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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 08:07:19 -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/t1197558067furm88zsdcwwkm4.htm/, Retrieved Thu, 13 Dec 2007 16:01:17 +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 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:

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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation intermediair-goederen[t] = + 38.7304827602253 + 0.621420888367847`totale-consumptie`[t] + 0.169178306430478`Duurzame-consumptiegoederen`[t] -0.195767517620194`Niet-duurzame-consumptiegoederen`[t] + 3.47440801073859`invoering-Euro`[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) 38.7304827602253 7.913233 4.8944 6e-06 3e-06 `totale-consumptie` 0.621420888367847 0.825965 0.7524 0.454191 0.227095 `Duurzame-consumptiegoederen` 0.169178306430478 0.102983 1.6428 0.104615 0.052307 `Niet-duurzame-consumptiegoederen` -0.195767517620194 0.717218 -0.273 0.785639 0.392819 `invoering-Euro` 3.47440801073859 2.325924 1.4938 0.13943 0.069715 Multiple Linear Regression - Regression Statistics Multiple R 0.690610406124864 R-squared 0.476942733047949 Adjusted R-squared 0.449046345477173 F-TEST (value) 17.0969352873341 F-TEST (DF numerator) 4 F-TEST (DF denominator) 75 p-value 5.26891974494959e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.59261586000023 Sum Squared Residuals 2345.80141181446 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 103.1 97.2962969767737 5.80370302322631 2 100.6 97.5484398736166 3.05156012638336 3 103.1 102.985972600501 0.11402739949926 4 95.5 95.6133576126502 -0.113357612650164 5 90.5 98.2366390633512 -7.73663906335116 6 90.9 102.844607884239 -11.9446078842392 7 88.8 89.4900351975311 -0.690035197531108 8 90.7 92.9979662136317 -2.29796621363169 9 94.3 102.293966106939 -7.99396610693868 10 104.6 107.704324131693 -3.10432413169319 11 111.1 101.000678368539 10.0993216314606 12 110.8 95.9877159705344 14.8122840294656 13 107.2 99.1468533208297 8.05314667917027 14 99 99.9855423728914 -0.98554237289136 15 99 104.122092043904 -5.12209204390369 16 91 101.396762088410 -10.3967620884101 17 96.2 101.316667810614 -5.11666781061418 18 96.9 103.517284941123 -6.61728494112332 19 96.2 94.3416657828942 1.85833421710579 20 100.1 93.1144734878168 6.98552651218321 21 99 105.555241130375 -6.55524113037466 22 115.4 108.751598250677 6.64840174932289 23 106.9 102.666754939568 4.23324506043218 24 107.1 99.960720289952 7.13927971004807 25 99.3 102.743896906620 -3.44389690661979 26 99.2 100.420614219356 -1.22061421935625 27 108.3 105.017996039321 3.28200396067914 28 105.6 103.020154172313 2.57984582768725 29 99.5 97.3193013431756 2.1806986568244 30 107.4 101.563764824036 5.83623517596357 31 93.1 96.2745451603384 -3.17454516033843 32 88.1 94.152987949309 -6.05298794930912 33 110.7 111.291753631358 -0.591753631357593 34 113.1 111.680912419700 1.41908758029981 35 99.6 103.995702349813 -4.39570234981285 36 93.6 107.090950413207 -13.4909504132075 37 98.6 96.2943273617142 2.30567263828579 38 99.6 98.9287860178254 0.671213982174624 39 114.3 107.745237945385 6.55476205461464 40 107.8 100.744999310461 7.05500068953882 41 101.2 98.6141922735433 2.58580772645669 42 112.5 110.615771947233 1.88422805276697 43 100.5 96.2390421945807 4.26095780541934 44 93.9 97.339079999368 -3.43907999936808 45 116.2 111.157711361463 5.04228863853704 46 112 107.125278911875 4.8747210881246 47 106.4 104.931534132020 1.4684658679798 48 95.7 108.556552787587 -12.8565527875873 49 96 98.8145318911902 -2.81453189119022 50 95.8 97.8797404091826 -2.07974040918265 51 103 105.904157371468 -2.90415737146767 52 102.2 101.208680401196 0.991319598804501 53 98.4 99.8939585858995 -1.49395858589952 54 111.4 106.479693742768 4.92030625723188 55 86.6 91.5808340899797 -4.98083408997972 56 91.3 96.7497775559254 -5.44977755592537 57 107.9 110.522973268329 -2.62297326832902 58 101.8 103.924013560252 -2.12401356025245 59 104.4 106.650236536952 -2.25023653695152 60 93.4 103.658597428649 -10.2585974286491 61 100.1 99.9066416161732 0.193358383826783 62 98.5 101.74457043159 -3.24457043159012 63 112.9 110.962582731882 1.93741726811799 64 101.4 99.7816258969023 1.61837410309773 65 107.1 105.134829545621 1.96517045437888 66 110.8 108.258378094683 2.54162190531722 67 90.3 92.7553941971589 -2.45539419715887 68 95.5 98.9865864521208 -3.48658645212083 69 111.4 109.278018804956 2.12198119504448 70 113 110.505752620967 2.49424737903276 71 107.5 107.533148743493 -0.0331487434925879 72 95.9 103.439375801052 -7.53937580105248 73 106.3 101.958930254546 4.34106974545445 74 105.2 100.93237445195 4.26762554804995 75 117.2 108.937734812573 8.26226518742705 76 106.9 99.6708049746522 7.22919502534776 77 108.2 102.126251235841 6.07374876415871 78 110 107.137897829646 2.86210217035410 79 96.1 98.38457960757 -2.28457960757003 80 100.6 99.8565769241726 0.743423075827347

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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Software written by Ed van Stee & Patrick Wessa

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