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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 15:03:54 -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/t1196891484hat6n09xv9c4a8w.htm/, Retrieved Wed, 05 Dec 2007 22:51:34 +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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Prod[t] = + 27.4744598687837 + 0.594073355286528Tot[t] -0.900469014278283Conjun[t] -0.174035113286912Mach[t] + 0.27617796977481`Elek `[t] + 1.48514691753448M1[t] + 0.941688379550246M2[t] + 2.16562533561343M3[t] + 5.1889958036742M4[t] + 3.27580560303855M5[t] + 6.75941325447884M6[t] -7.59023340780786M7[t] + 6.0747418129244M8[t] + 8.68269632502206M9[t] + 10.4660625083265M10[t] + 6.48427475697439M11[t] + 0.0154713738943704t + 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) 27.4744598687837 9.410858 2.9194 0.004859 0.002429 Tot 0.594073355286528 0.170605 3.4822 0.00091 0.000455 Conjun -0.900469014278283 2.050672 -0.4391 0.662085 0.331042 Mach -0.174035113286912 0.113368 -1.5351 0.129759 0.064879 `Elek ` 0.27617796977481 0.117704 2.3464 0.022116 0.011058 M1 1.48514691753448 2.910455 0.5103 0.611639 0.305819 M2 0.941688379550246 2.861187 0.3291 0.743153 0.371576 M3 2.16562533561343 2.805252 0.772 0.443007 0.221503 M4 5.1889958036742 2.667423 1.9453 0.056202 0.028101 M5 3.27580560303855 2.61039 1.2549 0.214147 0.107073 M6 6.75941325447884 2.886125 2.342 0.022353 0.011177 M7 -7.59023340780786 2.807738 -2.7033 0.008814 0.004407 M8 6.0747418129244 3.127472 1.9424 0.056564 0.028282 M9 8.68269632502206 3.066564 2.8314 0.006214 0.003107 M10 10.4660625083265 2.976712 3.516 0.000818 0.000409 M11 6.48427475697439 2.981425 2.1749 0.0334 0.0167 t 0.0154713738943704 0.049602 0.3119 0.756137 0.378068 Multiple Linear Regression - Regression Statistics Multiple R 0.958455806196206 R-squared 0.918637532431219 Adjusted R-squared 0.897974048604227 F-TEST (value) 44.4570499400122 F-TEST (DF numerator) 16 F-TEST (DF denominator) 63 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.21761989889206 Sum Squared Residuals 1120.66400952641 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 97.3 99.9464654707617 -2.64646547076166 2 101 101.689920523275 -0.689920523274765 3 113.2 115.072473642389 -1.87247364238852 4 101 103.943181949385 -2.94318194938462 5 105.7 107.503453733521 -1.80345373352119 6 113.9 115.112676016376 -1.21267601637615 7 86.4 80.015814344312 6.38418565568793 8 96.5 91.63973644116 4.86026355883995 9 103.3 108.287923598004 -4.98792359800426 10 114.9 114.649009551556 0.250990448444123 11 105.8 107.617207358914 -1.81720735891421 12 94.2 97.116677852328 -2.91667785232806 13 98.4 95.1387580249967 3.26124197500335 14 99.4 97.7595705070447 1.64042949295529 15 108.8 108.629363493477 0.170636506523263 16 112.6 109.419718217477 3.18028178252276 17 104.4 106.344512254108 -1.94451225410791 18 112.2 117.186910100135 -4.98691010013454 19 81.1 84.0839784976118 -2.98397849761182 20 97.1 93.3489570137545 3.75104298624553 21 112.6 113.501075953644 -0.901075953643509 22 113.8 120.863117493353 -7.06311749335305 23 107.8 106.460680456513 1.33931954348662 24 103.2 97.1489245562177 6.05107544378226 25 103.3 95.6819220852994 7.61807791470059 26 101.2 98.2618471213016 2.9381528786984 27 107.7 104.829123454865 2.87087654513516 28 110.4 103.975386238242 6.42461376175782 29 101.9 103.307198626419 -1.40719862641916 30 115.9 114.360942621436 1.53905737856404 31 89.9 85.9067647618848 3.99323523811523 32 88.6 88.1282065278777 0.4717934721223 33 117.2 111.227668962787 5.97233103721315 34 123.9 114.69398538343 9.20601461657009 35 100 104.191255810663 -4.19125581066347 36 103.6 104.611906209527 -1.01190620952737 37 94.1 95.0353548277077 -0.935354827707715 38 98.7 98.706496292179 -0.00649629217911918 39 119.5 115.787505272541 3.71249472745938 40 112.7 113.501970925708 -0.801970925707587 41 104.4 104.998225071626 -0.598225071625923 42 124.7 120.978758738953 3.72124126104663 43 89.1 87.5146604578774 1.58533954212256 44 97 105.247281739541 -8.24728173954143 45 121.6 120.277335861110 1.32266413888951 46 118.8 120.332819739776 -1.53281973977630 47 114 110.694517386978 3.3054826130219 48 111.5 109.467823722653 2.03217627734731 49 97.2 101.208794810194 -4.00879481019360 50 102.5 105.172340770713 -2.67234077071301 51 113.4 118.555301298810 -5.15530129880965 52 109.8 113.914936406828 -4.11493640682837 53 104.9 105.913727807735 -1.01372780773466 54 126.1 130.561198340229 -4.46119834022851 55 80 84.7691997625799 -4.76919976257989 56 96.8 100.705435912215 -3.90543591221513 57 117.2 120.509699143424 -3.3096991434235 58 112.3 115.583414908589 -3.28341490858865 59 117.3 120.916498499411 -3.6164984994108 60 111.1 115.064980101844 -3.9649801018442 61 102.2 105.992195777824 -3.7921957778237 62 104.3 109.213682872187 -4.91368287218674 63 122.9 125.859648263471 -2.95964826347137 64 107.6 111.868086806317 -4.26808680631702 65 121.3 121.704888311742 -0.404888311741646 66 131.5 133.052245352348 -1.55224535234832 67 89 90.322195106607 -1.32219510660698 68 104.4 105.324367476654 -0.924367476654207 69 128.9 126.996296481031 1.9037035189686 70 135.9 133.477652923296 2.42234707670379 71 133.3 128.31984048752 4.98015951247997 72 121.3 121.48968755743 -0.189687557429956 73 120.5 119.996509003217 0.503490996782732 74 120.4 116.6961419133 3.70385808669995 75 137.9 134.666584574448 3.23341542555173 76 126.1 123.576719456043 2.52328054395701 77 133.2 126.027994194849 7.17200580515049 78 146.6 139.647268830523 6.95273116947685 79 103.4 106.287387069127 -2.88738706912703 80 117.2 113.206014888797 3.99398511120298

Charts produced by software:

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Parameters:

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = 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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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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