6

*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 06:33:45 -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/t1229866491b7hpo8z2w3wug3g.htm/, Retrieved Sun, 21 Dec 2008 14:35:00 +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/t1229866491b7hpo8z2w3wug3g.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:

6

Dataseries X:

» Textbox « » Textfile « » CSV «

274412 0 272433 0 268361 0 268586 0 264768 0 269974 0 304744 0 309365 0 308347 0 298427 0 289231 0 291975 0 294912 0 293488 0 290555 0 284736 0 281818 0 287854 0 316263 0 325412 0 326011 0 328282 0 317480 0 317539 0 313737 0 312276 0 309391 0 302950 0 300316 0 304035 0 333476 0 337698 0 335932 0 323931 0 313927 0 314485 0 313218 0 309664 0 302963 0 298989 0 298423 0 301631 0 329765 0 335083 0 327616 0 309119 0 295916 0 291413 0 291542 1 284678 1 276475 1 272566 1 264981 1 263290 1 296806 1 303598 1 286994 1 276427 1 266424 1 267153 1 268381 1 262522 1 255542 1 253158 1 243803 1 250741 1 280445 1 285257 1 270976 1 261076 1 255603 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 3 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation WerklozenVrouwen[t] = + 288026.821555118 -51650.2475393702Kredietcrisis[t] + 5687.39799868752M1[t] + 1641.22500000003M2[t] -4177.1146653543M3[t] -8416.78766404194M4[t] -13418.7939960630M5[t] -10038.8003280840M6[t] + 20100.8600065617M7[t] + 25397.1870078740M8[t] + 18118.3473425197M9[t] + 7826.67434383204M10[t] -2476.16532152230M11[t] + 522.672998687666t + 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) 288026.821555118 6698.422456 42.9992 0 0 Kredietcrisis -51650.2475393702 5546.938164 -9.3115 0 0 M1 5687.39799868752 7637.770871 0.7446 0.459548 0.229774 M2 1641.22500000003 7617.96203 0.2154 0.830192 0.415096 M3 -4177.1146653543 7600.249127 -0.5496 0.584739 0.29237 M4 -8416.78766404194 7584.646844 -1.1097 0.271782 0.135891 M5 -13418.7939960630 7571.168232 -1.7724 0.08168 0.04084 M6 -10038.8003280840 7559.824648 -1.3279 0.1895 0.09475 M7 20100.8600065617 7550.625716 2.6621 0.010072 0.005036 M8 25397.1870078740 7543.579282 3.3667 0.001368 0.000684 M9 18118.3473425197 7538.691381 2.4034 0.01952 0.00976 M10 7826.67434383204 7535.966213 1.0386 0.303388 0.151694 M11 -2476.16532152230 7535.406125 -0.3286 0.743659 0.37183 t 522.672998687666 127.749123 4.0914 0.000136 6.8e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.881973132950892 R-squared 0.777876607247212 Adjusted R-squared 0.727216886093068 F-TEST (value) 15.3549326669275 F-TEST (DF numerator) 13 F-TEST (DF denominator) 57 p-value 3.97459842815806e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 12424.7501620641 Sum Squared Residuals 8799341745.6136 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 274412 294236.892552494 -19824.8925524944 2 272433 290713.392552493 -18280.3925524934 3 268361 285417.725885827 -17056.7258858267 4 268586 281700.725885827 -13114.7258858267 5 264768 277221.392552493 -12453.3925524934 6 269974 281124.05921916 -11150.0592191601 7 304744 311786.392552493 -7042.3925524934 8 309365 317605.392552493 -8240.3925524934 9 308347 310849.225885827 -2502.22588582670 10 298427 301080.225885827 -2653.22588582672 11 289231 291300.05921916 -2069.05921916005 12 291975 294298.89753937 -2323.89753937001 13 294912 300508.968536745 -5596.96853674519 14 293488 296985.468536745 -3497.46853674538 15 290555 291689.801870079 -1134.80187007871 16 284736 287972.801870079 -3236.80187007872 17 281818 283493.468536745 -1675.46853674538 18 287854 287396.135203412 457.864796587952 19 316263 318058.468536745 -1795.46853674538 20 325412 323877.468536745 1534.53146325462 21 326011 317121.301870079 8889.69812992127 22 328282 307352.301870079 20929.6981299213 23 317480 297572.135203412 19907.8647965879 24 317539 300570.973523622 16968.026476378 25 313737 306781.044520997 6955.95547900281 26 312276 303257.544520997 9018.4554790026 27 309391 297961.877854331 11429.1221456693 28 302950 294244.877854331 8705.12214566928 29 300316 289765.544520997 10550.4554790026 30 304035 293668.211187664 10366.7888123360 31 333476 324330.544520997 9145.45547900262 32 337698 330149.544520997 7548.45547900262 33 335932 323393.377854331 12538.6221456693 34 323931 313624.377854331 10306.6221456693 35 313927 303844.211187664 10082.7888123360 36 314485 306843.049507874 7641.95049212599 37 313218 313053.120505249 164.879494750809 38 309664 309529.620505249 134.379494750606 39 302963 304233.953838583 -1270.95383858271 40 298989 300516.953838583 -1527.95383858272 41 298423 296037.620505249 2385.37949475062 42 301631 299940.287171916 1690.71282808396 43 329765 330602.620505249 -837.620505249368 44 335083 336421.620505249 -1338.62050524938 45 327616 329665.453838583 -2049.45383858272 46 309119 319896.453838583 -10777.4538385827 47 295916 310116.287171916 -14200.2871719160 48 291413 313115.125492126 -21702.125492126 49 291542 267674.948950131 23867.0510498690 50 284678 264151.448950131 20526.5510498687 51 276475 258855.782283465 17619.2177165354 52 272566 255138.782283465 17427.2177165354 53 264981 250659.448950131 14321.5510498688 54 263290 254562.115616798 8727.8843832021 55 296806 285224.448950131 11581.5510498688 56 303598 291043.448950131 12554.5510498688 57 286994 284287.282283465 2706.71771653542 58 276427 274518.282283465 1908.71771653543 59 266424 264738.115616798 1685.88438320210 60 267153 267736.953937008 -583.953937007859 61 268381 273947.024934383 -5566.02493438304 62 262522 270423.524934383 -7901.52493438325 63 255542 265127.858267717 -9585.85826771656 64 253158 261410.858267717 -8252.85826771657 65 243803 256931.524934383 -13128.5249343832 66 250741 260834.19160105 -10093.1916010499 67 280445 291496.524934383 -11051.5249343832 68 285257 297315.524934383 -12058.5249343832 69 270976 290559.358267717 -19583.3582677166 70 261076 280790.358267717 -19714.3582677166 71 255603 271010.19160105 -15407.1916010499

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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