Model 4, kijken naar het verleden

*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: Wed, 16 Dec 2009 07:57:17 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/16/t12609755597k0k67stgje1d9n.htm/, Retrieved Wed, 16 Dec 2009 15:59:31 +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/2009/Dec/16/t12609755597k0k67stgje1d9n.htm/}, year = {2009}, } @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 = {2009}, 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:

Dataseries X:

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101.6 8.3 103.9 110.3 114.1 96.8 94.6 8.5 101.6 103.9 110.3 114.1 95.9 8.6 94.6 101.6 103.9 110.3 104.7 8.5 95.9 94.6 101.6 103.9 102.8 8.2 104.7 95.9 94.6 101.6 98.1 8.1 102.8 104.7 95.9 94.6 113.9 7.9 98.1 102.8 104.7 95.9 80.9 8.6 113.9 98.1 102.8 104.7 95.7 8.7 80.9 113.9 98.1 102.8 113.2 8.7 95.7 80.9 113.9 98.1 105.9 8.5 113.2 95.7 80.9 113.9 108.8 8.4 105.9 113.2 95.7 80.9 102.3 8.5 108.8 105.9 113.2 95.7 99 8.7 102.3 108.8 105.9 113.2 100.7 8.7 99 102.3 108.8 105.9 115.5 8.6 100.7 99 102.3 108.8 100.7 8.5 115.5 100.7 99 102.3 109.9 8.3 100.7 115.5 100.7 99 114.6 8 109.9 100.7 115.5 100.7 85.4 8.2 114.6 109.9 100.7 115.5 100.5 8.1 85.4 114.6 109.9 100.7 114.8 8.1 100.5 85.4 114.6 109.9 116.5 8 114.8 100.5 85.4 114.6 112.9 7.9 116.5 114.8 100.5 85.4 102 7.9 112.9 116.5 114.8 100.5 106 8 102 112.9 116.5 114.8 105.3 8 106 102 112.9 116.5 118.8 7.9 105.3 106 102 112.9 106.1 8 118.8 105.3 106 102 109.3 7.7 106.1 118.8 105.3 106 117.2 7.2 109.3 106.1 118.8 105.3 92.5 7.5 117.2 etc...

