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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 08:48:16 -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/t11975600021blsod22k2pk9j9.htm/, Retrieved Thu, 13 Dec 2007 16:33:22 +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 1 104.6 117.5 112.3 117.7 1 111.1 105.6 102.5 105.7 1 110.8 97.4 93.5 97.5 1 107.2 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:

WTC 9-11

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 intermediaire-goederen[t] = + 56.8144233107686 + 0.48733032890477`totale-consumptiegoederen`[t] + 0.0859384873333898`duurzame-consumptiegoederen`[t] -0.217827808454171`niet-duurzame-consumptiegoederen`[t] + 4.37494881242500`aanslagen-WTC9-11`[t] + 5.07926127284946M1[t] + 3.14424194856741M2[t] + 7.55592006481916M3[t] + 4.50318240294593M4[t] + 3.04115642517979M5[t] + 5.31492909401468M6[t] -0.439082047915904M7[t] -0.456107112610295M8[t] + 4.16331921146515M9[t] + 7.47935716091545M10[t] + 5.807952030928M11[t] + 0.0365005072086118t + 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) 56.8144233107686 18.921832 3.0026 0.003835 0.001918 `totale-consumptiegoederen` 0.48733032890477 0.903322 0.5395 0.591453 0.295726 `duurzame-consumptiegoederen` 0.0859384873333898 0.147705 0.5818 0.56276 0.28138 `niet-duurzame-consumptiegoederen` -0.217827808454171 0.826739 -0.2635 0.793042 0.396521 `aanslagen-WTC9-11` 4.37494881242500 2.595725 1.6854 0.096851 0.048425 M1 5.07926127284946 3.35979 1.5118 0.13559 0.067795 M2 3.14424194856741 3.387485 0.9282 0.35685 0.178425 M3 7.55592006481916 3.316311 2.2784 0.026103 0.013052 M4 4.50318240294593 3.382545 1.3313 0.187888 0.093944 M5 3.04115642517979 3.350049 0.9078 0.367446 0.183723 M6 5.31492909401468 3.300347 1.6104 0.112307 0.056153 M7 -0.439082047915904 4.496348 -0.0977 0.922518 0.461259 M8 -0.456107112610295 4.153569 -0.1098 0.912908 0.456454 M9 4.16331921146515 3.69528 1.1267 0.26416 0.13208 M10 7.47935716091545 3.675644 2.0348 0.04608 0.02304 M11 5.807952030928 3.298853 1.7606 0.08316 0.04158 t 0.0365005072086118 0.087651 0.4164 0.678511 0.339256 Multiple Linear Regression - Regression Statistics Multiple R 0.752262475930964 R-squared 0.565898832693784 Adjusted R-squared 0.455650917187443 F-TEST (value) 5.13296627963218 F-TEST (DF numerator) 16 F-TEST (DF denominator) 63 p-value 1.18416107863784e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.55899397910031 Sum Squared Residuals 1946.85208575943 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 103.1 96.9336992146612 6.16630078533878 2 100.6 95.1312943473176 5.46870565268241 3 103.1 102.810480024077 0.289519975922891 4 95.5 95.4938293054366 0.00617069456338041 5 90.5 95.5873505215899 -5.0873505215899 6 90.9 100.655133532570 -9.75513353257048 7 88.8 87.2314810385863 1.56851896141371 8 90.7 89.3567320157608 1.3432679842392 9 94.3 103.692277009603 -9.39227700960314 10 104.6 110.307607074989 -5.70760707498932 11 111.1 104.645208063827 6.45479193617345 12 110.8 95.8903894864117 14.9096105135882 13 107.2 100.922376503013 6.27762349698723 14 99 99.393646609288 -0.393646609288089 15 99 106.278762102654 -7.27876210265437 16 91 101.680983908455 -10.6809839084555 17 96.2 100.217736405432 -4.01773640543233 18 96.9 103.842409442453 -6.94240944245283 19 96.2 92.7713067560819 3.42869324391815 20 100.1 92.0691284026075 8.03087159739247 21 99 103.566252225004 -4.56625222500421 22 115.4 109.343988229322 6.05601177067831 23 106.9 103.571512784478 3.32848721552211 24 107.1 96.23010360947 10.86989639053 25 99.3 103.352834237749 -4.05283423774927 26 99.2 100.052710954735 -0.852710954734891 27 108.3 107.247111054689 1.05288894531093 28 105.6 103.028335880800 2.57166411920034 29 99.5 98.2120024183414 1.28799758165859 30 107.4 103.081548262215 4.31845173778486 31 93.1 94.2385915824697 -1.13859158246969 32 88.1 93.0009940456307 -4.90099404563074 33 110.7 107.826989769143 2.87301023085725 34 113.1 111.418654116674 1.68134588332648 35 99.6 105.206145116372 -5.60614511637239 36 93.6 101.307776825272 -7.70777682527167 37 98.6 99.9344529046976 -1.33445290469759 38 99.6 99.6186677632067 -0.018667763206698 39 114.3 109.332183675050 4.96781632495012 40 107.8 102.131862281132 5.66813771886757 41 101.2 99.4380375409958 1.76196245900420 42 112.5 108.924078500702 3.57592149929751 43 100.5 94.6076811406843 5.8923188593157 44 93.9 95.2788908834753 -1.37889088347529 45 116.2 108.199904404898 8.00009559510177 46 112 109.138790646158 2.86120935384172 47 106.4 106.197722913116 0.202277086884048 48 95.7 102.592141796973 -6.89214179697288 49 96 101.871148494700 -5.87114849469974 50 95.8 99.4219854386811 -3.62198543868115 51 103 108.672775912583 -5.67277591258282 52 102.2 102.842138879379 -0.64213887937857 53 98.4 100.628602044454 -2.22860204445407 54 111.4 106.885144082942 4.5148559170576 55 86.6 92.2413272612448 -5.64132726124481 56 91.3 95.3470983242375 -4.04709832423754 57 107.9 108.268708163685 -0.368708163684588 58 101.8 107.659967992119 -5.85996799211924 59 104.4 107.678669956679 -3.27866995667867 60 93.4 100.101020760107 -6.70102076010669 61 100.1 102.962789455149 -2.86278945514869 62 98.5 102.179031664515 -3.67903166451519 63 112.9 112.125552579987 0.774447420013413 64 101.4 102.438017807624 -1.03801780762376 65 107.1 104.201262014522 2.89873798547751 66 110.8 108.393631438155 2.40636856184481 67 90.3 93.3642122688959 -3.06421226889589 68 95.5 97.110213983921 -1.61021398392107 69 111.4 107.945868427667 3.45413157233291 70 113 112.030991940738 0.969008059262034 71 107.5 108.600741165529 -1.10074116552854 72 95.9 100.378567521767 -4.478567521767 73 106.3 104.622699190031 1.67730080996927 74 105.2 102.102663222256 3.09733677774361 75 117.2 111.333134650960 5.86686534903983 76 106.9 102.784831937173 4.11516806282651 77 108.2 102.815009054664 5.384990945336 78 110 108.118054740961 1.88194525903854 79 96.1 97.1453999520372 -1.04539995203718 80 100.6 98.036942344367 2.56305765563297

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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