.3 92.1 103.3 0 81.6 93.5 95.6 101.2 0 84.1 98.8 102.3 107.7 0 88.1 106.2 98.6 110.4 0 85.3 98.3 98.2 101.9 0 82.9 102.1 104.5 115.9 0 84.8 117.1 84 89.9 0 71.2 101.5 73.8 88.6 0 68.9 80.5 103.9 117.2 0 94.3 105.9 106 123.9 0 97.6 109.5 97.2 100 0 85.6 97.2 102.6 103.6 0 91.9 114.5 89 94.1 0 75.8 93.5 93.8 98.7 0 79.8 100.9 116.7 119.5 0 99 121.1 106.8 112.7 0 88.5 116.5 98.5 104.4 0 86.7 109.3 118.7 124.7 0 97.9 118.1 90 89.1 0 94.3 108.3 91.9 97 0 72.9 105.4 113.3 121.6 0 91.8 116.2 113.1 118.8 0 93.2 111.2 104.1 114 0 86.5 105.8 108.7 111.5 0 98.9 122.7 96.7 97.2 0 77.2 99.5 101 102.5 0 79.4 107.9 116.9 113.4 0 90.4 124.6 105.8 109.8 0 81.4 115 99 104.9 0 85.8 110.3 129.4 126.1 0 103.6 132.7 83 80 0 73.6 99.7 88.9 96.8 0 75.7 96.5 115.9 117.2 1 99.2 118.7 104.2 112.3 1 88.7 112.9 113.4 117.3 1 94.6 130.5 112.2 111.1 1 98.7 137.9 100.8 102.2 1 84.2 115 107.3 104.3 1 87.7 116.8 126.6 122.9 1 103.3 140.9 102.9 107.6 1 88.2 120.7 117.9 121.3 1 93.4 134.2 128.8 131.5 1 106.3 147.3 87.5 89 1 73.1 112.4 93.8 104.4 1 78.6 107.1 122.7 128.9 1 101.6 128.4 126.2 135.9 1 101.4 137.7 124.6 133.3 1 98.5 135 116.7 121.3 1 99 151 115.2 120.5 1 89.5 137.4 111.1 120.4 1 83.5 132.4 129.9 137.9 1 97.4 161.3 113.3 126.1 1 87.8 139.8 118.5 133.2 1 90.4 146 133.5 146.6 1 97.1 154.6 102.1 103.4 1 79.4 142.1 102.4 117.2 1 85 120.5

