2

*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Sun, 21 Dec 2008 06:24:07 -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/Dec/21/t1229865913fz8lj5l7k0088uk.htm/, Retrieved Sun, 21 Dec 2008 14:25:13 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Dec/21/t1229865913fz8lj5l7k0088uk.htm/}, year = {2008}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

2

Dataseries X:

» Textbox « » Textfile « » CSV «

519164 0 517009 0 509933 0 509127 0 500857 0 506971 0 569323 0 579714 0 577992 0 565464 0 547344 0 554788 0 562325 0 560854 0 555332 0 543599 0 536662 0 542722 0 593530 0 610763 0 612613 0 611324 0 594167 0 595454 0 590865 0 589379 0 584428 0 573100 0 567456 0 569028 0 620735 0 628884 0 628232 0 612117 0 595404 0 597141 0 593408 0 590072 0 579799 0 574205 0 572775 0 572942 0 619567 0 625809 0 619916 0 587625 0 565742 0 557274 0 560576 1 548854 1 531673 1 525919 1 511038 1 498662 1 555362 1 564591 1 541657 1 527070 1 509846 1 514258 1 516922 1 507561 1 492622 1 490243 1 469357 1 477580 1 528379 1 533590 1 517945 1 506174 1 501866 1

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 computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 5 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation WerklozenTotaal[t] = + 543630.189173228 -94863.0994094488Kredietcrisis[t] + 11509.5008530183M1[t] + 5500.84999999999M2[t] -5576.30085301837M3[t] -12928.7850393701M4[t] -23690.2692257218M5[t] -23150.4200787402M6[t] + 28927.9290682415M7[t] + 37250.2782152231M8[t] + 28664.1273622047M9[t] + 12813.8098425197M10[t] -4173.8410104987M11[t] + 1086.81751968504t + 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) 543630.189173228 11793.842977 46.0944 0 0 Kredietcrisis -94863.0994094488 9766.43652 -9.7132 0 0 M1 11509.5008530183 13447.743994 0.8559 0.395654 0.197827 M2 5500.84999999999 13412.866773 0.4101 0.683257 0.341629 M3 -5576.30085301837 13381.679846 -0.4167 0.678455 0.339227 M4 -12928.7850393701 13354.20907 -0.9681 0.337063 0.168532 M5 -23690.2692257218 13330.477417 -1.7772 0.080879 0.04044 M6 -23150.4200787402 13310.504887 -1.7393 0.087387 0.043694 M7 28927.9290682415 13294.308423 2.176 0.033718 0.016859 M8 37250.2782152231 13281.901839 2.8046 0.006878 0.003439 M9 28664.1273622047 13273.295762 2.1595 0.03503 0.017515 M10 12813.8098425197 13268.497587 0.9657 0.338258 0.169129 M11 -4173.8410104987 13267.511446 -0.3146 0.754221 0.37711 t 1086.81751968504 224.926557 4.8319 1.1e-05 5e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.876024537241298 R-squared 0.76741898984883 Adjusted R-squared 0.714374198059966 F-TEST (value) 14.4673767955094 F-TEST (DF numerator) 13 F-TEST (DF denominator) 57 p-value 1.37223565843669e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 21876.1288048348 Sum Squared Residuals 27278205654.6863 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 519164 556226.507545932 -37062.5075459323 2 517009 551304.674212598 -34295.6742125984 3 509933 541314.340879265 -31381.3408792651 4 509127 535048.674212598 -25921.6742125984 5 500857 525374.007545932 -24517.0075459317 6 506971 527000.674212598 -20029.6742125984 7 569323 580165.840879265 -10842.8408792651 8 579714 589575.007545932 -9861.00754593171 9 577992 582075.674212598 -4083.67421259838 10 565464 567312.174212598 -1848.17421259840 11 547344 551411.340879265 -4067.34087926507 12 554788 556671.999409449 -1883.99940944881 13 562325 569268.317782152 -6943.31778215212 14 560854 564346.484448819 -3492.48444881888 15 555332 554356.151115486 975.848884514445 16 543599 548090.484448819 -4491.48444881889 17 536662 538415.817782152 -1753.81778215221 18 542722 540042.484448819 2679.51555118111 19 593530 593207.651115486 322.348884514441 20 610763 602616.817782152 8146.18221784779 21 612613 595117.484448819 17495.5155511811 22 611324 580353.984448819 30970.0155511811 23 594167 564453.151115486 29713.8488845144 24 595454 569713.809645669 25740.1903543307 25 590865 582310.128018373 8554.8719816274 26 589379 577388.294685039 11990.7053149606 27 584428 567397.961351706 17030.0386482940 28 573100 561132.294685039 11967.7053149606 29 567456 551457.628018373 15998.3719816273 30 569028 553084.294685039 15943.7053149606 31 620735 606249.461351706 14485.5386482940 32 628884 615658.628018373 13225.3719816273 33 628232 608159.294685039 20072.7053149606 34 612117 593395.794685039 18721.2053149606 35 595404 577494.961351706 17909.0386482940 36 597141 582755.61988189 14385.3801181102 37 593408 595351.938254593 -1943.93825459307 38 590072 590430.10492126 -358.104921259847 39 579799 580439.771587927 -640.771587926524 40 574205 574174.10492126 30.8950787401495 41 572775 564499.438254593 8275.5617454068 42 572942 566126.10492126 6815.89507874013 43 619567 619291.271587927 275.728412073468 44 625809 628700.438254593 -2891.4382545932 45 619916 621201.10492126 -1285.10492125986 46 587625 606437.60492126 -18812.6049212599 47 565742 590536.771587927 -24794.7715879265 48 557274 595797.43011811 -38523.4301181102 49 560576 513530.649081365 47045.3509186353 50 548854 508608.815748031 40245.1842519685 51 531673 498618.482414698 33054.5175853018 52 525919 492352.815748031 33566.1842519685 53 511038 482678.149081365 28359.8509186352 54 498662 484304.815748031 14357.1842519685 55 555362 537469.982414698 17892.0175853018 56 564591 546879.149081365 17711.8509186352 57 541657 539379.815748031 2277.1842519685 58 527070 524616.315748031 2453.6842519685 59 509846 508715.482414698 1130.51758530184 60 514258 513976.140944882 281.859055118100 61 516922 526572.459317585 -9650.4593175852 62 507561 521650.625984252 -14089.6259842520 63 492622 511660.292650919 -19038.2926509187 64 490243 505394.625984252 -15151.6259842520 65 469357 495719.959317585 -26362.9593175853 66 477580 497346.625984252 -19766.625984252 67 528379 550511.792650919 -22132.7926509187 68 533590 559920.959317585 -26330.9593175853 69 517945 552421.625984252 -34476.625984252 70 506174 537658.125984252 -31484.125984252 71 501866 521757.292650919 -19891.2926509187

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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Software written by Ed van Stee & Patrick Wessa

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