paper: multiple regressie

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Fri, 04 Jan 2008 16:54:08 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Jan/05/t1199490864bkic4ef13nwe6hv.htm/, Retrieved Sat, 05 Jan 2008 00:54:35 +0100

User-defined keywords:

Tinne Van der Eycken met investeringen, seasonal dummies en trend

Dataseries X:

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86,5 109,2 104,1 126,3 110,9 104 114,5 96 112,2 262 96,4 89,8 92 86 102 92,7 99,7 126,8 102 92,8 98,9 87,8 87,4 100 94,4 72,4 109,3 104,9 116,4 52,3 101 65,3 105,5 110,2 97,8 54,4 95,5 47,5 113,7 65,2 103,7 69,8 100,8 53,6 113,8 116,1 84,6 56,6 95,3 47,2 110 90,6 107,5 60,4 107,6 59,3 116 131,6 96,9 59,4 97 65,5 108,1 70,5 101,9 81 107,2 73,3 110,2 107,5 78,7 88,9 96,5 55,8 115,2 80,5 104,7 86,3 109,1 112,6 108,4 148,6 95,5 47,1 97,8 57,8 115,1 81 96,2 60,1 112 76,1 111,8 82,5 82,5 66,8 100,8 58,7 116 54,2 116,3 103,3 116,6 77,8 112,9 118,4 100,9 64,9 104,1 40,8 117,4 77,7 103,3 66,8 111,6 69,2 115 82,4 92,6 62,7 105,2 58,2

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 Indpr[t] = + 76.9508311655516 + 0.0273171128015187Inv[t] + 12.3664224082476M1[t] + 27.0259492208726M2[t] + 27.3690912174461M3[t] + 25.7722913154589M4[t] + 24.8754300623079M5[t] + 13.6912581958045M6[t] + 13.3984779859362M7[t] + 26.7183798508353M8[t] + 16.1521944823323M9[t] + 21.9568778575105M10[t] + 24.3976771105950M11[t] + 0.171121815953736t + 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) 76.9508311655516 3.318038 23.1917 0 0 Inv 0.0273171128015187 0.02569 1.0634 0.293055 0.146528 M1 12.3664224082476 2.573191 4.8059 1.6e-05 8e-06 M2 27.0259492208726 2.696888 10.0212 0 0 M3 27.3690912174461 2.680757 10.2095 0 0 M4 25.7722913154589 2.678279 9.6227 0 0 M5 24.8754300623079 3.294987 7.5495 0 0 M6 13.6912581958045 2.702184 5.0667 7e-06 3e-06 M7 13.3984779859362 2.712634 4.9393 1e-05 5e-06 M8 26.7183798508353 2.668924 10.0109 0 0 M9 16.1521944823323 2.669705 6.0502 0 0 M10 21.9568778575105 2.668029 8.2296 0 0 M11 24.3976771105950 2.713573 8.991 0 0 t 0.171121815953736 0.034826 4.9136 1.1e-05 6e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.917448763333296 R-squared 0.841712233341794 Adjusted R-squared 0.797930510649099 F-TEST (value) 19.2251967618951 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 1.50990331349021e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.21534951973288 Sum Squared Residuals 835.151063955076 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 86.5 92.471404107679 -5.97140410767898 2 104.1 107.769175365163 -3.6691753651635 3 110.9 107.674267562217 3.22573243778312 4 114.5 106.030052573771 8.46994742622872 5 112.2 109.838953861626 2.36104613837392 6 96.4 94.1218969866548 2.27810301334516 7 92 93.8964335640945 -1.89643356409454 8 102 107.570481900718 -5.57048190071753 9 99.7 98.1069318947 1.59306810529995 10 102 103.153955250580 -1.15395525058041 11 98.9 105.629290755611 -6.72929075561101 12 87.4 81.7360042371483 5.66399576285171 13 94.4 93.5195961480277 0.880403851972294 14 109.3 109.238050942656 0.0619490573441767 15 116.4 108.315434621823 8.08456537817682 16 101 107.244879002210 -6.2448790022095 17 105.5 107.745677929800 -2.24567792980042 18 97.8 95.208332984926 2.59166701507407 19 95.5 94.898186512681 0.601813487319091 20 113.7 108.872723090121 4.8272769098794 21 103.7 98.6033182564583 5.09668174354169 22 100.8 104.136586220206 -3.33658622020570 23 113.8 108.455826839339 5.34417316066118 24 84.6 82.6039033330072 1.99609666699276 25 95.3 94.8846666968743 0.415333303125725 26 110 110.900878021039 -0.900878021038933 27 107.5 110.590165026960 -3.09016502696032 28 107.6 109.134438116845 -1.53443811684522 29 116 110.383725935198 5.61627406480226 30 96.9 97.3983803403784 -0.498380340378351 31 97 97.443356334553 -0.443356334553083 32 108.1 111.070965579413 -2.97096557941350 33 101.9 100.962731711280 0.937268288719855 34 107.2 106.728195133840 0.471804866159551 35 110.2 110.274361460691 -0.0743614606905861 36 78.7 85.5397078679411 -6.83970786794111 37 96.5 97.1730556584122 -0.673055658412168 38 115.2 112.678436973188 2.52156302681157 39 104.7 113.351140039964 -8.65114003996448 40 109.1 112.643902020611 -3.54390202061101 41 108.4 112.901578644268 -4.50157864426839 42 95.5 99.1158416443645 -3.61584164436451 43 97.8 99.2864763574262 -1.48647635742622 44 115.1 113.411257055274 1.68874294472572 45 96.2 102.445265845173 -6.24526584517324 46 112 108.858144841130 3.14185515887046 47 111.8 111.644895432097 0.155104567902546 48 82.5 86.9894614664724 -4.48946146647238 49 100.8 99.3057370769814 1.49426292301859 50 116 114.013458697953 1.98654130204668 51 116.3 115.868992749035 0.431007250964857 52 116.6 113.746728286563 2.85327171343702 53 112.9 114.130063629107 -1.23006362910736 54 100.9 101.655548043676 -0.75554804367637 55 104.1 100.875547231245 3.22445276875476 56 117.4 115.374572374474 2.02542762552591 57 103.3 104.681752292388 -1.38175229238826 58 111.6 110.723118554244 0.876881445756102 59 115 113.695625512262 1.30437448773787 60 92.6 88.930923095431 3.669076904569 61 105.2 101.345540312025 3.85445968797453

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

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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