Schatten van model met seizoenaliteit

*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, 26 Jan 2011 07:38:29 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Jan/26/t1296027547t6eajt8dxg09hap.htm/, Retrieved Wed, 26 Jan 2011 08:39:07 +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/2011/Jan/26/t1296027547t6eajt8dxg09hap.htm/}, year = {2011}, } @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 = {2011}, 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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81.71 84.86 87.703 85.03 90.09 85.61 100.639 85.52 83.042 86.51 89.956 86.66 89.561 87.27 105.38 87.62 86.554 88.17 93.131 87.99 92.812 88.83 102.195 88.75 88.925 88.81 94.184 89.43 94.196 89.5 108.932 89.34 91.134 89.75 97.149 90.26 96.415 90.32 112.432 90.76 92.47 91.53 98.61410515 92.35 97.80117197 93.04 111.8560178 93.35 95.63981455 93.54 104.1120262 95.07 104.0148224 95.39 118.1743476 95.43 102.033431 96.09 109.3138852 96.35 108.1523649 96.6 121.30381 96.62 103.8725146 97.6 112.7185207 97.67 109.0381253 98.23 122.4434864 98.29 106.6325686 98.89 113.8153852 99.88 111.1071252 100.42 130.039536 100.81 109.6121057 101.5 116.8592117 102.59 113.8982545 103.58 128.9375926 103.47 111.8120023 103.77 119.9689463 104.65 117.018539 105.12 132.4743387 104.97 116.3369106 105.58 124.6405636 106.17 121.025249 106.52 137.2054829 107.87 120.0187687 109.63 127.0443429 111.54 124.349043 112.47 143.6114438 111.63

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 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation LKI[t] = -32.3607428109777 + 1.57163858977850CPI[t] -18.3733655297165Q1[t] -12.3285261175605Q2[t] -14.5529109634028Q3[t] + 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) -32.3607428109777 3.330902 -9.7153 0 0 CPI 1.57163858977850 0.034001 46.2233 0 0 Q1 -18.3733655297165 0.742379 -24.7493 0 0 Q2 -12.3285261175605 0.741369 -16.6294 0 0 Q3 -14.5529109634028 0.741071 -19.6377 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.9914725479775 R-squared 0.983017813392995 Adjusted R-squared 0.981685877188525 F-TEST (value) 738.036709335832 F-TEST (DF numerator) 4 F-TEST (DF denominator) 51 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.96066508658799 Sum Squared Residuals 196.054586670020 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 81.71 82.635142387909 -0.925142387908967 2 87.703 88.9471603603273 -1.24416036032727 3 90.09 87.6343258965565 2.45567410344348 4 100.639 102.045789386879 -1.40678938687923 5 83.042 85.2283460610434 -2.18634606104343 6 89.956 91.5089312616662 -1.55293126166621 7 89.561 90.2432459555888 -0.682245955588817 8 105.38 105.346230425414 0.0337695745859119 9 86.554 87.8372661200757 -1.28326612007572 10 93.131 93.5992105860716 -0.468210586071613 11 92.812 92.6950021556433 0.116997844356717 12 102.195 107.122182031864 -4.92718203186378 13 88.925 88.843114817534 0.0818851824660364 14 94.184 95.8623701553527 -1.67837015535267 15 94.196 93.7480000107949 0.447999989205122 16 108.932 108.049448799833 0.882551200166906 17 91.134 90.3204550919257 0.813544908074257 18 97.149 97.1668301848688 -0.0178301848688156 19 96.415 95.0367436544132 1.37825634558677 20 112.432 110.281175597319 2.15082440268144 21 92.47 93.1179717817315 -0.647971781731469 22 98.61410515 100.451554837506 -1.83744968750586 23 97.80117197 99.3116006186108 -1.51042864861077 24 111.8560178 114.351719544845 -2.49570174484485 25 95.63981455 96.2769653471862 -0.637150797186257 26 104.1120262 104.726411801703 -0.614385601703362 27 104.0148224 103.004951304590 1.00987109540978 28 118.1743476 117.620727811584 0.553619788415865 29 102.033431 100.284643751121 1.74878724887858 30 109.3138852 106.738109196620 2.57577600338016 31 108.1523649 104.906633998222 3.24573090177780 32 121.30381 119.490977733421 1.81283226657945 33 103.8725146 102.657818021687 