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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = -6.79694103656072 + 1.05486730212581X[t] + 0.110965757067476Y1[t] + 0.391959746665791Y2[t] + 0.599520525239775Y3[t] -0.106726216223816Y4[t] -15.4550336799605M1[t] -10.4574260073356M2[t] -2.31357909367123M3[t] + 10.2745695704598M4[t] + 1.88615375451333M5[t] -1.91130093006396M6[t] + 4.78338037640562M7[t] -17.3903720895910M8[t] -8.15431671909183M9[t] + 9.7410438791364M10[t] + 21.7116429765906M11[t] -0.0196445345992148t + 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) -6.79694103656072 30.840317 -0.2204 0.826716 0.413358 X 1.05486730212581 1.855474 0.5685 0.572944 0.286472 Y1 0.110965757067476 0.158174 0.7015 0.48713 0.243565 Y2 0.391959746665791 0.136594 2.8695 0.006606 0.003303 Y3 0.599520525239775 0.14352 4.1773 0.000161 8e-05 Y4 -0.106726216223816 0.175443 -0.6083 0.546499 0.27325 M1 -15.4550336799605 4.849677 -3.1868 0.002831 0.001416 M2 -10.4574260073356 7.951912 -1.3151 0.196162 0.098081 M3 -2.31357909367123 7.859658 -0.2944 0.770043 0.385021 M4 10.2745695704598 6.311884 1.6278 0.111618 0.055809 M5 1.88615375451333 4.409779 0.4277 0.671207 0.335604 M6 -1.91130093006396 4.507512 -0.424 0.673877 0.336938 M7 4.78338037640562 5.474247 0.8738 0.387578 0.193789 M8 -17.3903720895910 5.774528 -3.0116 0.004544 0.002272 M9 -8.15431671909183 7.291104 -1.1184 0.270241 0.135121 M10 9.7410438791364 8.063551 1.208 0.234309 0.117154 M11 21.7116429765906 6.339742 3.4247 0.001462 0.000731 t -0.0196445345992148 0.057226 -0.3433 0.733231 0.366616 Multiple Linear Regression - Regression Statistics Multiple R 0.932735061561709 R-squared 0.869994695066524 Adjusted R-squared 0.813325715992958 F-TEST (value) 15.3522210791396 F-TEST (DF numerator) 17 F-TEST (DF denominator) 39 p-value 2.81630274656663e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.21808938618669 Sum Squared Residuals 693.898844724573 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 101.6 99.320475772464 2.27952422753588 2 94.6 97.6211072144157 -3.02110721441568 3 95.9 100.741156867006 -4.84115686700567 4 104.7 109.908862099633 -5.20886209963304 5 102.8 98.7192145119453 4.08078548805473 6 98.1 99.5614995911654 -1.46149959116536 7 113.9 109.896336866748 4.00366313325251 8 80.9 86.2741154292514 -5.3741154292514 9 95.7 95.512140351655 0.187859648344918 10 113.2 112.069515494952 1.13048450504796 11 105.9 110.081950047467 -4.18195004746746 12 108.8 106.689290255058 2.11070974494150 13 102.3 97.6926545071304 4.60734549286965 14 99 97.0527883318063 1.94721166819372 15 100.7 104.780776260850 -4.0807762608503 16 115.5 111.932578842080 3.56742115792044 17 100.7 104.442959207415 -3.74295920741531 18 109.9 105.944978980315 3.95502101968509 19 114.6 116.214905481883 -1.61490548188281 20 85.4 87.9075988955933 -2.50759889559334 21 100.5 102.715670536558 -2.21567053655809 22 114.8 112.657610208633 2.14238979136728 23 116.5 114.00086798874 2.49913201125992 24 112.9 110.126925356529 2.77307464347073 25 102 101.880679631808 0.119320368192365 26 106 103.836547660921 2.16345233907934 27 105.3 105.792543371155 -0.492543371154899 28 118.8 113.595164380482 5.20483561951772 29 106.1 110.077654515693 -3.97765451569272 30 109.3 108.979717338547 0.320282661453414 31 117.2 118.672757541408 -1.47275754140807 32 92.5 89.8720068120468 2.62799318795316 33 104.2 102.506960613425 1.69303938657547 34 112.5 116.077798358938 -3.57779835893824 35 122.4 117.884403659852 4.51559634014761 36 113.3 110.155470726990 3.14452927300966 37 100 101.489702705205 -1.48970270520455 38 110.7 106.579899915003 4.12010008499718 39 112.8 103.955171483312 8.84482851668796 40 109.8 113.631798383320 -3.83179838331952 41 117.3 113.126337604562 4.17366239543843 42 109.1 108.766164722165 0.333835277835293 43 115.9 115.870240677136 0.0297593228638166 44 96 97.2997642524604 -1.29976425246039 45 99.8 101.467741331825 -1.66774133182538 46 116.8 116.495075937477 0.304924062523 47 115.7 118.53277830394 -2.83277830394008 48 99.4 107.428313661422 -8.02831366142187 49 94.3 99.8164873833933 -5.51648738339334 50 91 96.2096568778546 -5.20965687785457 51 93.2 92.6303520176771 0.56964798232291 52 103.1 102.831596294486 0.26840370551438 53 94.1 94.6338341603851 -0.533834160385132 54 91.8 94.9476393678084 -3.14763936780844 55 102.7 103.645759432825 -0.945759432825444 56 82.6 76.046514610648 6.55348538935196 57 89.1 87.097487166537 2.00251283346307 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.36179619530423 0.72359239060846 0.63820380469577 22 0.206939083864356 0.413878167728711 0.793060916135644 23 0.181122517868897 0.362245035737793 0.818877482131103 24 0.152981680628758 0.305963361257517 0.847018319371242 25 0.158577893026211 0.317155786052423 0.841422106973789 26 0.100831739141817 0.201663478283634 0.899168260858183 27 0.0865948030615352 0.173189606123070 0.913405196938465 28 0.104714691215949 0.209429382431898 0.895285308784051 29 0.0952049913045044 0.190409982609009 0.904795008695496 30 0.0693642216866015 0.138728443373203 0.930635778313398 31 0.0709153084780533 0.141830616956107 0.929084691521947 32 0.0405759980767949 0.0811519961535898 0.959424001923205 33 0.0268404090670941 0.0536808181341882 0.973159590932906 34 0.386599205921636 0.773198411843271 0.613400794078364 35 0.431238347923233 0.862476695846465 0.568761652076767 36 0.301917166580482 0.603834333160963 0.698082833419518 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 2 0.125 NOK

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) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test 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)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$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') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$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() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() 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') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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