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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: Mon, 19 Nov 2007 10:36:43 -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/Nov/19/t119549488527yblhrgr990di5.htm/, Retrieved Mon, 19 Nov 2007 18:54:54 +0100

User-defined keywords:

Dataseries X:

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103,6500 0 103,8700 0 103,9400 0 105,3200 0 105,5400 0 106,0800 0 106,2100 0 105,5300 0 105,5600 0 105,1400 0 105,9700 0 105,4500 0 106,2200 0 106,3100 0 107,3800 0 109,3100 0 110,8200 0 111,2200 0 110,6600 0 110,7600 0 110,6900 0 111,0800 0 110,9700 0 110,2400 0 112,5100 1 111,5200 1 112,1300 1 112,2300 1 112,9200 1 111,8900 1 111,9900 1 111,5100 1 112,3300 1 112,0400 1 112,0900 1 111,4100 1 112,6100 1 113,1400 1 113,6500 1 114,2600 1 114,4000 1 114,9300 1 114,8600 1 114,9500 1 116,1700 1 114,6000 1 114,6200 1 113,8200 1 115,0200 1 115,1800 1 115,5900 1 116,6000 1 117,0700 1 116,9600 1 116,6600 1 116,0700 1 116,0400 1 115,8100 1 116,2200 1 115,8500 1 116,4300 1 117,3900 1 119,1700 1 119,2400 1 120,0300 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 y[t] = + 103.580115606937 + 0.515375722543355x[t] + 0.721733140655184M1[t] + 0.676048169556845M2[t] + 1.21036319845857M3[t] + 1.85301156069364M4[t] + 2.28232658959538M5[t] + 2.10610982658960M6[t] + 1.75875818882466M7[t] + 1.23940655105973M8[t] + 1.42605491329480M9[t] + 0.794703275529869M10[t] + 0.827351637764937M11[t] + 0.207351637764932t + 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) 103.580115606937 0.549905 188.3602 0 0 x 0.515375722543355 0.510016 1.0105 0.317022 0.158511 M1 0.721733140655184 0.654436 1.1028 0.275277 0.137638 M2 0.676048169556845 0.65267 1.0358 0.305173 0.152587 M3 1.21036319845857 0.651165 1.8588 0.068836 0.034418 M4 1.85301156069364 0.649923 2.8511 0.006274 0.003137 M5 2.28232658959538 0.648945 3.517 0.000927 0.000463 M6 2.10610982658960 0.680709 3.094 0.003202 0.001601 M7 1.75875818882466 0.679311 2.589 0.012511 0.006256 M8 1.23940655105973 0.678165 1.8276 0.073465 0.036732 M9 1.42605491329480 0.677273 2.1056 0.040184 0.020092 M10 0.794703275529869 0.676635 1.1745 0.245652 0.122826 M11 0.827351637764937 0.676252 1.2234 0.226787 0.113394 t 0.207351637764932 0.013145 15.7738 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.974801401456435 R-squared 0.95023777228143 Adjusted R-squared 0.937553282862972 F-TEST (value) 74.9133639465706 F-TEST (DF numerator) 13 F-TEST (DF denominator) 51 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.06904560245680 Sum Squared Residuals 58.2857835067429 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 103.65 104.509200385356 -0.859200385356096 2 103.87 104.670867052023 -0.800867052023139 3 103.94 105.412533718690 -1.47253371868981 4 105.32 106.262533718690 -0.942533718689817 5 105.54 106.899200385356 -1.35920038535646 6 106.08 106.930335260116 -0.85033526011562 7 106.21 106.790335260116 -0.580335260115619 8 105.53 106.478335260116 -0.94833526011562 9 105.56 106.872335260116 -1.31233526011562 10 105.14 106.448335260116 -1.30833526011562 11 105.97 106.688335260116 -0.718335260115623 12 105.45 106.068335260116 -0.618335260115614 13 106.22 106.997420038536 -0.777420038535735 14 106.31 107.159086705202 -0.849086705202322 15 107.38 107.900753371869 -0.520753371868994 16 109.31 108.750753371869 0.559246628131014 17 110.82 109.387420038536 1.43257996146434 18 111.22 109.418554913295 1.80144508670519 19 110.66 109.278554913295 1.38144508670519 20 110.76 108.966554913295 1.7934450867052 21 110.69 109.360554913295 1.32944508670519 22 111.08 108.936554913295 2.14344508670519 23 110.97 109.176554913295 1.79344508670519 24 110.24 108.556554913295 1.68344508670519 25 112.51 110.001015414258 2.50898458574174 26 111.52 110.162682080925 1.35731791907514 27 112.13 110.904348747592 1.22565125240847 28 112.23 111.754348747592 0.475651252408481 29 112.92 112.391015414258 0.528984585741808 30 111.89 112.422150289017 -0.532150289017342 31 111.99 112.282150289017 -0.292150289017344 32 111.51 111.970150289017 -0.460150289017339 33 112.33 112.364150289017 -0.0341502890173444 34 112.04 111.940150289017 0.0998497109826644 35 112.09 112.180150289017 -0.0901502890173395 36 111.41 111.560150289017 -0.150150289017340 37 112.61 112.489235067437 0.120764932562545 38 113.14 112.650901734104 0.489098265895956 39 113.65 113.392568400771 0.257431599229296 40 114.26 114.242568400771 0.017431599229298 41 114.4 114.879235067437 -0.479235067437372 42 114.93 114.910369942197 0.0196300578034815 43 114.86 114.770369942197 0.0896300578034766 44 114.95 114.458369942197 0.491630057803476 45 116.17 114.852369942197 1.31763005780348 46 114.6 114.428369942197 0.171630057803469 47 114.62 114.668369942197 -0.0483699421965219 48 113.82 114.048369942197 -0.228369942196527 49 115.02 114.977454720617 0.0425452793833593 50 115.18 115.139121387283 0.0408786127167793 51 115.59 115.88078805395 -0.290788053949889 52 116.6 116.73078805395 -0.130788053949897 53 117.07 117.367454720617 -0.297454720616568 54 116.96 117.398589595376 -0.438589595375715 55 116.66 117.258589595376 -0.598589595375709 56 116.07 116.946589595376 -0.876589595375717 57 116.04 117.340589595376 -1.30058959537570 58 115.81 116.916589595376 -1.10658959537571 59 116.22 117.156589595376 -0.93658959537571 60 115.85 116.536589595376 -0.686589595375709 61 116.43 117.465674373796 -1.03567437379581 62 117.39 117.627341040462 -0.237341040462409 63 119.17 118.369007707129 0.800992292870926 64 119.24 119.219007707129 0.0209922928709210 65 120.03 119.855674373796 0.174325626204258

Charts produced by software:

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Parameters:

par1 = 1 ; 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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