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 6 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation Prod[t] = + 27.0323618824689 + 0.587787983114033Tot[t] -0.756057202325195Conjun[t] -0.183109523021441Mach[t] + 0.29725078825593`Elek `[t] + 1.67156483034391M1[t] + 1.10325520722268M2[t] + 2.16417897807062M3[t] + 5.25039459411524M4[t] + 3.32183397931734M5[t] + 6.7371409579682M6[t] -7.536498510513M7[t] + 6.39162180834974M8[t] + 8.88554654979554M9[t] + 10.6224426006966M10[t] + 6.68380905729691M11[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) 27.0323618824689 9.237665 2.9263 0.004743 0.002371 Tot 0.587787983114033 0.168212 3.4943 0.000868 0.000434 Conjun -0.756057202325195 1.983584 -0.3812 0.704349 0.352175 Mach -0.183109523021441 0.108796 -1.6831 0.097238 0.048619 `Elek ` 0.29725078825593 0.095702 3.106 0.002826 0.001413 M1 1.67156483034391 2.828269 0.591 0.556588 0.278294 M2 1.10325520722268 2.793993 0.3949 0.694254 0.347127 M3 2.16417897807062 2.785394 0.777 0.440036 0.220018 M4 5.25039459411524 2.641323 1.9878 0.051117 0.025558 M5 3.32183397931734 2.58777 1.2837 0.203887 0.101943 M6 6.7371409579682 2.864821 2.3517 0.021779 0.010889 M7 -7.536498510513 2.782614 -2.7084 0.008662 0.004331 M8 6.39162180834974 2.936932 2.1763 0.033231 0.016615 M9 8.88554654979554 2.9756 2.9861 0.004 0.002 M10 10.6224426006966 2.91342 3.646 0.000536 0.000268 M11 6.68380905729691 2.891376 2.3116 0.024028 0.012014 Multiple Linear Regression - Regression Statistics Multiple R 0.958390257787248 R-squared 0.918511886221508 Adjusted R-squared 0.899413109554674 F-TEST (value) 48.092707833824 F-TEST (DF numerator) 15 F-TEST (DF denominator) 64 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.18776981498156 Sum Squared Residuals 1122.39462548932 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 97.3 100.023975200363 -2.72397520036250 2 101 101.723136845630 -0.723136845630392 3 113.2 115.096805355254 -1.89680535525428 4 101 104.146065661660 -3.14606566165953 5 105.7 107.768041528412 -2.06804152841156 6 113.9 115.244183411554 -1.34418341155397 7 86.4 80.1740026683116 6.2259973316884 8 96.5 91.71263531751 4.78736468249 9 103.3 108.427125349292 -5.12712534929224 10 114.9 114.871935853653 0.0280641463473881 11 105.8 107.775722679788 -1.97572267978820 12 94.2 97.273905325053 -3.07390532505305 13 98.4 95.2939680370481 3.10603196295189 14 99.4 97.9340246936277 1.46597530637228 15 108.8 108.758236860595 0.0417631394051853 16 112.6 109.642570085099 2.95742991490081 17 104.4 106.517560812103 -2.11756081210341 18 112.2 117.45974142387 -5.25974142386991 19 81.1 84.308926256684 -3.20892625668402 20 97.1 93.489875058188 3.61012494181193 21 112.6 113.674597230237 -1.07459723023742 22 113.8 121.062383022425 -7.26238302242527 23 107.8 106.466050493331 1.33394950666860 24 103.2 97.0189013753096 6.18109862469045 25 103.3 95.6904115809951 7.6095884190049 26 101.2 98.2970152689758 2.90298473102420 27 107.7 104.763336267696 2.93666373230412 28 110.4 103.839161783457 6.56083821654324 29 101.9 103.244501826037 -1.34450182603725 30 115.9 114.473726828405 1.42627317159528 31 89.9 86.003610922385 3.89638907761506 32 88.6 88.1151791630593 0.484820836940652 33 117.2 111.200710333194 5.99928966680645 34 123.9 114.637802560385 9.26219743961537 35 100 104.067764346291 -4.06776434629085 36 103.6 104.546859039602 -0.946859039602222 37 94.1 94.930304066866 -0.830304066865966 38 98.7 98.6505945037002 0.049405496299805 39 119.5 115.660626168618 3.8393738313824 40 112.7 113.483037117581 -0.783037117581143 41 104.4 104.865227708933 -0.465227708932678 42 124.7 120.718832225299 3.98116777470095 43 89.1 87.3218141994142 1.7781858005858 44 97 105.423248192910 -8.42324819291023 45 121.6 120.245374301055 1.35462569894487 46 118.8 120.122105481824 -1.32210548182368 47 114 110.515059638059 3.48494036194063 48 111.5 109.288055539146 2.21194446085364 49 97.2 100.983422934150 -3.78342293414957 50 102.5 105.036667309121 -2.53666730912132 51 113.4 118.393303422121 -4.99330342212055 52 109.8 113.749450565535 -3.94945056553545 53 104.9 105.621171059465 -0.721171059464924 54 126.1 130.304300871934 -4.20430087193357 55 80 84.4413086651588 -4.44130866515879 56 96.8 100.501645563630 -3.70164556363032 57 117.2 120.405682355108 -3.20568235510759 58 112.3 115.464054423415 -3.16405442341517 59 117.3 121.084338012142 -3.78433801214249 60 111.1 115.144090163815 -4.04409016381471 61 102.2 105.962917019409 -3.76291701940874 62 104.3 109.109397374814 -4.80939737481435 63 122.9 125.821864657597 -2.92186465759654 64 107.6 111.737992948693 -4.13799294869257 65 121.3 121.686968202349 -0.386968202348727 66 131.5 133.041036676119 -1.54103667611865 67 89 90.1969371592078 -1.19693715920777 68 104.4 105.245590217315 -0.845590217314555 69 128.9 126.846510431114 2.05348956888593 70 135.9 133.441718658299 2.45828134170136 71 133.3 128.291064830388 5.00893516961231 72 121.3 121.628188557074 -0.3281885570741 73 120.5 120.11500116117 0.384998838829993 74 120.4 116.749164004130 3.65083599586978 75 137.9 134.905827268120 2.99417273187967 76 126.1 123.601721837975 2.49827816202465 77 133.2 126.096528862701 7.10347113729855 78 146.6 139.65817856282 6.94182143717986 79 103.4 106.453400128839 -3.05340012883867 80 117.2 113.111826487387 4.08817351261252

Charts produced by software:

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Parameters:

par1 = 2 ; 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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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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