1.21469657831307 34 112.7185207 108.812672135127 3.90584856487253 35 109.0381253 107.468404899561 1.56972040043885 36 122.4434864 122.115614178351 0.327872221649358 37 106.6325686 104.685231802501 1.9473367974988 38 113.8153852 112.285993418538 1.52939178146206 39 111.1071252 110.910293411176 0.196831788823943 40 130.039536 126.076143424592 3.96339257540755 41 109.6121057 108.787208521823 0.824897178176927 42 116.8592117 116.545133996838 0.314077703162331 43 113.8982545 115.876671354876 -1.97841685487610 44 128.9375926 130.256702073403 -1.31910947340325 45 111.8120023 112.354828120620 -0.542825820620248 46 119.9689463 119.782709491781 0.186236808218625 47 117.018539 118.296994783135 -1.27845578313498 48 132.4743387 132.614159958071 -0.139821258070978 49 116.3369106 115.199493968119 1.13741663188066 50 124.6405636 122.171600148245 2.46896345175531 51 121.025249 120.497288808825 0.52796019117513 52 137.2054829 137.171911868429 0.0335710315713679 53 120.0187687 121.564630256722 -1.54586155672224 54 127.0443429 130.611299375355 -3.56695647535522 55 124.349043 129.848538418007 -5.49949541800693 56 143.6114438 143.081272965996 0.530170834004233 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.305157613555765 0.610315227111529 0.694842386444235 9 0.191719941009997 0.383439882019995 0.808280058990003 10 0.125717890437362 0.251435780874724 0.874282109562638 11 0.0666892610062384 0.133378522012477 0.933310738993762 12 0.315264280731399 0.630528561462797 0.684735719268601 13 0.327069617066949 0.654139234133898 0.672930382933051 14 0.263838828709626 0.527677657419252 0.736161171290374 15 0.182930657380930 0.365861314761861 0.81706934261907 16 0.284627898779411 0.569255797558822 0.715372101220589 17 0.264382403211650 0.528764806423299 0.73561759678835 18 0.215487218955775 0.43097443791155 0.784512781044225 19 0.156262590379953 0.312525180759906 0.843737409620047 20 0.204045780688491 0.408091561376983 0.795954219311509 21 0.168580431141206 0.337160862282412 0.831419568858794 22 0.206186361317140 0.412372722634281 0.79381363868286 23 0.265878764058893 0.531757528117786 0.734121235941107 24 0.437482965073152 0.874965930146305 0.562517034926848 25 0.46517222238026 0.93034444476052 0.53482777761974 26 0.555795625194257 0.888408749611487 0.444204374805743 27 0.484203260573369 0.968406521146738 0.515796739426631 28 0.521748807249713 0.956502385500575 0.478251192750287 29 0.508033750613353 0.983932498773295 0.491966249386647 30 0.542289328312792 0.915421343374417 0.457710671687208 31 0.56184381966141 0.87631236067718 0.43815618033859 32 0.520414824525521 0.959170350948957 0.479585175474479 33 0.454267053482617 0.908534106965234 0.545732946517383 34 0.507383494867183 0.985233010265634 0.492616505132817 35 0.447533996849486 0.895067993698972 0.552466003150514 36 0.482149363452539 0.964298726905077 0.517850636547461 37 0.394217845416260 0.788435690832521 0.60578215458374 38 0.311589265189983 0.623178530379966 0.688410734810017 39 0.279627966912246 0.559255933824492 0.720372033087754 40 0.335851734189754 0.671703468379509 0.664148265810246 41 0.260162209758527 0.520324419517054 0.739837790241473 42 0.207856014285556 0.415712028571112 0.792143985714444 43 0.259805901221162 0.519611802442325 0.740194098778838 44 0.383841530925345 0.76768306185069 0.616158469074655 45 0.370118610670568 0.740237221341137 0.629881389329432 46 0.294966373006053 0.589932746012106 0.705033626993947 47 0.235357997746689 0.470715995493378 0.764642002253311 48 0.430774206527488 0.861548413054976 0.569225793472512 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 0 0 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Quarterly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Quarterly Dummies ; par3 = No 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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